AMCP 706-247 Ammunition Series - Section 4 Design for Projection [Clean]

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01"C4 ENGINEERING DESIGN HANDBOOK'

AMMUNITION SERIES

SECTION 4, DESIGN FOR PROJECTION

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"PRFCst Available CopyPREFACE

This handbook is the fourth of six handbooks on artillery ammu-nition and forms a part of the Engineering Design Handbook Series ofthe Army Materiel Command. Information concerning the other hand-books on artillery ammunition, together with the Table of Contents,Glossary and Index, will L~e found in AMCP 706-244, Section 1, Artil-lery Ammunition--General.

The material for this series was prepaz.3d by the Technical Writ-ing Service of the McGraw-Hill Book Co., based on technical informa-

tion and data furnished prinnipally by Picatinny Arsenal. Final prepa-ration for publication was accomplished by the Engineering HandbookOffice of Duke University, Prime Contractor to the Army ResearchOffice-Durham for the Engineering Design Handbook Series.

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UNITED STATES ARMY MATERIEL COMMANDWASHINGTON, D. C. 20315

.31 July 1964

AMCP 706-247, Section 4, Design for Projection, formingpart of the Ammunition Series of the Army Materiel CommandEngineering Design Handbook Series, is published for the informa-tion and guidance of all concerned.

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FOR THE COMMANDER:

OFFICIAL: SELWYN D. SMITH, JR.Major General, USA

-Chief of Staff

R. 0. DA I SON

Colonel,/ S

Chief, mi strative Office.

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TABLE OF CONTENTSSection 4 - DVsign for Project~on

Page Paragraph&Propellants and Interior Ballistics 4-1Propellants, General 44 4-1 to 4-2Propellant Composition 4.2 4.3References and Bibliography 4-S

Manufacture of Propellants 4-6 4-4 to 4-6References and Bibliography 4-8Determination of Grain Design for a Specific

Weapon 4-9 4-7 to 4-8References and Bibliography 4-12De3ign of Dies and Pin Plates 4-13 4-9List of Symbols 4-13Control of Burning Surface 4-16 4-10 to 4-20References and Bibliography 4-29Theoretical M/ethods of Interior Ballistics 4-30 4-21 to 4-48r Tables of Symbols

4-30,-31,.32LeDuc System 4-80 4-49 to 4-51References and Bibliography 4-83General Problems of Propellant Ignition 4-84 4.52References and Bibliography 4-86

Calculation of Thermodynamic Properties ofPropellants 4-87 4-S3 to 4-64References and Bibliography 4-91,-92Propellant Characteristics and Test Methods 4-93 4-65 to 4-75References and Bibliography 4-94Tables

4-95 to 4-116

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TABLE OF CONTENTSSection 4- Design for Projection (continued)

Page ParagraphsCartridge Case and Gun Chamber Design 4-117

Introduction 4-117 4-76British Practice 4-117 4-77 to 4-93Notes on American Practice 4-129 4-94 to 4-100Dimensioning of Cartridge Case and Cham,,er 4-133 4-101 to 4-113Wraparound Cartridge Cases 4-135 4-114 to 4-116References and Bibliography 4-137Figures and Table 4-138 to 4-148

Rotating Band and Rifling Design 4-149Rotating Band Design 4-149 4-117 to 4-143Erosion of Rifling 4-162 4-144 to 4-148Rifling Design 4-169 4-149 to 4-154References and Bibliography 4-176

Stress in Shell 4-177List of Symbols 4-177Introduction 4-178 4-155 to 4-156Forces Acting on Shell 4-178 4-157 to 4-164 . ,

Stresses Resulting from Forces 4-181 4-165 to 4-171Yield Criteria 4-185 4-172 to 4-177References and Bibliography 4-190

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•. p SECTION

DESIGN FOR PROJECTION

PROPELLANTS AND INTERIOR BALLISTICS

PROPELLANTS, GENERAL The black powder* originally used as a militarypropellant has been completely displaced by

4-1. Introduction. The purpose of propellant propellant compositions at one time referred to

design is to select the correct formulation and as "smokeless powders," which invariably con-

granulation to satisfy a given set of conditions. tain nitrocellulose. Smokeless powder is a

The limitations imposed by these conditions misnomer, because these propellants are not

constitute the design problems. To achieve the used in the form of powder, and do liberatedesired results from a given propellant, it is varying amounts of smoke.

necessary to consider such factors as cartridgecase volume, rate of bore erosion, reduction in a composition basis, propellants are dividedof flash and smoke, ballistic uniformity, and nt t ingl three grops.high-velocity requirements balanced against i a. Sinclease Propella ofsitroe-basepressure limitations. It may not be possible to s the principal active ingredient of single-basesatisfy all of these considerations; therefore, propellant (see table 4-23). it may contain a

stabilizer (usually possessing plasticizing prop-a certain amount of compromise is necessary. erties) or any other material in a low state of

, oxidation, in addition to nitro compounds. andFrom practical considerations, propellants inhibiting or accelerating materials such asshould be made from relatively cheap, non- metals or metallic salts. M1 propellant is anstrategic raaterials which are available in example of a single-base propellant.large quantity. The rate of burning of the pro- b. Double-Base Propellants. "Double-base"pellant should be controlled so that the rate of generally defines propellant compositions can-gas evolution does not develop pressure peaks taining nitrocellulose and nitroglycerin. A bet-within the gun tube in excess of the gun stress ter definition describes adoouble-base propellantlimits. The burnt propeilant should leave little as one containing nitrocellulose and a liquidor no residue, since unburned material cor- organic nitrate which gelatinizes the nitroc-el-rodes bores, creates smoke, and reduces gun lulose. It may also contain additi es similarefficiency. It is also desirable that the explo- to the single-base compositions. Nitroglycermsion gases be as cool as possible at the muzzle propellants have not been used extensively into reduce flash and so prevent exposure of thegun position by night. By the same token, it is *Black powder is the generic name originally applied.desirable that the explosion be smokeless to to a mixtiare of charcoal, sulfur, and potas-iiumprevent obscuration of the target or revealing nitrate and now also applied to compositionsthe gun position by day. Cooler-burning pro- tamning bituminous coal and sodijun nitrate in.pellants decrease the tendency to erode bores. of the charcoal and potassium nitrate. The - aWhil-, nitrocellulose has a certain amount of ratio of the components of the potassiumcharcoal-sulfur has remained essentially L. r1einherent instability, it has retained its position for over 400 years, since any modificationas a general ingredient of propellants because ratio has been fo,'md to produce adverse rtesu..it can be made satisfactorily stable by the Although black powder is no longer used as a pr,addition of stabilizing materials and because pellant, it is still used an an igniting mater~ai forpropellants, time fuzes, base-ejecting shells, awdof the lack of a large supply of more stable the like. Black powder is coated with iraphite tomaterials possessing its advantageous char- increase its loading density and to reduce the build-acteristics. up of static charge.

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the United States as standard propellants to have desirable solubility and viscosity char-because their high explosion temperature makes acteristics as well as a specified nitrogenthem quite corrosive, reducing the service life cont qt.of the gun; furthermore, they may possibly bein short supply in an emergency. M2 propellant PROPELLANT COMPOSITIONis an example of double-base propellant.

c. Triple-Base Propellants. These pro-pellants have three basic active ingredients: 4-3. Criteria for Selection of Propellant Mate-nitrocellulose, nitroglycerin, and nitroguani- rials. In the manufacture of propellants it maydine, in addition to such other additives as be desirable to incorporate with the nitro-may be necessary. M15 propellant is an ex- cellulose other materials in order to modifyample of a triple-base propellant. the properties of the nitrocellulose. These

Table 4-23 is a breakdown of compositions materials may be either incorporated or coatedof standard propellants. In these compositions, on the surface, and are used to (1) increasethe dinitrotoluene and nitroglycerin act as stability, (2) decrease hygroscopicity, (3) changegelatinizing and moistureproofing agents which heat of explosion, (4) control burning, (5) re-contribute to the ballistic potential; diphenyla- duce muzzle flash, (6) reduce smoke, (7) in-mine and ethyl centralite are used as stabi- crease electrical conductivity, and (8) reducelizers; dibutylphthalate and triacetin are non- bore residue. Table 4-1 lists some of the ma-explosive gelatinizing agents which also con- terials used to achieve these ends, with spe-tribute to flashlessness; nitroguanidine is dis- cific applications.persed throughout the nitrocellulose-nitro- a. Stability. Since propellants nustbe storedglycerin colloid as a finely divided crystalline for log periods and then must function re-powder which contributes to ballistic potential liably when used, they must not decompose inand flashlessness; potassium sulfate and cryo- storage. Of primary concern is the fact thatlite are used as chemical flash reducers; while nitrocellulose by itself is not stable. In corn-tin is used as a decoppering agent. mon with other nitrate esters, nitrocellulose

breaks down autocatalytically to yield acid de-4-2. Forms of Nitrocellulose. Some types of composition products which accelerate thenitrocellulose are distinguished by name, in- decomposition rate once decomposition hascluding the following (see table 4-2). started. Stabilizers are added to the propellant

aw.Pyroxylin, or collodion, is soluble in a colloid to reduce the decomposition rate. 1

mixture of ether and ethanol and containsfrom about 8 to about 12 percent of nitrogen. Stabilizers react with the acid decompositionPyroxylin is distinguished from other types of products, as they are formed, to neutralizenitrocellulose by its partial solubility inethanoL them and thus prevent acceleration of the de-The pyroxylin used for military purposes con- composition. When daterioration has progressedtains 12.20 * 0.10 percent of nitrogen, while that to a point where the neutralizing action of theused in the manufacture of blasting explosives stabilizer is no longer significant, the de-has a nitrogen content of 11.5 to 12.0 percent. composition rate accelerates. The appearance of

b. Pyrocellulose has a nitrogen content of an acid odor and subsequently visible red12.60 ± 0.10 percent, and is completely soluble fumes indicate that the propellant has becomein a mixture of 2 parts of ether and 1 part of unsafe for further storage or use. (See para-ethanoi. Pyrocellulose for military use is graphs 4-65 through 4-75.)manufactured from cotton linters or wood cel- b. Hygroscopicity. Hygroscopic propellantslulose obtained commcrcially from wood pulp. are undesirable both because absorption of

c. Guncotton contains 13 percent or more of moisture reduces the ballistic power, and ren-nitrogen, that used for military purposes con- ders the propellant unstable chemically andtainng a minimum of 13.35 percent. Only 6 to physically, and because variations in moisture11 percent of this type of nitrocellulose is content alter the ballistic characteristics un-soluble in ether-ethanol mixture, but it is predictably. Propellants are made as non-completely soluble in acetone, as are prac- hygroscopic as possible by including moisture-tically all types of nitrocellulose. resisting materials in the colloid or by coating

d. Blended Nitrocelluloses are mixtures of the surface of the propellant grain with mois-pyrocellulose and guncotton. These are designed ture-resisting materials.

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"c. Heat of Explosion. The heat of explosion at the muzzle, immediately after the emer-is cuntrolled to reduce muzzle flash and bore gence of the projectile. The second flash, dueerosion, since high heats of explosion produce to the combustion of H2 and CO in the pro-muz le flash and high rates of bore erosion, pellant gases with atmospheric oxygen, occursesprcially at high rates of fire. F'or discussion a fraction of a second later same distance inof flash from guns see references 2, 3, 4, 5, front of the muzzle. Its illumination intersity6, 7, and 8. The heat of explosion is governed is far greater than the first flash. 2 Alkaliby the material included in the propellant metal salts have been found effective in re-composition. A high oxygen content produces ducing secondary flash, as they prevent thea high heat of explosion; therefore, it is ad- chain reactions which occur in oxidation ofvisable to formulate propellant compositions hydrogen to water; they also form nuclei in thewith low oxygen balance to lower the heat of emergent gases on which the explosion-pro-explosion, duced water vapor may condense, thereby cre-

d. Control of Burning. The rate of burning ating smoke. 3

is controlled to govern the pressure within the An alternative method of reducing flash is togun tube and to reduce flash. In addition tobeing controlled by proper grain geometry incorporate large amounts of nitrogen into the(paragraphs 4-10 through 4-20), the rate of propellant composition thereby diluting theburning may be further modified by coating amounts of inflammable H2 and CO in thethe propellant grain with a deterrent material zzle gases. Oxygen balance is important indiffsesintothe andthe reduction 31 flash and smoke because anthat diffuses into the grain and makes theoutside surface burn slower than the main adequate supply of oxygen reduces smoke bybody of the propellant. The depth to which the converting all of the carbon in an explosive todeterrent diffuses into the surface is con- gaseous form.trolled by the temperate,, a and duration of the . Electr:cal Conductivity. Graphite is coatedcoating process. on the grains to increase their surface elec-

e. Flash and Smoke. The importance of the tricarconductivity in order to reduce the danger

"elimination (or at least reduction) of muzzle arising from an accumulation of a static charge

flash and smoke lies in the elimination ol a during propellant handling..-The graphite also

source of detection of the gun battery and in serves to lubricate the grains and so increases

the pievention of target obscuration. The goal packi-g density.

in design for flash reduction is a propellant g. Residues. Propellant formulations arethat will be consumed close to the breech, compounded so that unoxidized carbon remains

thereby allowing the combustion products to low, since unburned carbon produces bore iies-cool' before they exit from the muzzle. This idue and smoke. Lead carbonate and tin aregoal is opposed to the high muzzle pressure materials that may be added to reduce copper-

necessary to produce high projectile velocities. ing.

Table 4-1 lists some of the more commonlyMuzzle flash may be resolved into two corn- used materials that are added to propellantsponents. The first flash is due to the burning and indicates their functions. It should beof incandescont propellant gases, 3ccurring noted that some items are muliipurpose.

"- ' 4-3

Table 4-1

Substizutes and additives

Function .. fU_ 0 . I. -S..M

Material Is

Nitroglycerin (NG) X x X

N-troguanidine . X

Dinitrotoluene (DNT) X X X X

Methyl centralite (Sym-dim ethyld•phenylurea) X X X X X

Ethyl centralite (Sym-

diethyldiphenylurea) X X X X X X X X

IDiethyleneglycoldinitrate (DEGN) X* X X

Diphenylamine (DPA) xt

Dibutylphthalate (DBT) X X X X X X X

Diethylphthalate (DET) X X X

Trinitronaphthaiene X X

Mineral jelly X X X X

Barium nitrate X

Potassium nitrate X

Potassium perchlorate X x

Potassium sulfate X

Tin (powdered)

Graphite X

Carbon black

Cryolite I _ X

* Thermally more stable than NG.t Stabilizer for single-base propc!lants only.

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REFERENCES AND BIBLIOGRAPHY

1. Davis, T. L., "Chemistry of Powder and Explosives," John Wiley and Sons, New York,1943, p. 266 ff.

2. "Internal Ba'.listics," The Philosophical Library, New York, 1951, pp. 3, 4, 80, 81.

3. Chemical Suppression of Gun Muzzle Flash, Franklin Institute Report, 15 January 1954,ASTIA No. AD-31197 (CONFIDENTIAL).

4. Laidler, K. J., "Chemical Kinetics," McGraw-Hill Bo'ok Co., New York, 1950, pp. 318-323.

5. Cocke et al, Study of Physical Mechanism of Muzzle Flash, CARDE Report No. 210/45.

6. Report on Muzzle Flash, BRL Report No. 426, 19 November 1943 (CONFIDENTIAL).

7. Muzzle Flash and Its Suppression, BRL Report No. 618, 10 February 1947.

8. Midwest Research Institute, Contractor's Reports on W-323-072-ORD-2163-27-4.

4-54.•

MANUFACTURE OF PROPELLANTS The grade of nitrocellulose in widest militaryuse contains 13.15 percent nitrogen. This grade

S4-4. Description of Propellant Manufacture. is blended from pyrocellulose (12.60 percentThe basic propellant material is nitrocellulose, nitrogen) and high grade guncotton (13.35 per-Thebasich propelant materialis nitrag le lsere cent nitrogen). See paragraph 4-5. The pyro-which is made by nitrating cellulose derived cellulose is soluble in the ether-ethanol solventfrom cotton linters or wood pulp. The manu- while the guncotton is soluble only to a limitedfacture of nitrocellulose propellants consists degree, so that the pyrocellulose acts as aof two distinct processes: (1) manufacture of binder.the nitrccellulose, and (2) manufacture of thepropellant from the nitrocellu lose. Njt•rocellu- Nirocellulose is softened or gelatinized bylose is a nitrate formed by esterification of Nitsolauioe i nd orvglati ntzedibycellulose. The wood pulp is. purified at a pulp various volatile and nonvolatile solvents, in-mill by either the sulfite or sulfate process to cluding ether-alcohol mixtures, acetone, nitro-yield a high alpha cellulose content, and sent glycerine and other nitrate esters, and di-to the nitrating plant in continuous rolls. Linters utylphthalate and other phthalates. In the gcla-cellulose is bleached and sent to the nitrating rolling.plant in bales. At the nitrating, plant the woodcellulose is shredded, and the linters are 4 Colloiding. The product obtained by dis-picked to expose the fibers, and then dried. solv idiro.luhe product ofther andNitration is accomplished by the du Pont me- solving nitrocellulose in a mixtire of ether andchanical dipper process. Theproper degree of ethyl alcohol is called the colloid. Since water-

Snitric wet nitrocellulose will not dissolve in the ethernitration results by adjustment of the cetrfuedtoairoi

acid-sulfuric acid-water ratio. When nitration alcohol solvent, it is

is complete, the contents of the nitrating vessel mately 30-percent moisture content- and then

f for re- dehydrated by forcing alcohol through the nitro-are centrifuged, and the acid fortified ore- cellulose under pressure. The alcohnl -saturated

use. The nitrocellulose is submitted to a cellulose as The are raced

lengthy series of acid'and neutral atmospheric blocks of nitrocellulose, as they are receivtdpressre boils to remove occluded acids. This from the dehydrating press, are put into a

thessure blsta ton pcess. This dough mixer, to which, afte- the blocks arecomprises thebroken up, the additional solvent is added. Thiscess also accomplishes a certain amount of sten the posisiontinsedvuntil a Tisviscositystep in the process is contined until a satis-lization the nitrocellulose must meet the sta- factory colloid is obtained.* Diphenylamine or

bility, physical, and chemical requirements of other stabilizer (dissolved in the solvent) is

Specification JAN-N-244. also added at this stage. From the mixer, thecrumbly mass is blocked under pressure, and

Table 4-2 is worked until it is freed from lumps.

M!i* ni-y grades of nitrocellulose In their colloided form, the constituents of the(Per Specification JAN-N-244) propellant are packed together so densely that

the hot gases d,. not travel through the massNitrogen, as they would if the propellant grain were

Grade Class percent porous, but instead, the gases travel across thegrain surface. Burning is stabilized by the

Grade A Pyrocellulose transfer of energy from the burning zone into

Ty¢pe I 12.-0 ± 0.10 the body of the grain. The burning surface re-Type If 12.60 ± 0.15 cedes into the solid at a relatively low velocity.

The linear rate is independent of the grain

Grade B Guncotton 13.35 minimum shape. The result is that the propellant burnsin layers at a rate that cpn be controlled by

Grade C Blended (guncotton) varying the pressure. The mass rate -is aGrade C1 Blende (gu1cttfunction of shape in addition to other things.Type I 13.15 ± 0.05 Proper rate of conversion of propellant to gasType If 13.25.+ 0.05

Grade D Pyroxylin (collodion) 12.20 ±. 0.10 *The determination of "satisfactory" colloid is still___an art.

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is brought about by dimensioning of the grain find very little application in artillery pro-to give the prope- surface area. The proper pellant manufacture.grain shape is produccid in the final manu-facturing operation by forcing the colloid For an alternative method of propellant manu-"through dies. (See paragraphs 4-7 through facture that has been successfully applied to4-9.) As the propellant comes from the grain- small arms propellant manufacture, see ref-ing dies, it contains almost 50 percent solvent, erence 3. This is the Ball Powder Processwhose recovery is an important consideration. used by the Olin Mathieson Chemical Corpora-The "green" grains shrink as they are dried tion. Although apparently competitive with theand this shrinkage must be allowed for in the conventional solvent-extrusior process fordesign of the graining dies. Purposeful solvent small arms propellants, it does not seemrecovery is carried on until the concentration suited for production of larger granulations.is reduced to about 12 to 15 percent, afterwhich it is no longer economically feasible. 4-6. Relative Costs of Propellant Manufacture.The remaining solvent, down to 0.2 to 3 per- It is not economically feasible for commercialcent, depending on grain size, is removed manufacturers of explosives to maintain plantseither by air drying or waterdrying.l, 2 Double- for production o( military explosives in peace-base propellants are not subjected to solvent time. For this reason, the Ordnance Depart-recovery or water drying. ment has established contractor-operated sys-

tems at Ordnance plants to handle wartimeThe process just described is the conventional military requirements and standby or reducedmethod of manufacturing artillery propellants, production in peacetime. Table 4-3, preparedwhich may vary in web from 0.014 to 0.100 by the Ordnance Ammunition Command, givesinch. When dimensions get larger than this, some indication of the relative costs of buyingsolvent recovery is such a difficult problem propeliant materials commercially (wherethat solventless methods are used. These available) and manufacturing in governmentmethods will not be covered here, since they plants.

Table 4-3

Ammunition component cost for ihe quarter ended 31 December 1954,propellants, explosives, and chemicals

Mfg. CostPurch. or or Purch. Indirect Total

Nomenclature Gov't.Plt. Price Cost-3% Cost Unit

Barium Nitrate, Class D, Granulation 140 Purchased $0.168 $0.005 $0.173 Lb

Dinitrotoluene Gov't. PiLt. 0.119 0.004 0.123 Lb

Diphenylamine GovIt P1t. 0.387 0.011 0.398 Lb

Diphenylanmine-Grained for Powder Gov't. Pit. 0.366 0.011 0.377 Lb

Ethyl Centralite (Carbamite) Class III Purchased 0.928 0.028 0.956 Lb

Mortar, 4.2", M8 (Increment Charge M6 andIncrement Charge M8) Gov't. Pit. 1.49 0.045 1.535 LbMortar, 60-mm and 81-mm, Increment Packaging

(Incremenlt MIA1, M2A1, and M3A1) Gov't. Pit. 3.18 0.10 3.28 Lb

Nitroglycerin Gov't. Pit. 0.204 0.006 0.210 Lb

Nitroguanidine Class A or B Purchased 0.26 0.008 0.268 Lb

Powder, Black, Grade A4 Purchased 0.33 0.01 0.34 Lb

4-7I,

44i

Table 4-3

Ammunitior component cost for the quarter ended 31 December 1954,propellants, explosives, and chemicals (cont)

Mfg. CostPurch. or or Purch. Indirect Total

Nomenclature Gov't. Pit. Price Cost-3% Cost Unit

Powder, Black, Meal Grade Purchased 0.32 0.01 0.33 Lb

Powder, Black, Grade FFFG Purchased 0.316 0.009 0.325 Lb

Powder. Black, Grade Al Purchased 0.311 0.009 0.320 Lb

Powder, Black, Sodium Nitrate, Class A Purchased 0.11 0.003 0.113 Lb

Propellant, M2 Purchased 0.67 0.02 0.69 Lb

Powder, Black, Potassium Nitrate, Cannon Grade Purchased 0.33 0.01 0.34 Lb

Propellant, M6 Purchased 0.574 0.017 0.591 Lb

Powder, M9, for Ignition Cartridge M4 and M5(60-mm Mortar) Purchased 1.03 0.03 1.06 Lb

Powder, M9, or Ignition Cartridge M3 and M6(8 1-rm Mortar) Purchased 0.82 0.025 0.845 Lb

Propellant, IMR 4895 Purchased 0.70 0.021 0.721 Lb



Propellant, M12, IMR 7013 Purchased 0.70 0.021 0.721 Lb

Propellant, Western Ball, Type II, WC 820 Purchased 0.799 0.024 0.823 Lb

RDX Gov't. Pit. 0.382 0.01 0.392 Lb

Solvent, Double Base Multiperforated Propellant(M2) Gov't. Pit. 0.783 0.023 0.806 Lb

Solvent, Single Base Ma1ltiperforated CannonPowder (Propellant MI, M6, and M10) Gov't. Pit. 0.42 0.012 0.432 Lb

Solvent, Single Base Single Perforated Propellant Gov't. Pit. 0.474 0.014 0.488 Lb

Solvent, Triple Base Single Perforated Propellant Gov't. Pit. 0.597 0.018 0.615 Lb

Trinitrotoluene Gov't. Plt. 0.145 0.004 0.149 Lb


1. Tschappat, W. H., "Textbook of Ordnance and Gunnery," John Wiley and Sons, New York,1917, ch. I.

2. Hayes, T. I., "Elements of Ordnance," John Wiley and Sons, New York, 1938, ch. I.

3. Chemical Engineering, McGraw-Hill Book Co., New York, December 1946, pp. 92-96, 136-139.

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DETERMINATION OF GRAIN DESIGN FOR A which a propelling charge is required.* WithSPECIFIC WEAPON a knowledge of the weapon characteristics and

of the functioning of other propellant com-positions in the weapon, an attempt is made

4-7. Fitting the Web to the Gun. The potential to manufacture these three propellants over athermal energy of a propellant when fired in a fairly wide web range; one lot will have a webgun is partially converted into the kinetic energy that burns slightly too slowly, one will burn atof the projectile. The proportion of the tctal nearly the correct rate, and one will burn aavailable energy that can be communicated to little too fast for the weapon.tthe projectile is limited by the length of travelof the projectile in the gun tube, maximum Each of the three lots of propellant is test-pressure, expansion ratio, friction and heat- fired in the weapon for which it is being de-conduction energy losses, and so on. The re- signed, in order to establish the charge-veloc-quired maximum pressure is controlled by the ity and charge-pressure relationships. This isballI4-1cian through the proper choice of pro- done by slowly building up the amount of chargepel. ranulation web. The web and propellant used until a quantity of charge is reached thatwei6., combination which produces maximum will produce the service velocity of the weapon,velocity at a specified pressure is the optimum or to a point where the firings must be dis-charge. continued either because the pressure limit has

been exceeded or because the chamber capacity

Propellant grains are commonly designated as has been reached. Since further calculations

either degressive or progressive. Adegressive are based on the results of these test firings,grain burns with a continually decreasing sur- they should be conducted with care.

face until the grain is completely consumed, The following is an application oi the principlewhile a progressive grain burns• with a con- Tefloigi napiaino h rnilwhil a rogrssie gain urn wit a on- described above: Figure 4-1 represents thetinually increasing surface. The burning rates desriedvel Fige-presentsrteare functions of the grain geometry (form). charge-velocity and charge-pressure curves(See paragraphs 4-f 0 thegraingeough ry 4-2) Bfor three experimental lots of propellant plotted(S e e pa rag raph s 4 - 10 th roug h 4 -20 .) B e cause on t e s m or i a . E x i i g th e c u v ,of nonsimultaneity of ignition, end-burning, on the same ordinate. Examining these curves,nonuniformity of web, and nonhomogeneities of it han be determined that Lot 1 does not meetvarious types, all propellants are somewhat the ballistic requirements ou the weapon be-degressive. In general, it is not practical to cause the rated maximum pressure (48,000manufacture grains that are wholUy degressive, psi)t will be exceeded before the desiredor wholly progressivae muzzle velocity of 3,500 ft per se-, is attained;the medium web propellant (Lot 2) also fails

to meet requirements for the same reason;A propellant designed to fit a given set of bal-listic conditions must have its burning ratc *From preliminary interior ballistic calculationscloseiy controlled, which is accomplished there probably is available an estimate of the webwithin close limits by proper design of the web required. However, it is usually considered ad-dimensions. Burning may also be controlled by' visabl, to test-fire webs slightly larger and slightlydiffusing a material, which decreases the rate smaller (±10 percent) than the estimr.tod web, in

addition to the one indicated, because of the lackof burning of the propellant, into the surface of of specific data providing an accurate value of thethe propellant grain. In this discussion, it is burning rate.assumed that the selected composition is com- tThe relative quickness of a propellant is defined aspatible with the severpl general requirements, the ratio of dP/dt of a test propellant to dP/dt of asuch as hygrosccpicity, stability, and so on standard propellant of the same composition taken

at the sisme initial temperature and loading density(see paragraph 4-3) which are prerequ~sites of a closed chamber (bomb). (See paragraphs 4-10for any propellant composition. Based on this through 4-20.)assumption, the proper design ard subsequent TThe rated maximum pressure for any type of gunacceptance of a particular composition for a is that value of the maximum pressure which i.,given weapon is made as follows, specified in the propellant specification as the

upper limit of average pressure which may be de-At least three small lots of propellant are veloped by an acceptable propellant in the form of

made for the particular weapon to which the propelling c~iarges which will impart the specifiedimproved composition is to be fitted or for muzzle velocity to the specified projectile.

4-9

the slowest propellant (Lot 3) can meet the re- curve (figure 4-2), the ordinate representingquirements. The completion of propellant selec- the service velocity. (3,500 ft per sec) can betion depends on the interpretation of these traced to the point of intersection with thecurves. curve, and the corresponding abscissa deter-

mined. This value represents the web thatFigures 4-2 and 4-3 are constructed from data will give a service velocity at 95 percent oftaken from the curves of figure 4-1. Figures the rated maximum pressure. In this example,4-2 and 4-3 are called "design curves." Figure the most desirable web to meet the ballistic4-2 represents the relationship between web requirements is found to be 0.099 inch. Pro-size and velocity at 95 percent of the rated jecting this web value vertically to figure 4-3,maximum pressure. Figure 4-3 is a web-charge it is found- that approximately 409 ounces ofcurve, at service velocity (3,500 ft per sec), propellant will be required.plotted from values taken from the charge-velocity curves. The values used for plotting While the determination of the optimum web,curve 2 are obtained by tracing, on the charge- was successful in this particular example, itpressure curve of figure 4-1, the abscissa may not be so successful under all conditions.which represents 95 percent of the rated maxi- For instance, it may be that the normal bal-mum pressure (46,000 psi). Wherever this trace listic requirements of a certain weapon areintersects a pressure curve, the ordinate of the too severe for a given propellant composition.intersection is traced to the right to where itintersects the corresponding charge-velocity 4-8. Determination of Web Range. Once thecurve. From this latter intersection, the cor- optimum web for a given composition has beenresponding velocity is obtained. This value is determined, it may not be feasible to manu-plotted against the web of the propellant in facture a grain with exactly the prescribedfigure 4-2. Having obtained the web-velocity dimensions. To meet this difficulty, a web

35000 40000 45000 50000 PRESSURE (PSI)

PRESSURE: .io-•0 I.092" • b. .. .-

420

400 , _" "-

380-____ _/®_ ...... ____ __ ___________

3_60i _aa

340 _ " .0__" •

VELOCITY:FPS) 3200 3300 3400 3500 3600

4-[0

range of thickness must be established. TheI •lower limit of web thickness is set by pressure

limitations, while the upper limit depends onI Ir such thirgs as flashlessness and chamber ca-

3500 33 pacity. To establish the web range, it is neces-sary to fire several propellant lots with webthicknesses approaching the maximum and mini-mum web limits in the particular gun for whichthe grain is intended. To indicate any tendency

3450 to produce erratic pressures, the charge weightsof these firings should be somewhat in excess

•"2/ of those required to give service velocity. The>2 web range established should be as wide as

0 possibl "vur manufacturing feasibilit) when the.i gun-ammunition combination is dpsired to de-

L> liver a velocity close to the maximum attain-

able. Under this condition, the web range thatwill satisfy the requirements is very narrow

3350 and requires tight control of manufacturingprocesses.

Since the optimum web was determined by30 assuming 95 percent of the rated maximum

3300 pressure, it is therefore the thinnest web that.085 .095 .105 can be used. Any material reduction of the web

WEB SIZE (IN) will 'end to develop a service pressure in ex-

cess of the allowable maximum. However, thin

430 webs (which tend to produce high pressures)are somewhat desirable since they requireless charge to meet a given set or ballisticconditions.

N410 Large webs tend to leave unburnt propellant

at the muzzle and to increase the muzzle_ pressure. Both factors inc'ease the tendencytU to flash. If the web is too thick, the chamber

_:t capacity may be exceeded before the velocity'"390LU 90level is attained. In certain large-chamber,

4 high -velocity guns the velocity at a constantM ,ressure may begin to decrease as the web

exceeds a certain value (this is not a common370 occurrence with normal guns).

SI

350.085 .095 .105

WEB SIZE (IN)

Figures 4-2 and 4-3. Figure 4-2 (above) rep-resents the relationship between web sizeand velocity at 95 percent of the rated max-imum pressure, and figure 4-3 (below) is a

web-charge curve

4-11


1. Alexander, Jerome, "Colloid Chemistry," D. Van Nostrand, New York, 1919, vol. 4, pp.117-120.

2. McFarland, "Textbook of Ordnance ar.d Gunnery," John Wiley and Sons, New York, 1929.

3. Marshall, "Explosives," Blakiston, New York, 1919, vol. 1, pp. 312-313.

4. Picatinny Arsenal Technical Report No. 165.

5. Proof Officer's Manual, Aberdeen Proving Grounds, February 1929, pp. 158-162.

4

4-12

BEJST AVA!LIABILE COPV'

DESIGN OF DIES AND PIN PLATES

"LIST OF SYMBOLS*

' D = maximum outer grain diameter Wig = green inner webDg = die diameter, or external diameter of WiD a dry inner web

green grain Wo = outer web, or. minimum distance be-DD = dry grain diameter tween an interior surface and a di-

d = inner diameter of grain perforation rectly opposing exitrior surfacedg = pin diameter, or green perforation di- Wog - green outer web

ameter WoD x dry outer webdD = dr7y perforation diameter Wa • average of the Inner and outer webs

L = grain length (usually 2 to 3 times the WaD = average dry webmaximum diameter) P = pin circle diameter

W = web, or minimum distance between Swo = percent shrinkage of outer webtwo directly opposing surfaces Swi = percent shrinkage of inner web

WI = inner web, or minimum distance be- Sd = percent shrinkage of perforationtween two directly opposite interiorsurfaces of the grain

in the grain design. As stated in the precedingparagraphs, a major factor in the control ofburning rate is the control of the web dimen-sions. Once the dry grain dimensions and per-centage shrinkage for a given composition havebeen established, the pr.ipellant can be madewith reasonable assurance that its dry dimen-sions -will be close to expectation. The follow-

-_ ing formulas are used.

*i V 8 Wog -WoD x ~~ (1)o Wog

Sw i = g x 100 (2)

Wig

Figure 4-4. Multiperfoiaoed grain Sd = dg m- dDx 100 (3)dg

4-9. In paragraphs 4-7 and 4-8, the procedure DD = 3dD + 4WaD (for multiperforated grain)(4)for establishing web size was described. Inthis section, the procedure for designing the dDproper-sized die to manufacture a grain of dg (pin size) = -desired web size will be described.

Wid + WodPropellants are shaped into their final form in WaD = - (6)

a plastic condition. This plasticity is the re-sult of the use of volatile solvents to disperse WoD 1.00 to 1.15 (for multiperforattd (7)the nitroc•elulose among the other ingredients iWd 1graans)W Lh coiluld. Subsequent evaporation of thesolvents during the drying ;rocess causes a Dg (bore) =3ug + 2Wog + 2Wig (8)shrinkage of the grain that i ,ust be allowed for

*See figure 4-4 for application of symbols. P (pin diameter circle) = 2dg + 2Wig (9)

4-13

* .-- * ----.

Wog WoD x 100 (10) g WiD(11)Wo -10-So i 100Swi - I0 (11)

0.0211100-i x 100 (11) 100 - 25 x 100 = 0.0281 in.

For example, to design the die and pin platenecessary for the manufacture of a propellant Dg (bore) = 3 dg + 2Wog + 2 Wig (8)with an average web of 0.0220 inch and a per-foration diameter of 0.0127 inch, assume the

,shrinkages for this composition for this webare Sd = 21.0 percent, Swo = 3.0 percent, D•= 3(0.0161; + 2(0.0352) + 2(0.0281) = 0.175

WoDSwi = 25.0 percent, and the ratio - = 1.04.

WiDThe solution is as follows. P (pin circle diameter) = 2dg + 2 Wig

0.0127dg (pin size) I- 10 1x 100 =0.0161 (5)) 00-21 P = 2(0.0161) + 2(0.0281) = 0.0883

This completes all the data required for multi-WoD = 0.0229 in. and WiD = 0.0211 in. perforated propellant except the length, which

is usually about 2.1 times the dry diameter (D).The dimensions of the die, pin plate, and length

WiD .WoD of cut are:WaD = W 0.022 in. (6) dg = (pin diameter) = 0.0161 in.

2 Dg = (bore diameter) = 0.175 in.P = (pin circle diameter) = 0.0883 in.

WoD L = (grain length) = 0.110 in.Wg= WD x 100 (10)

W 100- Swo This example is typical for web calculations.The shrinkage values actually vary widely for

0.0229 different propellant compositions. Representa--100 - 3x 100 = 0.0352 in. tive shrinkage data for some common pro-pellants are given in table 4-4.

4-14

iT .•V/i�'ELF C OP

Table 4-4

"Representative shrinkage data (percentages)

Web

Composition Type (dry) L Sd SWi Swo Wa

M1 MP .03 7 25 40 27 33

SP .02 3 40 ... ... 20

M2 MP .035 3 14 20 20 20

SP .03 4 33.5 ... ... 7

.09 1.3 14 ... ... 25.5

M6 MP .103 3.5 27 32 24.5 28.5

MIO MP .04 6 38 40 29 34

.024 9.5 40.5 ...... 34.5

.018 5,2 49 ...... 30.5

M15 MP .055 2 13 7.5 7.5 7.5

M17 MP .098 1 10 13 1 7.5

4-15

CONTROL OF BURNING SLRFACE measured at -40°C, +21°C, and +71°C, at pres-sures varying from atmospheric up to 50,000

4-10. Notation. Each of the authors of the psi at any specified pressure intervals.various bal'istics systems which we are about b. Closed Bomb. 2 This rrethod is used forto consider has used his own set of symbols to most gun propellants, which are not usuallydefine the parameters involved. Because this manufactured in the form of strands. Thecondition exists in the literature, it has been closed bomb is a thick-walled, steel-alloy cyl-difficult to standardize on any one set of sym- inder with removable threaded plugs in frontbols. However, where possible, an attempt has and rear which permit access to its interior.been irade to use consistent notation here. In The front plug contains the ignition mechanism,the instances where different notation has been aaid the rear plug contains a piezoelectric gage.used by different authors to define the same The bomb is cooled by a water jacket.quantity, the symbols havs been changed to readalike. Where apparently similar, but not iden-tical, quantities have been encountered, it has The closed bomb test is used to obtain data,been impossible to identify such parameters by under varying conditions of temperature anduniform notation, and, in such cases, the sym- pressure, for use in determining the interiorbols from the original treatises have been re- ballistic properties of propellants, such as thetained. Tables of the original notation found in linear burning rate, relative quickness, andthe references are given in table 4-7. relative force. This test allows a prediction

to be made of the behavior of any giver, pro-4-il. Burning of Propellants. The burning of pellant in any gun, serves as a manufacturingpropellants is a surface phenomenon. A pro- control test, and may serve as a substitute forpellant grain burns in parallel layers, in di- proving ground tests. Usually, the output of therections perpendicular to its ignited surfaces, gage is recorded as time-rate of pressure riseat a rate dependent on the initial temperature as a function of the pressure.and pressure. Under constant pressure, a pro-pellant burns with uniform velocity. An in- When the ciosed bomb test is used, a com-crease in initial t*emperature or pressurecauses an increase in the characteristic burn- parison is made between closed bomb results ofrae f cmpsiio, o ha araid a propellant under test and of p~revious lots of "ing rate of a composition, so that a rapid propellants o. the same composition of knownacceleration of burning rate results from burn- ballistic value. Mtthematical treatment ofing a propellant under confinement. Under closed bobues dP/t as atfunt ofvariable pressures, as in a gun, a grain will closed bomb results, dP/dt as a function of p,burnat pvaribessuraes, asitogether with propellant granulation form func-

tions (paragraph 4-20), yields the linear burn-

ing rate dX/dt. The actual method of obtaining4-12. Linear Burning Rate. The linear burning the data may vary at different establishments,rate is the distance (in inches) normal to any but at Picatinny Arsenal an oscillographicsurface that the propellant burns in unit time method is used, which measures the pressure(say, one second). Theoretically, this property developed in the bomb by means of a quartzis a function of the chemical composition of the piezoelectric gage. The circuitry used enablespropellant and is not a function ot propellant the charge generated by the gage to cause thegeometry. At present, there are two methods horizontal deflection (Vx) of an oscilloscopeused to determine burning rates, the strandbusned and dthermised burng rtrace to be proportional to the pressure (P) inburner and the closed bomb.

a. Strand Burner. This method is applicable the bomb, while vertical deflection (Vy) isproportional to the rate of change of pressureonly if the propellant is in the shape of a (dP/dt) at the same instant. The maximum

strand, or a strip, such as in rocket pro- presr develope insth bm i masur

pellants (in which it has its most pertinent pressure developer in the bomb is measured

application). This device measures the time as the maximum horizontal deflection of the

required for a propellant strand to burn a

predetermined distance (five inches betweenfixed electric probes). With this method, it is In this method, the data are obtained as oscillo-possible to measure burning rates at any tem- grams superposed on rows of calibration dots.perature. However, burning rates are usually (See figure 4-5, which illustrates a typical

4-16

/xV-1,:!;:•Liii C0 ,.

trace.) The dots are set 0.25 volt apart (cor- change of pressurx by equatons (12) adid (13),responding to approximately 5,60-lb pressure which are derived in appendix I of reference 3.*increments) and distances between dots aremeasured by use of a transparent interpolator, p = K(CxVx) (12)

shown in figure 4-6. The complete descriptionof the apparatus and test procedure may be K I r(13)found in reference 1. Interpretation of the data dlP/dt (13) ( ..

obtained from the oscillograms enables a de- Y L1 a mtermination of the ballistic properties of the X

propellant under test. where

P pressure developed by the burningpropellant

* * dP/dt time-rate of change of pressure ofthe burning propellant

*K =gage constant of te piezoelectric* *gage

Vx voltage across the capacitance CxVy voltage across resistance RCx capacitance of the pressure-meas-

V urirg circuitCy capacitance of the rate-of-change

measuring circuitR resistance in the rate-of-change

measuring circuitAm.= slope =V-/LVx at any point on

the curve.The expression

V C m

Figure 4-5. Pressure (P) versus rate ofchange of pressure (dp/dt) is a correction factor due to the capacitor Cy

* in the rate-measuring circuit. A nomograph hasbeen devived which enables this correctionfactor to be read directly from the dP/dt••l'• -- ~ ~~curve with a cossecminimum of mathematicalecoth

computation.

I I I - *For the sake of consistency within this section, the• -' - symbols of the original reference have been substi-

I 3 I tuted as follows:Original reference 3 This handbook

- - a covolw.,: nf propellant -- - at = covolume of kgii,.=-

* 1 JB = shortened notation forequation (15) -

C shortened notation forFigure 46. T.ransparent interpolator equation (16) = H

h = propellant web = W

This description is confined to methods of cal- mo= weight of unburned propellant = C

culat-on and interpretation of the data obtained, m; = weight of igniter = C1acw = grain *,idth = DThe values of Vx'and Vy may be converted Z = fraction of web burned = N/Crespectively. to ialues of pressure and rate of slope AV/JAV y =Am

4-17

To calculate a linear burning rate from the Z fraction of powder burnedoscillographic data obtained, a method used at - C =Picatinny, considered to be the best-balancedbetween accuracy and speed, uses equation (14). =, r I]

+ G()÷

dX dZ/dt (14)dZ/dt = rate of burning of fraction of powder

burned at time t = (17)

dP k1 - 1÷d

..........- ....... G dti T i~ piP)P

Sx/V° Sx/Vo= ratio of surface area to original volumewhen grain has burned a distance x,normal to grain surface.

whereP and dP/dt are obtained as described above Form functions of Z and Sx/Vo in terms of XPi is the pressure due to the burning of may be calculated for each grain geometry. Theigniter alone, which is obtained empirically. form functions for the most common geom-

About 300 psi are developed by two grams of etries are included in paragraph 4-20, whereblack powder in a 174-cc bomb. For rough they are correlated with their equivalent ex-approximation, Pi in equation (14) may be taken pressions in the Hirschfelder interior ballisticequal to zero. system.

G is calculated from equation (15). A consideration of dP/dt versus P, plus theappropriate form function, equation (14), yields

(Pmax - P1 ) 1-(07+ C-Qni )Do] the linear burning rate, dX/dt with respect toG - (I_ -_b)Do (15) P, for a particular grain geometry.

(',7-b)Do (5dX dZ/dt = linear burning rate (14)

in which dt - Sx/VoC = weight of propellant After the linear burning rates have been cal-

C i = weight of igniter= propellant covolume by the method of culated from equation (14), the procedure is to

reference 4. For sample calculation, plot these values against pressure on appropri-see reference 3, Appendix l-F, p. 19ff. ate graph paper (figure 4-7) to determine a

17i = igniter covolume, assumed to be 0.87 burning equation. The burning of most pro-cm 3/gm. (See reference 5.) pellants seems to follow one of three general

Do = loading density of propellant, alone, laws:C/VB dx/dt = a + BP (18)

b = specific volume of propellant; the re- dx/dt = BPn (19)ciprocal density before combustion.(For sample computation, see refer- dx/dt = a + BPn (20)ence 3, Appendix Il-G, p. 20.)

where a, B, and n are constants. (See para-H is calculated from equation (16). graph 4-15.)

( Ci ) 4-13. Relative Quickness. Relative quickness1- b +--T-j) Do is defined as the ratio of the average rate of

S b C (16) p L;sure rise of a propellant lot under test to(7(7- b)Do tUe average rate of pressure rise of a standard

4-18

1____0___ __ the relative quickness can be taken as the ratioat cthe Vy values without making any correctionsfor the circuit capacitance. When the quicknessof the test propellant and standard differ widely,Iw// I equations (12) and (13) must be used to obtain

5 the correction for Vy before comparison canX -. , be made. The values of dP/dt are plotted as

functions of P (calculated from the 0.25-volt3_- __ intervals of Vx). The values of dP/dt at 5, 10,

- 15, 20, and 25 thousand psi are taken from thegraph (figure 4-7) and the relative quickness

___• is calculated as in the example below. (Seea~~table 4-5.)

00 ,, 4-14. Relative Force. In interior ballisticsuse, the term "force" is related to the energy

...... ... --.- __released by a given propellant; that is, Force =3 4 10 20 30 (PV)r = nRTv, where (in closed bomb work) P

PRESSURE, psi X 10-3 is the maximum pressure developed and V Isthe volume of the bomb. Since the bomb volume

Figure 4-7. Linear burning rate versus is constant, relative force is defined as thepressure ratio of the observed maximum pressure de-

,,aloped by a lot of propellant under test, to themaximum pressure developed by a standard

propellant of the same formulation at the same propellant, when each is fired in the samespecified pressures when each is fired in the bomb under the same test conditions. Sincesame bomb under the same loading density and pressure is measured as P = KCxVx [equationtest conditions. When the test sample and (1)], if Cx is constant the relative force re-standard propellant are similar in quickness, duces to the ratio of the maximum x-voltages

Table 4-5

Relative quickness and relative force

P dP/dt x 10-6 Rel. quickness, Rel. force,ratio test/std. ratio test/std.

(%) (%)Prop. #1

(std.). #2 #3 #2 #3 #2 #3

05,000 1.03 1.32 1.27 123 123

6,000 1.18 1.55 1.46 132 124

10,000 1.82 2.44 2.27 134 125

15,000 2.73 3.50 3.35 128 123 1.77 1.761.81 1V

20,000 3.67 4.70 4.55 128 12498.0 97.2

25,000 4.66 6.09 5.82 131 126

Avg Max 130 124

V 1.81 1.77 1.76

*Value of dP/dt used, extrapolated.

4-19

recorded on the oscillograms. Values of maxI-Tmum Vx are obtained by measuring a vertical Itangent to the trace at the point of maximum 6

pressure, using the 0.25-volt interpolator. A . .sample calculation of relative force is included 5

above.

For a complete description of rluved bomb r,.4ý53xIo-3 0 .7

technique as used at Picatinny Arsenal, seereference 3. Another application of closed -bomb information as used by the Navy is 2

described in referenLe 7.

4-15. The Proportional Law of Burning Rate. 8 - -/-

The minimum distance between ary two ad-jacent surfaces of a propellant grPir. is called o .26the web. The rate at which the web decreases AVERAGE 20E:,4 2P 32,is a function of the gas pressure produced in agun due to the burning of prorellant grains. Figure 4-8. Proportional law to determineIt is assumed that burning proceeds only on the value of B for n a 1inner and outer grain surfaces, that is, burn-ing of the ends of the grains is neglected. Thetype of burning most usually encountered fol- at three-, six-, and nine-tenths of the maximumlows equation (19), dx/dt = BPn (in. per sec). value of an interval. The maximum value forFor M10 propellant this equation would be the intervals is called the peak pressure (Pp),

distinguishing it from all other values, whichare average pressure values. The slope of

-x-= 4.53 x 10- 3 P0 .7 (21) each of the straight lines thus obtained is B.It can be seen from figure 4-8 that, as the

For ease of computation, it is desirable to ex- peak pressure increases, the :slope decreases;press burning rate as proportional to pressure thus, the maximum value of B 'occurs at the

minimum peak pressure. Values of B aredx= r BP (22) plotted against peak pressures in figure 4-9.

4-16. Effect of Grain Shape on Burning Rate.or, to make equation (19) more useful in the Although the linear burning rate of a propellantHirschfelder system, an attempt is made to is characteristic of the formulation and the

make n equal to unity, in which we consider pressure, the granulation affects the overallwhat should be the value of the coefficient B to rate at which the propellant is transformed tomake n = 1, while the value of rI remains con- gas, since the surface exposed -is determinedstant. The value of B used in equation (22) is by the granulation. The best form .of propellant

an effective value. This effective value is obm grain from a ballistic viewpoint is one which,tained from a plot of the curve of equation (21). with the smallest weight of charge,will impart

(See figure 4-8.) A curve of this nature allows a prescribed velocity to a projectile without

a person desiring to use a proportional law to developing a pressure in excess of the per-

obtain a value of B that best represents the mitted maximum. In this connection, uniformityof ballistic effect must also be considered.

actual burning law over a desired pressure Figure 4-10 illustrates the relation betweenr . grain shape and ballistic effect. It should be

The abscissa is first divided into arbitrary noted that, for equal weights of identical pro-intervals. Then, for each of these intervals, pellant composition, the position of the pressure

the portion of the curve (from the start of the peak in the gun is very weakly dependent on

interva! to the maximum point of the curve in- the grain shape, while projectile velocity. de-

cluded in the interval) is replaced by a line of pends only on charge weight. The criterion

least-square fit. The least squares are obtained for the selection of a particular granulation isthe maximum pressure.

4-20

RFST AVAILABLE COPY

I0

VALUES OF *B"((NOTATION OF OSRD 1801) AREI DERIVED FROM FIGURE 4-8 BY THE LEAST-

8 SQUARES PROCEDURE, MATCHING AT THREE-,SIX-AND NINE-TENTHS OF Pp

a.

-4X

2

0 4 8 12 16 20 24 28 32Pp (IC00 psi)

Figure 4-9. Values of B determined by least-squares fit

The most important dimension of the propellant to the solution of workable form functiors, andgrain is the web thickness. The web size of show how the different systems way be cor-a multiperforated grain refers to its average related. Corner's 9 treatment is similar to theweb. Relatively slight changes in the average Hirschfelder 4 treatment, except that theformerweb of a propellant result in appreciable uses a form coefficient e, based on experiment,changes in the required weight of propellant whereas the latter uses a set of k's based oncharge and maximum pressure produced, for a geometry.given muzzle velocity of the projectile. Figure4-11 iliustrates the relation between surface 4-18. Corner Form Coefficient, 61 If a longarea and weight percentage burned for various cord of propellant, of initial diameter D, burnsgrain shapes. 10 When z (or N/C, the fraction under a pressure P, the rate of recession isburned), is zero, the ratio S/So must be unity uniform over the surface of the cord, and isfor all grain shapes. expressed as 1/2B(P). The amount of gas

generated up to time t is CO(t), where C is the4-17. The Form Function. It is assumed that initial weight of the cord and cgoesfrom 0 to I.all of the exposed surfaces recede at the same The diameter of the cord remaining at the timerate when propellant burns. Thus, there is a t is fD.simple relation between the fraction of pro-pellant burned and the distance tht each sur- Neglecting the small contributionfromthe burn-face has regressed. The mathematical ex- ing of the ends of the cord, we have the geo-pression of this relationship, for any par- metrical relationLicular propellant granulation, L- called theform function for that granulation. In the fol- 0 1 - f (23)lowing paragraphs we present two approaches

4-21

4.0MULTI- PERFORATED

3.5

o SINGLE PERFORATEDX' 3.0• v.•n• . •([PRESSURE • .,.. ..... ...VLCITY

2..

0o -rNGLE PERFORATEDW.

0

1 2.0

V

w

10 20 30 40 50 60 70 so 90 100 IIC 120 130

TRAVEL (IN.)

Figure 4-10. Pressure-travel and velocity-travel curves

in the other fundamental equations, we may1.5 -eliminate f, giving

SINGLE PERFORATED L B (1 )

Rd- 2- (25)1 dt D

These equations are true for any number oflong cords. The web size (D) is the minimum

05 Adistance between any two adjacent burningsurfaces; for cord propellant, the web is equi!to the diameter.

0.2 0.4 0.6 0.8 1.0 Analogous relations may be written down forZ other shapes. Sirgle perforated grains of initial

Figure 4-11. Surface area versus weight- external and internal diameters dl and d2,

percent burned for various grain shapes respectively, have D = I (d1 - d2), and fD as theannulus remaining at time t. The geometrical

and the expression of our definition of the rate relation is

of burning is S= 1 -f (26)

D -=df -B(P) (24) and the burning rate is still the same as in

dt equation (24), leading to

In the solution of the equations of interiorballistics, f is a convenient variable, but as d- B (27)it appears only in these two equations and not t

4-22

This assumes that the rate of burning is the final surfaces is (1 #. 0)/(l - e). Thus, thesame on all surfaces of the propellant, ar.d that larger the 6, the faster the decrease in surfacethe inner and outer surfaces are coaxia;. and the faster the drop in the rate of evolution

of gas at constant pressure. Shapes of positiveBoth cord and single-perforated grains may be 0 are said to be "degressive," and those ofbrought into the same scheme by clousinr.g the negative a to be "progressive." Shapes, suchdimension of the grain along a direction normal as tubes, with 9 = 0, are sometimes said to beto the surface at two points of intersection, "neutral."where the direction is ia one instance passing The possible range of 6 is restricted. 9 cannotinto, and at the other instance passing out of, be less than -1, for otherwise 0 would be nega-the propellant. The smallest such diameter is tive for f near unity. Nor can 0 be greater thancalled the web size. unity, for then 0 would be greater than unity

Next, we define fD as the remaining web when for some accessible range of f. This does nnta fraction 4b of the propellant has been turned mean that the cord, with its 9 = 1, is the most

into gas. From the definition of the rate of degressive shape possible. The sphere has a

burning, given in equation (24), surface which decreases even more rapidly(figure 4-12). In this case, D comes out, by ourprescription, as the diameter, and 4 = 1 when

Ddft-= -B(P) (24) the remaining diameter is zero. Equation (28)cannot express precisely the relation between f

For certain shapes, 4, - 1, when i = 0. For a and 0 for every geometric shape, alLhough a

still more restricted class of shapes, k and f satisfactory approximation can often be made

are related geometrically by by a proper choice of 6. The true geometricform function is - = I - 03 for a sphere. Al-

= (1 - f)(l +4) (28) though almost all grain shapes could be coveredby writing 0 as a cubic in f, this is not done

where 6 is a constant for a given shape. For because the analytical solutions of the ballistic

example, 0 = 0 for single perforated grains, equations would be much more difficult.

Pnd 9 = 1 for long cords.

It is seen that D is defined by reference to a I.0direction which will not exist for a shapechosen at random. For shapes of fairly high _____~

symmetry, D will have a meaning. The defi-

nitions of f and equation (24) then follow with- 0.8

out exception. There is, however, no guaranteethat when this dimension has been eaten away' 000,all %e solid propellant -will have turned into 0.6 +-- " / /gas; only for simple shapes does this occur. €, /#Finally, equation (28) is a very special form. .,We shall discuss the most common shapes toillustrate the variouz possibilities. 0.4

With long cords and single perforated grains,there is no difficulty. The web is easily found, 0.2 aand cquation (28) holds when 9 = 1 and 0, 1respectively. Equation (28) may be referred toas the "form function," with 0 as the "formfactor" or "form coefficient." a is a measure 0 -

of the change in the area of the burning surface 1.0 0.8 0.6 0.4 0.2 0

as burning proceeds. The burning surface of a flong tube remains constant (9 . 0), and the sur- Figure 4-1Z Relationship of form factorface area of a cord decreases to zero as the to rate of change of area ofburning proceeds. The ratio of the initial and burning surface

4-23

4-19. Form Coefficient for OFRD 6468. Let N c. Cord Propellant. Cord propellant is notbe the weight of propellant burned up to any used very much in the U. S. but is used ex-time t, so that N/C is the fraction of propellant tensively in Britain. The exact form function isburned. Let W be the web thickness, which inthe case of multiperforated grains is the mini- N/C = 1 - (1 - W2-W)f-3 (30a)mum thickness beforr the grains splinter. Let fbe the fraction of tWe web that remains un-burned at any particular time. The OSRD 6468 but replacing f 3 by its approximate equivalentballistics are based on a form function that (3/2)f2

- (1/2)f gives the approximate formexpresses N/C as a quadratic function in f; functicnthus N/C= 1 + (! 1 .f i,. f2 (30b)

N/C = ko -klf +÷k2f2 (29) For cord propellant

where ko, k1 , and k2 are all constants that ko = idepend on the granulation and grain shape. Theform functions for all grain shapes, except the kl W -

seven-perforated, can be expressed rigorously

as cubic equations. However, since this would k2 = - (1 +unnecessarily complicate the ballistics, and

since the f 3 -term is always quite small com-pared to the other terms, the quadratic ap- For a very long cord, neglecting the burningproximation is used in practice. This approxi- of the ends of the cord, where W/4L is nearlymation never differs from the exact expression zero, we can useby more than 0.05.

a. Constant Burning Surface. Theformfunc- N/C = 1 - f 2 (31)tion for a grain with a constant burning sur-. whereface is ko= 1

N/C= 1-'f (30) kl =-0•k2 =-1.

which is a simplification of equation (29). This d. Single-Perforated Grain. This granula-is the simplest of all the form functions. Its use tion is in common use in the U. S. for small-greatly simplifies our ballistic computations-. caliber weapons. The web of this grain is one-It is derived from a consideration of a grain " half the difference between the outer and innersuch as a sheet, whose web is so very small, diameters. The form coefficients arecompared to its length and width, that W/D and.W/L can be considered equal to zero., ko Il

ko01 = - W

kl= 1 . Lk2 =0 .

k2 =-

b. Strip Propellant. The web of this grain is No approximation was made here, but if'W/Lits thickness and the k-coefficients are: is quite small the form ior constant burning

surface may be used, and is recommended

ko= 1 except for very accurate work.e. Multiperforated Grain (Seven-Perforated).

- w 2 Form functions for the burning of this granula--k+ W tion, which is the most common in use in theL U. S. for large-caliber weapons, are morecomplicated than those described above. The

W2 burning is considered to occur in two stages,

L" D+ a progressive stage, before the web burns

4-24

through to the formation of unburned splinters; 2. Regressive Burning. Afler splintering,and a regressive stage during the burning of shown by the flex in the graph at f = 0, thethe splinters. The burning in each stage is slope decreases. This part of the curve isapproximated by a separate quadratic form represented by anoth'er quadratic of the formfunction.

1. Progressive Burning. The burning of N/C = k• - k'f + kkf2 (32)the grain before splinter formation may betreated analytically. Values of ko, k1 , and This is actually a continuation .of the cu.vek2 , to be used in equation (29) for various to the left of f - 0. It is shown in referencevalues of the ratios D/d (grain diameter to 4 that if the curve is made to pass throughweb diameter) and L/D (grain length to the points (f = fo, N/C = 0), (f = 0, N/C - ko),diameter), are given in table 4-6. The curve and (f - -0.5, N/C - 1), the resulting ex-of figure 4-13 (obtainEd from reference 4, pression is a satisfactory approximationbased on reference 6) is a plot of the burning to the form function in the regressive in-of a grain with D/d = 10, and L/D = 2.5. It terval. Accordingly, the form function to usewill be noticed that the slope increases up to in the interval after splintering isgiven b7f = 0, where the splinters form. the following equations.

Table 4-6

Form functions for seven-perforated propellant

1.5 2.0 2.5 3.0 3.5D/d

ko 0.8409 0.8362 0.8335 0.8316 0.8303

8 k1 0.9111 0.9300 0.9414 0.9490 0.9544

k2 0.0702 0.0938 0.1079 0.1174 0.1241

0ko 0.8498 0.8451 0.8423 0.8405 0.8191

9 kj 0.9298 0.9507 0.9633 0.9717 0.9776

k2 0.0800 0.1056 0.1210 0.1312 0.1385

ko 0.8563 0.8516 0.8487 0.8468 0.8455

10 kt 0.9447 0.9673 0.9808 0.9898 0.9963

k2 0.0884 0.1157 0.1321 0.1430 0.1508

ko 0.8612 0.8565 0.8536 0.8517 0.8503

11 kj 0.9569 0.9809 0.9Q52 1.0048 1.0116

k2 0.095? 0.1244 0.1416 0.1531 0.1613

ko 0.8652 0.8603 0.85'4 0.8554 0.8541

"12 k1 0.9673 0.9923 1.0073 1.0173 1.0245

k2 0.1021 0.1320 V.1499 0.1619 0.1704

k0 0.8682 0.8633 0.8604 0.8585 0.8571

13 kI 0.9760 1.0020 1.0177 1.0281 1.0356

k 2 0.1078 0.1387 0.1573 0.1696 0.1785

4-25

.' -I

1.0POINT OF

0.8 -SPLINTERING

0.6 ____

0.4

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6(I-f)

Figure 4-13. Actual versus theoretical burning curves

k= = ko thickness. With this adjusted web and thecorresponding f,

k 4fo (I - ko) + (ko/fo) C , I - f2fo + I

Stating this another way, we may say that a

4 (1 - ko) - 2 (ko/fo) seven-perforated propellant is ballistically(1 2fo + I equivalent to a sinrge-perforated propellant of

1.25 times its web thickness. The factor 1.25

3. Simplified Form Function for Seven- may vary somewhat between 1.23 end 1.28,Perforated Propellant. It is often convenient depending on the conditions of firfilg, and onfor the purpose of rough calculations to con- whether the ballistic equivalence of the twosider the seven-perforated grains as having propellants is based on the same muzzle veloc-a constant burning surface throughout their ities or the same maximum pressures.entire burning. This approximation cor-responds to replacing the true form function 4-20. General Form Functions. The particularby the dotted line in figure 4-13, which is equations (form functions) used to describe thea graph of N/C = I - f with specific values, change in grain geometry during burning as aSince it is desired to vary f between unity function of web or linear distance burned areat the beginning and zero when all of the determined by the ballisti:, method used. Para-propellant is burned, instead of between 1.0 graphs 4-18 and 4-19 have described the formand -0.25, as indicated by the dotted line in functions used in the Corner and Hirschfelderfigure 4-13, we must define an adjusted systems. The form functions of the most com-web equal tc 1.25 times the actual web mon granulations, as used in the method of

4-26

[ST AVA" ABL_ COPY

subparagraph 4-12b, are included here along Sx 2(LD+DW+LW)-8(L+D+W)X+24X 2

with their exact equivalents, since their deri- -S =

vation is time-consuming.11 The symbols used V° Lwh

in the various equations are listed below. 2(LD + DW + LW)X - 4(L + D + W)X 2 + 8X 3S.... • Z =Lwh

NN - fraction of charge burned

N = amount of charge burned b. Equations for Cord Propellant. The exactC = initial amount of charge equation for fraction of charge burned is

Vo = initial volume of grain N- 1 + LR - Lf2 L f3Vx = volume burned at any linear dis- N --_-L

tance (X)

So = initial surface of grainSx = surface of grain burned at any linear where R is the radius of the cross section of

distance (X) the cord. The Hirschfelder approximation for

Vx = fraction of propellant remaining this is

Vo (N/C= 1 -Vx/Vo) N (If)(1+ f) =1 -f 2

CX = linear distance burned to flame front,

perpendicular to burning surfacef perpnculan o burning on the basis that L is much greater than R, sof fract on of web remaining that H becomes negligible by comparison. Since

f is a decimal, it becomes insignificant when itis cubed, and the f 3 term drops cut. The other

s= progressivity equations, given without derivation, are as

follows.R, r = larger and smaller radii, respec-

tively, of grain geometry Vx 2(R2 + RL)x + 4R+ L X2 2 X3W = web, or thickness Vo R2L X R2L

L = lengthD = width Sx 2(R 2 + RL) - 2(4R + L)X + 6X 2

(Note that Z = I - Vx/Vo) So R2 L

a. Equations for Strip Propellant. The exactformula for fraction of charge burned is 2(R + RL)X - (4R + L)X 2 + 2X3

N + (LW+DWV- LD- W2) f R 2 L•= 1+LD

+ (2W 2 - LW - DW) f2 c. Equations for Single-Perforated Propel-L5 lant. The exact formula for N/C isW2 f 32

"•'D N= 1 + R- r- L R-rfL and D are both assumed to be much greater C L L

than W, and the f 3 term is assumed negligible, where the web (R - r) is assumed much lessWith these assumptions, the Hirschfelder form than the length (L), so that N/C becomes equalcan be shown to be to (1 - f). This again is the Hirschfelder

equation for a constant burning surface. TheHirschfelder equivalent, before simplification,

N I -f isC

which is the Hirschfelder form function for a N I + k2f2constant burning surface. The other equations Care as follows.

4-27

where In the Hirschfelder system, the equivalent formkI - W function is represented by a cubic equation

L [see reference 4, p. 129, equations (14) and(15)) that is simplified to a pair of quadratics

W of the form

N/C= ko-klf * kf 2

(See subparagraph 4-19c.) The other equationsare given below, where the roefficients ko, kl, and k2 are ex-

pressed in terms of grnin diameter, grain

Sx 2(R .. r + L) - 8X length, and web. (See subparagraph 4-19d.) The

Vo L(R - r) other equations are

2(R- r + L)X - 4X2 Sx 2 [(R + 7r)L + (R 2 - 7r 2)]Z = L(R -r) V = -

Vo L(R2 - 7r2)

Vx 1- 2(R- r+L) 4 -4[2(R+7r)- 3L]X- 36X 2

Vo L(R- r) X + L(R -r) X2+ L(R 2 - 7r 2 )

d. Equations for Multiperforated Grain. Theexact formula for NIC is

N R3 - R2 r- 5R 2 r- 3r 3 z=2 [(R + .7r)L + (R2 - 7r 2)]X

C 16(R2 - 7r 2 ) L(R 2 - 7r 2)

14R 2 L - 4RL - 114r 2 L 2 [2(R + 7r) - 3L]X2 - 12X 3

4- 1 6 (R 2 '/ 2 ) +2- L(R 2 - 7r 2 )

9R 3 - 49R 2 r + 35Rr 2 + 93r 3 - 20R 2 L

+ 16(R 2 - '7r 2 )

40 RrL + 60r 2 L16(R 2 - 7r 2 )

-i3R 3 + 77R 2 r - lllRr2 - 9r 3 + 6R 2 L

6(R2 - 7r 2)

- 36RrL + '54r 2 L+ f2

16(R2 - 7r 2)

3R3 - 27R 2 r + 81Rr 2 - 81r 3

+ 16(R2 - 7r 2 ) Q

4-28


"1. Jackson, W. F., "Closed Bomb Method of Powdor Testing," E. I. Du Pont de Nemours &Co., Explosives Dept., Carney's Point Works, 1941.

" p

2. Proof Directive-12, Rev. 3, Supplement to U. S. Army Specification 50-12-3, Powder,Cannon, Propellant.

3. Pallingston, A. 0., and M. Weinstein, Method of Calculation of Interior Ballistic Propertiesof Propellants from Closed Bomb Data, Picatinny Arsenal Technical Report No. 2005, 7.A•le1954.

4. Interior Ballistics, A Consolidation and Revision of Previous Reports, Office of SnientificResearch and Development Report No. 6468. Juiy 1945.

S. Closed Bomb Burning of Propellants and High Explosi"Ves, Office of Scientific Researchawid Development Report No. 6329, January 1946.

6. Tschappat, W. H., "Textbook of Ordnance and Guniaery," John Wiley and Sois, New York,1917.

7. Atlas, K., A Method for Computing Webs for Gun Propellant Grains from Closed-VesselBurning Ratcs, Naval Powder Factory, R. and D. Dept., Indian Head, Md., MemorandumReport No. 73, 'anuary 1954.

9. Hughes, S. G., Summary of Interior Ballistics Theory for Conventional Recoilless Rifles,Frank-ord Arsenal, Report No. R-1140, September 1953.

9. Corner, J., "Theory of Ihterior Ballistics of Guns," John Wiley and Sons, Inc., New York,1953, p. 30ff.

10. Hunt, Co. F. R. W., et al, "Internal Ballistics," Philosophical Library, New York, 1951,p. 52.

11. Julier, B. H., Form Functions for Use in Interior Ballistics and Closed Chamber Calcula-tions, Naval Powder Factory, Indian Head, Md., Memorandum Report No. 3, February 1951.

4-29

THEORETICAL METHGDS OF INTERIORBALLISTICS

Table 4-7Table of symbols

Symbol T Unit 1 Definition

A In.2 Cross-sectional area of bore

a in. 3 per lb. 7

ao ... 23,969 (-1)

B (in. per sec) Burning constant(lb per in. 2 )

b ft 2 per sec 2 2C Fnl'fý - 1)

C lb Charge weight

C,, ... Specific heat (constant volume)

e2 ft per sec j 1CF(B/W)A

e 3 ft-lb per in.3 e2 2 mt

Vc

F ft Powder impetus

f ... Fraction of web remaining unburned

fo 'Initial value of f.

g ft per sec2 Acceleration due to gravityoz z dz

J ... exp dq. q+z-uz

2

No

C

JI" k, - 2k 2 fo

2- k2

ko, k1, k 2 ... Form-function constants

L in. Travel of the projectile

M lb Weight of projectile

m slug Effective mass of projectile

mr slug Modification of m

N lb Weight of powder burned

No b Weight of powder burned when projectile beginsto move

P lb per in. 2 Space-average pressure

4-30

Table 4-7

Table of symbols (cont)

Symbol Unit Definition

PO lb. per in. 2 Initial value of P

pO lb. per in.2 aoP

Pr lb. per in.2 Pressure resisting projectile motion (friction)

Px lb. per in.2 Pressure on base of projectile

2 1 YAl~z) ( -77 0) -

JoZb

R energy Gas constant(gm-moleOK)

94oJ2 for..

Zb

Z dZs J -T

T ok Absolute temperature of gas

To ok Isochoric flame temperature

t sec Time from beginning of motion of projectile

k2 fo

S2 - JZb

V ft per sec Velocity of projectile

VC In. 3 Chamber volume

W in. Web of powder

X in. Distarce from the basoi of the projectile 0• apoint fixed with respect to Lhe gun

Xo in. Effecti-e length of chamber !LcA

x ... X - ro

xoXO

y ... X

yo ... y - rZ

z Ve2

Zb ... Value of Z at the time the powder Is all burned

4-31

Table 4-7

Table of symbols (cont)

Symbol 1 .. Unit Definition

Geometric density of loading

r ... Function of Zb (or Zs) and Ppo

Ratio of specific heats

S..Pseudoratio of specific heats

* lb per in. 3 Average density of gas

* gm. per cm3 Density of loading. A = 27.68 Ao

S... Constant depending on ratio of charge weight Cto projectile weight M

7 in. 3 per lb Covolume of gas

lb per in.3 loom

ý11Jo -k2 fo(f)

aA

p lb per in. 3 Density of eolid powder

a€ •"Yo " P

Table 4-8

Symbols proper to the RD38 method only

Symbol Unit Definition

D in.2 Initial web size

E in.3 Al (initial free space behind shot)

fD in. Remaining web

M1 .Central ballistic parameter

RT° ft-lb Force constant

ft-lb per lb Effective mean force constant

4-32

1EST AVAII-ABLE COPY

4-21. Introduction. When a gun is fired, the 4-22. Fundamental Equations of interior Bal-

primer delivers energy in the form of hot listics. Interior ballistics attempts to predict

gases to the individual propellant grains in the mathematically the effects described quali-

S ~ propelling c'iarge, 2nd initiates the decomposi- tatively above. The fundamental mathematicaltion reactions of the propellant. It Is known relations are: (a) equation (43), representing

that in many artillery rounds deficiencies of t.e the rate of burning; (b) equation (33), repre-ignlt'l.- system cause nonuniform distribution senting the motion of the projectile; (c) equationof primer energy and, consequently, time dif- (42), the energy balance equation; (d) equationferences in initiation of various parts of the (34), the equation of state of the powder gas;charge. For ease of mathematical treatment, and (e) e-aation (47), an equation expressinghowever, it is assumed that all grains are ig- the variation of weight fraction of propellantnited on all surfaces instantaneously. The rate remaining with fraction of web burned.at which the solid propellant is transformed togas depends on total exposed suriace and on Interior ballistics is concerned with the simul-

the pressure surrounding the grains. If there taneous solution of these equations, which arewere no mechanism serving to increase the correctly modified to take into account pro-

volume available for gas (chamber volume jectile friction, the distribution of the gas, the

minus the volume taken up by the solid, un- heat lost to the bore, and other second-orderconsumed propellant), the pressre would rise effects.at an increasingly high rate until the propellantwas all transformed to gas. This is the action The variety of systems of interior ballistics

in a closed bomb, %here the loading density that have been proposed differ in the number

(propellant weight divided by chamber volume) of simplifying assumptions made in order to

seldom exceeds 0.2 g/cc, and the pressure obtain a solution of these equations. If time is

may be as high as 45,000 psi. At the loading no object, or if automatic computing machines

densities usual in guns, however, if the volume are availabie, it is possible to solve these

did not increase during propellant burning the equations by maintaining a strict analogy to

pressure would become excessively high. This the physical phenomena. A quick hand com-

increase in volume is provided by the forward putational technique, nowever, requi:es some

motion of the projectile with an acceleration simplification. Two excellent compromises be-

proportional to the force exerted by the chain- tween exactness and ease of calculation are

" ' ber pressure on the projectile base. The pro- outlined in references 1 and 2. We reproduce

jectile begins to move as soon as the force on below the method of reference 2, and two very

its base is high enough to overcome the crimp much simpler techniques, one in use in the

and to inscribe the rotating band in the forcing United Kingdom (RD38) and the other in con-

cone. As the volume increases, the bulk gas siderable use by the U. S. Navy (Le Duc).temperature decreases, and the internal energychange of the gas is mostly accounted for by 4-23. Basic Problems. The basic problems to

the kinetic energy acquired by the projectile, which solutions are desired are of the follow-In the beginning, when the projectile is moving ing two general types.slowly, the pressure increases as a result of a. Given the type, web (essentially a mea-

propellant burning. A proper balance of the sure of available bumning surface), and weightfactors that influence propellant burning and of the propellant; the weight of projectile; andprojectile motion determines the maximum at- the characteristics of the weapon, calculatetainable pressure. After this, the rate of vol- the expected maximum pressure and muzzleume increase more than compensates for the velocity.rate of gas production, and the pressure be- b. Given the characteristics of the weapon;gins to drop. The point of maximum pressure the weight of the projectile; and the muzzle

occurs when the original volume has about velocity and maximum permissible pressure,doubled. After the propellant is completely find the weight and web of propellant requiredtransformed to gas, the pressure drops more (to this problem, there may be no practicalrapidly. The projectile continues to increase solution).in velocity, at an acceleration prcportional tothe pressure until it emerges from the muzzle In each of these cases it may be necessary toof !be gun. (See figure 4-14.) establish the point-to-point relationship among

9 1% 4-33 ...1j,

* - i ll

No -\

0.)la/et IU \S ao" ,\01O M -

W It

0 W 30 30 " so X s 0 "Wo 1" 10 .30 W

LENGTH OF TRAVEL (IN)-7,, -4* o~ -4ti -10O --2* -6*

TIME (MSEC)

Figure 4-14. Pressure versus time and pressure versus travel curves

time, position of the prnjectile, velocity and Px is the pressure on the base of the projectile,pressure; or the muzzle velocity, maximum and t the time measured from the beginning ofpressure, charge, and web may be the only motion of the projectile. Normally, the cross-values desired. sectional area of the chamber is larger than

that of the bore. It is convenient to define the4-24. Development of the Fundamental Equa- zero point of X so that AX is the total volumetions. The equation of motion of a projectile behind the projectile available to gas andis one of Newton's laws. This equation states solid powder. However, the zero point may alsothat the force is equal to the product of the be the position of the projectile base beforemass and the acceleration. In the case of a motion occurs. In that case the distance trav-gun, the iorce causing the acceleration of the eled is denoted as X and the equation of motionprojectile Is the product of the pressure and isthe area on which it acts. Thus,

M d2XAPx = - -

Md 2 X M dV g dt 2 (33)APx .(33)

g t2 g dX

4-25. Equation of State. The equation of state

where A is the cross-sectional area of the base of the powder gas is the relation among theat the beginning of motion of the projectile, and pressure, the density, and the temperature ofX is the distance the projectile has moved. M is the gas. This equation is to some extent em-the weight of the projectile, so that M/g is its pirical. The virial equation of state is the mostmass (g is the acceleration due to gravity), general form. This equation gives the pressure

4-34

BEST AVAILABLE COPY'.

in terms of a power series in the density. How- Simplifying, we getever, it is apparent that such an equation wouldconsiderably complicate the equations of in- pV c aN-NFT (39)terior ballistics. It can be shown that the Abel V I +AToequation of state applies with sufficient ac-curacy under the conditions of the gas in thegun tube. The Abel equation of state is the 4-26. Energy-Balance Equation. The energy-van der Waals equation with the constant a balance equation simply states that the loss of

omitted because it is negligible at the high internal energy of the gas is equal tothe kinetictemperature prevailing in guns. The Abel equa- energy cf the projectile. Thustion of state is 1fT° CvdT = 1/2 _Mv2

S(40)JT gP( = - nRT (34)

Where V is the velocity of the projectile, N theamount oi powder that has been burned, To the

where a is the average gas density; 17 the co- flame temperature, and CV the specific heat ofvolume of the gas; P the space-average pres- the gas at constant density. We assume that CVsure; T the absolute temperature; n the number is constant in the region of temperatures in-of moles of gas per unit weight; and R the usual volved, so thatgas constant.

The volume available to the propellant and the NC, (To - T) = 1/2jV- (41)

propellant gas is Vc + Ax, where Vc is theoriginal volume (the volume of the cartridge Then the equation of energy balance becomescase corrected for the volume occupied by theprojectile extending into the case before firing). NF - = 'r V (42)If p is the density of the solid propellant, then, -- 1I To 2gsince C - N is the amount of propellant remain- 4-27. Burning Rate Equation. The equation of

ing unburned, C -. N is the volume occupied by the rate of burning is the equation that givesP the rate of regression of the surfaces. It has

the solid propellant remnaining. The volume been found empirically that the rate of burningavailable to the gas is of the powder depends primarily on the pres-

(C__N) sure of the gas surrounding the burning grains.Vc + Ax- Other factors apparently affect the rate to only

a small extent. It has been found that the de-pendence of the rate on the pressure can be

and the gas density is given by given by an equation either ad the form

N dr

Vc+AxC - N (35) d--= a + bP (43)

or

Let us define two constants characteristic of dr nthe powder. dt= BP (44)

1a = (36) where r is the distance the surface has re-

gressed. It has been found that both forms fitF = n RT (37) the experimental data equally well. In the case

of equation (43) it has been found that the con-The equation of state becomes stant a is small; and in the case of equation

(44) the exponent n is near unity. An equationof the form

Vc + Ax-(C - N)/P] T (38) d=Bp (45)N -- "rB(5

" - 4-35

therefore fits the existing data with reasonable 4-29. Equations of Motion and Energy Balance.accuracy over the range of high pressures ex- The motion of the powder gas is represented byisting in guns. In addition, the use of an equa- the usual partial differential equations of fluidion of thiis type permits an analytic solution lf flow. A solution of these equations applying to

the ballistic differential equation. For these the motion of a gas in a gun tube with the pow-reasons, we adapt the approximate equation for der burning has not been found. A solutionthe rate of burning, equation (45). The web of under certain restricted conditions was de-the powder grain is defined to be the minimum veloped by Love and -Pidduck. I However, thisdistance between the surfaces of the grain, that solution involves the motion of waves of finiteis, the distance which must be burned before amplitude, and is entirely too cumbersome to

the grain is completely consumed (or in the use in the., equations of interior ballistics. Acase of seven-perforated grains, before the solution developed by Kent represents a limit-grain splinters). The equation of the rate of ing condition, that is, a stable• equilibriumaburning to be used in this ballistic system is situation. The development of this solution is

described in section 57, reference 2.dfdt BP (46) According to this solution, the pressure on the

base of the projectile is related to the averagewhere B is' the burning constant (a constant gas pressure by

characteristic of the type of powder); W theweb of the powder; and f the fraction of the web [M + C1which remains unburned. The quantity f is re- P = *P (50)lated to the fraction of the powder burned by Mpurely geometric reiations based on the geom-etry of the grain. It is shown in section 52 of and the projectile base pressure is related toreference 2 that this* relationship can usually the breech pressure by Pbreechbe represented satisfactorily by a quadraticequation of the form Px IM + C1

N/C = ko- klf + k2f 2 (47) M (51)

where 6 is a constant depending on the ratio ofThe values of coefficients ko, kl, and k2 depend the charge weight (C) to the projectile weightonly on the shape of the grain. C

(M). In the usual cases, when the ratio - is

Equation (47) is expressed in the RD38 method about 1/3, 8 is about 3.1. (In RD38, the valueas of 8 is taken as 3.) It is also shown in section

N 57 of reference 2 that the kinetic energy of the-=(-f)(1 + ef) (48) CVpowder gas is given -by CV2

= 1 + (e- 1)f-f 2 (49) It becomes convenient to define an effective

4-28. The Second-Order Effects. In the previous mass of the projectile,section a necessary distinction was made be- (M + C/O)tween the pressure on the base of the projectile, m = (52)and the space-average pressure. The gas must gfollow along behind the projectile, yet the In terms of this quantity the equation of motion,breech. element must remain stationary. This equation (1), becomesmotion of the powder gas causes a pressure d2Xgradient to develop, in which the pressure on APav = m (53)the base of the projectile is lower than that at " dt2the breech. The kinetic energy of the gas ,nu:tbe included in the energy-balance equation, and the equation of energy balance, equationand the existence of the pressure gradient must (33) becomesbe taken into account in relating the motion ofthe projectile to the space-average pressure. NCv (To- T) 1/2 mV2 (54)

4-36

ITFS AVAiLABLE COPY

4-30. Energy Equation Including Heat Loss. divided by the cross-sectional area A. From"The heat lost to the bore surface up to any equation (59) and V i this term becomesinstant is taken to be proportional to the square -t

S," of the velocity. Thus if h is the amount of 1/2 mV2Cenergy lost to the bore of the gun, then

h = 1/2 (mV2 B) (55) This correction term must be added to the righthand side of the energy-balance equation, equa-

where B is a constant. Some justification for tion (56), to give

this form is given in section 55 of reference 2. .N. (1-7 - 1 To (62)

This term is now included in the energy equa- = (1 + B) 1/2 mV2 + 1/2 mV2Ction, equation (54) so that Equation (62) can be written in terms of m' as

NFF _ T)(1- )=(1+B) 1 mV2 (56) (63)

V--I To 2= (I + B) 1/2 mtV2 - 1/2 CpmV2

4-31. Energy Equation Allowing for Friction.We take the friction of the projectile~ to be The final term is dropped as negligible, to giveWe tke he ficton o th proectle t be as the modified equation of energy balance

equivalent to a resisting pressure on the baseof the projectile equal to a constant fraction of NF Tthe actual average pressure. The resisting - (1 -o) = (I + B) 1/2 m'V 2 (64)

pressure is taken to be

4-32. Solution of Equations by the SchemePr + P RD38. The simplifying assumptions are asPr =• P 57) followa.

a. There is no initial resistance to motionBecause of this friction, the equation of motion, by cartridge-case crimp, or the need for en-

" ' equation (53) must be modified. Pressure caus- graving the rotating band.ing acceleration is no longer P, but rather b. The temperature of the gas during burn-" Pr. Thus ing is constant, thereby reducing the simul-

taneous equations to be solved.

A 1 d2 X c. The covolume is assumed to be equal toI m (58) the specific volume of the solid propellant.

dt2 These assumptions permit an aigebraic solu-

tion of the remaining simultaneous equations.or

= d2X By assumptiou b the right hand side of equa-AP dt2 (59) tion (39) becomes XN, and by assumption c,

a = o. The equation of state, equation (39), then

where becomes

S= (1 + c)m (60) Pav. [e+ Ax -•G].= XN (65)

The work done against friction must be in-cluded in the energy-balance equation. This or, in terms of breech pressure (P). See equa-work is tions (50) and (51).

AI Pr dX -, Af P dX (61) + C)

0 o0 P Vc + Az- =• (66)

where Xo is the effective length of the cham- 3W1)ber, defined as the volume of the chamber

4-37

The assumption c introduces an error that may pN (1 + C/2M1 )be considerable at high densities of loading, P(x+t) =A (1 + C/3M1 ) (74)since ,7 is about I g/cc, and I/p is 0.6 g/cc.The result is that the peak pressure is higher dVthan the calculations would predict. This can (MI + C/2) "Y t- AP (75)

be compensated for by increasing either B ork., which then becomes dependent on peak with the initial conditions x 0 at f = 1.pressure. It is more convenient to hold \constant, and to vary B as required to cor- Eliminating P from equations (73) and (75) andrespond with ballistics, integrating, we get

We can write V = AD (I - f) (76)B(MI + C/2)

VC E At (67) If we use equation (76) in equation (75), andelimi.nate P by using equation (74), then

where E is the initial free space behind the dx Ix+1\shot. The length t is a convenient measure. - = - M' (77)Hence, equation (66) becomes df 1 +of

( C whereA N 1 +P(X+ = (68) M1 A2 D2 (1 + C/3M1)32.2

+ B 2 MICX,( + C/2MI) 2 (78)

The equation of motion of the shot is Integrating equation (46) with 9 • 0,

MdV AP x+ = (+ e + Mf 9 (79)

dt C (69)2W1 whereas, if 9 = 0,

neglecting resistances to motion, the recoil of x+ = teM'(i " f) (80)the gun, and the rotational inertia of the shot.To include these we replace equation (40) b•" The pressure P can now be obtained from

equations (39) and (48) asdV AP ei• : (81)

MI 1 C (70) XC(I + C/2M1 ) (1 - f) (1 +,90) (1 + efM2 P =E,%I + C/3MI) .T• ..,

where MI = mM and \C(l +C/2MI)9 =0:P = - (I - f)e (82)

m = 1.02 (approximately) (71) E(1 + C/3MI)This completes tIe determination of x, V, andP as functions of the parameter f.

The fundamental equations are thus:

NX is an energy per unit mass, the square of aN= (1 - f) (1 .+1) = 1- (.- 1)f- &f2 (72) velocity; AD/BMi is a velocity. Hence M' is

dimensionless, as it should be in order to beconsistent with equation (77). M' is the "central

D_ f- BP (73) ballistic parameter" of this method. M' or andt equivalent can be identified in nearly all of the

ballistic theories that lead to explicit solutions.

4-38

can be thought of as a dimensionless param- The last equation (91) is simplified aseter showing the importance of the shot motion"in reducing the pressure from the vn":c that x.C(1 + C/2M1)((I+would be attained in a closed vessel. PM= (93)

p ~~E(: + C/3M1 ) (eM' +40) (34-33. Values at "All Burnt." The suffix B willbe used to denote quantities at the instant at This is exact ior 9 = 0.which the propellant is just burnt, f 0. Fromequation (76), 4-35. Solution After "Burnt."

AD Let X + (94)VB = B(M1 + C/2) (83) - i

Integrating equation (77), At any travel x greater than xB, the pressure is

xB+ t =t(l +9)M'/6 (& •0) (84) PfPBr-V (95)

= teM' (e = 0) (85) The velocity is given by

From equation (74), V2. -C(M + (6Ml + C/3 (96)

X C(I + C/2M1)P (1 + C/3MI) (I + a)M'/O (8 / 0) 76 whrre) (97)

-M' where 5 is the equivalent specific heat ratio,,\C(1 + C/2MI) e (= 0) (87)

- E(1 + C/3M1) defined by equation (44).

4-34. Values at "Maximum Pressure." Quanti- For details on the derivations of the equationsties here are denoted by the suffix m. Differ- for the last three conditions, refer to referenceentiating equations (48) and (49) gives 1, pages 138 and 139.

M' + 9 - 1 (88) 4-36. Summary c the Working Formulas. Afm- M' + 2( solution of the equations given above leads to

the expressions given below.'for all 8. Also

If M'> (I -8),N (1 + C)2 (M' + 6) xC(i + C/2MI) (1 + &)2

C m h )2Pin = (98)C (M' + 26)2 (89) E(I + C/3M1 ) (eM' + 46)

Xm+ t2)t MI + 2 0) Otherwise, the maximum pressure is

\,C(1 + C12M1)PB =(9W• 0) (86)

= -e e -= 0) (90 E(I + C/3MI) (I + C )M'/(

andPm (91) XC(l + C/2Mj) • (6= 0) (87)

XC(1+C/2M,)(1+8) 2 (M'+ 6)1+(M'/6) ( 0) E(l+C/3M1 ) eM'

E(1 + C/3M1 ) (M' + 2 )2 + (M'/&) The position of "all burnt" is given by

XC(l + C/2M1 ) (92) xB + t = t(l + e)M/8 ( 0) ,84)

E(14.C/3M,)eM' ==0teM'- ( = 0) (85)

4-39

* ~- - . - - . .. -.- -.-- -

If the muzzle is at travel x, and used in assessing charge for production lotscf propellant for various weapons. In the prob-

x + ( lem worked out below, we will take item 21r= X(94) (from table 4-22) as the one for which a solu-

B tion is known. Then we will try to find the max-

and imum pressure and muzzle velocity for items10 and 14.

Q 2 (1 - rI - X) (97) Knowing the value of the maximum pressure as

given for item 21, we find the value of M' foritem 21. We check this value of M) with the 9

and X /RTo used to see if the correct velocity

V2 M1C 3 (96) will be obtained. The final value of 9 andMI + C/3 ( X/RTo that we will use will be the one that will,

give us the correct velocity. Then, with thecorrect value of M' for item 21, we can calcu-late M' for items 10 and 14.

4-37. Sample Solution by Use of the RD38System. The equations developed include twoconstants whose value cannot easily be found In the first set of calculations, we shall assumeeircept with experience obtained through the use that 9 = 0, and then take various .'alues forof this scheme in the analysis of past firings. X/RTo to see whfrh of the'e wil! bp correct for

Since X/RTo is equivalent to •--, where T' is our problem.

the correctly avcraged temperature assumed In the standard calibration chart (table 4-22) itto exist during propellant burning, X/RTO should will be noticed that the maximum pressure isbe a fraction, probably between 0.8 and 1.0. given as 39,500 psi, whereas the value used in0 can be assigned from considerations of this example, as well as for Hirschfelder andgeometry of the grain alone, but there are other Le Due is 45,400 psi. This is so as the presrfactors :,uch as nonideality of ignition and im- Lure g is 4,0 p hirts is sh oater ges-perfect pi ,pellant grains that make a better sure given in the charts is the copper gage~ t b 02 reaerthn he eoetic pressure, which is a lower reading. To con-value at 6; to be 0.2 greater than the geometric vert to the actual pressure, we must multiplyvalue. The actual values have to be fitted in a e copper pressure by 1.15.particular problem to match the observed prop-erties to calculated ones. When no results offirings are available for the particular case Using the basic formula for pressure, we havedesired, it is necessary to obtain values of 9and X from an analysis of a sir ilar case where xC(1 + C/2M1 ) (1 + 9)2

ballistic firings are available. Pm= (98)E(1 + C/3MI) (eM' + 49)

The burning constant B is of p ime importancein determining the maximum pressure, as is -However, since 8 = 0, the formulacanbe slightlyclear from various equationsý However, it is simplified.difficult to correlate values of B determinedfrom closed-chamber firings with thcse ob- Assuming 9 = 0, and ,/RTo = 0.9, we havetained in guns. Hence, whene.er possible, Bshould be determined from the observed max-imum pressure or muzzle velocity in a bal- 45,400 = (0.9) (3.18) (3.12) (1e15) (12) (105)

listic firing of a similar case to the one under (1.58) (L.1) eM1

consideration. This can be done once values are M' = 1.50assigned to x and 0.

An illustrative example, of the manner in which Checking the velocity with this value, we findthis scheme may be used, follows. Table 4-22 that the velocity is 2,680 ft/sec, which is toocontains the ballistics'of reference propellants low.

4-40

We then try a higher value of X/RTo. Trying t for item 10 = 2.31S= 0 and X/RTo = 0.93, we have 0 for item 14 1.62

M'= 1.54 v2 -(0.98) (3.82) (3.18) (3.76) (32.2)5V02 18.2

This value of M yields V as 2,710 ft/sec. Hence VIO = 2,560 ft per secwe raise the value of X/RTo to 0.96, and obtaina velocity of 2,780. We try.X/RTo = 0.98? and (0.98) (3.39) (3.18) (2.87) (32.2)obtain a velocity of 2,800. The value of M that 0 ( (9 .6we choose for item 21 is 1.69. Using this valueof M we can calculate the burning rate, using V14 2,180 ft per sec

the formula We now assume a value of & as 0.15, and then

A "2 D2 + C/3M 1] 32.2 try various values of k/RTo to see which is

M I - (78) correct. We again use the formula for max-

B 2 MtC,\ •+ C/2M' 12 imum pressurexC(1 + C/2M1) (I + 0)2

B2 102 (2.97 x 10-3) (1.1) (32.2) E(1 + C/3M1) (eM' + 4e)

(1.69) (26.5) (8.12) (0.98) (3.18) (1.32)-8 Trying successively the values of x/RTo as

B2^ 7.ýF x 10 0.85, 0.87, 0.90, and 0.92, we find thatX/RTO = 0.88 will yield the correct velocity

Using this value of B, we can find M' for items for item 21. The correct value of M' for10 and 14. item 21, using 6 = 0.15 and x /RTo = 0.88, is

1.79.(49.3) (1.76 x 10-3) (1.08) (32.2) B2 is obtained as 7.19 x 10-8M'10 = t2i banda .9x1-

(7.55) (16.9) (3.82) (0.98) (3.18) (1.21) M10 = 1.830 = 1.59 M1 -= 1.61

PrM10 = 44,400 lb per in. 2

M = (49.3) (1.35) (1.07) (32.2) Pm14 = 23,100 lb per in. 2

(7.55) (16.5) (3.39) (0.98) (3.18) (1.23) Checking the velocities in these, we obtain

M'14 = 1.57 010 = 1.65

Calculating the pressure for items 10 and 14, 0 14 = 1.24

we get V10 = 2,610 ft per sec

(0.98) (3.18) (3.82) (1.12) (12) V14 = 2,230 ft per secPml- (7f(.8)(.4

m10 = (73) (1.08) (3.94) We again repeat the problem, but assume

Pr10 49,400 lb per in. 2 0 = 0.30, and in the first case, thatx/RTo= 0.95.= • Usi,. the formula

(0.98) (3.18) (1.:1) (12) (3.39; Pm=xC(, + C/2M1) (1 + 9)2Pm14 = (130) (1.07) (3.40) E(1 + C/3M1) (eM+(93)

we getPm14 = 26,400 lb per in. 2

45,400 = (0.95)(8.12)(3.18)105(."15)(1.69)(12)

To calculiate the velocities for both of these (158)(1.1)(eM + 1.2)

items, we have to obtain the values of 0. M' 2.10

4-41

Trying this value of M' for velocity, we obtain (0.88) (3.18) (3.39) (1.11) (1.69) (12)

V = 2,950Pmt14 =25,300 psi

which is too high. 2 5,30M'psi

2 k C(M' + 't)

We then try t = 0.30 and x /RTo = 0.90. With Vic =these values we obtain M' -- 2.06 and the veloc-ity V = 2,650, which is still too high. V1O2 (0.88)(3.18)(3.82)(1.79 + 2.57)(32.2)

V = 18.2Then we try 6 = 0.30, and ),/RTo = 0.88. Withthese values M' = 2.03 and V = 2,800. This V10 = 2,590 fpsvalue ot M is then correct for our 6 andX/RTo. With this value of M' we can calculate 2 (0.88)(3.18)(3.39)(1.29 + 2.08)(32.2)B for M6 propellant. We can then use the value V1 4 = 17.6of B obtained for item 21, and use it for items10 and 14 to obtain M' for theze. V1 4 2,300 fps

We obtain B from the formula for M' 4-38. Derivation of Equations by Method Out-2 lined in CSRD 6468. For the tabular solution

M1 + C/3MIJ 32.2 we assume that : = 1.3; and that the startingM 2 2 (78) pressure is what is developed when one per-

B 2 MIC% [i + C/2MI] cent of the charge has burnt when the projPctilebegins to move. The covolume of the propellant

B2 = (102)(2.97 x 10- 3 )(1.1)(32.2) is considered.(2.03)(26.5)(8.12)(0.r8)(3.18)(1.32) Equation of State. The equaLion of state (34),

as derived in paragraph 4-25, is transformedB 2 = 6.75x 10-8 by taking Vc= AXo and AX=Vc + Ax. The

equation of state (34) then becomesHence, we obtain M 10 from

= (49.3)(1.76)(1.08)(32.2) P aN0 -(9MI0 16 ( 75) (16.9) (3. ý'2)(0.88)(3.181(1.28) - -. . .Multiplying this equation by vc, dividing by

M'10 = .995 its equivalent AXo, and remembering thatC/Vc = 6o, we get

We obtain M 14 fromSpcC 'o aANcfiN T.T

(49.3)(1.35)(10.7)(32.2) P -2- - - anx0 = NF (100)4 (6.75)(16.5)(3.39)(0.88)(3.18)(1.25) xo p

M14= 1.795 Equation of Motion. By equation (52), equa-tion (33) can be expressed in terms of the

We can now use these values of M to cplculate average gas pressure ast-he pressure and velocity for both items 10and 4. AP =- M (+ /) V (101)

SC(1 + C/2M I)(1.69)(12) ( dV

E(l + C/3MI)(eM' + 1.2) or AP mV d- (102)dX

Pm10 = (0.88)(3.18)(3.82)(1.11)(1.69)(12) where(73)(108)(5.12)

M = 5 (103)Pm10 = 46,400 (0

4-42

To account for frictional resistance, engraving 1 ( -) V +-- Vcresistance, etc., m' is substituted for m, the 2 Arelation being m' = 1.02m. The qu..ntity m' is I m' B Nodefined as an effective mass. +[TX - -- k2) - -V- 2Ao

The three equations, the energy of m.ition (33),

the equation of state (34), and th7 energy bal- dV No in' B (109)

ance equation (40), derived previ,,usly in para- + V- = CF 7--+ (kl - 2k2fo) - -Vgraph 4-26, are combined to give one equation dx L C Wvalid before and alter the powder is all burned. !)n B\ 21The rate of burning will then be used to obtain + k2(- w) 1v2a differential equation applicable only during A Wthe interval of burning of the powder.

First eliminate T/To between equation (34) and Here, in the term a,50 N/C, which is a smallequation (40), and then eliminate P between this correction term, we have approximated theequation and equation (45). This gives value of N by replacing f2 by If. Thus

m = FN (104) 1; dV N ko (k1 -k 2)f (110)vc / X Ao a^ NAA_,)= W -=dV C" 2

k3---- _P 0 C -V-XThe equation for the rate of burning (43) may and, correspondingly, we have introducedbe rewritten in terms of velocity to give No'

-mBT= ko - (k, - 2k2)fo- df=n_.' B dV CI5

dt A KW d(04-39. The Solution of the Differential Equation.

This eq,,ation is integrated to give Let us define the follswing:

m' B No (III)fo f= IA W V (06)

where fo is the value of f when the velocity As J1 = kl - 2k 2 to (112)zero, that is, fo is the fraction of the web thatis unburned when the projectile begins to move. 1It is convenient to let No be the weight of the J2 kl - k 2 (113)powder burned when the projectile begins tomove (equation (47) evaluated at f = fo). Equa- AOS-- + a ISO (ko - J2fo) (114)tion (106) can be used to eliminate f from the C

form-function equation, equation (47), to give(107)

N No m' B m' 2 V2 Zb 10 (115)C C j~+ (k, + 2k2fo)- w 2A W V+k2 j, C F m' (B/W)2 (1)

The value of No is related to the starting pres-sure Po by the equation of state, equation (48), In terms of these quantities, equation (109)evaluated at the start of motion, that is, when becomesP= Po, N = No, T/To = 1, and X/Xo= 1, gives

No0 Po(l - Ao/lo (108) X0 am'B1!n V dV C F joC -o(F + aPo) Xo .-a.oJ2 V V AX= ml

* Eliminating N in equation (104) by means of (116)"equation (107) gives the fundamental ballistic CF BV - (" I)- k | V2

* equation for the interval of burning +i A j I(Z1). V

4-43

This is an equation relating the length of so that equation (125) becomestravel (X) of the projectile to its velocity (V). dys yIt now becomes convenient to define dimen- -d r (127)sionless variables related to the travel and dZ q + Z - uZ 2

velocity:X Thus we obtain a linear first-order differential

Y =O Xo.(117) equation, with a solution as follows

and V y' =J(k - rf 5 zt (128)

e2 = -- (118)

where Where k is the constant of integration,

j1 C F (B/W)e2 - A z Z d3 x 5 Z dZ(19

In terms of these variables, equation (116) exp (129)

becomes 0 q + Z - uZ2

anda aoJ2 'b/Z oZdZdy 7b z (120) S = 3J (130)

CFjo I k2 fo~ 0- + Z - (- - ) - Z2

e2 2 m, 1.2 "'1ZbI Then by using the definition of y' from equation

(126) and of y from equation (117)Let us define the following:

X/Xo = k3+ a - r(S - Z) (131)a A j2 fo (121) The function I is elementary, but the expres-

Zb sions developed by the explicit integration are

u ) f°- (122) of view. The function S is, in general, notShJlZb elementary, ard must be calculated either by

numerical integration or by some type of seriesand expansion.

Jo Zb(13ij fo (123) The integration constant k is obtained by use

of the initial situation, X/Xo = 1 when Z = 0,

In terms of these quantities, equation (120) 3 = 1, and S = 0.

becomesThis gives the following equation for X/Xo as

(y rZ)Z = q (124) a function of Z.(y

X/A = 3J-a (I3- 1)- r(S- Z) (132)

which may be arranged to giveThis is the relation between the travel and the

dy Z (y - rz) velocity of the projectile. It will be noted thatdZ - q+ Z - uZ 2 (125) in this equation the i elocity is the independent

variable and the travel is the dependent vari-

We define able. This is not the c'ioire that would havebeen desired. However, it is not possible togive

y'= y - rZ (126) a simple equation for the velocity in terms ofthe travel.

4-44

F.,ST AVAILABME ,CQFY

The pressure may be obtained as a function of (136) and the etl of dP , 0 1the velocity as follows. From equation (45) and sX o , eads [seethe definitions of Z and y in equations (117) equation (117)] toand (118) (v/ ) - rZp) ( - 2 uZp)

P= e3 Z dZ (133) -q Zp - UZp2 (139)Te dIf a position of true maximum pressure (that

dPwhere is, d = 0) occurs during the range of the eaua-

e 22 m' tion (LUhat is, during the burning of the powder),

e3 =-- (134) equation (137) may be combined with equationVc (125) to give

The constant e 3 may be written in terms of q Zp - uZp2 (1 . 2u)Zp- Imore fundAmental quantities as follows: yp - r Zp r (I•0)

Fjl fo %o Thus, from equation (136) we obtain on re-e 3 - Zb (135) arrangement

Equations (124) and (133) may be combined to Zp = (141)give 1 + 2u

q + Z - uZ 2 This is a relation between the value of Z, andP = e3 - (136) the value of P at thetimeof maximum pressure.

X/Xo - o - rZ The numerical value of the term (r/e 3)Pp is

of the order of 0.1, so that the numerieal valueThe relation between position and time can be of Z is only slightly dependent c . the value ofobtained only by means of numerical integrals. Pp. This fact is made use of in a recursiveThis can be carried out by use of either of method of obtaining Zp and" P numerically.two equations

4-41. The Point at Which the Powder Is All

t dX 137) Burned. The velocity at the time the powder isV all burned is o udred from equation (106) byletting f, the fraction of the web left unburned,

or equal zero. Thusm VdV Afo

(138) Vb = (142)

The first equation leads toan improper integral. \IFor this reason, it is always convenient to It is convenient to let the subscript b indicatebegin the in'ezration by use of equation (137). that the quantity has been evaluated at the timeThis equation leads to infinite times in the case that the powder is all burned. From the defi-Po = 0. This is true because the ballistic equa- nition of Z equations (117) and (118)tions give solutions for the case Po = 0 only ina limiting sense. If the pressure is initially - foA2zero, the powder (according to the rate-of- Zb= - (-143)burning equation used) will not burn. Therefore, J, C F m' (B/W) 2

the pressure will not rise, and the situationwill remain unchanged. Thus the quantity previously denoted by Zb is

4-40. The Maximum Pressure. The position of seen to be simply the value of Z at the time thethe maximum pressure is found by setting powder is all burned [equation (120)].dP

aI a 0. Let a subscript p indicate that the 4-42. The Equations for the Period After All

quantity has been evaluated at the time of maxi- the Powder Is Burned. In the derivation (para-mum pressure. The differentiation of equation graph 4-38), it was stated that equation (104) is

'p 4-45

applicable both before and after the powder is The pressure is found by combining equationsall burned. After the powder is all burned, (34), (146), and (147). ThusN = C and equation (104) becomes

1F v ml X (142P m'(5- 1) (h- V2) (152)1 ,-2 F c m' '_X 7 dV P V (152)7602- (• -1I) A(i- '- j• '•L~ v~ .

2Vc (X/Xo - •o

It is convenient to introduce W, as defined inLet . equation (150), into this equation to give.

2CF P14)p o FQ (X/Xo - 7io)" (153).b = C (144)

n'(i- .1) .4-43. Summary of Equations. The equationsof

interior ballistics developed previously can.be

and summarized and rewritten in a form moresuitable for use in the solution of problems..

SX( 145) The equations are given in an order consistent

0X with their use. The constants are expressedin a somewhat different manner, that is, in amanner which permits more direct calculation

Then, since of their numerical values. Equations for the-

dV V dV I dV2 gas temperature and for the fraction of the.V - _ (146) powder burned are included. These equations

dX Xo dX 2Xo dX are derived directly from equations (34) and(107). First we have the subsidiary quantities -

equation (143) becomes functions of the form function constants ko,kl, and k2, and the fraction of' the powder

dV2 (5 - 1) b(7 - 1) burned to create the starting pressure, jo:- + V2 - (147) /dX X X2 * 4k/2 ( 5 )

il= [k1 2. 4 2 (ko - 'This differential equation can be sclved to give i

V2= - + b (148) J2= k, -" k2 U155)

where k is the constant of integration. • (kl - jl)fo 2k if k 2 •0

This constant is evaluated so that V = Vb when 2k2

X = Xb. Thus, (156)S(ko - jo)

V b2 2 b) t( jX)(v-) + b (149) 10=:kl if .2 -0

it is convenient to define Al = Jo - k2 fo(fo - J) (157)

One of the important parameters is Zb. This"Q (-' JfoZb) (Xb/Xo- o7f(0 - 1) (150) quantity introduces the burning rate, and is de-fined

as

Then, by use of equations (142), (144), (145),and (14S), Zb = foA2 /iICFm' (B/W) 2 (158)

, (151)

V2 2CF [I _ Q(X/X. - b"( 1)] The quantity a, which is essentially the geo-'- 1) metric density of loading, that is, the ratio of

4-46

the density of loading 6o = C/Vc to the density The gas temperature Is given byof the powder P, is defined by "F.A T T .1 /2(•'-1) Z2 1

P 0+360I(159) T [1 T q-- Z-u +12-1)21(168%,p a~o•'l(q.:.Z uZ')÷I /2&'., 1) Z2 1'

The quantity r introduces the covolume of the The fraction of the powder burned N/C is

powder gas (77) through given by (169)1

(36) N Jifo u fZ /z(v-i)z2.= P Ll Z +12(F-1 2

so that C -b

r aJ2 f0oA (160) The point of maximum pressure is given byZb Zp, where

The two parameters that enter into the functions Zp ( +1 aJ 2 (170)3 and S are q (related to the starting condi- 1 + 2u• 12FJ 1

tions) and u (related to the pseudo-ratio ofspecific heats, 5): unless Z > Zb. If tUis is true, all the powder

'oZb is burned before the pressure has risen to aq =if- (161) point of zero slope. The maximum pressure

then occurs at the time the powder is all burned,

I k2fo that is, at Z = Zb. It will be noticed that Zu 2 ( 1)- (162) depends on Pp. However, this is a weak de-

2 1 lZb pendence, so that a method of successive ap-

The physical quantities for the interval before proximations converges quite rapidly.

all the powder is burned (that is, Z I Zb) are 4-44. Tables for the Calculation of Muzzle- - given4inTterms ofrtheeparameteriZ. TheMtrave

given in terms of the parameter Z. The travel Velocity and Maximum Pressure. Tables 4-9of the projectile is given by through 4-15 show the interdependence of the

V-( four functions r (a function related to theVC muzzle velocity, PpO (a function related to theL= --A (X/Xo - 1) (163) maximum pressure), - (a function related to the

where density of loading), and Zb (a function relatedtothe burning rate or web). These tables permit

_X= 3(1 - a) - rs + a + rZ (164) the rapid solution of problems involving only0o the maximum pressure and muzzle velocity.

The pressure is given by The tables cannot be used to obtain the completecurves. The use of the tables i; restricted

12FJlfoAo q + Z - uZ 2 somewhat by the fact that certain of the minorP = (165) parameters are fixed; in general, this is not a

Zb J(1 - a)r serious restriction.

A new constant, dependent only upon the char-The velocity is acteristics of the powder, is

V= Z(166) a°= 23,969 (F) (171)

The time since the beginning of motion is The numerical constant was chosen to makegiven by a°= 1, for M-1 powder. A new pressure

t= dZ function defined ast f -P (167)Zb 0 PO aop (172)

4-47

-. . . . . . .- - .

The travel function is A2 /B_ 2

a Ao Zb = 0.99 C-F m (176)= - o(173)

(x__0 ,,o) for seven-perforated grainsA2 m )B 2

and the density of loading function Zs = 1.369 m ) (177)

a (174) b. The pressure function

" Fo 10 aP m= P = 2.3969x F- P 178)

As in the case of the other variables, a sub-script p, b, or m on PO or f indicates that the c. The velocity function for the period afterquantity is evaluated at the time of maximum burning is complete ispressure, when the powder is all burned, orwhen the projectile reaches the muzzle, respec- F(Zb Pp°)=(1 - 0.1 4 8 5Zb)fb 0.3 (179)tively. In the case of seven-perforated grains,the subscript s refers to the instant the powder Two of the minor parameters have been fixedsplinters. The use of two of these tables is by the tables. The starting pressure has beenshown in the solution of the problem worked out. fixed by taking j = 0.01. The heat loss and ratio

of specific heats has been fixed by takingA function rFhas been defined so that 5 = 1.30. Provided that these quantities are

not changed, the results obtained by use of

Vm 2 = 2CF. 1 - r (175) these tables are numerically identical with(7- 1) m' / those obtained by the cumbersome fundamental

equations.provided that

6 (F - 1) C (1 -f OoZb) 4-45. Solution by the Hirschfelder System. The( - uFo) example worked out by the RD38 System will .m F- now be worked out by the OSRD 6468 System,

and the results will be compared in table 4-20.or, in the case of the seven-perforated grain We again assume that item 21 is known, andtables, provided that will calculate the maximum pressure and muzzle

( - 1) =< (I - 0.2420Zs) velocity for items 10 and 14.

F Knowledge of C, Pmax, and type of propellantpermits calculation of PpO and 6. Table 4-11

(These conditions are neccssary to ascertain provides t..e value of Zs for the calculatedthat the powder is all burned whenthe projectile values of Pp0 and o. From Zs, B/W andreaches the muzzle.) therefore B can be calculated. B is dependent

on the propellant formulation Ully, and may beReference 2 has two sets of tables showing the used to estimate B/W for any other round (thatinterrelations, of F', ppO, , and Zb (or s). One is, items 10 and 14) using the same formula-set applies to the problems involving the burn- tion. Zs and 0 may then be calculated for itemsing of constant-burning-surface grains. The 10 and 14, which qre used to obtain values ofother applies to the burning of seven-perforated Pp 0 and r. From P 0 and r the maximumgrains. In this latter case, Zs replaces Zb as pressure and muzzle velocity for items 10 andthe variable in the tables. 14 are obtained.

There are three other fundamental parameters The maximum pressure for item 21 is givenor auxiliary variables that enter intothe simpli- as

fied tables. They are: as:

a. The reduced velocity at the completion ofburning, for constant-burning grains Pmax = 45,400

4-48

From this we determine Pp by: from table 4-11, we get PpO = 46,000 lb perin. 2 . The value was obtained with a value of4' as 0.679.

M + C/3 p 46,000M /2 max Pp= -ý-- =46,400 lb per in. 2

0.991

2 P 4640 r15.4 +. 3.82/21Pmax = 4 3 ,100 lb per in. 2 Pm~x 4 6 ,40 0 15.40+ 3 J

The value of a, 12.98, is obtained from table 48,100 lb per In. 2

4-15. The value of au, also from table 4-15, is For item 14:0.991. B 0.0033455

Pp0 = aOp = 0.991 (43,100) - 42,700 W - 0.00941

a 12.98 0 8.8 2(1/"ýo - 11/) 19.5 = .6 =8.85 x 10-5

8.12 Zs = 1.483= -- "-= 0.027

Zs = 1.5890 (frorm table 4-11) €= 0.313

m= (1.02) (24.1 + 8.12/3.1) hence, from table 4-11,

32.17 PpO = 19,010 lb per in. 2

m' = 0.8467 Pp = 19,200 lb per in. 2

B = (1.369) (102.1) Pmax = 19,800 lb perW (8 12) (3.18)105(0.8467) (1.5890)

Checking the velocity, we use the basic formula

B 0.006341- F 1.

Therefore, B = 0.0003455.For item 10:

Using this value of B, we may now calculate the Vm =

ratio of B/W for items 10 and 14, since web 1(6.667) (3.82) (3.18) 105.sizes are known. (1 -(1.3379) (0.3955' L 0.528

For item 10: The value of r is obtained frow table 4-13.

B 0.0003455 0.00825 m is obtained from the formula

W 0.0419 A ar.0m (Xm/Xo - ,7LO)

(B) 2 = 6.81 i0-5 Hence

W 12.98 (6.0273)

m= 8.63 - (30.49) (0.0273)

(1.369) A2

s CFm' (B/W) 2 - 1.54 = 0.3955 (table 4-14)

4-49

.3 p

The value Xm/Xo is obtained from the formula made for each of these values to determineoptimum loading density (subparagraph 4-46a

Xm Vc + AL above) and velocity. The selection of these

X0 Vc assumed values for chamber volume and travelis based upon the characteristics which are

Hence desired for the gun; for example, in tank guns

Xm 140 + (6.82) (156) it is desirable to keep gun length as short as= 8.63 possible. The desired characteristic could also

Xo 140 be a light gun. The design should be a coopera-tive effort among the interior ballistician, the

Vm = 2,680 ft per sec gun designer, and the man familiar with tacticalrequirements. As an example, if there is a

The actual velocity is 2,600 ft per sec. maximum length limitation that cannot be ex-ceeded, the initial calculation may be based on

Checking for velocity in item 14: this maximum barrel length, and the velocitycalculated for several assumed values of cham-

r = 1,7813 ber volume. If the chamber volume at whichthe desired muzzle velocity is obtained is low

m= 0.0336 enough, and it is desired to shorten the gunlength at the expense of a larger chamber vol-

0 .3613 ume, the calculation may be repeated for aXm shorter barrel length. This relationship ofS= 7.19 chamber volume versus barrel length to obtainX- a given velocity at a given pressure is asymp-

totic to both axes, and there is a smallest1 1practical chamber and shortest practical gun

= - (1.7813) (0.361) (7.19) 106 as shown in figure 4-15. Pressure enters intoN L 0.509 .this problem by its effect on gun weight; and if

"the lightest gun is desired, the method outlinedV = 2,340 ft per sec above has to be repeated for several pressure

levels, and at each pressure level the lightest4-46. The Optimum Conditions gun is selected. For tank guns, weight is not

a. Optimum Loading Density. Given a gun too important, and considerations of shortwith its maximum rated pressure• and the length prescribe using the shortest possibleweight of the projectile to be fired from it, gun, which implies working at the maximumthe question often is asked what i$ the maxi- pressure level permitted by practical con-mum velocity that can be obtained. In most siderations, such as cartridge case design.cases of guns encountered it turns out that themaximum velocity occurs at max mum loading Table XVII of OSRD 6468 has approximatedensity, that is, at the maximum charge that solutions of velocity and loading density versusthe case will hold. To avoid ignition diffi- gun dimensions and pressure which may be usedculties, and as a consequence of the packing to restrict the number of trial calculations tocharacteristics* of propellants, this maximum be made as outlined above.loading density should seldom exceed 0.75 g/ccof chamber volume. The optimum loading den-sfty in the general case. is dependent on pres- 4-47. Example for Optimum'Loading Density.sure, however, and at low pressures, or with In the example worked out below, there is avery light projectiles, the optimum loading fixed gun-projectile combination, with one typedensity may leave a void in the cartridge can. of propellant. The loading density and quick-

b. Optimum Gun. If the gun is in the design ness (B/W) are varied in order to attain max-stage, with the required velocity and weight of imum velocity at the required pressure.the projectile known, the method of solution forthe optimum gun corresponds to a trial anderror solution for several Assumed values of In this example, we again use a 90-mm gun,chamber volume and travel. A calculation is but of different type. Also, we change the

4-50

B[ST A.\'ALABLE COPY

Table 4-9 (OSRD 6468)

Table Of Zb as a functio, of p and P., single-perforated grains

0.05 0.1 0.15 0.20 0.25 0.30

2000 2.45884000 "_I1748 2.49146000 0.7767 1.6185 2.52428000 0.5448 1.2047 1.8626 2.5574 3.2903

10000 0.3591 0.9636 1.4819 2.0242 2.5q06 3.181812000o 0.2034 ----PAP58 ..... 1.2349 1.6810 2.1439 2.624114000 0.0691 0.68405 1.0618 1.4417 1.9342 2.239516000 0.5783 0.V338 1.2655 1.6071 1.9586

18000 0.4830 1 0.8354 1. 1304 1.4334 1.744420000 0.3966 0...7543----- ! 1.0236 1.2964 1.575822nno 0.3176 0.6803 0.9370 1.1856 1.439824000 0.2448 0.6121 ...... 0.8654 1.0941 ?.327626000 0.1771 0.5488 -.8045 1 1.0174 1.233728000 0.1139 0.4897 0.7482 0.9520 1.153830000 0.0547 0.4343 0.6956 __ 0.8958___ 1.085132000 0.3821 0.6460 0.8468 1.025334000 0.3329 0.5991 G.8018 0.973036000 0.2861 0 5547 0.7592 0.926638000 0.2417 0.5124 0.7187 0.885440000 e..1993 0.4722 0.6800 0.848042000 0.1588 0.4337 0.6432 0.812444000 0.1201 0.3969 0.6078 0.778346000 0.0829 0.3616 0.5740 0.745748000 0.0471 0.3277 0.5415 0.714350000 0,0127 0,2950 0,5102 0,684152000 0.2635 0.4800 0.655154000 0.2332 0.4509 0.6270"56000 0.2038 0.4228 0.599958000 0.1754 0.3956 0.573760000 0,1479 0,3693 0,548462000 0. 1213 0.3438 0.523864000 0.0954 0.3190 0.499966000 0.0703 0.2950 0.476868000 0.0458 0.2716 0.454570000 0.0221 0.2489 0.432472000 0.2268 0.4111.4000 0.2052 0.390476000 0.1842 0.37027800C 0. 1637 0.350480000 0. 1437 0.331282000 0.1242 0.312484000 0. 1051 0.294186000 0.0864 0.276188000 0.0682 0.258690000 0.0503 0.241495000 0.0073 0.2001

100000 J 0.1608

4-51

Table .1-9 (OSRD 616198)

Table of Zb as a functio. of n a ) ) 0 stntgle-pe)-foiatd q'rati:; (copt)

0.35 0.40 0.45 0.50 0.55 0.60

12000 3.1 1814000 2.6578 3.0O,9216O00 2.3201 2.6917 3.0737

18000 2.0634 2.3905 2.725s 3.069420010 1.8619 2.15.15 2.4539 2.7601 3.073122000 1.6995 1. 9648 2.2357 2.5123 2.7946 3.0"272.1000 1.5659 1.8089 2.0567 2.3094 2.5669 2.829326000 1.4511 1.6786 1.9073 2.1402 2.3773 2.61S6.8000 1.3591 1.5681 1.7808 1.9971 2.2171 2.410730000 1.2776 1.4733 1.6722 1.9744 2.0799 2.21S632000 1.2067 1.3910 1.5781 1.7682 1.9612 2.15703r400 1.1446 1.3189 1.4958 1.6753 1.8574 2.042236000 1.0898 1.2553 1.4231 1.5934 1.7660 1.941038000 1.0409 1.1987 1.3586 1.5206 1.6848 1.8513•10000 0.9973 1.1480 1.3008 1.4556 1.6123 1.771142000 0.9579 1.1025 1.24e9 1.3971 1.5472 1.6991-14000 0.9223 1.0612 1.2019 1.3443 1.4883 1.63414I6000 0.8899 1.0238 1.1592 1.2963 1.4349 1.575218000 0.8595 0.9896 1.1203 1.2525 1.3862 1.521450000 0.8303 0.9583 1.0846 1.2124 1.3416 1.4722520C0 0.1022 0.9295 1.0519 1.1756 1.3007 1.427154000 0.7750 0.9028 1.0217 1.1417 1.2130 1.385556000 0.7,18,83 0.8774 0.9937 1.1103 1.2281 1.347058000 0.7204 0.8528 0.9678 1.0812 1.1957 1.311460000 0.69R9 0.8289 0.9437 1.0542 1.1657 1.278362000 0.6751 0.8058 0.9211 1.02S9 1.1377 1.247464000 0.6520 0.7835 0.8994 1.0054 1.1115 1.218666000 0.6296 ').7617 0.S782 0.9834 1.0870 1.19176C000 0.6079 0.7406 0.S577 0.9627 1.0641 1.1664

9 0.5867 0.7201 0.8377 0.9432 1.0425 1.1-1427600 0.5661 0.7001 0.8183 0.9243 1.0222 1.1203

74000 0.5461 0.6;07 0.7994 0.9059 1.0031 1.099376v00 0.5265 0.6617 0.7810 0.8879 0.9851 1.079478000 0.5075 0.6433 0.7631 0.8704 0.9679 1.060680000 0.48,9 0.6252 0.7455 0.8534 0.9513 1.042982000 0.4708 0.6077 0.7285 0.8368 0.9351 1.026084000 0.4530 0.5905 0.7118 0.8205 0.9193 1.010086000 0.4357 0.5737 0.6955 0.8046 0.9038 0.994788000 0.4188 0.5573 0.6795 0.7891 0.8887 0.980090000 0.4022 0.5412 0.6639 0.7740 0.8739 0.965695600 0.3623 0.5026 9.6264 0.7375 0.8383 0.9309

100000 0.3244 0.4659 0.5908 0.7028 0.8046 0.8980

4-52

Table 4-9 (OSRD 6.168)

Table of Zb as a.functiopi of; atd ppO, single-perforated grains (cot;!;

I 0.65 0.70 0.75 0.80 0.85 0.900

24000 3.096726000.r 2MC•2 3.111228000 2.,6682 2.,1293 3.134330000 2.5006 2.7160 2.9347 3.156s'2000 2.3559 2.5576 2.7621 2.9702.34000 2.2295 2.4 196 2.612;3 2.8071 3.005936000 2.1184 2.29,12 2.1804 2.6051 2.8522 3.041I38000 2.0198 2.1906 2.3636 2.53,8 2.7163 2.896040000 1.9319 2.094 7 2.2595 2,4263 2,5952 2,766242000 1.•529 2.0086 2.1661 2 3255 2.4867 2.64994-1000 1 7816 1.9309 2.0818 2.234I5 2.3889 2.545146000 1.7170 1.8604 2.0055 2.1521 2.3004 2.450348000 1.6581 1,7963 1.9360 2.0772 2.2199 2.564150000 1.6042 1.7376 1.8724 2.0087 2.1463 2.285352000 1.55.1b '.6838 1.8141 I.'!58 2.0788 2.213254000 1.5092 1.6342 1.7605 1.8880 2.0167 2.146856000 1.4671 1.5885 1.7109 1.8346 i.9595 2.085558000 1.4281 1.5460 1.6650 1. 852 1.9064 2.028860000 1.3919 1.5066 I.E224 1.7393 1.9572 1.9762

-- 62000 1.3582 1.4700 1.5828 1.6966 1.8114 1.92726.1000 1.3267 1.43o7 1.5457 1.6567 1.7687 1.881666000 1.2972 1.4037 1.5111 1.6,94 1.7287 1.838968000 1.2696 1.3737 1.4787 1.5845 1.6913 1.798970000 1.2437 1.3455 1.4482 1.5518 1.6562 1.761472000 1.2193 1.3190 1.4196 1.5209 1.6231 1.726274000 1.1963 1.2940 1.3926 1.4919 1.5920 1.692976000 1.1745 1.270M. 1.3671 1.4645 1.5627 1.6616

- 78000 1.1540 1.2482 1.3430 1.4386 1.5350 1.632080000 1.1346 1.2271 1.3202 1.4141 1.5087 1.604082000 1,1162 1.2071 1.2986 1.3909 1.4839 1.577584000 1.0987 1.1881 1.2782 1.3689 1.4603 1.55246000 1.0821 1.1701 1.2587 1.3480 1.4379 1.5285

88000 1.0663 1.1529 1.2402 1.3281 1.4166 1.505790000 1.0512 1. 1Vs.6 1.2225 1.3091 1.3963 1.484195000 1.0166 1.0990 1.1820 1.2655 1.3496 1.4343

100000 0.V944 1.0654 1.1458 1.2266 1.3080 1.3900

4-53

T:zble 4-9 (OSRD 6468)

Table of Zh as a function of p and p.O, single-perforated grains (cant)

p o 0.95 1.00 1.10 1.20 1.30

38000 3.078040000 2.9392 3.114312000 2.8149 2.981944000 2.7031 2.862846000 2.6018 2.7550 3.066348000 2.5098 2.6571 2.956350000 2.4258 2.5677 2.855952000 2.3488 '..4858 2.7639 3.047554000 2.2780 2.4106 2.6795 2.953556000 2.2127 2.3412 2.6016 2.866958000 2.1523 2.2769 2.5296 2.7 869 3.04A860000 2.0962 2.2174 2.4629 2.7127 2.969962000 2.0441 2.1620 2.4008 2.6438 2.891064000 1.9955 2.1103 2.3430 2.5796 2.820266000 1.9500 2.0621 2.2890 2.5197 2.754168000 1.9075 2.0169 2.2384 2.4636 2.692370000 1.8675 1.9745 2.1910 2.4110 2.6634472000 1.8300 1.9347 2.1465 2.3616 2.580074000 1.7947 1.8972 2.1045 2.3151 2.528976000 1.7613 1.8618 2.0650 2.2713 2.480778000 1.7298 1.8284 1.0277 2.2300 2.435280000 1.7001 1.7968 1.9924 2.1909 2.392282000 1 6718 1.7669 1.9590. 2.1539 2.351584000 1.6451 1.7385 1.9273 2.1188 2.312986000 1.6197 1.7115 1.8972 2.0855 2.276388000 1.5955 1.6859 1.8686 = -- 2.0538 - 2.2415 - . .90000 1.5725 1.6615 1.8414 2.6237 2.208595000 1.5196 1.6054 1.7788 1.9545 2.1324

100000 1.4724 1.5554 1.7231 1.8928 2.0647

4-54 ,

_________

Tcbfe 4-10 (OSRD 6468)

Table of r as a function of p and Po singleyperforated graixs

Pp 0.05 0.10 0.15 0.20 0.25 0.30

p0

2000 3.73344000 .... 2,9?89_ ... 3.03706000 2.7228 2.5375 2.69358000 2.6248 2.3530 2.3380 2.4751 2.X762

10000 2.5510 2.2367 2.1716 2.2007 2.3191 2.538212000 2.4922 i 2.1976 2.0749 2.0525 ZINC, 2.2000140(0 2.4434 - 2.1541 2.0115 1.9595 L9639 2.012816000 2.1170 1 1.9667 1.8955 L$758 1.893518Co0 2.0847 ... 9.33 ------- .. 1.8487 L$128 1.810420000 2.0532 1.9067 I 1.8130 L7655 1.749222000 2.0307 1.8828 1.7849 L7286 1.702124000 2.0076 1.8612 1,76_22 ... L6991 1.664826000 1.9866 1.8415 1.7431 L6748 L.em428000 1.9673 1.8234 1.7258 1.6,545 1.609130000 1.9494 1.8067 1.7099 1 1.6374 1.587932000 1.7911 1.6950 L622; L E.M69734000 1.7766 1.6811 1.6093 1 1.553936000 1.7630 1.6681 L5967 1.540238000 1.7502 1.6559 L5849 1.528140000 1.7381 1.6443 L5737 1 --- "42000 1.7266 1.6334 1.5631 1.506944000 1.7157 1.6230 1.5531 L497246000 1.7054 1.6131 L5436 1.487948000 1.6956 L6037 L3345 1.479050000 1,6861 1.5947 1,5257 1.470552000 1.5860 1.5174 L462454000 1.5777 1.5094 1.454656000 1.5696 1.5017 1.447158000 1.5621 L4943 L439"60000 1.5548 L4872 1.433062000 1.5477 L4803 1.42G64000 1.5408 1.4736 1.419866000 1.5341 L4672 1.413668000 1.5277 1.4610 1.4076lOC 1.5215 1.4550 1.401772600 1.4491 1.396074000 L4435 1.390576%100 L4380 L3851780'0 1.4326 L379980000 L4274 1.374882000 1.4223 1.369984000 1.4174 1.365186000 L4126 L360488000 1.4079 L355890000 1,4033 1.351395000 1.3923 L3406

10000O 1.3305

"4-55


Table of r as a function of • and p , single-perforated grains (cont)

p 0.35 0.40 0.45 0.50 0.55 0.60

p 0

12000 2.371814000 2.1050 2.246616000 1.9437 2.0268 2.147718000 1.8352 1.8850 1.9608 2.067020000 1.7569 L.7856 1.8345 1.9048 1.999422000 1.6978 1.7118 1.7428 1.7904 1.8559 1.941724000 1.6514 1.6548 1.6730 1.7051 1.7515 1.813126000 1.6140 1.6093 1.6180 1.6390 1.6718 1.716928000 1.5831 1.5721 1.5735 1.5860 1.6089 1.642030000 1.5573 1.5411 1.5368 1..426 1,5578 1,582052060 1.5353 1.5149 1.5058 1.50C3 1.5155 1.532734000 1.5163 1.4924 1.4794 1.4755 1.4798 1.491436000 1.4998 1.4729 1.4566 1.4491 1.4492 1.456338000 1.4853 1 #558 1.4366 1.4260 1.4227 1.4260

1.4725 1,4407 1.4191 1.4058 1,3995 1,399642000 1.4610 1.4272 1.4035 1.3878 1.3791 1.376444000 L__AýQ457 ------ 1.4151 1.3895 1.3718 1.3609 1.355846000 1.4415 1 1.4143 1.3770 1.3575 1.3446 1.337448000 1.4328 1 1.3945 1.3656 1.3445 1.3299 1.320850000 1.4245 1.3855 1,3553 1.3327 1,3165 1.3058

51.166 1 .3773 1.3459 1.3220 1.3044 1.2922

54000 1.4090 1.3698 1.3372 1.3122 1.2933 1.279756000 1.4017 1.3626 1.3293 1.3031 1.2831 1.268358000 1.3946 1.3557 1.3220 1.2948 1.2737 1.257860000 1.3873 1.3491 J1.3152 1.2871 1.2651 1.248'G2000 1.3813 1.3427 1.3088 1.2799 1.2570 1.2391 --64000 1.3750 1.3365 1.3027 1.2733 1.2495 1.230866000 1.3689 1.3305 1.2968 1.2671 1.2426 1.223068000 1.3630 1.3247 1.2911 -.... 1.2613 ..... 1.2361 1.215770000 1.3572 1.3191 1.2856 1.2558 I 1.2,299 1.2089

1.3517 1.3136 1.2803 1.2505 1.2242 1.202574000 1.3463 1.3083 1.2751 1.2454 1.2188 1.196576000 1.3410 1.3032 1.2700 1.2404 1 '.2138 1.190978000 1.3359 1.2982 1.2651 1.2356 - "-N62"---- 1.18,5680000 1.3310 1.2933 1.2603 1.2309 ' 2043 1.1805

""*82'00 1.3261 1.2886 1.2557 1.2263 1.13M8 1.175784000 1.3214 1.2840 1.2511 1.2218 1.1954 1.786000 1.3168 1.2795 1.2467 1.2174 1.1911 1.167088000 1.3124 1.2751 1.2424 1.3132 1.1869 1.162890000 1.3080 1.2708 1.2382 1.2091 1.1828 1.158895000 1.2975 1.2605 1.2280 1.1991 1.1729 1.1490

100000 1.2876 1.2508 1.2185 1.1897 1.1636 1.1398

4-56

b Table 4-10 (OStiD 646:')

Tablc of F as a function of; and p sing. -perforated grains (€cont)

0.65 0.70 0.75 0.80 0.85 0.90Pp

24000 1.892126001, 1.7752 1.8486119000 1.6859 1.7415 1.8102nm000 1.6153 1.6581 1.7113 1.776232U00 1.5578 1.5911 1.0329 1.684134000 1.5101 1.5360 1.5692 1.6101 1.659536000 1.4699 1.4898 1.5162 1.5492 1.5893 1.637338005 1.4354 1.4505 1.4714 1.4981 1.5310 1.570440900 1.4054 1.4166 1.4330 1.4546 1.4817 1.51444""20 1.3791 1.3569 1.3996 1.4171 1 4394 1.466744000 1.3559 1.3608 1.3703 1.3843 1.4026 1.425446000 1.3252 1.33 76 1.3444 1.3553 1.3703 1.389448000 1.3166 1.3169 1.3213 1.3296 1.3417 1.357750000 1.29.,8 !.2982 1.3005 1.3066 1.3162 1 329452000 1.2846 1.2813 1.2818 1.2858 1.2933 1.304154000 1.2707 1.2659 1.2647 1.2670 1.2725 1.181256000 1.2580 1.2518& 1.2491 1.2498 1.2536 1.U60558000 1.2463 1.2388 1.2348 1.2341 1.2364 1.241660000 1.2356 1.2268 1.2217 1.2196 1.2206 1.224362000 1.2256 1.2158 1.2095 1.2063 1.2060 1.208464000 1.2163 1.2056 1.1983 1.1940 1.1925 1.193766000 1.2077 1.1961 1.1878 1.1825 1.1800 1.1801

68000 1.1996 1.1872 1.1780 1.1718 1.1684 1.167470000 1.1921 1.1789 1.1689 1.1618 1.1575 1.155672000 1.1850 1.1711 1.1604 1.1525 1.1473 1.144574000 1.1.84 1.1638 1.1523 1.1438 1.1378 1.134276000 1.1721 1.1569 1.1448 1.1355 1.1288 1.124.578000 1.1662 1.1504 1.1377 1.1278 1.1204 1.115480000 1. 160G 1.1443 1.1310 1.1205 1.1125 1.106882000 1.1554 1.1385 1.1246 1.1135 1.1050 1.098684000 1.1504 1.1330 1.1186 1.1070 1.0978 1.090186000 : 1.1457 1.1278 1.1129 1.1008 1.0911 1.083688000 1 1.1412 1.1228 1.1075 1.0919 1.0847 1.07679*00 j .j_--L369 --- 1.1181 1.1024 1.0893 1.0'46 1.0701

1.1271 1.1073 1.0906 1.0764 1.0647 1.0550S 100000 1.1180 1.0977 1.0800 1.0650 1.C522 1.0416

4

S4-54

4.57


Table of F as a fimction of p and Ppo, single-perforated grains (contj

0.95 1.00 1.10 1.20 1.30

Pp0,p

38000 1.617140000 1.5532 1,59874200W 1.4992 1.537544000 1.4529 1.485446000 1.4127 1.4404 1.510148000 1.3774 1.4011 1.461250000 1.3461 1.3664 1,418552000 1.2182 1.3356 1.3808 1.441154000 1.2931 1.3080 1.3473 1.400356000 1.2703 1.2831 1.3173 1.364058000 1.2496 1.2604 1.2903 1.3315 1.385460000 1.2307 1,2398 1,2657 1,3023 1.350362000 1.21-34 1.2209 1.2433 1.2757 1.318764000 1.1974 1.2035 1.2228 1.2515 1.290166000 1.1826 1.1874 1.2039 1.2293 1.264068000 1,1688 1.1725 1.1864 1.2089 1.240170000 1.1560 1.1586 1.1702 1.1900 1.218172000 1.1440 1.1457 1.1552 1.1725 1.197774000 1.1324 1.1336 1.1411 1.1562 1.178976000 1.1223 1.1123 1.1280 1.1410 1.161478000 1.1125 1.1116 1.1156 1.1268 1.145080000 1.1032 1.1016 1. 1040 1.1135 1.129782000 1.0944 1.0921 1.0931 1.1009 1.115384000 1.0861 1.0832 1.0828 1.0891 1.101886000 - 1.0782 1.0748 1.0730 1.0780 1.089188000 -1.0707 1.0667 1.0638 1.0674 1.0771 * -90000 1.0636 1.0590 1.0550 1.0574 1.065795000 1.0474 1.0416 1.0349 1.0345 1.0397

100000 1.0329 1.0260 1.0171 1.0142 1.0167

BEST AVAILABLE COPY

4658 "ZZW

Table d-11 (OSRD 6468)

"Table of Zs as a function of; and ppO, s~ren-perforated grains

0.05 0.10 0.15 0.20 0.25 0.30

2000 1.99494000 1,0725 ------ 2.01771000 0.'143 1.3927 2.04068000 0.4493 1.0960 1.5684 2.0636

10000 0.9038 1.2965 1.6344 2.0866 2.503112000 0.7432 1.1198 1.4400 1.7700 2.1096140G0 0.6048 0.560 1.2695 1.5503 1.838016000 0.4329 0.8714 1.1438 1.3889 1.639418000 0 7721 1.0448 - 1.2655 1.4878^2l000 0.6794 0.9564 1.1680 1.3684

0.0 5o.7 0.8754 1.08N. 1.27192. 000 0.5166 0.8010 1.0166 1.19232•000 0.4442 0.7319 0.9501 1.1255 12800C, 0.6675 0.8880 1.065530000 0.6071 0.0299 1 0092 L.32000 0.5503 0.7753 0.9r6334000 0.4967 0.7236 0.906336000 0.1459 0.6748 0.85'038000 0.3976 0.6283 O.SL.*040000 0.5641 0.771242000 0.5418 0.730344000 0.5014 0.691246000 0.4626 C.653848000 0.4254 0.617850000 0.583252000 0.549854000 0.517756000 0.4867

" 58000 0.456660000 0.427562000 0.3993

- - 4-59

Table 4-11 (OSRD 646881

Taule of Zs as a function of; and P seven-perforat'd grain.s (cont)

0.35 0.40 0.45 0.50 0.55 0.60

12000 2.459114000 2.1328 2.434416000 1.8930 2.1559 2.422018000 1.714.2 1.9447 2.1791 2.4176LI00100 1.3720 1.7790 1.9891 2.2024 2.418822000 1.4574 1.6456 1.8364 2.0297 2.2257 2.4241

"". 24000 i.3630 1.5360 1.71j' 1.8883 2.0676 2.249026000 1.2140 1.4443 1.6064 1.7702 1.9359 2.103228000 1.2169 1.3665 1.5176 1.6703 1,8244 1.980130000 - 1.1391 1.2996 1.4414 1.5846 1.7290 1.874732000 . .1076. . 1.2416 1.3754 1.o103 1.6464 1.783534000 1.0590 1.1907 1.3175 1.4453 1.5741 1.703836000 1.0130 1.1454;f 1.2664 1.3880 1.5104 1.633638000 0.9693 1.1028 1.2210 1.3370 1.4538 1.571340000 0.9278 1.0623 7 I.1803 1.2914 1.4032 1.515612000 0.8881 1.0236 I.i4' 1.2505 1.3577 1.465644000 0.8501 0.9867 1.1065 1,2134 1.3166 1.4204

46000 0.8136 0.9512 1.0719, 1.1794 1.2793. 1.379448000 0.7788 0.9172 1.0387 1.1469 : 1.2452 1.342050000 0.7452 0.8845 1.0067 1.1157 1.2141 1 1.307752000 0.7128 0.8530 0.9760 1.0857 1.1847 1.276354000 0.6817 0.8227 0.9464 1.0567 1.1563 1.247256000 0.6515 0.793A 0.9178 1.0288 1.1289 1.220353000 0.6224 0.7650 0.8902 1.0018 1.1025 1.194460000 0.6943 0.7376 0,8634 0.9756 1.0769 1.169462000 0.5670 0.7110 0.8375 0.9503 1.0522 1.145164000 0.5405 0.6353 0.8124 0.9258 1.0282 1.1216 -

66000 0.5148 0.M663 0.7881 0.9020 1.0049 1.098868000 0.4899 0.6360 0.7644 0.8789 0.9823 1.0767 . -70000 0.1656 0.6125 , 0.7414 0.8565 0.9604 1.055272000 0.4419 0.5895 0.7191 0.8347 0.9390 1.034374000 0.4189 0.5672 .... 0.6973 0.8134 0.9182 1.013976000 0.3964 0.5454 0.6761 0.7927 0.8980 0.994178000 0.5242 0.6554 0.7725 0.8783 0.974880000 0.5035 0.6353 0.7529 0.8591 0.956082000 0.4833 0.6156 0.7337 0.8403 0.937784000 0.4636 0.5965 0.7.49 0.8220 0.919786000 0.4443 0.5777 0.6966 0.9041 0.902288000 0.4255 0.5594 0.6788 0.7867 0.8852"90000 0.4070 0.5414 0.6613 0.7696 0.868495000 0.4983 0.6192 0.7285 0.8283

100000 0.4573 0.5793 0.6895 0.7901

4-CO r "

Table 4-11 (OSI 168)

Table of Zs as a frpwtio of O and se'vn -perforated grains (conij

S0.65 0.70 0.75 0.80 0.85 0.90

210 -- 2.4.125

26;000 2.27,23 2.41432

28000 2.1372 2.2957 2.455830000 2.0216 2.1G98 2.3192 2.469832000 1.9.'17 2.0610 2.20 13 2.3427 2.485034000 1.8345 1.9661 2.0986 2.2319 2.3662 2.501336000 1 1.7577 1.8825 2.0082 2.1346 2.2618 2.389738000 1.6895 .1.8045 1.9281 2.0484 2.1694 2.291040C00 1.6287 1.7424 1.8567 1.9716 2.0870 2.203142000 1.5740 1.6830 1.7926 1.9026 2.0132 2.124344000 1.5247 1.6295 1.7347 1.8404 1.9466 2.053346000 1.4799 1.5809 1.6823 1.7341 1.8863 1.989048000 1.4391 1.5366" 1.6345 1.7328 1.8315 1.930550000 1. I7 1.4961 1.5909 1.6859 1.7813 1..77052000 1.3674 1.4589 1.5508 1.6429 1.7353 1.828054.00 1.3358 1.4247 1.5139 1.6033 1.6930 1.782956000 1.3066 1.3931 1.4798 1.5667 1.6539 1.741358000 1.2796 1.3638 1.4482 1.5328 1.6177 1.702860000 .--- 1,2544 ---- 1.3365 1.4188 1.5014 1.5841 1.667062000 1.2306 1.3111 1.3915 1.4721 1.5528 1.633764000 1:2076 1.2875 1.3660 1.4448 1.5236 1.602766000 1.1852 1.2653 1.3422 1.4192 1.4964 1.573768000 1.1635 1.2-40 1.3198 1.3952 1.4708 1.546570000 1.1424 1 2233 . 1,29s . 1.3727 1.4468 1.521072030 1.1219 1.2032 1.2790 1.3516 1.4242 1.497074000 1.1020 1.1836 1.2598 1.3316 1.4030 1.474376000 1.0826 1.1646 1.2411 L 1.3128 1.3829 1.453078000 1.0637 1.1460 1.2229 1.2949 1.3639 1.432980000 1.0452 1.1279 1.2051 1.2775- 1.3460 1.413882000 1.0272 1.1103 1.1878 1.2605 1.3290 1.395884000 1.0097 1.0931 1.1709 1.2439 1.3127 1.378686000 0.99Z6 1;0763 1.1545 1.2277 1.2968 1.362488000 0.9758 1.0599 1.1383 1.2119 1.2813 1.346990000 .0.9595 1.0439 1.1226 1.1965 1.2661 1.3320 ,95000 0.9201 k.0053 1.0848 1.1593 1.2296 1.2961

100000 0.8828 0.9687 1.0489 1.1242 1.1951 1.2622

. . *1

4-6


Table .f Z. as afunctiopr of and p 1 , ser'in-pe'rforated gramls (cont)

0.95 1.0 1.1 1.2 1.3

ppO

36000 2,518538000 2.4133 2.536340011 2.3197 2.4369"-200 2.2359 2.34804.11000 2.1604 2.2679 • 2.484246000 2.0920 2.1954 2.403448000 2.0293 2.1295 2.329950000 1.9731 2.0694 2,2629 2.457G52000 1.9210 2.0113 2.2016 -. 389954000 1.3721 1.9636 2.1452 2.327656000 1.8289 1.9168 2.0931 2.2703 2.448158000 1.7880 1.8735 2.0450 2.2172 2.390160000 1,7501 1,8334 2,0004 2,1681 2,336362003 1.7148 1.7960 . 1. %89 2.1224 2.286364000 1.6819 1.7612 1.9203 2.0798 2.239F.66000 1.6511 1.7287 1.8841 2.0400 2.196466000 1.6223 1.6982 1.8503 2.0028 2.155770000 i.5952 1.6696 1.8186 1.9680 2.117672(00 1.5698 1.6427 1.7.388 1.9352 2.081874000 1.5458 1.6174 1. 707 1.9043 2.048276000 1.5233 1.5935 1.7343 1.8753 2.016478000 1.5019 1.5710 1.7093 1.8478 1.986580000 1.4817 1.5497 1.6857 1.8219 1.958282000 1.4626 1.5295 1.6333 1.7973 1.931484000 1.4445 1.5103 1.6421 1.7740 1.9060 lot86000 1.4272 1.4921 1.6220 1.7519 1.881988000 1.4108 1.4748 1.6028 1.7309 1.8590

....- b 9600 1.3952 1.4584 1.5846 1.7109 1.8373 1%950606- 3593 1.4205 1.5427 1.6550 1.7872

100000 1.3259 1.3867 1.5054 . 1.6241 1.7427

rEST AVA''ABLE COPY

4-62

I.


Table of r as a function of Zs and p seven-perforated grains

pp0 7s 0.5 0.6 0.7 0.8 0.9

p 'S

2000 3.9415 3.8859 3.8306 3.7758 '. 21340nO 3.2004 3.1552 3.1103 3.06.58 j.u2156010 2.8328 2.7928 2.7531 2.7137 2.674580C" 2.5976 2.5609 2.5245 2.4884 2.4525

10000 2.4285 2.3942 2.3602 2.3264 2.292912000 2.2984 2.2660 2.2338 2.2018 2.170014000 2.1937 2.1628 2.1320 2.1015 2.071216000 2.1008 2.0771 2.0476 2.0183 1.989218000 2.0329 2.0042 1.9758 1.9475 1.919420000 1.9639 1.9412 1.9136 1.8862 1.-P ?1022000 1.9127 1.8857 1.8590 1.6324 1.8t6024000 1.8627 1.8365 1.8104 1.7845 1.758826000 1.8179 1.7922 1.7668 i.7415 1.716428000 1.7772 1.7522 1.7273 1.7026 1.678130000 1.7402 1.7157 1.6913 1.6671 1.643132000 1.7062 1.6821 1.6583 1.6345 1.611034000 1.6748 1.6512 1.6278 1.6045 1.581436000 1.6457 1.6225 1.5995 1.5766 1.553938000 1.6186 1.5958 1.57:)2 1.5507 1.528440000 1.5933 1.5709 1.5486 1.5265 1.5045-4600 1.5696 1.5475 1.5255 1.5037 1.482144000 1.5472 1.5255 1.5038 1.4823 1.461046000 1.5262 1.5047 1.4833 1.4622 1.441148000 1.5062 1.4850 1.4640 1.4431 1.441350000 1.4873 1.4664 1.4456 1.4250 1.404552000 1.-.694 1.4487 1.4282 1.4078 1.381554000 1.4523 1.4319 1.4116 1.3914 L371456000 1.4360 1.4158 1.3957 1.3758 L356058000 1.4204 1.4004 1.3806 1.3609 1.341360000 1.4055 1.3857 1.3661 1.3466 1.327362000 1.3912 1.3717 1.3522 1.3329 1.313864000 1.3775 1.3581 1.3389 1.3198 1.300866000 1.3643 1.J452 1.3261 1.3072 1.288468000 1.3517 1.3327 1.3138 1.2950 1.276470000 1.3394 1.3206 1.3019 1.2834 1.264972000 1.3277 1.3090 1.2905 1.2721 1.258374000 1.3163 1.2978 1.2794 1.2612 1.243176000 1.3053 1.2870 1.2687 1.2507 L232778000 1.2947 1.2765 1.2584 1.2405 1.222780000 1.2844 1.2663 1.2184 1.2306 1.213082000 1.2744 1.2565 1.2387 1.2211 1.203684000 1.2647 1.2470 1.2293 1.2118 1.194586U00 1.2554 1.2377 1.2202 1.2029 ;.185688000 1.2463 1.2288 1.2114 1.1941 1.177090000" 1.2374 1.2200 1.2028 1.1857 1.168795000 1.2163 1.1992 1.1823 1.1655 L148j

100000 1.1966 1.1798 1.1631 1.1466 1.1301

4-63

pq


Table of a-cs a function of Zs avd pp serew-perfo rated grains (colt)

zs1.0 1.1 1.2 1.3 1.40p .0

2000 3.5672 3.6154 3.5771 3.5520 3.53794 COO 2.9776 2.9351 2.9032 2.8821 2.87006000 2.0357 2.5978 2.5688 2.5494 2.5381'1000 2.4169 2.3819 2.3546 2.3363 2.3254

10000 2.2596 2.2267 2.2006 2.1829 2.172212000 . .1345 2.1073 2.0820 2.0641t 2.054114000 2.0412 2.011-3 ....... 1.9865 1.9695 1.958918s00 1.9603 1.9317 1.9073 1.8904 1.8798MO0 1.8916 1.8639 1.$399 1.8231 1.8125

20000 1.8320 1.8053 1.7815 1. 7 A48 1.754122000 1.7798 1.7538 1.7303 1.7136 1.702824000 1.7333 1.7080 1.6847 1.6680 1.657126000 1.6915 1.6668 1.6438 1.6271 1.616028000 1.6537 1.6296 1.6068 1.5900 1.578830000 1.6193 1.5956 1.5731 1.5562 1.544932000 1.3177 1.5645 1.5422 1.5252 1.513734000 1.5585 1.5357 1.5136 1.4966 1.484936000 1.5314 1.5091 1.4872 1.4701 1.458338000 1.5062 1.4843 1.4627 1.4454 1.433440000 1.4827 1.4611 1.4397 1.4223 1.410242000 1.4506 1.4393 1.4182 1.4007 1.388444000 1.4398 1.4189 1.3980 1.3804 1.367946000 1.4203 1.3996 1.3790- 1.3612 1.348648000 1.4017 1.3813 1.3610 1.3431 1.330350000 1.3842 1.3640 1.3440 I 1.3260 1.313052000 1.3675 1.3475 1.3278 1.3097 1.2966 ,54000 1.3516 1.3319 1.3124 1.2943 1.2809

56000 1.1364 1.3169 1.2976 . 1.2795 1.266038000 1.3219 1.3027 1.2836 1.2655 1.251860000 1.3081 1.2890 1.2701 1.2520 1.238262000 1.2948 1.2759 1.2572 1.2392 1.225164000 1.2820 1.2634 1.2449 I 1.2268 1.212666000 1.26)9 1.2513 1.2330 1.2150 1.200668000 1.2580 1.2397 1.2215 1.2037 1.189170000 1.2466 1.2285 1.2105 1 1.1928 1.178072000 1.2257 1.2177 1.1999 1l.1822 1.167474000 1.2251 1.2073 1.1896 :. 1.1721 1.157176000 1.2149 1.1972 1.1797 1.1624 1.147178000 1.2050 1.1875 1.1701 1.1529 1.137580000 1.1955 1.1781 1.1609 1.1438 1.128382000 1.1862 1.1690 1.1519 1.1349 i 1.119384000 1.1772 1.1601 1.1431 1.1263 1.110686000 1.1685 1.1515 1.1347 1.1180 1.102288000 1.1600 1.1432 1.1265 1.1099 1.094190000 1.1518 1.1351 1.1185 1.1020 1.086295000 1.1322 1.1158 1.0995 1.0833 1.0675

100000 1.1138 1.0977 1.0817 1.0658 1.0501

4-64.

7nble 4-12 (OSRD 64681

Table of r as a fwctiom of zs aWd P,,, sevex -perforated Mims (cocl)

S1.5 1.6 1.7 1.8 1.9p0

2000 3.5333 3.5371 3.5483 3.5466 3.54164000 2.9657 2.8682 2.8769 2.8914 2.91126000 2 5338 2.5356 2.5429 2.5553 2.57258000 2.3209 2.3221 2.3284 2.3395 2.3550

10000 2.1076 2.1683 2.1738 2.1838 -.1.98012000 2.0493 2.0496 2.0545 2.0636 2.076814000 1.9540 1.9539 1.9582 1.9464 1.978916000 1.8746 1.8742 1.8781 1.8859 1.897418000 1.8071 1.8063 1.8096 1.81TO 1.827920000 1.7485 1.7475 1.7505 1.7572 1.767522000 1.6970 1.6956 1.6982 1.7045 1.714324000 1.6511 1.6494 1.6517 1.6576 1.666826000 1.6098 1.6079 1.6098 1.6153 1.624128000 1.5724 1.5702 1.5718 1.5769 1.585330000 1.5383 1.5359 1.5371 1.5418 1.549832000 1.5069 1.5042 1.5052 1.5096 L517234000 1.4779 1.4750 1.4757 1.4798 L487036000 1.4510 1.4479 1.4483 1.4520 L458938000 1.4260 1.4226 1.4227 1.4262 L432740000 1.4026 1.3989 1.3988 1.4020 1.408242000 1.3806 1.3767 1.3764 1.3792 1.385144000 1.3599 1.3558 1.3552 L3578 L363446000 1.3404 1.3361 1.3352 1.3375 1.342948000 1.3219 1.3174 1.3163 1.3184 L323450000 1.3044 1.2996 1.2983 1.3001 1.3049"52000 1.2878 1.2828 1.2812 1.2828 1.287354000 1.2719 1.2667 1.2650 1.2663 1.270556000 1.2568 1.2514 1.2494 L2505 1.254558000 1.2424 1.2368 1.2346 1.2354 L239260000 1.2286 1.2228 1.2203 1.2210 1.224562000 1.2154 1.2094 1.2067 1.2071 1.210464000 1.2027 1.1965 1.1936 1.1938 1.196866000 1.1905 1.1841 1.1810 1.1810 1.183868000 1.1788 t.1722 1.1689 1.1686 1.171270000 1.1675 1.1607 1.1572 1.1567 1.159172000 1.1567 1.1496 1.1460 1.1453 1.147474000 1.1462 1.1390 1.1351 1.1342 1.136176000 1.1361 1.1287 1.1246 1.1235 1.125278000 1.1263 1.1187 1.1144 1.1131 L114680000 1.1168 1.1091 1.1046 1.1031 1. 104482000 1.1077 1.0997 1.0951 L0934 1.094484000 1.0989 1.0907 1.0858 1.0839 1.084886000 1.0903 1.0819 1.0769 1.074888000 1.0820 1.0735 1.0682 1.065990000 1.0739 1.0652 1.0598 1.057395000 1.0547 1.0456 1.0397 L0367

100000 1.0369 1.0273 1.0210

4-65

- mE


Table of F as a function of Zs and ppO seveen-perforated grains (cont)

z0 20 2.1 2.2 2.3.

p 2.4

2000 3.6229 3.6605 3.7044 3.7546 3.81154000 2.9363 2.9665 3.0018 3.0424 - 08836060 2.5944 2.6208 2.6518 2.6874 2.72788000 2.3747 2.3987 2.4269 2.4593 2.4961

10000 2.2162 2.2384 2.2645 2,2945 2,328712000 2.0937 2.1145 2.1390 2.1672 2.199414000 1.9949 2.0144 2.0376 2.0643 2.094816000 1.9125 1.9310 1.9530 1.9786 2.007618000 1.8422 1.8599 1.8809 1.9053 1.933220000 1.7811 1.7980 1.8182 1,8417 1.868522000 1.7273 1.7435 1.7629 1.7855 1.811424000 1.6793 1.6949 1.7136 1.7354 1.760426000 1.6360 1.6510 1.6691 1.6902 1.714528000 1.5967 1.6112 1.6287 1.6492 1.672730000 1.5604 1.5748 1.5917 1,6116 1,634532000 1.5277 1.5413 1.5577 1.5770 1.599334000 1.4972 1.5102 1.5262 1.5450 1.566736000 1.4687 1.4814 1.4969 1.5152 1.536438000 1.4422 1.4544 1.4695 1.4873 1.508040000 1.4173 1.4292 1.4438 1.4612 1.481442000 L3939 1.4054 1.4197 1.4367 1.456444000 1.3718 1.3830 1.3969 1.4135 1.432846000 1.3510 1.3619 1.3754 13916 1.410548000 1.3312 1.3418 1.3550 1.3708 1.389350000 1.312 1.3227 1.3356 1.3510 1.369152000 1.2946 1.3045 1.3170 L3322 1.349954000 1.2775 1.2872 1.2994 1.3142 1.331656000 1.2612 1.2706 1.2825 1.2970 1.314058000 1.2456 1.2547 1.2663 1.2805 1.297260000 1.2307 1.2395 1.2508 1.264762000 1.2163 1.2249 1.2359 1.349564000 1.2025 1.2108 1.221666000 1.18 2 1.1973 1.207868000 1.1764 1.184270000 1.1641 1.1716

1.152274000 L140776000 1,1195

4-66

31


Table of f its a functiowe ofp and P seven -perforated grains

i 0.05 0.10 0.15 0.20 0.25 0.30

PP0

2000 3.62114000 2.9461 2.94136000 2.7474 i 2.5387 2.60468000 2.6162 L 2.3----2.3213 2.3895

10000 2.2916 2.1833 2.126 2.2351 2.3685•000 2.2199 2.10q6 2.0513 2.705 ruff-14000 2.1613 2.04144 1.9739 L9533 1.970916000 2.1119 1.9966 1 920 .. 1.8800 L875218000 1.9554 1.8791 1.8282 1.807520000 1.9193 1.8438 : 1,7883 - 1.754922000 1.8872 1.8124 1.756d 1.7175624000 1.8584 1.7842 1.7291 L..Jff•..26000 1.8322 1.7587 1.7033 L.660628000 1.7354 1.6810 1.637930000 1.7139 1.6599 L617132000 1.6941 L6404 1.5978,34000 1.6756 1.6223 1.579936000 1.6583 1.6053 1.563238000 1.6421 1.5894 1.547640000 1.5744 1.532841000 L5603 1.518944000 L5469 1.505746000 L5342 L493248000 L5221 1.461350000 1,46"

S.52000 1.459154000 L448756000 L4387

" - 58000 L429160000 1.419962000 1.4111

4I

;iI

, ,V

i6

Table 4-13 (OSRD 646R)

Table of r as a fimction of • and p Seven -Perforated grains (cony

* o 0.35 0.40 0.45 0.50 0.55 0.80

0pp12000 2.220314000 2.0216 2.106216000 1.896" 1.9429 2.014518000 1.8106 1.8338 1.8762 1.938520000 1.7473 1.7555 1.7794 1.8187 1.873922000 1.S989 1.6963 1.7077 1.7318 1.7684 1.818124000 1.6005 1.6500 1.6522 1.6655 1.6895 1.7239

2600 1.6294 1.6127 1.6079 1.6133 1.6280 1.651628000 1.6036 1.5820 1.5717 1.5710 1.5787 1.594230000 '1.5.1. 1.5563 1.54 6 1.5359 1.5382 1.547532000 1.5627 1.5344 1.5161 1.5064 1.5042 1.508634000 1.5450 1.5155 1.4942 1.4812 1.4754 1.475836000 1.5285 1.4990 1.4752 1.4594 1.45C5 1.447638000 1.5130 1.4836 1.4585 1.4404 1.4289 1.423240000 1.4984 1.461.443. 1.4236 1.4099 1.401842000 1.4847 1.4556 1.4303 1.4087 1.3930 1.382844000 1.4717 1.4427 1.4175 : 1.3954 1.3780 1.366046000 1.4593 1.4304 1.4054 1.3832 1 1.3645 1.35084$000 1.4475 1.4188 1.3938 1.3718 L-_3523.. 1.337250000 1.4363 1.4077 1.3828 1.3608 1.3412 1.324852000 1.4256 1.3971 1.3723 1.3504 1.33C8 1.313654000 1.4153 1.3869 1.3622 1.3404 1.3209 1,303356000 1.4054 1.3771 1.3525 1.3308 1.3113 1.293758000 1.3960 1.3678 1.3432 1.3216 1.3022 1.284760000 1.3869 1.3588 1.3343 1.3127 1.2934 1.275962000 1.3781 1.3501 1.3257 1.3042 1.2849 1.267564000 1.3697 1.3417 1.3174 1.2960 1.2768 1.259486000 1.3615 1.3336 1.3094 1.2881 1.2689 1.251568000 1.3536 1.32S8 1.3017 1.2804 1.2613 1.243970000 1.3459 1.3183 1.2942 1.2729 1.2539 1.236672000 1.3385 1.3109 1.2869 1.2657 1.2467 1.229574000 1.3314 1.3038 1.2799 1.2587 1.2398 1.222676000 1.3244 1.2970 1.2731 1.2520 1.2331 1.215978000 1.2903 1.2665 1.2454 1.2266 1.209580000 1.2837 1.2600 1.2390 1.2202 1.203282000 1.2774 1.2537 1.2328 1.2140 1.197084000 1.2712 1.2476 1.2267 1.2080 1191086000 1.2652 1.2417 1.2208 1.2021 L 185288000 1.2594 1.2359 1.2151 1.1964 1.179590000 1.2537 1.2302 1.2094 1.1909 1.174095000 1.2166 1.1960 1.1775 1.1607

100000 1.2038 1.1833 1. 1649 1.1482

BEST AVAILABLE COPY

4-68 t


table of F as a fiaction of; and pp setven -perforated grams (cong)

p 0.65 0.70 0.75 0.80 0.65 0.90

Ppp0

24000 !.769326000 1.6841 1.726028000 1.6.174 1.6483 1.687230000 .1,5636 1.5863 1.6158 L662332000 1.5192 1.5357 1.5579 1.5862 1.6206:4000 1.4819 1.4934 1.5100 1.5319 1.5590 L5918 ,3G000 1.4501 1.4575 1.4696 1.4864 1.5078 L534138000 1.4226 1.4266 1.4351 14477 1.4646 1.485640000 1.3985 1.3998 1.4051 1.4144 1.4275 1.4443

42000 0.3774 1.3762 1.3789 1.3853 1.3953 1.40874!000 1.3586 1.3513 1.3558 1.3597 L3670 1.37754G000 1.3417 1.3366 1.3351 1.3370 1.3420 L350048000 1.3266 1.3198 1.3166 1.3166 L3196 1.325550000 1.3128 1.3n47 1.2999 1.2983 1.2996 L303652000 1.3003 1.2909 1.2848 1.2317 1.2.815 1.283854000 1.2889 1.2783 1.2710 1.2656 1.2650 1.2659"56000 1.2784 1.2668 1.2584 1.2.528 1.2499 L243558000 1.2688 1.2562 1.2468 1.2402 1.2362 1.234560000 1.U599 1.2464 1.2361 1.2285 1.2235 1.220862000 1.2516 1.2374 1.2262 1.2177 1.2118 1.208164000. 1.2435 1.2290 1.2170 1.2077 1.12009 1.196366000 1.2357 1.2084 1.1984 1.1908 1.18546RO000 .1.2282 1.2136 1.2004 1.1897 1.1814 1.173370000 1.2209 1.2063 1.1930 1.1816 1.1726 1.165872000 1.2138 1.1993 1,1859 1.1740 1.1644 1.156974000 1.2069 1.1925 1.1791 i 1.1669 1.1567 L 148676000 1.2003 1.1859 1.1726 1.1602 1.1494 1.140878000 1.1939 1.1795 1.1662 1.1538 : L1426 1.133480000 1.1876 1.1733 1.1600 1.1476 : 1.1361 1.126582000 1.1815 1.1672 1.1539 1.1416 ; .1 L119984000 1.1755 1.16"3 1.1480 1.1357 1242 1.113786000 1.1697 1.155b 1.1423 1.1300 1.1185 1.107888000 1.1641 1.1499 1.1367 1.1245 .1130 1.102290000 1.1586 1,1444 1.1313 1.1191 1.1076 .09681,95000 1.1454 1.1313 1.1183 1.1061 L0947 1.0839

100000 1.1330 1.1189 1.1059 1.0938 1.0824 1.0718

4IR

I1

Tble 4-13 (OSRD 6468)

Table of r as a fwctjon of ; and ppO seven-perforated grains (cont)

P 0.95 1.00 1.10 1.20 1.30

36000 1.565338000 1.5110 1.541040000 1.4650 1.489642000 1.4255 1.445844000 1.3911 1.4079 1.451346000 1.3609 1.3747 1.411248000 1.3341 1.3454 1.376050000 1.3102 1.3193 1.3450 1.380852000 1.2886 1.2958 1.3172 1.348054000 1.2691 1.2746 1.2923 1.318756000 1.2514 1.2554 1.2698 1.2924 1.323258000 1.2352 1.2379 1.2494 1.2686 1.295460000 1.2203 1.2218 1.2307 1.2469 1.270362000 1.2066 1.2070 1.2136 1.2271 1.247564000 1.1939 1.1934 1.1978 1.2089 1.226666000 1.1821 1.1807 1.1831 1.1921 1.207468000 1.1712 1.1689 1.1696 1.1766 1.189670000 1.1610 1.1579 1.1570 1.1622 1.173272000 1.1514 1.1477 1.1452 1.1488 1.158074000 1.1424 1.1381 1.1342 1.1362 1.143876000 1.1340 1.1291 1.1239 1.1245 1.130578000 1.1261 1.1206 3.1142 1.1135 1.118080000 j 1.1187 1.1126 1.1050 1.1031 1.1063"82000 1.1116 1.1050 1.0964 1.0934 1.095384000 1.1049 1.0979 1.0683 1.0842 1.085086000 1.0986 1.091i 1.0806 1.0755 1.075288000 + 1.0926 1.0L 7 1.0733 1.0672 1.065990000 L1.Q0069 --- 1.0786 1.0663 1.0593 1.057195000 1.0738 1.0646 1.0504 1.0414 1.0370

100000 1.0617 1.0522 1.0363 1.0255 1.0192

4-70BEST AVAILABLE COPY

_____.-


Values of N 0 .3

N 0 2 4 8 Avg.Dill.

0.010 0.25119 0.25269 0.25416 0.25582 0.25706 1460.011 0.25847 0.25988 0.26126 0.26263 0.26396 1370.012 0.26531 0.26663 0.26793 0.26922 0.27050 1290.013 0.27176 0.27301 0.27424 0.27546 0.27667 1220.014 0.27787 0.27905 0.28023 0.28139 0.28254 Vot0.015 0.28368 0.28481 0.28593 0.28704 0.28814 1110.016 0.28923 0.29030 0.29138 0.29244 0.29349 1060.017 0.29453 0.29557 0.29660 0.29761 0.29862 1020.018 0.29963 0.30062 0.10161 0.30259 0.30356 960.019 0.30453 0.36549 0.30644 0.30738 0.30832 940.020 0.30925 0.31017 0.31109 0.31200 0.31291 910.021 0.31381 0.31470 0.31559 0.31647 0.31735 80.022 0.31822 0.31908 0.31994 0.320680 0.32166 850.023 0.32249 0.32333 0.32416 0.3249" 0.32582 833.024 0.32664 0.32745 0.32826 0.32906 0.32986 800.025 0.33066 0.33145 0.33224 0.33302 0.33380 780.026 0.33457 0.33534 0.33611 0.33687 0.33763 760.027 0.33838 0.33913 0.33988 0.34062 0.34136 740.028 0.34210 0.34283 0.34355 0.34428 0.34500 720.029 0.34572 .0.34643 0.34714 0.34785 0.34855 710.030 0.34925 0.34995 0.35064 0.35133 0.35202 690.031 0.35270 0.35338 0.35406 0.35474 0.35541 660.032 0.35608 0.35674 0.35741 0.35807 0.35873 60.033 0.35938 0.36003 0.36068 0.36133 0.36197 65

- 0.034 0.36261 0.36325 0.36389 0.36452 0.36515 63-0.035 0.36578 0.36641 0.36703 0.36765 0.36827 62

0.036 0.36888 0.36950 0.37011 0.37072 0.37133 610.03, 0.37193 0.37253 0.37313 0.37373 0.37432 600.038 0.37492 0.37551 0.37610 0.37668 0.37727 590.039 0.37785 0.37843 0.37901 0.37958 0.38016 5s0.040 0.38073 0.38130 0.38187 0.38244 0.38300 570.041 0.38356 0.38412 0.38468 0.38524 0.38579 560.042 0.38634 0.38690 0.38744 0.3879" 0.38854 650.043 0.38908 0.38962 0.39016 0.39070 0.39124 540.044 0.39177 0.39231 0.39284 0.39337 0.39390 530.045 0.39442 0.39495 0.39547 0.39599 0.39652 520.046 0.397033 0.39755 0.39807 0.39858 0.39909 510.047 0.39960 0.40011 0.40062 0.40113 0.40163 510.048 0.40214 0.40264 0.40314 0.40364 0.40413 500.049 0.40463 0.40513 0.40562 0.4-3611 0.40660 490.050 0.40709 0.40758 0.40806 0.40855 0.40903 490.051 0.40952 0.41000 0.41048 0.41096 0.41143 480.052 0.41191 0.41238 0.41286 0.41333 0.41380 470.053 0.41427 0.41474 0.41520 0.41567 0.41614 470.054 0.41660 0.41706 0.41752 0.41798 0.41844 460.055 0.41890 0.41935 0.4 1981 0.42026 0.42072 450.056 0.42117 0.42162 0.42207 0.42252 0.42297 450.057 0.42341 0.42386 0.42430 0.42474 0.42519 440.058 0.42563 0.42607 0.42650 0.42694 0.42738 440.059 0.42781 0.42825 0.42868 0.42912 0.42955 430.060 0.429968 0.43041 0.43084 0.43126 0.43169 430.061 0.43211 0.43254 0.43296 0.43339 0.43381 420.062 0.42423 0.43465 0.43507 0.43548 0.43590 420.063 0.43632 0.43673 0.43715 0.43756 0.43797 410.064 0.43838 0.43879 0.43920 0.43961 0.44002 4'.

4-71

-I----o


Values of N (coal)

2 4 6 8Avg.I Diff.

(1.o6e 0.44043 0.44083 0.44124 0.44164 0.44205 400.066 0.44245 0.44285 0.44325 0.44365 0.44405 400.067 0.44445 0.44485 0.44524 0.44564 0.44603 400.068 0.44d43 0.44682 0.44722 0.44761 0.44800 390.069 0.44839 0.44878 0.44917 0.44955 0.44994 390.070 0.45033 0.45071 0.45110 0.45148 0.!5187 .... 380.071 0.45225 0.45263 0.45.701 0.45339 0.45377 380.072 0.45415 0.45453 0.45 191 0.45528 0.45566 380.073 0.45603 0.45641 0.4O678 0.45715 0.45753 370.074 0.45790 0.45827 0.45464 0.45901 0.45938 370.075 0.45975 0.46011 0.46048 0.46085 0.46121 370.076 0.46158 0.46194 0.46230 0.46267 0.46303 360.077 0.46339 0.46375 0.46411 0.46447 0.46483 360.078 0.46519 0.46555 0.46590 0.46626 0.46661 360.079 0.46697 0.46732 0.46768 0.46803 0.46838 350.080 0.46873 0.46909 0.46944 0.46979 0.47014 350.081 0.47048 0.47083 0.47118 0.47153 0.47187 350.082 0.47222 0.47256 0.47291 0.47325 0.47360 340.083 0.47394 0.47428 0.47462 0.47497 0.47531 340.084 0.47565 0.47599 0.47632 0.47666 0.47700 340.085 0.47734 0.47767 0.47801 0.47835 0.47868 340.086 0.47902 0.47935 0.47968 0.48002 0.48035 330.087 0.48068 0.48101 0.48134 0.48167 0.48200 330.088 0.48233 0.48266 0.48299 0.48331 0.48364 33-0.089 0.48397 0.48429 0.48462 0.48494 0.48527 32iv- .U09- 0.48559 0.48592 0.48624 0.48656 0.48688 320.091 0.48721 0.48753 0.48785 0.48817 0.48849 320.090 0.48881 0.48912 0.48944 0.48976 0.49008 320.093 0.49039 0.49071 0.49103 0.49134 0.49166 320.094 0.49197 0.49228 0.492C0 0.49291 0.49322 310.095 0.49353 0.49385 0.49416 0.49447 0.f8 310.096 0.49509 0.49540 0.49570 0.49601 0.49632 310.097 0.49-63 0.49694 0.49724 0.49755 0.49785 310.098 0.49816 0.49846 0.49877 0.49907 0.49933 300.099 0.49968 0.49998 0.50028 0.50058 0.50089 30

N __.3

10 1.995262

102 3.981072

103 7.943282

104 15.84893

105 31.62278

106 63.09573

107 125.8925

108 251.1886

109 501.1872

4-72

o ~ 0 0 0

0.f f I- f

f. i f

o 0 a0 0

Pt* "- f 0

vi

- ~--

4-7

powder to M2. The' constant. that we use inthis evaluation are listed .- dow.

)A 4a I ILhVe - 457 in.3 MAXIMUM PRESSURE FIXEDL a 185.2 In. MUZZLE VELOCITYA ,, 10.1 in.2Pm " 59,800

Propellant Composition: M2 >}1 - 26.95 in. 3 /lb 0:p - 0.0596 lb/in.3 w

F - 384,000 ft-lbs/lb 4a 10.17 in. 3 /lbao - 0.635B , 0.5 x 10- 3 (in./sec)/(lb/in.2 )

To start, we select three values for 0: LENGTH OF TRAVEL

, Fgwre 4-15. Optimum conditions

0.40 0.50 0.60=10 - 1/(a/0 + i/o) loading density, lbs/in.3

a= 25.4 20.33 16.941/p= - 16.78 16.78 16.78

MAO - 42.18 37.11 33.72AO a 0.02372 0.02695 0.2968

Aa 27.688o loading density, gms/ccA a 0.657 0.746 0.822C a AoVc charge, lbs

Vc - 457 45? 457C a 10.84 12.33 13.56

Pmax a 59,800 59,00 59,800

p p. (Pmax)(M ,_C 8aO)

M II 11 11a 3.275 3.300 3.320

C/s 3.31 3.74 4.09M . C/3 - 14.31 14.74 15.09

Ma 11 11 11C/2 a 5.42 6.16 6.78

M + C/2 = 16.42 17.16 17.78

S0.872 0.858 0.849

(M + C/2XPmax • + C/2) 52,200 51,300 50,800

po = 33,200 32,600 32,200Xm/Xo (Vc AL)/Vc 1 + AL/Vc

Vc- 457 457 457/

AL a 1852 1852 1852Vc + AL = 2309 2309 2309xm/xo 5.05 5.05 5.05

4-74

- ao/(XM/'Xo- 17Xm/Xo a 5.05 5.05 5.05

Io 0.640 0.726 0.800Xm/Xo -" 0 4.41 4.32 4.25

aAo a 0.2412 0.2740 0.3015am 0.0545 0.0632 0.071

Use table 4-14 for values of N0"3

fm0'3 = 0.41775 0.43673 0.45225

Use table 4-9 or 4-11 for Z and tables 4-10 and 4-13 for r as indicated.

f = 1.5250 1.4988 1.5043ZS or Zb = 1.2110 1.4908 1 7755

2CFVm =i( -rTxm 0 "3) 23.

1.02(M + C/3.1)m3= 2.174

M 11 11 11 11C/3.1 3.31 3.74 4.09 3.88

M + C/3.1 = 14.31 14.74 15.09 14.88m= 0.454 0.467 0.478 0.472

0.3m' = 0.1361 0.1385 0.14342CF = 8330000 9470000 10420000

2CF/0.3m' - 6120000 6840000 7280000CF = 4665000 4732000 5210000

r *m0"3 = 0.636 0.654 0.6811 - rl'm 0 " = 0.364 0.346 0.319

Vm 2 . 22.2 x 106 23.68 x 106 23.18 x 106Vm = 4710 4865 4810

When using a multiperforated propellant, follow this method:

.m 0 "3 (U - 0.242Zs)/f0.242Zs = 0.293 0.361 0.43

1 - 0.242Zs a 0.707 0.639 0.57(I - 0.242Zs)/r' = 0.464 0.426 0.379

The point of optimuir efficiency is when fm 0 .3 and (1 - 0.242Zs)/A are equal, hence we use

B/W= V1.3 6 9 _

A2 = 100

1.363A2 = 136.9

CFm'Zs a (12.05) (384,000) (0.472) (1.4315) = 3.19 x 10+6

(B/W)2 - 43.7 x I0-6

B/W = 6.61 x 10-3

4-75

Now. having all the values, we plot the curve From the example for the optimum loadingfor :mO. 3 and for 01 - 0.242 Z,)/F,. The value density, we found B/W to beo( (and therefore C and Vm) selected should .1x0-be the one corresponding to the point of inter- 66se~tiu. of these curves, or the one corres- We shall use this value of B/W for our calcu-ponding to the highest velocity, whicheveroccurs latlons -below. As explained previously, thefirst. Values of -1 beyond the point of inter- pressure-time trace is divided into three in-section are undesirable because they imply tervals - before splintering, after splintering,unburnt propellant released at the muzzle. The and after burnt. There are different formulasgraph is shown in figure 4-16. for each interval; accordingly the problem

worked out below is done in fthree sectior~s.

We know -the value of Zs to be 1.4315, and A toFFVFT-4T be 0.462. We break our interval before splinter-

~-' t-~ttj4 t~tIng into increments of Z of 0.2, starting with0 46 A 4 0.2,. and going up to 1.4315, omitting 1.40. The

form function constants frthis first interval0 are

0440 -" ko 0.848o

=0.9808

7 k 0.1321

E Also, we have

10 Z0.017TTA = 1.30

0400 0.72028J2 0.9!475

2-/r fo 0.98607. A . Al -0.53315

A =l 0.439+1~f3] ~ M -0.01422

.~ ~ ~ . 0.42478a 32 f oto= 0.2405

0.400.500.60r = 0.1679* 3Z 5 = 0.014315

Fipire 4-16. Optimum value of s 31 f0 0.711q 0.02014

The constants calculated are listed below. (5-1) =0.15

C = 12.05 lbs k2 fo0 = 0.1302A= 0.725 gins/cc t . 3Zs = 1. 03

Vm- 4,855 ft/sec .. k2f0/3AZs = 0.1264Zs= 1.4315

Using theý formula

4-48. The Complete Solution for a Pressure- u (- 1) -k2fd/lZ 5sTtime Trace. Utilizing the formulas of the pre-ceding derivation for the OSRD 6468 System, we get u = .0.0236.

we shall make a complete solution, and plot theresultant prebsure-time curve. Our gun is again With our values of q, u, and Z we can get the

.-the 90-mm, WTV-F1951, the same as in the values of 3 and S from tables. These values areexample for the optimum conditions, given here in table. 4-16.

4-70

Table 4-16 This is the space avenge pressure. To con-vert to maximum pressure, we multiply by

Values of J and Sfor values of Z

Z 0.2 T 0.4 0.6 0.8 1.0 1.2 1.431 U, C/5

J 1.1647 1.4065 1.7082 2.0812 2.5427 3.1131 3.9327 We get

S 0.2180 0.4834 0.8082 1.2064 1.6945 2.29511 3.1633 20,900 34,700 43,800 49,300-. 151,500 51,400 49,200

We then find the pressure for each intervalfrom the formula We find the time before splintering by the

12F Jlfo a q÷ Z - uZ 2 equation

Z (1-a)- rs o fz dZ

The steps in the calculatien are tabulated below. Z 5 (B/W) P

0 To solve this integral, we plot Z versus li/P,0.2 0.4 (j.6 0.8 and find the areas under the curve for the

various intervals. These values of the area12FJlfoo/Zb 59.900 59.900 59,900 59,900 give us the value o the time. The curve is

Z2 0.04 0.16 0.36 0.64 shown in figure 4-17. The outline of the calcu-lations for the curve is given below.

uZ 2 0.000936 0.00374 0.00842 0.0149?

q + Z - uZ 2 0.2192 0.41640 0.61172 0.80517__..... - Z 0.2 0.4 C.6

1J(1 - a) 0.669 3.809 0.182 1.195 =

J(- - - :S 0.6324 0.7273 0.8463 0.990 fo/Zs(B/W) 104.2 104.2 104.2

q + Z - uZ 2 0.3405 0,573 0.723 0.513 I/P x 104 0.483 0.292 0.2J1T(1 - a_) - F 0340 =7 .2 .

P 20.700 34,360 43,300 46.700 1.2z 19-5 0.744 x 0.512z10

S1648 [ 2.022 2.554

z 1.0 1.2 1.4315 Z 0.8 1.0 1.2 1.4315

12 FJlfo-o/Zb 59,900 59,900 59,900 fo/Zs(B/W) 104.2 104.2 104.2 104.2

Z2 1.0 1.44 2.043 1/P x 104 0.2052 0.1972 0.1976 0.2060

uZ 2 0.023 0.0337 a.0478 dZ 0.432 x 10U 0.400 0.392 0.460

q + Z - uZ2 0.99674 1.1864 1.4038 _ P_t [ 3.003431 49 387 0.0

J(1 - a) 1.462 1.789 2.260 3.419 3.827 4.306

J(1 -l ) - rS 1.1775 1.404 1.7297

qg+ Z -uZ2

J(+ - ru 0.846 0.845 0.812 The plot ao the P - t curve for the intervalJ(1_____- _ ___-_rfrom t = 0, to t a 4.306 (splintering), can be

P 50,700 50,600 48.600 seen on figure 4-18 as par-t of the complete---i curve.

4-77

t The equations used in the solutions for the apply. The form function constants for theInterval before spLinteriing no longer apply. burning of splinters areFrom the point of splintering to the point whenall the powder Is burned, the following values k. -0.49037

4j - -0.3755

iJ 31.231

0'" J2 0.39648

0"2 0.45774-~042

`'3 0.66817--------- 0.241r,

036~~ ol 0.439

a~2a 0.122

30.561

O~n aAoP3 0.179r -0.125

OH - 1) XO.150.22

0.2 ki- -0.3700.19

0.20 Q40 010O 0.00 1.00 1.20 1.40 j1Z5 1.03

Figure 4-17. Evaluation of time integral in k~f0 /J1 Z5 - -0.359interval before splintering

Using the formula

ii' ~ ~ k a/~ -)-1fiz 0.68751

KOOSPUINTNt 1 he physical quantities for the Interval ofburning of the splinters are given in terms ofthe parameter Z' in the region

............ where Z. jIZ5 /j1 0.837, and Zb (foL--. Z,/= 1.262.

In addition, we use the following two quantities:

AL 8(1~ u'Zs .iu=2.99

- z'- (I.+ z 0.62299

AM where Xs/X 0 is the value of X/X 0 at the endof the previous interval (2.3848).

We take our interval during burning from00 10 2.0 3.0 4.0 so O 0 0 &0 Zs: Z' :5 4. Hence, v.! break this interval

Tom 6b012M) Into four parts, as shown In the calculationsFigure 4-18. Pressure-time curve below. To calculate 3', we use the formula

4-78

I'. (1 - u'Z')"l/u'. The values for the various We again solve this Integral by plotting Z'intervals are given in table 4-17. versus l/P, and finding the area under the

curve for the increments. The values are givenTable 4-17 In table 4-19.

Values of J' The equations for the interval after all thepowder is burned are in general the same as

Z 0.837 0.900 1.000 1.100 1.262 those for the intenal after splintering. First,-.-...- we find Q, as

uVZ' 0.426 0.458 0.509 0.560 0.632

1 - u'Z' 0.574 0.542 0.491 0.440 0.367 Q = ( "4%s) 7- "

l/J 0.336 0.3095 0.247 0.199 0.140 The values that we have are

J' 2.97 1 3.230 4.050 5.020 7.140- - - - - 4 U= .24191

Zs a 1.4315For this interval, S is absorbed in the equa- 4Zs a 0.346tions. To calculate the pressure, we use the (1-,4Zs) - 0.654formula *o a 0.706

P a 12F J1 fo ko Z' (I - u' Z') Xb3.992Z• k Jr + i -- "' 1-u '

+ U,(I -U, I) ! 3.1.515

The outline of the values for *he increments is

given in table 4-18. Q a 0.991

The physical quantities for the interval after allS, The value o the time from the beginning of the powder is burned are given in terms of

motion is given by X/Xo as the parameter. "The pressure is given" t "+; fo f' dZ' by

t . 0 (BM ÷f P P - 12 FOQ VC/Xo -7

Table 4-18

Maximum pressure in interval after spliatering

Z 0.8"7 0.900 1.000 1.100 1.244

KJ' 1.67 1.814 2.270 2.820 4.01

r' / 1 + u' 0.0829 0.0829 0.0829 0,0623 0.0629

12FJ'l fo4,!Z• 175,000 175,000 175.000 175,000 17,000

Z'(1 - U'Z') 0.4805 0.4880 0.4910 0.484 0.458

r + ') 11 - u'Z'] 0.0476 C.0449 0.0407 0.038 0.0306

PI v. 49,000 46.,00 37.100 23.650 19.840

Pam 49,700 46,800 37,700 30,200 20,100

4-79

Table 4-49 port from theory. The system depends on as-suming a simple algebraic relation between

Time in ixter•l after splintering velocity and shot travel.

zo 0.837 0.9 1.00 1.10 1.244 The basic assumption of the Le Duc System isthat the velocity space curve for the travel of

fo/Z4(B/W) 178.2 178.2 178.2 178.2 178.2 the projectile up the bore of any gun can be

t/p X 104 0.204 0.2175 0.2695 0.238 0.503 represented by the hbperbolic functionaz (180)

f i- o.136X 10-6 0.245 0.300 0.597 (18-"

. .-4.306 4.548 -4.94 5.51816.578 This curve passes through the origin, risesFor our X/Xo values, we take the value Xb/Xo, steeply at first, and gradually flattens out.and Xm/Xo. We have Xb/Xo = 4.698, Pm This curve resembles the velocity-space curve19,740; and Xm/Xo a 5.05, Pm 17,700. in general form, but the equation is not always

-accurate.S The time is found from the integral To determine the significance of a, it will be

XM/ X noticed that as x tends to infinity, tendst/tho+ d2X/fd to unity, and. v thus tends to a. Therefore, a is

Xb/Xo the theoretical velocity of a projectile firedfrom a gun with the given loading conditions,

To find the value of V, we use the formula but from a gun of infinite length. Under theseconditions the kinetic energy of the projectile

V2 2CP [I (X/X Q)1- IF is experted to be However, by con-S1-sideration of the energy equation

vb2 - 2.754 x 106 (1 - 0.991 (4.698 - 0.706)'0.3] 'Cz pcz(,, b) (X

Vb = 976 ft/sec 7- Ps dx (1

In 2.754 x In [1 - 0.991 (4344)-" it Is seen that the energy released by theburning propellant Is FC/ y - 1. Neglecting

Vm = 1,012 ft/see losses, and equating the twoenergy expressions,

5. 05 - we gett 6.578 + d FC I wa 2

12 -a -. (18)'4.698 ( 1-) 2 g

1 orv' (103) = 1.025 2gF[] (1/2

a1L-;- (103 (1SU1 (l0V ) 0.9U8 Adapted for American naval pyro powder, the

In formula becomes

t a6.578 0.352 a6.930a ,. 6823(C/w)i (27.68C/,,) (184)

LE DUC SYSTEM with7

"4-49. Introduction. The Le Due System is al-most completely empirical, deriving little sup- C aUJ w are in lb, Ko Is in cubic inches.

4-Ot

For other propellants, the constant term in We can use the computed value of a in eitherr * the formula for pressure or the formula for

modified in the ratio of L( - J velocity. Wlth the constant b, however, we canonly use the b value calculated from maximumpressure in the formula for maximum pres-

By consideration of the equation of motion cd a pesiei h oml o aiu isByconsider fthe fr ula tn f or mn p r a sure. The b value which Is calculated from the

projectile, the formula for maximum pressure velocity formula can be used only in computingis derived as -velocity. This is explalied by the fact b takes

4.48 wa 2 somewhat different values in each case. In ourIn * 27Agb (IdS) example, we will first calculate the value of a

It can be shown that b is travel to maximum for item 21. With this, we *Il calculate the

values of b from the pressure formula and fromthe velocity formula. We then calculate the value

It is assumed that the shot travel to maximum ol a for items 10 and 14, and by changes in

pressure id proportional to some function of equation (191), we can calculate the b value for

the quickness of the propellant, to Initial air velocity for items 10 and 14. Then, with our

space, and to some power, positive or negative, values l b and a for Items t0 and 14 a simple

cd the chamber volume and of the weight cd the calculation yields the velocity.

projectile, that is To calculate the maximum prersure in items 10b •q(Ko - C/6)K "L lw'k and 14, we use the a values computed for 10

q0 and 14 and make the proper changes in the bfrom pressure in item 21 to obtain the b value

Sq(1 - C/ Ko)Koa wk (18M) for pressure In items 10 and 14. With these

values, the maximum pressure can be calcu-

where q is a constant depending on the con- lated directly.

position and ballistic size of the propellant. ForAmerican pyro powders, a and k have been de- For item 21termined as approximately 2/3. Hence the for- (64.411%38,000) (8.12)mula becomes a(.4 5 0) (2.1)

b - q(1 - C/S Ko) (K1 /w)2 /3 (187) a 5 5,189Finding the b value for maaimum pressure, we

4-50. Example by Le Duc System. The four obtainbasic equations that are used in our calcula- (0.65) (24.1) (2.692) 1tions are given below. 45,400 (10. 7) (2.2) b(10.7) (32.2) b

axV a f (188) b - 7.l It

1/2 blO(for pressure) -

a C (189)L5 _1 (1 - CAI Ko4i0 (Kv1o(l02/ 71

4.48 wa2 (0 - CA Kl) 2 1 (K2w) 212 / 3

PmI 27Agb (190)

bnaq l- C~l% 2 / 3 (191) - 3.82 1O

(0.0571) (140)1M.4)By the Le Duc syst em, we first Lalculate the b 10 S [ 8.12 J300N2/value of a, directly from equation (189). With V 20457) (30) .1this value of a, and by use of equation (190),with the known maximum pressure of item 21,we can calculate the value of the constant b. bl 0 75.74 ft

4-6

I~q..1

To got the value of b for item 14 that is needed Checking for velocity in items 10 and 14, wefor pressure, we solve in the same manner, first have to obtain the b value for velocity inand obtain item 21.

fi (0.0571) (2R0 )J -) (7.126)(5:189)( 156- 133 in.

28.2 Applying this value of I to find the values of

b14 =10-1b in 10 and 14, we obtainM1b - (0.522)(4.36)(133) . 107 In.

The a value for item 10 is b (0.526) (5.36)

a 64.4) (3.18 X_ _0S 3.8211/2 b (0.703)(5.61)(133) , 186 in.-" i - 1 .4,455 Am4 2.82[ 0.256 15.4] /j428a (4,455)(136) , 2,490 ft per sec

a2-1.85x 106 V10" 107 , 136

The a value for item 14 I 6 (4250)(158

[ (!64.4) (3.-18) . 4,250 4-51. Comparison of Results. Since the same.256 15.0 Jproblems have been worked out by the threesystems, a comparison of the results may be

a2 = 18.08 x 106 made. This is done in table 4-20. Since only twoproblems have been worked out, a general com-

(0.166)(15.4)(19.85)106 ment cannot be made as to the relative accuracy10 a 39,100 lb per in. 2 of the three systems, although it seems that

both the RD38 (Corner system) and Hirsch-

P 14 ) ( 19,810) 01 per in.2 felder (OSRD 6468) systems give results whichare about the same in value.

Table 4-20

Cop,,anson of results

.D38 method

Value e- 0 8=0.15 e a 0.30 0SRD 6468 Le Duc Firing values

Pin 43,600 44.40C 46,400 48,100 39,100 48,64010

V10 2,560 2,610 2.590 2.680 2.490 2,600

P 14 21,800 23,100 25,300 19,38.0 19,800 33,000

V14 2,180 2,280 2,300 2,340 1,960 2.400

4-82

REFERENCES AND IIBLIOGRAPHY

1. Corner, J., "Theory of Interik' Ballistics of Guns," John Wiley and Soam, New York, 190.

2. Curtiss, C. F., and J. W. Wrench, Jr., Interior Ballistics, Division 1, OSRD, NDRC ReportNo. A-397, Washington, D. C.

3. Hypervelocity Guns and the Control of Gun Erosion, Summary of Technical Report ofDivision 1, NDRC, Vol. 1, Washington, D. C., 1946.

4. Hayes, T. J., "Elements of Ordnance," John Wiley and Sons, New York, 1938. -

5. "Internal Ballistics," Philosophical Library, New York, 1951.

48

,p 4-83

p 4

GENERAL PROBLEMS OF PROPELLANT effective. This is the explanation of why somea IGNITION primers with a small black powder charge -

perform better than larger primers in certain4-52. The standard method of igniting fixed rounds.and semifixed rounds of ammunition is by theiong artillery primer, usually the longest As a consequence of the nonuniform distributionprimer allowed by the cartridge case and of a po wde r gase non gn ther axis t he

round lengths is used, in the hope of distribu- of black powder gases along the axis of theting the igniter gases uniformly in the pro- primer or the time delay which exists in mann

tingtheIgnier asesuniorml Inprimers before any 6..ses emerge fromn thepelling tharge. Few conventional primers jus- piesbfr n -e mrefo hpelin eare.Fe cnvntonl rier js- forward vent holes, some parts ofthepropellant

tify this intent (see references 1, 2, and 3), forw ar t holes, sod parts thepressure

because tht black powder charge within the bed start burning, and increase the pressurenarrow primer tube imposes a resistarhe to locally, earlier than others. This is believed to

rapidrflow primerstusewimposes tube. For a be conducive to sporadic high pressures underrapid f nalysis ow the action ohthe primer the several conditions listed earlier. For ansimplified anlsi oferat thetess actie reftheeprimergases, see reference 4; for design information alternate hypothesis, see reference 5.regarding standard primers, see reference 7.

During the past few years there have beenManifestations of improper ignition vary from several proposals made bor overcoming themisfires and hangfires to sporadic high pres- deficiencies of the conventional long artillerysures and poor velocity uniformity. Theoretical primers.analysis indicates, and experience confirms, a. The fraction of the black powder chargethat problems of ignition are more severe under emitted from each section of the primer canthe following conditions: more nearly be equalized by using small vents

1. High propellant loading density (over 0.7 where the pressure normally is highest andgm/cc) large vents where pressure is low. An example

2. Long cartridge cases of this is the T88E1 primer.3. Small granulations of propellant b. An empty channel can be built into the4. Low flame temperature propellants primer, so that the percussion element flash5. Low ambient temperatures is transmitted rapidly along the whole primer6. Low projectile sectional densities and axis.

starting forces. c. Some correction is effected if the blackThese conditions are met more frequently in powder charge is positioned forward, rathermodern ammunition, because there is a need than in close contact with the percussion ele-to attain high velocties and to extend gun life. ment. The distance forward has to be precisely

determined in order to prevent hangfires.There is still much to be learned about ignition d. The igniter charge may be placed in aof propellants and there may be disagreement closed magazine at the rear, from which theamong workers in the field on the principles gases then issue into a highly vented, emptyto follow. There appears to be no difference forward section. Since room fer the igniterof opinion, however, that in artillery rounds material is limited in such an arrangement,the index of satisfactory ignition is a pressure- something with a higher heat of reaction thantime record of the firing that exhibits no dis- black powder must be used. In a practical de-continuities. There has been general acceptance vice designed by the Canadians, a propellantof this rule, which was first proposed by with high nitroglycerine content is used. 6

British workers in 1942, and most proving e. The resistance to flow along the axis,grounds are equipped to record the pressure- characteristic of haphazardly packed blackpow-time relationship in experimental firings. der granules, can be drastically reduced by

using an igniter material in the form of longIt is obvious that the ignition interval is com- sticks. A proper rate of burning is provided byplete when the pressure in the gun has reached inducing porosity in the igniter sticks duringsome high value. It follows that the primer manufacture. 7

must have discharged its igniter gases by thattime. If the primer used does not accomplish Practical considerations often dictate the dc-this, only part of its black powder charge is sign of the ignition system on terms directly

4-84

opposed to the requirement for optimum ignition. In separate-loading ammunition (no cartridgeAs an example, there was one experimental, case), no primer is used. The ignition systemfin-stabilized round whose lin extended within consists of pancake bags loaded with blacka few inches of the cartridge-case base, leav- powder and positioned along the charge. Aning no room for a primer. Fortunately for the attempt is made to allow a free channel forengineers responsible for the ignition system, passage of igniter gases by using propellingthe project was cancelled. The problem is charges of smaller diameter than the chamber.present to a varying extent in other finned There is evidence to Indicate that the loadingammunition. density must be very low to prevent sporadic

high pressures.

4-85


1. Ekstedt, E. E., and D. L. Wann, The Discharge Characteristics of Certain Artillery Primers,BRL Report No. 972, November 1955.

2. Vest, D. C., et al, On the Performance of Primers for Artillery Weapons, BRL ReportNo. 852.

3. Unpublished experimental data available at Picatinny Arsenal on several standard and specialprimers.

4. Hicks, B. L., Some Characteristics of the Practical IgniLion Of Propellants, BRL Memo-randum Report No. 640, December 1952.

5. Frazer, 3. d., eL al, One View of the Ignition Process for Nitrccellulose Propellants, Bulle-tin of the First .1,ymposium on Solid Propellant Ignition.

6. McLennan, D. E., Studies in Ignition, Part VIII: Further Experiments with the "Hot Gas"Primer, CARDE Report No. 296/54, April 1954.

"7. Vest, D. C., A General Discussion of Extruded Igniter Compositions, BRL MemorandumRaipurt No. 894.

8. Price, 3. R., Experiments on the Ignition of Cool Granular Propellants in the Q. F. 3" 70 calGun, CARDE Memorandum (P) 14/55.

4-86BEST AVAILABLE COPY

CALCULATION OF THERMODYNAMIC Example. Ethylene diamine dinitratePROPERTIES OF PROPELLANTS (C2 H1oN4 0 6 ):

4-53. Introduction. From a knowledge of the 377composition of propellants, the thermochemical Q =8580 - 67,421 (4 5 - 6)

properties of their constituents, and of the 186

products oi explosion, it is possible tocalculatethe ballistic properties of propellants. Because = 945 ral per gmthe propellant is a colloid rather than a corn- b. The leat of explosion (Q) is calculatedpound, the individual contributions of the cor.- for a propellant composition (the colloid) bystituents are additive. The following methods obtaining the algebraic sum of weighted valuesof calculation, based on reference 1, use the for all constituents.summation of tabulated values of these additive Example. Calculation for a propellant con-properties.* Gun performance depends, es- taining 20 percent nitrocellulose (11.15 N), 30sentially, on three properties of the propellant percent triethylene glycol dinitrate, and 50per-gas: n, the number of moles of gas formed per cent ethylene diamine dinitrate is as follows:gram of propellant burned (reciprocal of the 1033* x 0.20 = 206.2mean molecular weight of the gas); C, the mean 619 x 0.30 = 186.

heat capacity of the combustion gases in the 945 x 0.50 - 473.range of temperatures and densities attained in Q = 865.2 cal per gmthe gun; Tv, the adiabatic (constant volume)ilame temperature (the temperature a gas 4-55. Gas Volume (Volume of Products of Ex-would attain if all th'i energy of the propellant plosion). Calculations are based on the assumedwere used to heat the gas, without energy loss complete reaction to yield maximum volume.to surroundings). Auxiliary quantities are de- Below 3,000°K, n is additive (by this method;fined in terms of these three. The constituent values are given in table I of reference 1).properties of propellants that are calculated Above 3,000'K, dissociative equilibrium be-by these methods are: comes important, but does not affect values

Heat of explosion Q cal per gm of n at densities encountered in guns."Gas volume n moles per unit mass a. The gas volume (n) is calculated for anRelative energy organic chemical constituent by the formula

in gas E cal per gm C*H i.NMean heat capacity C cal per gm per deg n =o ar wgForce F 't-lbs/lb molecuiar weightUnoxidized Example. Triethylene glycol dinitratecarbon UC percent in ,as (C6 H1 2N2 0 8):

Density D gins per ccn = 6 5 -1 1I= 0.0542 moles per gr

4-54. Heat of Explo3ion. Calculations are based 24 1on the assumption that the carbon, hydrogen, b. The gas volume (n) is calculated for apro-nitrogen, and oxygen of the solid propellant are pellant composition by cbtaining the sum oftransformed into CO or C0 2 , H2 or H2 0, and weighted values for all constituents.N2 ; and that no free oxygen or dissociation Ei ales for consituents.results. Example. For composition as in subpara-

a. The heat of explosion (Q) is calculated for graph 4-54b, above:

an organic chemical constituent by the formula 0.0392 x 0.20 = 0.007840.0542 x 0.30 = '.01625

= -AHc) -67,421 (2C + 1H - 0) 0.0484 x 0.50 = 0.02420molecular weight n =.0.34829 moles

where AHc f heat of-combustion, in cal per mole. per gru

*These are simplified equations. For more detailedmethods, see paragraph 4-64 and associated ref- *The Q value for nitrocellulose is obtained fhrmerences. reference 19, p. 276.

4-87

4-56. Energy Released (Relat.ve Energy) is the wherechange in internal energy of the propellantgases nRwhen they cool from the adiabatic flame tem- = 1 , Cvpe rature to the temperature at which the relativeenergy is being calculated inthscase, 2,500*K). z1I + 1.987ý-(See paragraph 4-5e.)

a. The relative energ-,, in the gas is cal- where the units co R are BTU per lb-mole perculated for an organic chemical constituent *R, or cal per gm-mole per *K.by the formula:

4-59. Isochoric Adiabatic Flame Temoerature.E ( 132771 C 40,026 H (See reference 2, pp. 19-22.) This value (T.)

molecular weight 2,500 + E/Cv. If Tv is found to be over+ 5§18t9l 0 -_6724 N 3,000°K, a better approximation can be obtained

molect.ar wejLht, from the formula:

where -A E is the heat co combustion. TV = 3000 + 6046 I*(Cv + 0.01185)Example. Ethylene .diamine -dinitrate 3 -r(E 3.308 x

(C2HlN' 6): + [(Cv + 0.01185)2 3.08 x 10 0C)]

-132,771 x 2 ='-265,542 4-60. Isobaric Adiabatic Flame Temperature.This value (Tp) = Tv/-.

- 40.026 x 10 = -400,260ý%E 377,580 4-61. Force. This term is a property of a

- 6,724 x 4 =- 26,896 propellant composition that is convenient for6 x 0 3914 -692,698 use in interior ballistic systems. It is defined

688,494688494 as- 4,204

E --4 •20 22.59 cai per gm F nRTv186

". TFor the composition given in subparagraphb. The relative energy is calculated for a

propellant compositionby obtaining the algebraic 4-54b above,

sum of weighted vwiues for all constituents.Example. For composition as in subpara-

graph 4-54b, above: where 1.8 x 1543 is the gas constant.283.1 x 0.20 = +56.6

-169 x 0.30-= -50.5- 22.6 x 0.50 = -11.3 Experimental values of force fora new compo-

- 5.2 cal per gm sition relative to a known composition may beobtained as the ratio of maximum pressures

4-57. Mean Heat Capacity (see reference 9, obtained in the closed bomb upon firing equalp.19ff), weights of propellant. This is justified as

a. The mean heat capacity is calculated for follows.an organic chemical constituent by the formula:

5 + The equation of state of satisfactory assuracyC = 1.62 C +3.265 H 5.193 O N under closed bomb conditions ismolecular weight

P(V - =nRTv = Fb. The mean heat capacity. is calculated for

a propellant composition by obtaining the sum of where i is the covolume and TV (neglectingweighted values for all constituents, cooling) is the adia-atic flame temperature.

For equal covolumes,4-58. The Ratio of Specific Heats.

P1 (nRTv)1

Sp. Ht. Constant Pressure *C"Y = Sp. It. Constant Volume =v P2 (nRTv)2

4-88

Note that the cooling uf the system affects the d. Unoxidized Carbon. This value canbeob-results, if widely diffe-rent granulations (see tained by multiplying the oxygen deficiency byparagraphs 4-7 and 4-8) are tested. 12/16. In the example in subparagraph 4-62c,

,, 0, abo e:

4-62. Unoxidized Carbon. -212a. This value is determined for the purpose -12.15k°1612.9.12% unoxidized

ol estimating by calculation the amount of car- 4-63. Density. The density ofapropellant com-bonaceous smoke produced from propellants in 4 position can be calculated by obtaining the sumballistic tests. For the purpose of simplicity of weighted values for all constituents. This isin calculationr, the following assumptions are the densitv of the solid propellant.made:

1. Propellant gases consist only of C02,CO, H2 0, H2 , and N2. 4-64. Alternate Methods of Calculation. Some

2. N2 is not involved in smoke and re- important quantities used to determine thelated oxidations. thermochemical chtracteristics of propellants

3. All CO2 and H2 which are :ormed can and explosives are heat of combustion (.Hc),be considered as equivalent amounts of ad- heat of explosion (Q), heat of formation (,nHf),t itional CO and H2 0 formed, without affect- and heat of reaction (:Hr). These quantities

ing fuel-oxygen balance. are all interrelated and are usually determined4. All H2 burns to H2 0; all remaining 02 by some form of calorimetric test. The de-

burns some C to CO; remaining unoxidized C tailed descriptions of the many methods of cal-represents carbonaceous smoke. culating these quantities are given in the ref-b. The excess (or deficiency? of oxygen inan erences (see bibliography at end of this section).

organic chemical compound, for rearrangement The exact definition of each term is given inof the atoms to CO and H2 0, can be calculated the glossary.by the formula.

The calorimetric quantities are related by theOxygen deficiency percent formula:

deficient no. atoms oxygen x 16 x 100 aH a 2'Hf(products) - LzH1(reactant) (192)molecular weight where

AH* beat (energy) evolved

Example. Ethylene diamine dinitrate: A Hf (products) = beat of formation of the pro-ducts of the reaction

16 AHf(reactant) a heat of formation of the re-Oxygen deficiency 16 x 100 - -8.6 percent actant (explosive).

The principal methods of calculating theseThe value of this estimation is that it allows a properties are described in references 4, 5, 6,comparison to be made between a new formula- 7, and 10.tion and a known formulation whose smokecharacteristics are favorable. To calculate the heat of explosion (Q) for any

c. The percentage oxygen deficiency of the explosive or propellant, it is necessary to knowproducts of combustion of a propellant compo- the heat of formation (AHf), or the heat of com-sition can be calculated by obtaining the alge- bustion (LiHc), of the substance, as well as thebraic sum cf weighted values for all constituents. products of explosion.

Example. For the composition (given in sub- a. Methods for Calculating AHf. Based onparagraph 4-54b, above: chemical structure of the molecue, it is pos-

sible tn estimate the heats of formation of corn-+0.81 x 0.20 - 0.162 (20% NC; pxunds by the following methods:

13.15% N) 1. Kharasch method, references 4 and 8;--- 8.01 (30% TEN) 2. Bond, group, and atomization energies,

-26.7 x 0.30 -references 5, 5, and 9;

- 8.6 x 0.50 a - 4.30 (50% EDDN) 3. Group contribution method, referenceOxygen deficiency = -12.15 % 7.

4-81

A simpler, but generally satisfactory, method Table 4-21(for heat of combustion) consists of adding thecontribution of the various structural groups, Heat of combustion values fromas given in table 4-21. Special experimental structural featuresstudies have been made on heats of formationof nitrocellulose, reference 11, and nitrogly- (h20 is calculated as a liquid. see reference 6.)

cerin, reference 12.b. Calculation of 6 Hc. Heat of combustion,

He, may be calculated by (1) a modification of C-H 52.44formula (192),

C-C 49.79AHC a AHf(products) - !AHf(reactant)c*C--O (Aliphatic) 13.96

or (2) by direct summation of heats of com- C--O (Aromatic) 4.16bustion of the molecular structural units (ifthe values are known). Substituting the known C-N (Altihatic) 27.91values from table 4-21 for TNT (C 7 H5 0 6 N3 ),AHc may be calculated thus: C-N.(Aromatic) 33.70

O--H -14.28Heat liberated

Structural feature (kcal per mole) N-H 21.34

3 C=C 3 x 116.43 C=C 116.43

4 C-C 4 x 49.79 C=o (Ketone) 11.25

5 C-H 5 x 52.44 C=O (Amide) 16.15C---O (Aldehyde) 19.09

3 C-NO2 (Aromatic) 3 x 16.66

O-NO2 -12.90Resonance of benzene nucleus -40.00 C-NO2 (Aliphatic) 10.76

Hc calculated 820.6 C-NO2 (Aromatic) 16.66kcal per mole

Hc experimental 820.7 N-NO2 6.55kcal per mole Resonance of benzene nucleus -40.00

c. Calculation of Q. The heat of explosion Resonance of naphthalene nucleus -77.00cannot be predicted as accurately as the heatof combustion because the products of explosion Resonance of amide -27.00are uncertain. Various procedures have beenadvanced for estimating the products of ex-plosion. See subparagraph 4-54b and references2, 13, 14, 15, 16, 17, and 18.

4-90


"1. I'1rsh•elder, J. 0., and J. Sherman, Simple Calculation of Thermochemical Properties for

Use in Ballistics, Office of Scientific Research and Development Report No. 935, October1942.

2. "Internal Ballistics," Philosophical Library, New York, 1951.

3. Hirschlelder, 1. 0., et al., Interior Ballistics, Office of Scientific Research and DevelopmentReport No. 6468, July 1945.

4. Kharasch, S., Heats of Combustion of Organic Compounds, Bu. Std. Jr. Res., RP 41, voL2, p. 359, 1929. This paper gives determined and calculated vah.es for hundreds of com-pounds.

5. Springall and Roberts, ARD Explosives Report No. 614/44, Bristol Research Report No.126, July 1944.

6. Report on Study of Pure Explosive Compounds, Arthur D. Little, Inc., 2 April 1947.

7. Anderson, Beyer, and Watson, National Petroleum News. vol. 36, May-August 1944.

8. Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and RelatedCompounds, American Petroleum institute Research Project 44, 19.53, Carnegie Press.

9. Pauling, "Nature of Chemical Bond," Cornell University Press, 1948.;

10. Laidler, K. J., Prugress Report, Catholic University of America, NORD 10260. December1949.

11. Jessup and Prosser, National Bureau of Standards Report RP 2086, vol. 44, April 1950.

12. Taylor and Hall, Journal of Physical Chemistry, p. 593, 1947.

13. Kistiakowsky and Wilson, NDRC Report No. 1352.

14. Robinson, C. S., "Thermodynamics oZ Firearms," McGraw-Hill Book Co., New York, p.41 f" I

15. Corner, J., "Theory of Interior Ballistics of Guns," John Wiley and Sons, New York, 1950,p. 89 ff.

16. "Handbook of Chemistry and Physics," 34th ed., Chemical Rubber Pub. Co., Cleveland,Ohio, pp. 1631-1640, 1952-53.

17. Perry, J. H., ed., Chemical Engineer's Handbook," 3rd ed., McGraw-Hill Book Co., NewYork, 1950, pp. 236-246, 344, 345.

18. Gilman, Henry, ed., "Organic Chemistry," John Wiley vnd Sons, New York, 1953, vol.IV, p. 953 ff.

19. Hickman, C. M., Rocket Fundamentals, Office of Scientific Research and Development Re-port NA. 3992, 29 December 1944 (CONFIDENTIAL).

20. Tomlinson, W. R., Properties of Explosives of Military Interest, Picatinny Arsenal Tech-nical Report No. 1740, 20 June 1949 (CONFIDENTIAL).

4-01

REFERENCES AND BIBLIOGRAPHY (cont)

21. Garner, W. E., and C. L. Abernathy, Heats of Combustion and Formation of Nitro Com-pounds (Benzene, Toluene, Phenol and Methylaniline Series), Chemical Abstracts, vol.15, 3748, 1921.

22. Blatt, A. H., Compilation of Data on Organic Explosives, Office of Scientific Research andDevelopment Report No. 2014, 29 February 1944 (CONFIDENTIAL).

23. Stegeman, G., Heat of Combustion of Explosive Suhstances, Office of Scientific Researchand Development Report No. 5306, 4 July 1945 (CONFIDENTIAL).

24. Sheffield, 0. E., Long range Basic Research Leading to the Development of Ideal Pro-pellants -Compounds of High Nitrogen Content in Propellant Powders, Picatirmy ArsenalTechnical ReportrNo. 1694, 26 May 1948 (CONFIDENTIAL).

25. Taylor, I., C. R. Hall, and H. Thomas, Theraoc.emistry of'. pellant Explosives, J.Phys. & Coiloid Chem:, vol. 51, 580-592, 1947.

26. Hell, S., Long Range Research Leading to the. Development of Ideal Propellants - Com-pounds of High Nitrogen Content in Propellant Powders, Picatinny Arsenal Technical Re-port No. 1752, 7 November 1949 (CONFIDENTIAL).

27. Castarina, T. C., Long Range Research Leading to the Development of Ideal Propellants- Explosives Plasticizers for Nitrocellulose, Picatinny Arsenal Technical Report No.1755, 30 December 1949 (CONFIDENTIAL).

28. Second Re"ort on Synthesis and Testing of High Explosives to Office of the Chief of Ord-nance, Arthur D. Little, Inc., I March 1951 (CONFIDENTIAL).

29. Picatinny Arsenal Technical Report No. 1841.

30. Jessup, R. H., and E. J. Prosen, Heats of Combustion and Formation of Cellulose and Nitro-cellulose, National Bureau of Standards Research Paper, Report No. 2086, vol. 44, 3January 1950.

31. J. Soc. Chem. ind., vol. 55, 291-2T, 1936.

32. Stohmann, Ir., Colorimetrische Untersuchungen, Journal Praktische Chemic (2), vol. 55,263, 1897.

33. Karrer, P., and W. Fioroni, Heats of Combustion of Carbohydrates, Chemical Abstractsvol. 17, 2416, 1923.

34. Picatinny Arsenal Physical Chemistry Laboratory reports.

4-92

BEST AVAILABLE COPY

PROPELLANT CHARACTERISTICS AND TEST" might cause deterioration, rather than a testMETHODSI of Irherent instability. After being properly

prepared and dried, the sample !a heated (nitro-* 4-65. Sensitivity is a measure of t."- ease with ceAlulose to 65.50C, nitroglycerin to 82.2'C) inwhich an explosive material can be made to a glass tube maintainedatconstanttemperature,burn or explode. Propellants, as manufactured, into which is suspended a potassium iodide-are relatively insensitive to shock and friction, and starch-impregnated paper. The test isHowever, they are required to be sufficiently continued until the paper becomes discolored.sensitive to ignition by flame so that initiation The minimum time required for discolorationmay be positive and burning may be uniform of the paper is considered to be the test value(see paragraph 4-52). of the sample. This test is gradually being

eliminated from general use.4-66. Stabilit is a measure of the period oftime that an explosive material can be safelystored before it begins to decompose. Pro- 4-69. 65"C Surveillance Test. This test ispellant stability is concerned primarily with applied only to finished propellants. It consiststhe stability of nitrocellulose, which, being hy- of placing the samples in sealed bottles in agroscopic, is the most vulnerable component of magazine kept at a constant temperature ofpropellant compositions. Tests for stability 65C. The end point is reached when red fumesare made during the manufacture of the proof nitrous oxide appear in the bottles. Minimumpellant, immediately after the completion of times of appearance of the fumes are statedeach lot, and as long as the lot remains in for each size of gratmlation.service. After propellants are issued for serv-ice use, it is not possible to subject them tothe heat tests described here; therefore, visual 4-70. 115f C Heat Test. This test applies onlychecks, such as the methyl violet test, are used. to finished propellapt. It consists of exposingwhole grains of the propeLlant to a temperature

4-7. Methyl Violet Test. This test Is used as of I1°C for six 6-hour days and noting the

an acceptance test for both nitrocellulose and weight loss. The loss in weight must be !s

finished propellaxAt. The test prevents accept- than a specified limit for each size of grama-

ance of improperiv stabilized nitrocellulose and .ation. This test is not In general use.

detects deterioration of the propellant in serv-ice. It consists of heating the sample with 4-71. Compression Test. Propellant grainsmethyl violet test paper in a glass tube •while should be designed to withstand the stresses tothe temperature is maintained at a constant which they may be subjected during the firing134.5S0.5"C, or 120"C, and noting the time re- of a gun. Little has been done to determinequired for the test paper to turn salmon pink, what theoretical factors are involved, but it isimd for the onset of NO 2 fumes; in addition, the known that Ihe chamber pressure builds up toosample must not explode in less than live hours. sharply if the grains fracture (exposing moreActual minimum time requirements of indiv idual burning surface). Therefore, it is desired thatpropellants are given in the propellant specifi- the grains do not fracture during firing. Thecations. This test is run at 1350C for single- compression test is a routine testfor measuringbase propellantb, and at 120"C for double-base the percent compression to failure under staticpro"eliants. A related test (for nitrocellulose) load. It is a very simple test, and unsatis-is the Bergmann-Junk test, in which a quanti- factory as a measure of the propella:t's abilitytative determination is made of the amount of to withstand stresses imposed by the gun. Ingas liberated. the test, the grains are cut to form cylinders

whose lengths are equal to their diameters,4-68. kI-Starch Test. This test is used as an and are then compressed between parallel sur-acceptance test to prevent acceptance of nitro- faces until the first crack appears on thecellulose containing traces of oxidizing im- cylindrical surface. Specification JAN-P-270purities that tend to accelerate the decomposi- requires that the average compression of ation. It is a test for traces of impurities that grain at the point of cracking he not less than

30 percent. Nitroguanldine propellants are*See Section 2 for tests applicable to high explosives, excepted.

fi •4-93

ti.

4-72. Maximum Pressure (see Glossary, under decreasing its effectiveness. It is determined"PERI'ISSIBLE INDIVIDUAL MAXIMUM PRES- by routine chemical analysis.SURE"). Proof firings are made to determinethe pressure developed by a propellant. The 4-74. Total volatiles is a measure of the in-easiest way to measure this pressure is by the corporated solvents. The tests and require-use of a device called a crusher gage, which is ments for specific propellants are as per speci-inserted in the gan chamber. In this type of fications.

gage the gas pressure developed is transmitted, Vacuum itability tests have been found suitableby means of a piston, to a copper cylinder con- Vacuum ta bility ts h b ound nstained within the body of the gage, and the for determining the compatibility of propellantsamount of deformation of the copper cylinder in or explosives with each other. (See table 4-27used as a measure of the maximum gas pres- anSetn2.ThsIaco liedbtsigsure to which the gage has been subjected. 2 the stability of the proposed mixture of ma-

Tho crusher gage is used in two forms: a fixed terials under vacuum and determining whether

gage, which ib threaded into the breech block, the volume ct gas liberated is significantlyand a loo, e gage, which is loaded loosely with greater than the sum of the gas volumes lib-

the propellant charge. Because of the high erated by the materials when tested separately.

strain rate of the gage, the deformation of the When used for this purpose, the test generally

copper cylinder is smaller than the deformatiorn Is made at 100C, 120C, or 150C. or any otherthat wouMd be obtained for the same stress under desired temperature, but 100" or 120"C are most

static conditions. Accurate piezoelectric meas- commonly used. Vacuum stability tests yieldurements indicate that the true pressure stres- reproducible values; and when a material issing the gage is approximately 1.2 times the subjected to this test at two or more tempera-

static pressure required to produce the meas- tures, a rather complete picture of its chemi-

ured strain of the copper cylinder. Although cal stability is obtained. In some cases, tests

the crusher gage does not record true pressure at two or more temperatures are required tolevels, it Is still of value as an indicator of bring out significant differences with respectrelativels t irssul oto stability between explosives, but a test atrelative pressure. 100"C is sufficient to establish the order of

stability of an explosive.Crusher gages can only measure the maximumpressure developed at the position of the gage 4-75. Taliani Test (110C). One gram of finely

in the gun. The piezoelectric gage is used to ground propellant is placed in a sample tube-helix combination with constant volume of 8 niL

obtain a history of the way pressure builds up. his asmbly is censan alumn blo

This device operates on the principle that This assembly is placed in an aluma1um block

pressure applied to certain types of crystals heater man ome t i pp, with a level-will produce a charge which is proportional t to a mercury manometer equipped with a level-that pressure. A piezoelectric gage can be ing device. The system is evacuated and thenused in conjunction with an oscilloscope and infused with nitrogen or oxygen. The mercurysweep generator to measure, as the projectile is leveled to a fiducial mark on the helix, andsweep geeratorh gat progressive readings at 30-minute intervals,travels~ through gun, the variation of pressure thmeur slvedotis ak.Wh

with time, producing a photographic time-pres- the mercury is leveled to this mark. Withsure rcordtemperature and volume constant, the evolution

sure record.of gas is reflected as increased pressu'e. Theseries of readings is plotted as pressureversus

4-73. Hygroscopicity is the tendency ofthepro- time and the resulting curve is examined forpellant composition to absorb moisture, thereby slope.


1. Purchase Description and General Specification for Methods of Inspection, Sampling andTesting, MIL-P-11960, 24 April 1952.

2. "Internal Ballistics," Philosophical Library, New York, 1951, pp. 98, 99.

4-94

Table 4-22

Staidard propelapit cal;.brati

(TANK• AND ARTILLERY WEAPONS)

Proicetile C"rt caseItem WeiKht Primer Pull Pr'ui.ellant

Canfton a jo. Type -(po-inds) Fuze type N-e Grairs Type lbs Lot Type Web

"76mm G, 9 HE. M42A1 12.80 Dummy, M73 M28B2 300 M25 Min 17636-R M6 .0419.MP U.-1MIA2, MIAIC WP, M312 of

1800

10 APC-T, 15.40 BD. M66AI M40AI 270 M26 17635- H M6 .0419-MP LM62AI 1/2

leaontS' ~pro

It- AP-T, 14.60 None M4982 400 M26 2000 35718- 1 M17 .0547-MPT166F2. toTP-T304 8500

12 HVAP-T, 930 None M2882 300 M26 2000 18891-R M2 .0595- MP LoM93 to

8500

13 HVTP-T, 9.30 None M2882 300 M26 2000 18891 R M2 .0598-MPM315AI to

8500

"76mm G. T91, 14 HE, T64 15.00 PD, MSIA5 M58 400 TI9EIBI 5000 35036-S M6 .0367-MP BaT124 to Gr.

11000 s1119.,

12479-R M6 .0377-MP15 WPT140E2 A15.71 PD, MSIA5 T70 300 T19EItt 5000 35036-S M6 .0367-MP Di5I WP T,1oo

to11000

-If AP-T, 14.50 Nine M58 400 TI9EIBI 2000 38313-R Mi0 .0615-M4PS T128F6 to

STP-T.T212 8500

17 HVAP- T, 7.0 None M62 300 TI9EIBI 2000 13050 M6 034-MP LT66E4, toHVTP-T, 8500T74E1

18 HVAP-DS-T, 8.22 None T88EI 300 TI9EIBI 5000 34482-R M17 .0495.-MP LSM331A2 to

11000

Item No. 9 - Data valid in issessment for Shell. WP., F1312; test round- M42AI loaded to 12.80 lbs.. std. rds. Hadled to 12.80 tbs.I- Std. rds. loaded to 9.30 lbs. and test ids. loated to 9.38 lbs. Assessment of prop. to be made for M93AI shot weighing 9.38 "is.14 - Prop. to be std'z. with distance wadding if i.,,h.crized by 000.?- Prop, lot 34700. M17, MP, web size '0448 tj be std'z. in the near fulure.

Bullet pull requirements have not been established, a minimum of 5000 lbs. is recommended, how(.ver, the mnximum i.I11000 lbs. will ne-ed further investigation

AV

ble 4-22

it calibration data cha'rt

Gun Rtvitqim 3. dated: I April 1954Calihration rated

Ftndard charge v'alues maX. Prp.s'WeignhI VolT Press press gages Last check Valid STDZ

ieb Loading Desig. Zone (ounces) fps -psi pI used fired date data FR NO.

9-MP Looise 60.40 2700 36600 43000 2-M3 To be %td Yes (R) JP0109261w, M40AIprimer.Jan 45Check duewShell Lot

., LOP- SOS- 2

9-MP Loos w, 61.17 2600 42300 43000 2-M3 Feb 53 Yes (R) JP0124947, 2 on. pure Lot LM-3

lead foil (a) Checkon top of Firing dueprop.

7-MP Loose 57.84 2700 39500 43000 2- M3 Estb. Aug Yes (S) P5702053

d-MP Loose 61.73 3400 39800 43000 .2-M3 June 52 Yes (R) P37413Lot CM-73CHK w/GP-1-35(a)

%I MP Loose 61.98 3400 39500 43000 2-M3 June 52 Yes (R) P51796P51797

7-MP Bag. Sleeve 54.21 2400 28700 46000 2-M3 Std.Aug 52 No (S) P52483Gr. "E" Shell To be Re-s;Ik RMP Stdz w/19" x 3" 30000 Dist. Wad,

T70 Primer.Prop Lot 6'0105

7-MP Loose 55.94 2400 28109 2-M3 Yes (R) P49108

I-MP Dist. Wad 2400 46000 2-MI To be StdzShell w, Dist. Wad.RMP + T70 Primer,30000 Prop Lot

60105, Web.0365-

i-MP Loose 89.43 3200 44200 46000 2-M3 Estb. Jan Yes (R) JPG17268553 Incom-plete. Pdr.To be stdlz.YPG conductedTemp. Ref.

MP Loose 84.64 4135 44700 46000 2-M3 E'tb. Kit No (A) P4898252

i-MP Loose 91.05 4125 43800 46000 2-M3 Estb. Jan. Yes (R) P5858354 Prop Lotto be std'z.

(S) - Valid Standard•'s. (R) - Valid Reference(A) - Not valid, limited reference(a) - Pros. lot used in latest check

4-95

a

Table 4-22

Standard propellant calibration drta

(TANKS AND ARTILLERY WEAPONS)

Projectile Cart ease

Item Weight Primer Pull pr liantCaftoo No. Type (pounds) Fuse type Tfp ains Type lbs Lot -- .- W LoMW_

90mm G, 19 HE. 7I1 13.40 PD, MSIAS M28D2 300 MI1 Min 17665.3 M6 .0496.MP Loose

MI, 3iAl, TP, M7il o1Mn, U3, TO WP, M313 5000

7g , me .041-KP LOW"

20 HE, NIl 23.40 PD, MSIAS U49 400 U19 38422-$ MiS .0550-UP LooseTP, 1471WP, UI313

It APC-T 24.10 OD, U60 M49 400 M19 " 10632-R M6 .0545.P Dist.M42 Wad-

2oN.IP.an tooc chg.

22 UVAP-T 16.75 None U4..A.i 2-10 1I9 5000 14677-R M6 .0469-6 P Dist.N304 to Wad.

11000 20os.

of chg.

23 HVTP-T 16.75 None M40AI 270 M19 5000 14677-H M6 .0469- MPMUM7A to

U1000

24 HVAP-T, 12.44 None M49 400 M19 5000 3571B Mi7 .0547- MP Dist.U331AI to Wad.

HVTP-T, IIOW-M333AI

25 HEAT 14.60 P1-DO. T69 400 T27 Not 35258 Ml .0344- MP Loose

TIMM8E4 T209 approx. Est. +TI08E40 16.20 in boom. K2SO4

26 Canister 23.29 None M49 400 1419 5000 33840-R M2 .0924- MP Loxcse

M336 to approx.11000

90mm Gun, 27 RET21 18.60 PD, MSIA5 T70 300 T24BI 5000 38740-6 MI .0267-MP Dist.

T119, T139 WP,T92 to Wad.

23 AP-T, 24.10 None M58 400 T24 5000 34478 M17 .073-MP LooseT33E7 to 2 as.

TP-T 11000 Ign.on topT225 of c

29 HVAP-DS•-

T, T137

30 HEAT 16.20 PI-BD, T6S 400 T27 Not 35258-R MI .0344-MP Loose

TI08E40 T209 Est. +K2 04

Item No. 22 and 23 - Differences in band materials result In different prop. charges for M304 and U317AI .ell.25 - Present production round is TI08E40.26 - SheU, HE, 3(71 loaded to 23.29 lbs. used to simulate Canister, M336. Chg. based on tube have 9 prey. rds.27 - Standardized with M28B2, screw head primer (T70 primer was not itvailable at tht time of test).

Fired also with various lots modified TIO Brass cases. Comparison teý.t with T2481 cases wereconducted. 12 fps less vel. with steel case.

23 - Standard row.ida loaded to 16.75 lbs., test rounds (M317A2) fired at 16.31 Wb.

As

Table 4-22

mt calibration data chart (cont)

Gun Ievialon 3, doted: I April 1954Calibration rated

"f•tanard chart# values max. Presssat Vel. Press press pges Last check Valid JIDZt WE Loading Desig Zoe ss fps pal pal used fired daMt data Il NO.

.049&-UP Loose 7 .3.13 2700 36600 380C) 2-M3 Oct 51 Lot Yes (m P-41010IDOW- 70 CHKv/VG3- 1- 13

(a).0491-UP Loose 7 1.7 2700 36200 .38000 3-M1 To be replac.d Yes (3 P-64229

v/Prop. Lit4 63215

.0550-UP Loose 7 1.12 2700 34200 38000 2-MS3 stb. Ag Toes (3) P. 5A8302953

.0545-UP Dist. 1 . 2.1 2800 39500 41500 Z-.M3 Jum 48 Yes (Rm P32409Wad. 88-36 (a)

On topo chg.

.0469-6UP Dist. 8 5.22 J3!50 .0600 41500 2-MS3 June 52 Yes (R) P37523Wad. Lot HCO-72 0o. and CAA- I-Ig. 8 (a)on topof chg.

.0469-.M 8 3.10 3350 41100 41500 2-M3 Yes (R) P51784

.0547-UP Dist. 8 . 0.27 3875 41400 41500 2.MS Chg. Est. Yes (R) P58912Wad. conducted

March 1954

.0344- UP Loose 5 6.58 2800 22700 41500 2-MI No (A) P47615

5 13.34 900 28700 41500 2-MI Yet (R) P58913

.0924-UP Loose 7 11.2 2870 39200 41500 2-M3 Estb. Mar. Yes (Pl P59164approx. Shel. 1954

8.58 RMP415,00

.0267-MP Dist. 4 8.46 2400 26300 47000 2-MI Stdz. Sept. Yes (S) P57202Wad. Shell 1953

RUP30000

.072OMP Loose 8 4.21 3000 47400 47000 2-M3 Prop. Gran. No (A) P532772 ox. Tests toIgk. be continuedon topof ehg.

47000 2-M3 Dey. incom-plete

-0344-UP Loose 5 13.34 2800 28700 47000 2-MI Estb. Dec. Yes (R) P589g31953

(3) - Valid standard(R) - Valid Reference(A) - Not valid. ligi'ed referencr(a) - ProS. lot uwed in latest chft ,

4- #78.4

Table 4-22

Slandar propellant caltbiahop

(TA4'KS AND ARTILLERY WEAPONS)

Prjc ie t __________ rasenCannoeni ht Primer Cart Pull Pr ntCannon No. Type (pounds) Fuze :ype t".pe Grains Type lbs Lot W ' Web

105mm How. 31 HE. MI 33.00 OPI, MSIAS M28F12 300 P14BI None 61090-S MI .0143-SPM2. M2AI. 31080-S MI .0143-SPM4. 1ltg0-s MI .0262- MP

61180-S MI .0262-UP61180-S MI .0262-MP61180-S MI .0262-MP61 10-S MI .0262-UP

32 HEAT-T 28.80 BD, M91 MIBIA2 to0 M14 None 065&-S M1 .0i46.SPM67

33 HEAT 24.00 ilt-BI" (Mod) 700 (Mod) Not 3328 M6 .0240- MPT31331 T208 M23A2 M14 Estb.

105mm How. 34 HE, MI 33.00 PD, MSIA5 M28B2 300 M14(l) None 9525-S Ut .0154-SPM3.

35 HEAT, M67 28.80 BD, M91 M28B2 300 M14(fl) None 9525-S MI .0154-SP

105mm Gun, 36 AP-T- 35.0 None T48 400 T6 None EXA- M17 .0852- UPT140 T182. 6905

TP-T,"T79

120mm Gun, 37 HE, M73 50.000 MT, M51 MIRIA2 100 M24 None 38470-S MG .0674-MPMI

120mm. 1 38 HE. TISE2 50.40 PD, MSIA5 M"57 1000 M54 None 38723-S MI5 .034-SPGun, T123 WP, T16E2 or or

M67 T25E3

I 39 AP-T, 50 0 None M67 1000 T25EI None EXA M17 .V'23-MPTIS6E5 7069 Approx.TP-T,T147F3

40 HEAT 32.0 M57 800 M134 Mod None M6 .0469-MPT153E8 Mod 18 1/2"

Length

Item No. 33 - Charge weight in primer includes the amount of black powder obtaoehi in primer and shell bcom.32 - Standardization conducted with prop. loose in case and crimped. Test rounds should be fired in bag and staadard

loose in case when firing for calibration. New values will be set for standard using Gr. "E" silk bag if requirement exists.31 - Propellants recently made the new standard by matching the velocity levels of propellant lots 36172/17395.40 Data shown is approximate.

A t BEST AV/LAiBLE COPY

Table 4-.22

uxt calibratsopt data chart (>•ot.

Gun Revisinm 3. dated I April 1954Calibration rated

Stat, !_-I 'h&rfe value, max. Pres!.ant W V-• P; - , pres-s Kages Li-t check Valid STDZ

SLoading Design 'one TS' ois fps piI ps u,,ed fired date daim FR NO

.0143-SP Dualgran Zone 1 855 IF 5 .00 Stdt Mar Yeq (S P58846

.0143-SP Rayon I * 2 2 9.98 710 b200 1954

.0262-MP Bag 1, 3 SP Pdr. 3 12.51 780 9000

.02•6-MP oz, 60" MP 111 4 16.31 875 11000

.0262-MP 40 lead other 5 22.96 1020 14300

.0262.-MP toil zones. 6 30.85 1235 19800

.0262-UP sewed to 7 45.24 1550 31000 32500 2-M3Zone 5Bag

.0146-SP Bag Single 24.42 1250 23500 32500 2-M3 Ian 48 Lot Yes (SI U14542Sect. 11, IR RA-3..6 (a)Gr. "Er altP Chk firingSilk 20000 dueBag

.024C-MP Loose 60.50 1750 20600 32500 2-Mi To be stda No (A) P49276Shell if require-RMP ments exist.approx.25000

.0154-SP Bag Gr. "E" 9.75 650 7800 25000 2-U0 Apr 47 Yes (S) M23114Silk 11.36 710 9100

13.34 780 1080016.23 875 1380021.24 1020 19900

.0154-SP Bag Gr E 24.42 1020 17400 25000 2-U0 Apr 47 Yes (S) M22294SilkIPCsleeve

.0852-MP S us. 274.90 3500 45500 480(0 2-M3 Coot. dev. No (A) P49350ign. on Chg.on top to be done-cf chg.

.0674-MP 8 ox. ign. MISE1 230-5.07 3100 37200 38000 2-M3 Stdz. Nov. 53 Yes (R) P577116Dist. Wad,M2E2closingplug, noreta ine r

.034-SP T23 Plug. T21EI 12 3.82 2500 38500 48000 2-M3 Additional Yes (R) P58630Bag Silk Chg. firings to".E" 25 x 5- be conducted* Dist. Wad. to establish

Prop. asStandard

.l123,.MP Loose 4 T38EI 29 5.0 3500 45600 48000 2-M3 Dev. Prop. No (A) P55152Approx. o0. on Chg. incomplete

ign. topof chi.

.0469- MP Loose. T41 18 8.0 3450 33000 48000 2-U3 Dev.Plastic Chg. incompletePlug

(S) - Valid Standardexists. (R) - Valid Reierence

(A) -. Not valid, limited referenceja) -- Prol. lot used in latest check

.4-99

.•..

Table 4-2,2

Standard propellant calibration

(TANKS AND ARTILLERY WEAPONS)

ft*~Cart csItem Pro/etil!;eigh[lt Primer Catcs ul Pr: Iant""

Cannon No. Type (pounds) Fuse type Type Gaii Type Tbe I,• eb

135mm Gua. 41 HE, MIl 911.0 PD, MSIAS MK hA4 17 Noe Non 32809-. MG .ow51-MP GOMI. MIAI Cand M!

155mm How. 42 HE, M107 95.00 PD. MAS NIXK TtA4 17 None None 3742-S MI .0165-SP Gr.MI and MU C

43 HE. M107 95.0 PD. MSIAS MI l1A4 I? None None 38250- MI. .0334-MP Gr.

K2 301

8" Gun, 44 HE. M103 240.0 PD. MSIAS MK I1A4 1? None None 8501-S Ms 1366, ., MMl

45 "E, MI03 240.0 PD, MS1AS MK I1A4 17 None None 16697-R MNO 0839.-MP MI

1" How.. 46 liE, M106 Zu 4 V. MSIAS MK UA4 17 None flone 8295-S 141 .0161-sp MI

47 14F, M 106 200.0 PD , % fSIA ! M K '!A 4 17 None N on ~ 10567-S M I 04" .4- UP MN

240mm How., 48 HE, M114 360.0 PD, MS5145 MK IiA4 17 None None 17014-S Mt .6%J.,-M-P MUMl

280mm Gun, 49 HE. T122 600.0 VT, T27 MK 15. 30 None Nw.i, 38834-R M6 * I T:03-MP TT13 Ir Mod. I 30271-R M6 .0993- MP

PD. MSIA5 Ele . 30271-R U6] 30271-R MN

Item No. 44 and 45 - Check firings due, however, no firings will be conducted due to propellant being of limited standard.

A.

Table 4-22

sit calibration data chart (co1t)

Gum Itirvislom 3, daedh: I Alwil11IOUCalibration rated

Standard charge values mal Press!Wight Vel. Press press gages Last check Valid UrD2

SLoading Dasitn Zone lbs oss fps psi psi used fired date data im NO.

.0552-UP Gr. *"C" ormal 20 4.6 2100 17300 40000 2-M13 rae 4 Tes (3 P04103Colton Super 30 10.6 2800 38400 40000 21-M3 Lot (W-

Mil 3-32 (a)ChI. to be lired

'with Lot

JDC-I 62Check dee

.0165-SP Gr. '" M3(: i 1 63U 4600 Ian 52. Aide- Yes (a M3 1803Cotton 2 2 7 0 710 6200 I and NCC-35

3 3 1.40 6S0 6400 (a) Chit. firing4 3 1570 1020 12000 doe w/L45 5 8.0 1220 1l900 32000 2-MS USK-1-2I-

.0334.MP Gr. "A" M4AI 3 4 4.00 860 5200 2-M3 Eat. Mar 53 Yes (3) P55450Cotton Chg 4 5 704 1020 7000

5 7 3.20 1220 101006 1 ., 0.44 t57-1 17000" " 3 * 4 1f,'. 29700 32000

069.1 M• IChg RW-kuerd S3# 0.0 2100 10700 38000 4-MS Apr 44 IC- Yes (Q 1 M2644Nirmal 140 8.0 2600 33500 3MOO0 4-MS 2-4 (a)Gr. "D" Check d€e

.0s0,.6MP MI Chg. Normal 80# 14.25 2600 29300 38000 4-M3 May 4 -,C- Ye (i) P3723920 4.25 2850 37600 38000 4-MS3 2-0 (a)

Check dieCo,,a. u/LU-*0

,0161-SP M1 Chig Green I So 53 esig 7600 33000 4-10 Aug 47 Yes (S) SW G00H:; 2 6S 4.$ 900 9600 OW- IGr. "B" 3 76 8 3 1000 12400 40(a)Cotton 4 9g 6.6 1350 17100 Check due

5 133 2.5 1360 217000 33000

0414.MP M2 Chg White 5 166 10.0 1380 12900 Aug 47 OWl- Yes (0 P31806Bad 6 210 13.4 1C40 39800 1-49 (a)Gr. "E" 7 286 0.6 1050 32000 33000 4-M3 Check dueSilk

*..-MP M23 Chg Gr. ")" 1 420 2.0 1500 10900 Juse 48 Yes (a I131811Cotton 2 526 10.0 1740 1,'00 ACF-55-

3 65o 7.0 2020 23100 23145 (a)4 78e 10.4 2300 34600 36000 4-M3 Check due

i.;o3-MP T44 Chtg. silk 1 53.7b6 1380 8700 36000 4-M3 Est. Him 1952 Yes (a) PS3814.0993. P Class 2 90.056 1780 16000""B 3 118.261 2100 22700

4 156.701 2500 35200

(S3 - Valid Standard(R) - Valid Refereace(a) - Prol. lot used is latest check

4-101

Table 4-2"

Calculated thermochemical valucs for standard proo(including residual rolalies) ]

Use _ _Artil'cry _ _ __o_ _

Prpellant Ml TM2 IM51 M6_M_4 M1 M17 T0__

Specification JAN-P JAN-P-JAN-P- JAN- P- PA-PD- PA n-, PA-PD- PAPD

Specification___ 309 323 323 309 309 26 26- 231 329____________ - + . ... . INattC.IlIulose 45.0 77.45 41.95 87.0 90.0 20.0 22.0 20.0 94.0 72.0

I Nitration 13.15 13.25 1:1.25 1z. 15 13.15 13.15 13.15 13.15 13.15 13.15

Nitroglycerin 19.50 15.00 ... ... 19.0 21.5 13.0 ... 19.75

Barium nitrate 1.40 1.40 ... ... ... *.. 0.75

Potassium nitrate 0.75 0.75 ... ... ... 9.70

Potassium perchlorate ... ... ... ...

Nitroguanidine . 54.7 60.0Diiitrotoluene 10.0 ... 10.0 8.0 ... ...

Dibutylphthalate 5.0 ... 3.0 2.0 5I ... .. ".'.0

Dicthylphihalate ... . .. .Potassium sulfate "'"i .r.

... ..... .....

Diphenylamine 1.0, ... ... h.0 1.00 ... ... ... 1.0

Ethyl centralite ... 0.60 0.60 ... ... 6.0 1.5 2.0 ... 6.50

Graphite ... 0.30 0.30 ... .. . O.t O' .0t 0.30

Carbon black ... ... ... ... ... ......

Cryulite ...... ...... 0.3 0.3 ...

Ethyl alcohol (Residual) 0.75 2.30 2.30 0.90 1.00 0.30 0.30 0.30 1.50 1.20

Water (residual) 0.50 0.70 0.70 0.50 0.25 0.00 0.00 0.00 0.50 0.30

Lead carbKmate ... ... ... ... ... ... 1.0* ......

Isochoric flame temp. OK 2417 3319 3245 2570 2710 2594 3017 2348 3000 2938

Force. ft-lbs/lb. x 10-3 305 230 355 317 327 336 364 314 339 346

Unoxidized carbon. 5 S.6 0 0 6.8 5 9.5 3.9 11.6 4 3.4

Combustibles. % 65.3 47.2 47.4 62.4 58.9 51.0 38.7 53.1 54.3 39.1

Heat of explosion. cal/gml 700 1080 1047 758 809 796 962 712 936 910

Gas volume. moles/gm 0.04533 0.03900 0.03935 0.04432 0.04338 0.04645 j0.04336 0.04794 0.04068 0.04219

Ratio of specific heats 1.2593 1.2238 1.2258 1.2543 1.2496 1.2557 1.2402 1.2591 1.2342 1.2421

Isobaric flame temp, OK 1919 2712 2647 2050 2168 2066 2433 1897 2431 2365

Density, Ibs/in. 3 0.0567 0.0597 0.0596 0.0571 0.0582 0.0600 0.0603 0.0602 1.0583

Covolume. in. 3 ilb 30.57 27.91 27.52 29.92 29.54 31.17 29.50 30.41 27.76 29.13

*Added tGlared tCoating Added

As

Ta b~e 4 -ý.U3i

tkwrpMo(he'mical lucs 1 ,r standard propellantstincludm•, residu~al t olatiles)

Recoilless Mortar Sm: arms1i

______ -ýVI M7 mg NE MB '19 *M18~IA-P- JA--'l MIL•P- JA- P-- IA•N-P-- FA-'PD-

D- PA-PD- PA-PD- PA-PD- PA-PD-IPA-PD-AJAN-P- AN-P - A I--26 123 329 329 329 659 381 20306 733 528 26A

a 22.0 20.0 9,..0 72.0 73.25 I . -4. I 32.15 57.75 1000 97.7 80015 13.13 1.3.15 13.15 13.15 13.1.) 13.15 13.15 13.25 .3.:-- 13.15 13.15 13 15

3) 21.5 13.0 ... 19.75 20.00 25.00 35.5 43.00 40.00 ...... n.0

0.75 0.75 0.75

0... 0.I 0.70 0.70 ... 1.25 1.50

I ... ... ... ... I .. o ...... ....... 0.54 60.0 6.50 .. . . I .60

... ...... 8.0. ......5.0 ..... ... ....... ...... . ..... 9.0S... .'... .. . ..... 3.0 O... . ..... ...

3 .. 1.0 1..2 1.2 ..0 0.0 0. 1.00 0.75... . .... ... 0.75..

0.0 "0.00 .50 .0.30.3 0.0 0.0 0.7 0,80 1.0

" "1.5 31 30 2.50 5.00 6.00 0390 0.609 37...2

..11 .6 4 0.30 0.30 0.30 ... ... .. . .....1.20 38. .6

1 "6.3 7 9.... .. 0 12 6 1 19 8.6,0 o.10 -.30 1.50 1.0 1.20 i.0 0 i 0,4-0 0.50 o0.o0.0 0.50)0 0.03 0.00 0.50 0.3n 0.30 1 0.3017 0.03 0,03 0.00 . 0 .0.03 0.047

)4 3017 1897 3000 2938 3071 3081 3734 3605 3791 2827 2996 257716 6 1 339 346 353 356 368 382 382 32536 31

0 3.9 11.6 4 3.4 1.8 2.2 0 0 0 1.9 6 6.817 38.7 53.41 54.5 59.13 ...6 ... 27 .4 37.2 32.9 59.2 53.66 66.6)6* 962 712 936 i 910 962 966 M•5 1244 1295 866 933 17215• 0.04336 0.04 79N 0.04068 [0.04219 0.04133 0.04157 0.03543 0,0 3711 0.03618 0.04137 0.04037 0.04457

i7 t 1 .2 402 1.2591 1.234• 2 11.2 421 1.2373 ,.23 83 1.2100 1 .214 8 1.2102 1.2 4•00 1.2326 1 .252 3'1i 2•433 1897 2431i 2365 2482 2488 3NS 304 3139 2280 243 2058A o.oO__ . __. 0.062 11.5_3 0.055 0.0585 ... ... .. . ...t7 29.50 30.41 27.76 ]29.13 28.66 29.77 ... 216.63 25.97 28.87 27.1 30.21

ko~ating .\dd,.-d

4-103

8,

Table 4-24

Characteristics* of propellant compositions

Heat o Productst of explosion Forcecombustiort Heat Burning (1,000

(cal (cal Gas ratel (at ft-lbCompositiom per gin) per gin) (ml per gin) 25 0 C) per Ib)

MI 2.975 744 858 15 314

M2 2.275 1,13, 65s 29 368

M3 2.430 S20 1304 12 310

M4 2.945 797 783 ... 325

M5 2,389 1.032 .729 ... 362

M6 2.780 796 842 14 328

M7 ... 1.262 587 59 370

MS ... 1,225 671 67 380

M9 ......... 43 384

MIu ... 949 762 38 352

M12 ... 950 760 38 356

M13 ... 1.244 640 55 390

M14 ... 879 337

MI5 ... 800 836 I8 337

T2 ... 935 821 31 353

T3 .. 798 874-

T5 ... 1.259 610 ......

T6 ... 473 842 28 338

T", ... 752 864 20 306

T9 ... 65

i'yrocellulose 8..... 61 792 19 339

Cordite ML) 1.025 910

' For units, meaning. tnd inethwis of determination see pairagraphs 4-53 through 4-64.

" At constant volume.Water produced in liquid form.

¶ In. per see per Ib. per sq in.'x 10-5

4-105

BEST AVAILABLE COPY

• . .. .,I

"rable 4-25

Thermochemical characteristics of ritrocellulose

Nitroý-en conte,,:, n,''-,1nt

Characteristics 12.60 13.15 13.35 0

HIeat of ombustion (cal per gin) m

At c(.nstant volume 2.4 15 2. -A 5 2.32G 2.2'37

At constant pressure 2,409 2.33e 2,313 2.224

Heal, of formation ical per g-n)

At constant volume 616.7 575.5 560.9 512.5

Heat of explosion Ical per gm)

At constant volume, with

Water, liquid 936 1,017 1,0.6 , 1.140

Water, gaseous 855 935.5 90 1'0.5

Gas produced (ml per gin)

At constant volume, with

Water. liquid 744 721.6 7 1:1.5 I67

Water. gascous 91,8.5 '92.7 +R3.2 $53

4-106

Table 4-26

Thermoch/mical properties of propellant constituents

Heat of

Molecular combustion N CConstituent Formula weight (cal/mole) (moles/gm) (cal/gm/do

Acetone C3 H6 0 58 J"6,800 .10345 .5111

5-Amino Tctryl CII3 N 85 254,500 .05882 .3333

Acid Ammonium Tartrate C4 H9 NO 6 167 341,700 .05389 .4216

Ammonium Alum (Anhvd' AIH4NS208 237 .020 .2400

Ammonium Nitrate Nil 4 NO3 NH 4 N0 3 80 49,200 .03750 .4426

Ammonium Picrate C6 H6 N4 0 7 246 677,130 .04472 .3219

Ammonium Thiocyanate NH4SCN -4 340,100 .05260 .2830

Barium Nitrate Ba(N( 3 ) 2 BA(N0 3 )2 261 .00765 .1574

Barium Sulfate BaSO4 BaSO4 233 .00430

N-tBensovlalanine CI1H01NO3 193 1,168,100 .08390 .3683

Butane Triol Trinitrate C4 H7 N3 0 9 241 522,480 .03734 .3578

Butyl Malonate CIIH2 0 0 4 216 1,484,40n .09722 .4810

Butyl Stearate BS C22H4402 340 3,342,330 .12941 .5579

Camphor ClOH 16 0 152 1.411,000 .11842 .4844

Cartbn Black CB C 12 .0?333 .1350

Cellulose Acetate CIoH 14 0 7 246 1,106,000 .06911 .3994

('vanurie Trihvdrazide C3 H Nj 171 623,979 .07018 .378439 %('vclohexane llexanone.ll 20 C H160 14 312 366,000 .04487 .3718

Cyclotetramethylene Tetranitramine HMX C41-8N808 296 666,610 .04054 .3419

Diamylphthalate C1 8 H2 6 0 4 306 2,359.000 .10131 .4406

Dibutylphthalate DBP C1 6 H2 2 0 4 278 2,056,000 .09712 .4263

Dibutyltartrate C12 112,0; ( 262 1,533,000 .08779 .4673

Diethanolnitraminediniti ate DINA C4 115N4 0S 240 576,060 .04167 .3653

Diethyldiphenylurea F. C C1 7 1i120 N20 268 2.266,700 .10448 .3910

Diethyleneglycoldinitrate DEGN C1 H N07 196 548,400 .0459 .3862

Diet hv:lphthalate DEP C1211404 222 1,432,000 .08559 .3870

Diathvlmalonamide C7 H14 N2 0 2 158 994,800 .0949. .4696

Dimethyldiphenylurca C 5 H6N2O 240 1,950,000 .10000 .3688

A.

Table 4-26

"nochemical properties of propellant constituents

Heat of N Heat ofMolecular combustion N C E Q Oxygen N combustion

weight (cal/mole) (moles/gm) (cal,'gm/deg) (cal/gm) (cal/gm) balance (111.3 | Density reference

426,100 .10345 .3111 -2756 -1911 -138 '

85 251,500 .05882 .3333 -376 360 -47.1 28

167 341,700 .05389 .4216 -1470 -578 1 4

237 .020 .2400 -600

80 49.200 .03750 .4426 365 1458 20 22.83 1.725 17

246 677,130 .04472 .3219 -97 560 -13 23

76 340.100 .05260 .2830 445 926 -42.1 1.30 35

261 .00765 .1574 131 1139 15ý34 3.240

233 .00430 234

193 1,168,100 .08390 .3683 -2338 -1808 -104 4

241 522.480 .03734 .3578 653 1469 10 1.52 20

216 1.484,400 .09722 .4810 -2635 -1867 -126

340 3,342,330 .12941 .5579 -3636 -2861 -198 58.91 .855 6

152 1.411,000 .11842 .4844 -3324 -2t;93 -179 4

12 .0,333 .1350 -3330 -133

246 1.106,000 .06911 .3994 -1704 -985 -65 42.10 34

171 623.979 .07018 .3784 -1141 -491 -70.2 24

312 366,000 .04487 .3718 -1117 -123 0 6

296 666,610 .04054 .3419 595 1341 0 1.92 23

306 2,359,000 .10131 .4406 -2824 -2206 -141 58.81 1.022 31

278 2,056,000 .09712 .4263 -2667 -2063 -132 56.97 1.05 31

262 1,533,000 .08779 .4673 -2404 -1611 -104 6

240 576,060 .04167 .36V 469 1277 0 23

268 2.266.700 .10448 .3910 -2808 -2360 -155 ' 62.60 1.11 25

IS6 548,400 .0459 .3862 2.7 1078 -8.2 22

222 1.432.000 .08559 .3870 -2315 -1749 -108 4

158 994,800 .09494 .4696 -2561 -1811 -122 4

240 1,950.000 .I0o0o .3688 -2682 .- 2269 -147 " 25

4-107

2?4

Table 4-26

Thermochemical properties of Propellant constituents (c

Molec- Heat ofular combustion N C

Constituent Formula weight (cal/mole) (moles/gin) cal/gm!/

Dilnethylphthalate DMP CIoHI 0 0 4 14 1,119,700 .07732 .3589

Dinltrodlmethyl Oxamide DD Oxam C4 1 6N 4 06 206 511,910 .04369 .3433

Dtni I roethylb.nzene DNEB C8HsN204 196 1,011,800 .06633 .3399

Dlnitrotoluene DNT C7 A6N204 182 855,200 .06043 .321i

Dipnenylamine DPA C2 H IN 169 1,536,200 .10651 .3476

Diphenylurea C13 H12 N2 0 212 1,614,500 .09434 .3406

Diphenylurethane C1 5 H15 NO 2 241 1,866,090 .09544 .3612

Ether (Dimethyl) C2H60 46 347.600 .10870 .6092

Ether (Diethyl) r4H1100 84 660.300

Ethyl Alcohol ETOH C2 H6 0 46 327,600 .10870 .609

Ethylene Diamine Dinitrate EDDN C 2H10N406 186 374,700 .04839 .4332

Ethylenedinitramine HALEITE C2 H6 N4 0 4 150 371,690 .04667, .3809

Food Meat .06785 .4215

Glucose C6H1206 1I0 673,000 .06667 .4148

Glucose Pentaacetate (lnsol.) C 16H 220 390 1,726,300 .06923 .3971

Glycine C2 H NO2 75 233,400 .06667 .4445

Graphite G C 12 94,272 .,Q1!33 .1350

Guanidin(. Nitrate CH 6N 403 122 209,230 .0-1918. 4 5

Guan :: i i: urea (Stab. Insol.) C2 H5 NbO3 147 288,900 .04080 340

Guanylurt anitrate (Stab. Soluble) C2 IN5 04 165 296,500 .04840 38

ll::xanitroethane HEXANE C2 N6 0 12 300 130,000 .01666 2 62

llcxani'rn tjxaniide IINO C14 H6 N8 014 510 1,421,030 .04118 .2t85Hydrazinc Nitratw. H5N 95 112,200 .04210 .4427

5N303 9 1,0 42

llydrazine ,Ir g•en Oxal','- C If N,04 122 189,100 .04920 .41202 6'

llydroxylamine Nitrate IIYDROX N NIi 2OH.HNO3 96 49.740 .03125 .429[ ,i, C .,!.,nate PbCO, PbCO .67 .00374 .06443

Mclamine C3HsN6 126 478,926 .07143 .355I

Metriol Trin:, i te C5H9N30 9 255 673,710 .04314 .37.01

il..

Table 4-26

Femical proberties of propellant constituents (cont)

Molec- Heat of Heat ofular combustion N C E Q Oxygen combustio

weight (cal/mole) (moles/gm) (cal/gm/degl (cal/gm) (:aligr..' balance 1n."/1b) Density reference

194 1.119,700 .07732 .3589 -2067 -1527 -91 4

206 511,910 .04309 .3435 120 849 -7.76 21!

196 1.011.800 .066Z3 .3399 -911 -342 -65.3 43.0 1.32 6

182 855,2C0 .06043 .3213 -662 -117 -52.7 40.44 1.27 21

169 1.535,200 .10651 .3476 -293:j -2679 -166 65.41 1.16 20

212 1,514,500 .094.4 .3406 -2610 -2243 -136 4

241 1,866,090 .09544 .36i2 -2609 -2183 -136 6

46 347,600 .10870 .6092 -2310 -I'•8s -139 4

34 60.300 -261( -1141 4

46 327.600 .10870 .6092P -2715 -1672 -139 56.35 .789 4

156 374,700 .04839 .4332 -3s. 1 j27 -8.6 1.59 23

150 371,690 .04667 .3809 30, 1130 - I•.G 33.90 1.71 22

.06795 .4215

IqO 673,000 .06667 .4 148 -162c -75G -53.3 4

190 1.726,300 .06923 .3971 -I117 -1105 -66 4

75 213,400 .06667 .4445 1901 -933 -55.3 1.60 4

12 94,272 .,4333 .11'50 -3208 3370 -133 60.53 2.10

122 209,230 .04918 .4125 -288 610 -13.1 22

147 288,900 .04080 .3540 -374 360 -16.3 1.93 26

165 296,500 .04840 .3860 -457 367 -14 1.54 20

300 130,000 .01666 .2862 14bM) 2231 53.3 4

510 1.421,030 .04118 .2785 -12 539 -9.4

95 112,200 .04210 .4427 499 1536 -13 1 29

122 189.100 .04920 .4120 -1007 -108 -13.1 27

96 49,740 .03125 .4229 855 1923 33.3 17

"167 .00374 .0644 618 .315

126 473,926 .07143 .3552 -1587 -1015 -76.2 1-57

255 673.710 .04314 .3701 375 1188 -3.1 117 201

4-109

Table 4-26

Thermochemical properties of propellant constituents

Molec- Heat olular combustion N

Constituent Formula weight (cal/mole) (moles/gm) cali

Mineral Jelly (Vistanex) C3 0 H6 2 423 4,695.000 .14i21

Nitrocellulose 11.1'N NC C6 HS 2 0 9 252 657,000 .04390

Nitrocellulose 11.2%N NC .04129

Nitrocellulose 11.6%N NC C6 H7 5 5 04 N2 .4 4 9 09 8 9 9 2 272 651,800 .04041

*Nitrocellulose 13.15%N C6 H7 . 3 6 4 5 N2 . 6 7 0 0 0 1 0. 2 7 1 0 281 651,700 .03920

Nitro.ellulose 13.25N NC C6 H7 . 3 3 0 0 N2 . 6 7 2 6 010. 3 4 00 282 650.000 .03898

Nitrocellulose 13.35%N NC .03876

Nitrocellulose 13.45%N NC C6 H7 .26 0 4 N2 . 7 3 9 6 0 1 0 .4 7 92 281 649,000 .03854

Nitrocellulose 14.14%N NC C6 H7N3 0 297 647,000 .03704

Nitrodicyanodiamidine .04761

2-Nitrodiphenylamine 2NDPA C12 H1 0 N2 0 2 214 .08400

Nitroglycerin NG C3HAN 309 227 370`237 .03084

Nitroguan'dine NG"a CH4 N4 0 2 104 211.300 .04808

4-Nitro-N-MetI.ylanaline 4NNMA C7 HsN 2 0 2 152 925.200 .07887

Oxalic Acid C2 H2 04 90 60.200 .03333

Oxamic Acid C2H3NO3 89 128,600 .0450

Oxam ide C2 H4 N2 0 2 88 203,280 .05682

Paracyanogen (C2 N2 )X (52)X 250,000 .05769

Pentaerythritol Tetranitrate PETN CAH8 N4 0 12 316 619,360 .03481

Potassium Aluminum Flouride CRYOLITE K.3ALF 6 258

Pctassium Nitrate KNO 3 KNO3 101 .00989

Potassium Sulfate K2'0 4 K :74 .00574

Potassium Perchlorate KC104 KCI0 4 139 .00722

Sodium Aluminum Flouride CRYOLITE Na 3 ALF 6 210

Starch .06785

Sucrose C12H2 2 0 1 1 342 1,349,600 .96725

* Thp values for nitrocellulose depend linearly on the degree of nitration.X = A + B (13.15 - %NB,); NB = % Nitrogen of component B

NC-F N .00218 C = .0060 E = -153 Q f -140

A * BEST AVAILABLE COPY

Table 4-26

Thernuchemical propertrics of prope'llant ccnstiuents (cont)

•Molec- Heat of .. Heat U(ular cor-bust.on N C E Q Oxygen c Coibus-

weight (cal/mole) (moles/gm) (cal/gm/deg) (cal/gm) (cal/gm) balance (In. ,.lb) Density tion re-S23ference

423 4.695,000 .14421 .5935 -4184 -3405 -231 (0.64 0.92 6

252 657.000 .04390 .3545 -27.4 734 -6.3 29.61 11

.04129 .3478 28.51 11I

1449609.8992 272 651,800 .04041 .3454 183 941 0.77 29.11 11

1.6700010.2710 281 651,700 .03920 .3421 268.4 t 1024 3.4 27.56 1.66 11

1.6726010.3400 282 650,000 .03898 .3415 278.5 1034 3.95 27.46 11

.03876 .3409 291 4.4 27.36 -11

1.7396010.4792 285 649,000 .03854 .3403 305 1061 4.8 27.26 II297 647.000 .03704 .3362 407.2 1160 8.3 26.57 11

.04761 .3541 -252

214 .08400 .3240 -1960 -1575 -112 53.73

227 370,237 .03064 .3439 960 17V! 24.7 22.78 1.601 22

104 211,300 .04808 .3712 -46.5 735 -15.4 31.77 1.50 22

152 925.200 .07S87 .3560 -1671 -1141 -94.6 21

90 60.200 .03333 .3393 -868 -80 17.8 1.65 4

89 428.600 .0450 .3600 -1222 -449 -9 4

88 203.280 .05682 .3801 -1502 -755 -3C.' 36.26 1.67 24

(52)X .250.000 .05769 .1925 -5575 -3785 -61.6 4

316 619,360 .03481 .3483 729 1533 15.2 24.88 22

258

101 .00989 .2158 25 1434 23.61 2.109

174 .00574 .1250 -800 300 9.36 2.662

139 .00722 .2467 891 1903 46.1

;.10

.06785 .4215 -1606

342 1,349.600 .06725 .4339 -1620 -785 -56 1.59 4

Itation.

40

4-111

Table 4-2b

"hermochemical properties of propellant constituents

I'• IMolec- Heat of

•[ula r combustion N CConstituent FormuLa weight (cal/mole) (moles/gm) (cal/g.

Tetranitro Diphenyleneimine TNC CI 2 H5 N5 0 8 347 1,332.250 .04899 .27

Tetranitro Oxandilde TNO C1 4 H8 N6 0 1 0 420 1,492,590 .05000 .28

Triacetin C9 H14 0 6 218 1,100,620 .07339 .41

Tricresyl Phosphate TCP C, IH 2 1 PO4 368 2,539.568

Triethvleneg;ycol. TEG C6H 150 857,800 .08667 .44

Triethyleneglycol. Dinitrate TEGN C6 H12 N2 0 8 240 822,270 .05417 .40

T."imethylenetrlnitramrine RDX C3 H6 N6 06 222 507,270 .04054 .34

Trinitrotoluene TNT CAH5 N3 0A 227 816,900 .04846 .30

Urea CNN 20 60 151,600 .06667

Water HOH H20 18 .05556 .65

A . BEST AVAILABLE COPY

Table 4-26

hermochemicul properties of propell•t constituents (cont)

Heat olMolec- Heat of combus-

ular combustion N C E Q Oxygen N tion ref-weight (cal/mole) (moles/gm) {cal/gm,'deg) cal/gm) (cal/gm) balance (In. 3/lb) Density erence

347 1.332.250 .04899 .2716 -231 245 -30.0 6

420 1,492.590 .05000 .2882 -497 22 -30.5 G

218 1,100,620 .f-'339 .4195 -1577 -827 -73 43.77 1.161 G

368 2,539,568

150 857,800 .086G7 .4427 -1146 .349 -96 32

240 822,270 .05417 .4051 -223 -617 -26.7 33.60 1.33 20

222 507,270 .04054 .3419 628 1374 § 28.51 1.816 221

227 816,900 .04846 .3039 -96 480 -24.6 34.31 1.654 22

60 151,s00 .06667 .4440 -1715 -844 -53.3 4

18 .05556 .6513 -1568 0 0 24.60 1.00

4-113

B3

Table 4-27

Propellant stability test ralues

Surveillance test Vacuum stabili'y tesSurveillhect test (Ml gas per 5 graz•s p•

I _ _ 40 hours)

Composition (Days to red fumes) 2 0°Cheat test min SP, hn IExps. min 'A0. h At

AtR 655 0 C A 1 5~0 C 300+ 50 :to 0- 2.5__

wC Ball 1,000 . . . 85 300÷ 25 300. 1.2 6.5

MI 1,700 400 50 300+ 0.2 3.5M2 50a 90 1o5 300+ ... ... 1.0 2.0

M5 600 100 119 300+ . .. 2.0

M6 1,700 400 ... ... 55 300+ 0.5 5.0

M7 (DPA)* 400 75 85 300+ ... ... 7.5

M7 tEC)* I 800 200 115 300+ ... 2.0

M8 (DPA)* 200 40 50 300+ 15 90 7.0

M8 (EC)* 370 75 60 300+ ... ... 4.0

M9 210 ... 50 300+ 20 35 6.5

M10 500 150 ... ... 90 300+ 1.0 5.0

M12 800 ... .. . ... 50 300+ . . . 2.5

M15 1,00ot . .. 100 300+ 35 300+ 2.0

M17 1.000" .... 150 300+ 35 100 1.3 6.0

TIS ... ... 60 300+ 25 300+ 6.5

T20 ... .. 95 300+ .

ECBF S00 . .. 150 300+ 40 240+ . .. 6.0

*Stabilizers: diphenylamine (DPA); ethyl centralite (EC).

t Surveillance Test of nitroguanidine propellants does n,,tproduce red tumes by normal procedure. Fires appear onopening of te-;t bottle after approximately 1,000 days.

A.

Table 4-27

Propllal stabilrtY test ralues

- Vacuum stability test Taliani test (1 10oC)heat test 134. 5(C heat test (M gas per 5 gragns per

- 40 hours)

Sm E . Slope at Min to Slope at4-q- 2t 0 A -0°.Mdu 100 .nm 100 mm 100 mm

Expl, rain S . min I Expl. t wC AtIOO Mdun10nioomr

300+ 50 300. 0.. Sitrogun 0.30 400 0.25

300+ 25 310+ . 6.5 N itrogen 0.90 175 0.35

50 300, 0.2 3.5 Nitrogen 0.25 300 0.10

300: ... 1.0 2.0 Nitrogen 0.95 145 0.70

300 ... ... 2.U Nitrogen 1.54 139 0.85

. . 55 300+ 0.5 5.0 Nitrogen 0.34 324 0.25

300. ... 7.5 . . . Nitrogen 2.22 52 1.95

300+ ... ... 2.0 . . . Nitrogen 0.60 200 0.60

300+ 15 90 7.0 . . . Nitrogen 3.45 44 2.50

300+ .... 4.0 . . . Nitrogen 0.80 250 0.65

300+ 20 85 6.5 . . . Nitrogen 2.38 76 2.50

- . . 90 300+ 1.0 5.0 Nitrogen 1.47 43 0.95

* . . 50 300+ . . . 2.5 Nitrogen 0.30 360 0.2!

300+ 35 300. 2.0 . . . Nitrogen 0.75 170 0.80300+ 35 100 1.3 6.0 Nitrogen .55 245 0.50

S 300+ 25 300+ 6.5 . . . Nitrogen l. 1 74 1.38S 300+ . .. .. .. . .... Nitrogen .. .. .. .

300+ 40 240+ . . . 6.0 ._._...._._. .. .

lite (EC).

Joes nutPs appear on

lays.

4-115

B.

CARTRIDGE CASE AND GUN CHAMBER DESIGN

4-76. Introduction. The primary function of a expected to protect the propellant charge dur-cartridge case is to facilitate the handling of the ing storage and handling, and to provide ef-propellant charge. When the projectile and fective obturation during the firing of the gun.charge are short enough and light enough to behandled as a unit, and when adjustment of the BRITISH PRACTIC,charge Is not required, fixed ammunition isused. When provision for adjustment of the 4-77. Design of Drawn Cartridge Caser - Brit-charge is required, semifixed ammunition is ish Practice. The report by the British Arma-used. When the combined overall length or ments Design Department of the Ministry oftotal weight of a case and projectile is too great Supply on the design of drawn cartridge casesto permit both to be handled as aunit, and there is acknowledged by both the Picatinny and Frank-is no need for adjustment of the charge, sepa- ford Arsenals to be the best assemblage ofrated ammunition is used. In very large guns, design material available for this type of car-where the weight of a case for the propellant tridge case. Paragraphs 4-78 to 4-93 arecharge would be a liability, separa.te loading taken directly from this report. The onlyammunition is used. (See paragraphs 1-1 changes that have been made are changes inthrough 1-12, "Types and Classification of nomenclature, where British nomenclature dif-Complete Rounds," for a description of these fers from American, and the insertion of a fewtypes of ammunition.) parenthetical remarks to indicate some points

where American practice is at variance withIn a separate loading gun, the chamber must the British.be designen for a volume determined by the in-terior ballistician. This volume must be suf- It is highly probable that other variations thanficient to hold the propellant charge andprovide those indicated exist between American andthe desiredi loading density (see paragraphs B.-itizah practice. This must be borne in mind4-21 through 4-51, "Theoretical Methods of In- when making use of thas "nfurmation.terior Ballistics"). The shape of the chamberis determined, within the limitations of this 4-78. Requirements in Design. The require-volume, by the gun designer. From the latter's ments for the production of a cartridge casestandpoint, the diameter of the chamber should are that:be kept low to reduce the diameter and weight 1. It shall be easy and cheap to manufacture.of the breech of the gun. A further limitation 2. It shall effectively protect the propellantis set, however, by the fact that the diameter charge against flash and moisture during themust not be so small as to cause the breech of storage.the gun to be excessively long or to require 3. It shall not be corroded by moisture.the use of powder bags that are difficult to 4. It must not develop cracks or split duringhandle. storage or undergo dimensional changes.

5. It must be strong enot:gh to withstandIn separated, fixed, and semifixed ammunition, rough usage and the force of the gun extractorsthe propellant charge is not loaded directly intoa after firing, and in the instance of fixed ammuni-the gun, but is contained in a cartridge case tion rigid enough to carry the projectile withoutwhich may or may not be attached to the pro- distor+ion in handling.jectile. This cartridge case must be designed 6. Ut shall withstand the high temperaturesso that it has the volume desired by the propel- and pressures encountered during firing.lant designer. The shape of the case is subject 7. It shall be of suitabie hardness to ensureto the same limitations as the shape of the that it will expand to the chamber and obturatechamber, in addition to the !imitation that it satisfactorily during firing, but will be resilientmust be capable of being extracted from the enough to recover after firing to allow free ex-chamber of the gun. Moreover, the case is traction.

//6 4-117

S. . . ~ . . . . . . . .. ... . .. ... . . .. . .

8. It shall preferably be capable o0 being re-formed to size a number of times after firing. MOUTH MOUTHS~THICKNESSThe following paragraphs (4-79 to 4-93) con-31der'the above requirements and attempt to NECKRcover those points in cartridge case design, (PARALLEL)which can, to some degree, be standardized. Itis emphasized, however, that successful casedesign involves experience and a knowledge ofthe methods of manufacture and of the function- SEPARE LOA

ing of the case during firing. SEPARATE LOADINGAMMUNITION WITH

4-79. Theory of Functioning. Figure 4-19 RAMMING LIDSshows a typical cartridge case with the namesof the various parts. The closeJ end of thecase is known as the "base" or the "head" butthe term "base" is mote consistent with thenames of the other parts.

When firing a cartridge case in a gun, the caseis supported by the gun Adthl:. nkcluL the caseis subject to plastic flow; therefore, strengthcalculations by elastic theories do not apply. BODY-

When a gun is fired, the propellant charge isignited and the resultant internal gas pressure --- WALL

causes the case to expand to the diameter of thechamber, after which case and gun expand to-gether. The gun expands elastically; the metalof the case will be stretched beyond its yieldpoint and plastic strain will occur. Forthecaseto extract freely, the recovery of the case fromi1ring strain must exceed that of the gun, or in UNDERother words, the permanent expansion of the HEAD PRIMER 3OSScase after firing must not exceed the initialclearance in the chamber. This is illustrated FLANGE-\in figure 4-20, which shows a stress-straincur.e for the material (brass) of the case wall.

AB represents the initial clearance between the BASE OR P Rcase and chamber, and BC represents the elastic HEAD "-ý-PRIMER HOLE

expansion of the gun on firing. Stress and Figure 4-19. Cartridge casestrain are proportional up to the yield point Y,and hence the graph follows a straight line, modulus but lower yield. It will be seen thatwhose slope is a measure of Young's modulus this case would, on recovery, follow the linefor the material. Beyond the yield point, plas- FG, which would result in an interferencetic extension takes place up to a point E; on re- between case and chamber (represented by BG),lease of the pressure, elastic recovery takes causing stiff extraction.place along line ED (which may be assumed tobe parallel to YA). The factors, then, influencing the freedom of

extraction represented by distance BD in figureAD then represents the permanent expansion of 4-20 are:the case. Provided that the expansion of the 1. Yield stress of material, indicated bygun is completely elastic, the chamber will re- point Y;turn to B after firing; the distance BD thus 2. Young's modulus of elasticity for the ma--epresents the clearance between chamber and terial (given by the slope of the straight portioncase after firing. The dotted line AF repre- AY of the stress-strain curve Pnd assumed tosents a case made from material of the same be also the slope of the recovery line (ED);

4-118

N C4-80. Effect of Gun on Extraction The pre-, C.,LtA III, SI(W(BtR CFITRINGO CS ANSR ,000 ceding theory is based only on the oehavior of

S- il, k IRING the case across a plane perpendicular to theI axis, and would be true for a chamber with a

"0"" -very smooth surface finish, no extractor pock--/_-f "*-- .w+.o.'.oets, and n, longitudinal expansion. In these

./ circumstances, a case made as thin as manu-/ facturing considerations permit would be ex-

pected to extract freely. In British practice,however, the gun usually has extraLtor pockets,

S// and during the war the surface finish of cham-A ExpAesNoN (STRAINqI o 11 C bers was permitted to deteriorate. This has

resulted, on occasions, in stiff extraction ofFigure 4-20. Functioning of cartridge case cartridge cases. The precise reason for this

is a little obscure, but is probably due to the3. Elastic expansion of the gun (BC)., internal gas pressure expanding the mouth of4. Initial clearance of the case in the cham- the case to the chamber. The chamber expands

ber (AB). longitudinally, and the pressur- forces backthe base of the case, together with the breech.

With brass, there is a good correlation between Owing to the roughness of the gun chamber, thehardness and yield stress, so in cartridge case mouth of the case will not slide, and the casemanufacture great importance is attached tothe is thus stretched. In this condition the case ex-hardness. It is emphasized, however, that the pands into the extractor pockets, and when thefactor influencing extraction is yield stress and gun recovers after firing the bulged portion ofnot hardness, the latter being merely a con- the case is longer than the extractor pocket andvenient method of measuring the former. the edge becomes jammed inthechamber. Sim-The elastic expansion of the gun for a given ilar trouble will be experienced if the radius atpressure will depend on the materials and de- the junction of chanibui and brecch face is toopssurofthe will d ighepn on thesmaterials andgd small. Shots striking this edge during loadingsign of the gun. Higher gun pressures or guns will bruise it and form small projection.3 in

with a reduced factor of safety will lead to wron so It whc the c all psetion in

higher elastic expansion, with accompanying front of it, which the case will upset on firing,

extraction difficulties. It will be seen from causing sUff extraction. A further possible

the cause (.f stiff extraction occurs when the gun isfigure 4-20 that the initial clearance of rhe cvrnatefingndhebehtaelcase in the chamber has little influence on ex- forwrd ate to the brelph thetraction conditions. forward relative to the barrel, pushing the

cartridge case in front of it. The gas pressure

Figure 4-21 gives two further diagrams to am- may be sufficient to hold the mouth of the caseplify the theory of extracticn. Figure 4-21a against the rough chamber, preventing sliding.shows the effect of an increased elastic expan- In these circumstances the case will be sub-sion 3f the gun, due to raising the pressure or jected to a longitudinal compressive force,reducing the factor of safety. It will be seen which may cause "barrelling" and stiff extrac-that a case which extracts freely on the normal tion. If the breech-block face is rough or if thechamber expansion will be hard to extract with firing-hold bushing sets back on firing, theincreased expansion. Figure 4-21b shows a pressure of the expanded case thereon will makecomparison of steel and brass cases. It will operation of the sliding block very difficult.be seen that the steel case, owing to its highermodulus, will require a much higher yield stressthan the brass to give the same recovery. With The Ordnance Board has now recommended thesteel cases, a small increase in the elastic ex- adoption ol the following design policy:pansion of the gun wotld necessitate a relatively f. To provide full support for the cartridgelarge increase in the yield stress of the cdse, cases (no breakthrough extractor pockets).and a condition is eventually reached when the 2. The provision of breech blocks withoutnecessary yield stress is unoitainable by work- firing-hole bushings when possible.hardening during manufacture, and a heat- 3. The specification of a smooth finish tothetreated steel b1.,comes necessary. chamber and front face of the breech block.

4-119

ELASTIC EXFANSIONOF GUN STEEL

/ Ii

CLEARANCE BETWEEN IsCARTRIDGE CASE AND I

CHAMBER BEFORE FIRING INICREASED /Q b •I I

. - --- -I I

// II I I

I II~II

:(A)()

Figure 4-21. Functionin~g of cartridgýe case

If pressures in new designs of guns are raised a. Failures Due to Case.appreciably, with a corresponding increase in 1. Cases too soft (yield stress too low),eldAstic chamber expansion, it is unlikely that a resulting in hard extraction (see figure 4-20).brass case or work-hardened, low-carbon steel 21. Cases too hard, resulting in splittingcase will have sufficient elastic recovery to caused by the low percentage elonwation ofextract freely. In that case the only solution the material.(for a solid-drawn metal case) would probably 3. Cases with inherent metal faults orbe a case made of alloy steel of high yield ob- folds, causing "blow-throughs" and gas wash.tained by a combination of %ork-hardening and 4. The use of cases of different lengthsheat treatment. in the same gun, causing stiff extraction.

n.b. Failures Due to G Causing Hard Ex-

4-81. Effect of Case on Extraction.A further cause of stiff extraction is the use of 1. 'Sxtractor pockets.

difeen lngh ass*inthe same gun. With 2. Rough chamber and,/or breech-blockdiffren legth ase inface.

the shorter cases,* constant firing will cause 3 ebc ffrn-oebsigan annular depression to be eroded in the 3. Brseatbc jufcfiring-ole buhamng. an

Figure4.-Burrs attjunctionf ofrchamber and

chamber near Wte mouth of the case. When a breech face, caused by the shot striking onlonger case is fired in the same gun, the mouth an insufficient radius.

af the case will expand into the depression andfextractr in tt ate 4-83. Data Required to Design a Cartridge

4-82. Summary of Causes-of Case Failure. The Case. Before a derign e a be initiated, thecauses of "case faillrest can be summario-1 following data will be required:as follows: 1. Details of gun chamber

4-120

2. Details of projectile and rotating, band The tolerance of the length of the case, lot3. Gun pressure. fixed or semifixed ammunition. may be. taken

approximately as 0.01 inch per inch of caliber,but this tolerance can be reduced, if necessary,

With regard to the details of the gun chamber, without rausing s,,rious manufacturing prob-dimen.sions of the gun chamber should not be hm;

finalized until the cartridge-case desi.,ner has ltn .

confirmed that a case to suit the chamber is amanuactringproositon.For separated ammunition, the length (A themaniufacturing proposition, case should be calcuflated so that after ramming

The gun designer is not always permitted a free the projectile there is a minimum clearance of0.075 in. between the base of the projectile

hand in the shape of chamber. Often there is a 0n7 in. between the base tcomplete round length restriction to suit stow-.age or other special conditions. For a speci- 4-85. Cle'irance in Case in Chamber. withlied chamber capacity, then, it may become fixed ammunition, and separated ammunitionnecessary to design a chamber with a large (closed v ith plastic plug), the clearance should

back end; but this is objectionable from the

gun designer's point of view, as it results in be constant along the body taper and the tapered-..a large breech and heavy gun. Such a design portion in .ront of the shoulder. An exception

also causes diffiuhties, in. cartridge-case to this -ule occurs with f bred ammunition, whenmanufacture; it is difficult to taper the case it is necessary to increise the lengtl (it p,,ral-

from the large back end to the comparatively lei to improve shot attachment, which may besmall emergent calibern done, for a given length of case, by increasing

the taper of the portion of the case in front cf

the shou!der. The clearance has hitherto beenTo ensure ease of extraction, it is desirable obtained by issuming minimum clearance (Athat the main body taper should not be less 0.004 in. on diameter per inch of caliber. Thisthan 0.02 inch per inch on diameter. The is excessive for the larger calibers; figure 4-22tapered portion of the case, between shoulder shows a suggested clearance curve. (Ameri-and parallel, should not have a tarer in excess can practice for 37-mm to 120-mm calibers isof 0.3 inch per inch on diameter, or manufac- to allow 0.006 in. clearance on diameter forturing difficulties will be encountered. brass cases, and 0.008 in. on diameter for

steel cases. The larger clearance for steel isWhen designing new vquipment, a "basic de- specified to allow 0.002 in. for the varmshsign," showing the chamber ind rifling with the coat.)cartridge case and projecti.o in position, en-sures close cooperation between the various When estimating the clearance at the paralleldesign sections, which is obviously very de- portion of fixed-ammunition cases, it must besirable. borne in mind that the projectile is an inter-

ference fit in the case, and hence the mouth

4-84. Length of Cartridge Case. On fixed am- ol the case expands upon assembly.

munition the mouth of the cartridge case should Tibe in contact with a projection on the projectile . e parallel portion of the gun chamber mustknown as the "case stop," controlling the over- he designed to give the correct clearance overth-e rotating band. Once the case mouth thick-all length of the round. On conventional pro- ne has bend, the the case me-

jectiles, the rear Ice of, or a step on, the

rotating band forms the case stop. signer has no means ci controlling the clearancein the chamber at the mouth of the case. Theclearance between the gan chamber and the

The length of case should be calculated by as- parallel pcrtion of the case (alter insertion ofsuming a minimum run-up of 0.015 in. in a new the projectile) should ,aot be less than0.01 in. ongun; that is, with a high length of case and high diameter per inch of caliber; if this cannot tlerotating band in a low chamber the projectile ac.iieved, the chamber and projectile dimen-should have a travel of 0.015 in. before the ro- sions should be reconsidered. At this point ittating band contacts the taper portion (known as .s better to err on the side of too much ratherthe forcing cone) at the front of the chamber, than too little clearance, as maltreatment of a

4-121p

.025

WI-. Iw

_ n_ _OI_ _ _"

cW.02Z• STRAIGHT LINE PLOTTED ONo MINIMUM CLEARANCE ON DIAMETERWIU 0O.004 (DIAMETER OF BORE)Z Z .015

•E O.OI -- *

2 -.005

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0BORE OF GUN

Figure 4-22. Clearance of cartridge case in chamber

fixed round will sometimes cause a slight boll- cartridge, however, .Ae latter is closed with aing of the mouth cf the case, and if the clear- white metal or plastic plug. In such cases it isance is too small troubles in loading may be now common practice to strengthen the mouthexperienced, of the case, and to increase the support for the

plug, by rolling a crimping groove into theIn separated ammunition closed with a white mouth of the case (see figure 4-19). For themetal plug, the clearance at the "under head" 3.25-in. case the radius (R) is 0.2 inch, and forposition should be on the lines outlined above. other sizes the radius should be adjusted in theThe clearance should then decrease uniformly ratio of the calibers.along the taper toward the mouth, so that thehigh mouth diametar of the case is equal to the For white metal plugs, the empty case is slottedlow chamber diameter at that pohit. at the mouth to form tangs which may be bent

over the recesses in the plug to secure theWith a plastic plug, however, the mouth of the latter.cartridge case alter closing is very rigid andwill not "give" to the chamber, as woulda case The present tendency is to close with a plasticclosed with a white metal plug, should slight plug, this being secured by "coining," no tangsdiscrepancies (due, for instance, to ovality) be being required.present. Therefore, with a plastic plug it isnecessary to allow clearances of the case with- 4-87. Flang Design. The flange (figure 4-19)in the chamber in the same manner as for fixed performs the dual function of acting as a stopammunition, except that the clearance at the . when loading the round, and providing a projec-short parallel portion should be approximately tion on the case against whichthegunextractorsthe same as at the taper. operate to eject the case after firing. The

force exerted by the extractors when a case is4-86. Crimping Groove Design. With separated tight may be considerable, and flange strengthammunition, where the projectile is rammed is therefore of importance.before the loading of the cartridge (as is -thecase in howitzers), the cartridge case is nor- Figure 4-23 shows several types of flanges.mally closed with a simple glazed-board cup. With.any type of flange the cartridge head spaceWhen the projectile is rammed by means of the (the clearance between the base of the case and

4-122

With a simple flange witkJut step 'igure 4-43,a and b) the extractors are usually located in

r, recesses at the mouth of thr chamber. These

is pockets leave small areas of cartridge case' j unsupported; when there is insufficient thick-

.04R ness under the head, the case is likely to expand

.0R4" into the pockets, causing hard extraction. (See.05R paragraphs 4-79 through 4-82.) German de-

H. 0-2 signs for Q.F. guns incorporate a lipatthe rear

255 1. of the chamber (see figure 4-23e), which ob-L.245 -" viates extractor pockets; it is understood that

(A) 20 PR (8) 2 PR extraction troubles with German cases are very

CONVENTIONAL FLANGES rare.

!2 'With a stepped flange (figure 4-23c), the stepo .N - acts as a stop in loading, and positions the

_ -J • •. 1 flange proper at a fixed distance from thek 0n chamber face. The extractors are located In_J

.03R L,] the space so formed, leaving a portion of the

heavier base. A few early case designs have aL.0 step locat.ýd in the chamber. This step appears

H. 25 H. 305 4.,15 L.S1 to serve no useful purpose, and the design is

L.25• not likely to be repeated.(C) 17 PR (D025 PR

4-88. Design of Mouth of Cartridge Case. FromSTEPPED FLANGES a functional aspect, the internal surface of the

mouth of the case is quite satisfactory "asNOTE: BRITISH PRACTICE USES HIGH B drawn." In production, however, forming the

TO INDICATE MAXIMUM PERMISSIBLE

DIMENSION AND LOW IL) TO INDICATE mcuth within the specified tolerances, par-MINIMUM PERMISSIBLE DIMENSION. ticularly with fixed ammunition, could oaly be

effected at the exense of repeated tool re-placements.

It is usually considered more economical tothicken the cases at the mouth when taperingand necking, and to bore on a lathe to withinthe specified tolerances. (InAmericanpractice,

(E) ARRANGEMENT OF GERMAN CHAMBER this is not usually done; instead, the case isSHOWING LIP AT MOUTH OF CHAMBER TO used "as drawn.'"OBVIATE EXTRACTOR POCKETS.Figure 4-23. Flange design To obtain a rigid fixed round, there must be

adequate interference between the cartridge

the face of the breech block when the case is case and the projectile. Excessive interference

pushed right home into the chamber) should be is objectionable as it causes stretching of thelow*cartridge-case mouth in the plastic range with-lowcnes 0.0ange. Whighen 0.015in. w nithahigh out giving additional strength of attachment, andthickness flange. When designing ammunition increases the work necessary to insert thefor a new gun, the case designer is usually prectie.permitted a free hand on flange thickness, and projectile.the breech is then designed to give the correct The interference depends on the diameters andcartridge head space. tolerances of both the case mouth and the base

of the projectile; it is Often necessary to corn-*Low refers to the minimum dimension, promise. Figure 4-24 shows recommendedfHigh refers to the minimum dimension. maximum and minimum interferences. The

4-123

"' {{ 4

Reference should bt made here to the mnethodof dimensioning the mouth of the case. With

I separate-loading ammunition, the internal ui-MAXIMUM ANO W! .UM INTERFERENCEFOR EXISTING AMI JNIT,- ameter of the mouth of the case is not critical,

. / and the mouth is usually controlled by an ex-ternal high and low diameter and a high and low

J wall thickness. The wall thickness toierance03- also 4rols the eccentricity of the mouth

borirg.

-e - Assuming a. internal diameter tolerance of10 rs 0.005 in. and a wall thickiiess tolerance of

- 0.01 in. the above method of dimensioning wouldpermit a tolerance cn .i. internal dia.neter of0.025 in., which woul4 J .;eneral be ace -ptable

--- o. -- for separate-loading amrrunition.

W E OF OVN With fixed ammunition, however, the internalI -outh diameter is critLal s it controls the

SO CL~c!G CASE ANO PROJECT. minterference of tha case on the projectile; andFigure 4-A;4. Interference of cartridge case the wall thickness is critical because it con-

and projectile trois the strength of attachment as well as theclearance of the assembled round in the gun

dotted curves show the maximum and minimum chamber.interferences for selected existing ammunition.

Having fixed these two dimensions, one cannotThe thickness of the case mouth is governed logically add external high and low dimensions,by .wo considerations: but the manufacturing and inspection depart-

1. Strength of attachment of the cartridge ments insist on a control at this point. Acase to the projectile rather unsatisfactory compromise has there-

2. Sealing in the chamber upon firing, fore been agreed, of giving a high (only) externalFor a given hardness, a thin mouth would be diameter calculated from the additions of twoexpected to seal better than a thick mouth, but high wall thicknesses to the low internal mouththe thickness must be adequate for the strength diameter.of attachment. It should be borne in mind thatonce the dimensions of the chamber have been 4-89. Internal Contour of Case. After drawingfixed, the mouth thickness car. only be increas- and before tapering, a cartridge case is paralleled at the cost oi reduced clearance in the externally, but to facilitate stripping the casechamber. from the punch the inside of the case will have

The length of the parallel inouth of the cartridge a constant taper from th.• mouth to a pointcase is controlled by thE shape of the chamber where the thickening for tria base commrnces.and the width cf the rotating band. However, togive the maximum possible strength of attach- The internal contour in the base must be con-ment, it is desirable that the case parallel be sidered in conjunction with the gun design andat least as long as the portion of projectile to working conditions, but the general trend isthe rc-ar of the rotating band. indicated in figure 4-25. The contour of figure

4-25a is favored for the smaller sizes of case,For conventional projectiles, the surface finish but in the larger sizes (over about 3 in.) theafter mouth boring is unimportant, but for contour of figure 4-25b is preferred.skirt-banded projectiles (for example, discard-ing-sabot shot) and for projectiles where the The distance to points x and y is stated on thecase is attached over the rotating btnd a smooth design. The radius (R) is invariably left open,case mocth is essen'ial; the case design should but is virtually fixed by being centered on acarry a note to the effect that the "mouth of case line through x parallel to the base and drawnmay be bored, but a smooth finish is essential." tangential to xy and to the base thickness line.

4-124

B[ST AV~iLABLL COPY

Early designs of the case showed a radius0.4 D ,approximately equal to the internal diameter

1-0.2 0 of the case, connecting point y to radius R.This contour, *while possibly permitting a bet-ter flow of metal in drawing, wave a very tTickwall in the region of point x. The contour hasbeen replaced in new designs by the contour

PR_ THIS ANGLE TO BE shown in figure 4-25a or b, except for an oc-AFPROX. 40 BUT TO BE casional case design for medium- or low-pres-

•,D DMEN SION S AT X sr us..FIXED BY THICKNESS sr us.0 6 D * A U- Y

A__D ___ The base thickness and wall thickness at pointsy and x are at present controlled by low dimen-sions only. The high dimensions have pre-

CONTOUR ."A" viously been controlled by specifying the maxi-mum weight of the case.

In estimating the minimum chamber capacity,it may be assumea that the base thickness will

0.5 r be low* +10 percent and the high wall thick-ness low +20 percent for sizes up to- and in-

2 cluding 6 pounder, and the low A40 percent forsizes larger than 6 pounder. The high figures

__ are not, however, specified at present.

x YR 'SEE NOTE ABOVE 4-90. Additional Notes on Cartridge Case De-

R, a. Number of Draws. The minimum number

4,of draws and anneals required: during manu-S3i _facture used to be stated on the design with the

object of controlling, to some extent, the workhardening of the final product, but this practice

CONTOUR "B" has been discontinued as unsatisfactory sincethe case is now fully annealed between draws.

Figure 4-25. Internal contour c"'carlidgc An insufficient number of draws may result incases overworking the brass and producing a case

which would split upon firing, but this wouldRadius R can be fixed, but as it ip ;.,A critical be brought to light at proof.it is usualiy left to the manufacturer's discre- b. Hardness of Cartridge Case. The hard-tion. Theue radii will affect the flow of metal, ness figures of the finished case are quoted inand hence the hardness under the flange, and it the relevant inspection- department specifi.a-is undesirable to restrict the manufacturer un- tions, but as a rough guide, the hardness of tuenecessarily, mouth for fixed ammunition should be 60 to 75

D.P.N., and the "underhead" approximately160 D.P.N. Between these two points the hard-

The question of a blending radius at point y or nes3 should approximate to a straight lineof a targe radius joining point y to radius R has gradient.caused some controversy. Each manufacturerusually has a definite opinion on what he con- The hardness of the case (see p- ragraphs 4-79siders the best contour to avoid a hard spot at to 4-82) is particularly criticalforcertainhigh-the junction of the wall and base (point y). It pressure guns having a large elastic setback ofis usual therefore to allow, as an alternative to the breech bloc%; the gas pressure tends toholdcontour figure 4-25a, a blending radius at point the mouth of the -ase to the chamber while they equal approximately to 2 1/2 times the insidediameter of the case at that point. *See notes to paragraph 4-87.

4-125

(.4

base of the case is being forced back. The necessary. The effective chamber capacity forcase then must stretch, and if the metal will fixed ammunition is the volume contained bythenot stretch sufficiently separation will occur. cartridge case, up to the base of the shot, lssThis type of failure is more common in small the volume of the empty primer (Americanarms than in larger calibers. Too high a practice considers the filled primer). Thehardness will result in a high yield stress but volume of an empty rather than a filled primerlow ductility. To insure correct functioning in is subtracted, ar the primer magazine containssuch guns, it is desirable to work to both high gunpowder which may be considered part of theand low hardness figures on the case. propellant charge. The internal volume of the

c. Notes on Experimental Case Design primer thus becomes part of the effective chain-Drawings. On experimental cartridge-case de- ber capacity.signs, the following information should be given,in order that a complete history of the design The effective chamber capacity for saeparated

can be referred to: ammunition is the same as for fixed ammunition,1. Chamber design number and date extcept that the volume of the gun chamber2. Projectile design number and date around the base of the projectile to the rear3. Rotatilg band design number and date of the rotating band must be added, and the4. Diagram showing clearance of car- volume of the plug with which the cartridge case

tridge case in chamber is closed must be deducted.

5. Volume of projectile to the rear of the To determine the internal volume of the car-rotating band (case stop) tridge case, -the case is drawn accurately to

6. Effective chamber capacity with pro- scale and divided up into frustums of cones, andjectile in position. (In the ca-ce of an irregular portion in the base of the case. Theseparate-loading or separated ammu- volume of the frustums m=.y be calculated by thenition this will include the space around usual formulas. The volume of the irregularthe base of the projectile.) portion in the base of the case may be obtained

d. Control of Flatness of Base. Inaccuracies by the use of an integrator or by mensuration.and wear in the lathes may produce concavity In capacity calculations it is necessary to as-or convexity of the base in machining. Con- sume a thickness for the tapered portions ofcavity will reduce the thickmess of the base the wall to the rear of the mouth parallel, andtoward the center ard will increase the distance for this purpose the thickness at the junction ofbetween the primer and the breech block, thus the taper and the parallel istakenasbeing equal . -

reducing-the effective striker blow when per- to the high mouth thickness.cussion firing is being used. Convexity willresult in a reduced cartridge head space to- When a new gun is designed, the effective chaim-ward the center of the base, which if excessive ber capacity (E.C.C.) is first obtained by themay cause difficulty in closing the breech. gun designer, who calculates the gross capacity

of the chamber and subtracts an estimated4-91. Marking on Bases of Cartridge Cases. amount for the volume of the cartridge cace.Marking is one of the last operations in manu- This preliminary E.C.C. can only be regardedfacture, and is usually carried out with a group as an approximate figure that is subject to cor-stamp on a light power press. During stamping rection after the cartridge case has actuall)the case must be supported on a bolster which been designed. A small variation in the finalis small enough to pass through the mouth of figure from the original estimate of chamberthe case. It is therefore very desirable (though capacity is not serious, as the charge is de-not always practical) that all stamping should be termined with the cartridge case to give thewithin the diameter of the bolster (that is, the required ballistics. Once the charge has beendiameter of the mouth); otherwise, tilting of the determined, however, it is important that thecase and distortion of the base may occur case-to-case variation of the actual volumeduring stamping, of metal shall be within a defined percentage

tolerance.4-92. Effective Chamber Capac:ty. For a given 4weight of propellant, the resultant ballistics are -93. Typical Calculations for a Cartridge Caseinfluenced by the volume of the chamber; an Design to Siit a Given Chamber.* Figure 4-26

accurate estimation of this volume is therefore *See notes to paragraph 4-87.

4-126

__..........- 25.68 - .05

"- • _____24.0+.05• rL_ 22.17+.05 •

I ~18.5 +.05

. IDIMENSIONS OF CHAMBER 0 i

H A , '0 -- 0-C q

, -TAPER .02 INCHES PE!t INICH +1 0L.245 ON DIAMETER

H 24.09 L 2k.O4 -PR LLE

E)TERNAL DIMENSIONS OF CASE

.2554

.25 ,. .25

CASE STOP•

ENLARGED VIEW OF-SHOT SEATING

DETAIL OF DRIVING BAND

Figure 4-26. Typn:al chamber and details of rotating band

shows "t typical chamber together with details Low BB' 1/2 ',3.465 - 0.005, - 3.3 = 0.08 (196)

of the rotating band.DD' = 1/2 (3.44 - 3.3) = C.07 (197)

Assuming a minimL'm run-up to be 0.015 inchesand supposing D) to be the point at which the Thnbrtiwegtha

front edge E of the rotating band first meets the Thnbrrto;egttaforcing cone,

.168x0.01

The 24D 0.08 = 0.21 (198)

Dstace rommouh ofcas topoit ELow distance of D from chamber face (AD)== high 0.35 (193) 24.0 0.21 = 24.21 (199)

(See detail of rotating band in figure 4-26.) Substituting in equation (194) gives

High length of case from chamber faceHigh length of case (from chamber face) =23.845

, 0.35 .. 0.015 = low distance of D from AFR0T ENAETT

CAS STOP E TO DEAETT

IV - D

chamber face fTo) 14 s LOW S A D VIEW OF

AFille g urt-6 yi hame and details ofn roatn 'b-----MNd

DD 256 1/ (3.40 - 3.68 =15 C.0 (197

(Note that subtracting high AB from low ACIe 0

would give a shorter length for BC, but we re- A' 3' C C

quire the shortest length AD to ensure that a LO raIGH LO (HIGH)

high lengt c-se will not foul. See figure 4-27.) Figure 4-27. Slope of forcing cone

I

16 x-12.01

ThenB D .08 .21 198

LowditaceofD ro camerfae ADD~~stance~I fro mout of cas to pon 40 .1=24219

high 0.5 (193

MINI

*Assuming low thickness of flange 0.245 Length from flange to shoulder of case

High overall length of case 24.09 (200) = low length of chamber = 18.5

(As the precise position of the shoulder is

Allowing a tolerance of 0.05 gives somewhat indeterminate, tolerances are notgiven for this dimension.)

Low overall length of case = 24.04 (201)Diameter of chamber at shoulder

= H.4.985 L.4.975Clearance on Main Taper. This should be a

parallel clearance (see figure 4-22) of lowO.013 High case diameter at shoulderon diameter = low 0.0065 on radius. = low chamber - low clearance

= 4.975.- 0.013

Diameter of chamber at rear face = H.4.962 (205).- 5.35 t 0.005

Low case diameter at shoulder= high chamber - high clearance

Taper of chamber = 0.02 inches per inch = 4.985 - 0.003on diameter = L.4.952 (206)

Assume mouth thickness of case afterDiameter of chamber at 0.07 inches bra .6L0

from chamber face bor".ng = H.06 L.05

= 5 35 - (0.02 x 0.07) ± 0.005= 5.349* 0.005 Diameter of rear end of projectile= H.5.354 L.5.344 H.3.29 L.3.28

External diameter of neck of case after pro-

High diameter of case under head jectile is inserted:= low chamber - low clearance= 5.344 - 0.013 = H.5.331 (202) High = 3.29 4 0.12 = 11.3.41 "

Low = 3.28 + 0.10 = L.3.38

Allowing a tolerance of 0.01 gives the low di-. Diameter of chamber parallel = 3.465 ± 0.005

ameter of case = L.5.321 (203) = H.3.47 L.3.46

Low clearance on diameter = 3.46 - 3.41= L.0.05

(For calibers less than 3-inch, tolerance shouldbe reduced to 0.005 inch.) High clearance on diameter = 3.47 - 3.38

= H.0.09

Then Assume interference of L.0.01 H 0.025 (See

figure 4-24.)High clearance = high chamber - low case -

= 5.354 - 5.321 Mouth bore diameter (high) = 3.28 - 0.01

= H.033 on diameter = 3.27H= H.0165 on radius "204)

Mouth bore diarmeter (low) = 3.29 - 0.0253.265L

*The length of a cartridge case is invariablytaken from the bnslt to the mouth, that is, in- High external diam,:t,?r of moutheluding the flange. Had the high thickness of = low mouth bore diameter + 2the flange been used in the ibove calculation, 'high iouth thickness)then in manufacture it would be possible toobtain a high length cf case from the chamber = 3.265 + 0.12 = H.3.385 (209)face in excess of 23.843. (See paragraph 4-88.)

4-128

°*..

To Obtain Length of Parallel Mouth. The The volume of metal containpd in the case isclearance of the conical portion of the case ordinarily obtained by using the volume of aabove the shoulder within the chamber should similar, previously designed, case for an ap-be constant and equal to the clearance on the proximation. When possible, Frankford Ar-main body taper. senal solves the design problem by finding a

case already manufactured and having approxi-Using mean dimensions mately the same volume as the required case,

but which takes a larger caliber projectile. tByTaper of coned portion of chamber necking this case down to the required size, a

4.98 - 3.465 satisfactory new design can be established. This- 3.67 procedure not only simplifies the design prob-= 0.4128 in. per in. on diameter (210) lem, but also expedites manufacture, since,

with the exception of the tapering dies, existingMean diameter of shoulder of case = 4.957 dies may be used.

4-95. Trend in Specifications for Cartridgeinsertion of shot cas 3.395 Cases. Frankford Arsenal recommends that

the major reliance of quality in the production

Length of coned portion of case of cartridge cases be placed upon functionaltests. They feel that the fewer the restrictions

4.957 - 3.395 placed upon a manufacturer, the more likely0.4128 he is to find it possible to reduce the cost of

= 3.783 (211) producing a satisfactory product. It is recog-nized that in some instances the effect of

rheoretical length of parallel mouth of case changes in accepted methods may net be im-mediately perceptible. One example of this

= High overall length of case type was the high notch sensitivity of the bases- (low flange thickness + length to shoulder of non-heat-treated steel cartridge cases at

i length of coned portion case) low temperatures. This high notch-sensitivity= 24.09 - (0.245 . 18.5 ! 3.783) = 1.56 was not predictable, and did not show up until

low-temperature firing tests were performed."In instances of this sort, it is necessary, of

To obviate fouling in the chamber this must be course, to make definite specific-tions for heatregarded as a low dimension; allowing a tol- treating.erance of ±:0.02 inch gives a dimension of

Figure 4-28 shows the format used for draw-1.58 ±0.02 (212) ings of steel cartridge cases. Figure 4-29

shows the format for brass cases.NOTES ON AMERICAN PRACTICE

4-96. Bullet Pull. Bullet pull refers to the4-94. Design Procedure for Cartridge Cases. straight pull necessary to remove the pro-In order to design a cartridge case, the re- jectile from the crimped case in a round ofquired internal volume and the maximum length fixed ammunition. Correct bullet pull is re-of the case must be specified. The external quired in order t, obtain proper Internal bal-volume of the case is determined by adding to listic characteristics. Propellant pressurethe required interior vohlme the volume of the must be allowed to build up to a minimum valuemetal in the case, the volume occupied by the 'efore the projectile leaves the case. Exces-portion of the projectile that projects into the t ive variations in bullet pull from round tocase, and the volume of the primer. (The r,'und may cause the muzzle velocity of the pro-primer charge is not considered to add to the jet tile to vary accordingly, and consequentlyeffectiveness of the propellant, hence the volume ma., result in excessive dispersion of theof the primer tube is considered as if it were rou,,ds. Bullet pull is also highly importanta solid rod) When'determining the length of the in rounds used in automatic weapons. If In-case, the maximum length perrmlssible is usual- suffirien. iullet pul'l exists, the case may be-ly used in order to obtain minimum body di- come detached from the projectile during theameter. loading cycle.

. 4-129

0,

-0 o

, Ll* 1~1i-14

-0 #

lilit l~it

4--4-3-

I, i ifil I, i .=

c. it] i ý,

YIN;

.. . . . ,13- 'I i -"

H !I.

"i .- a

.3 :• • r--I -- I, i

:'I i ~ l+..t •- + hI I.

li--• -i- ii ' •

I i1 --.. . .""" -- I' 1-1.1 Il

Is ----. -, J ",,.

II

4-131

4-97. Methods of Achieving Desired Bullet culties. Under the action of the propellantPull. The desired bullet pull may be obtained gases, the metal in the crimp expands to theby means of (1) press fitting of the projectile wall of the chamber and, due to the highlyin the cartridge case and (2) by machining a strained condition of this metal, sufficientcrimping groove into the projectile and crimp- recovery does not take place.ing the case into this groove.

a. Press Fit. The amount of bullet pull 4-98. Effect of Method of Crimping. Twothai may be obtained by means of the press methods of crimping are in use: (1) press-fit is limited by two considerations. Both type crimping, and (2) rubber-die crimping.cjasiderations ire dependent on the fact that, a. In press-type crimping, the case isfor a metal of a given modulus of elasticity, crimped to the shell by means of a form toolth.- tangential force that can be applied by the in a mechanical or hydraulic press. Thispress fit is determined by the thickness of method has an inherent difficulty in that thethe neck of the cartridge case. These limits- tool must be properly alined with the crimp-tions are: ing groove. Since the projectile is inside the

1. The absolute limit is set by the fact case, the alinement cannot be done visually butthat the outside diameter of the case at the must be done by means of an alining jig. Var-neck must be 'css tha, the outside dia.meter iations in the position of the crimping grooveof the rotating .ani. may result in the tool's iot falling at the exact

2. The manufac'uring process (drawing) position required. This results in the metal ofimposes a practical limit on the thickness the case beicg excessively strained in the areaof the neck; this practical limit is usually where the crimping tool forces it against thewell below the absolute limit, edge of the crimping groove. This effect is notb. Crimping. The amount of bullet pull re- easily noticed during inspection, but has given

quired, beyond that obtained by means of the rise to extraction difficulties during firing.press fit, must be obtained by crimping th±! b. In rubber-die crimping, the projectile iscase to the projectile. The amount of pull placed inside the case ard a closed rubber bagobtained depends upon (1) the physicals of the or a sclid rubber ring is fitted over the neck ofmetal of the case, (2) the length of the crimp- the case. In the use of the rubber bag, hydraulicing groove, (3) the depth of the crimp, (4) the pressure applied on the inside of the bag forceswidth of the crimping groove, and (5) the num- the metal of the case into the crimping groove. ..ber of crimping grooves. In the use of the solid rubber ring, compressing

1. The physicals of the metal are not the ring by a mechanical or hydraulic pressordinarily controlled in order to affect the forces the case into the groove. Rubber-diebullet pul). In the case of steel cases, how- crimping does not present the alinement diffi-ever, the mouth must be soft enough to per- culies that press-type crimping does. It ismit the crimp to be made without cracking difficult, however, to make an interruptedthe metal. For that reason, cases that have crimp by this process.been overall heat-treated must be mouth-annealed before crimping. 4-99. Materials for Cartridge Cases. Brass

2. The length of the crimp may vary from strips or disks of 70/30 composition were useda full crimp, around the entire periphery of almost exclusively in the manufacture of car-the case, to an interrupted crimp that makes tridge cases prior to World War II. Presentuse of only a small portion of the available specifications allow:circumferential length. Aninterruptedcrimp 68.5 to 71.5 percent coppercan be used only when press-type crimping 0.07 percent maximum of leadis employed. 0.05 percent maximum of iron

3. The depth of the crimpi-,g groove is 0.15 percent other materials butlimited, for any given width of groove, by not over 0.006 percent bis-the physicals of the metal. Depth is further muth and 0.0001 percent mer-limited by the requirement that the crimping cury; remainder, zinc.groove must not be so deep that it weakensthe wall of the projectile. In the annealed state, the minimum tensile

4. Excessively wide crimping grooves strength may vary between 40,000 and 45,000have been found to cause extraction diffi- pounds per sq in. (depending upon the thickness

4-132

BEST AVAILABLE COPY

of the sheet or disk) with corresponding mini- cases. The height of the primer boss is shownmum elongation of from 60 to 40 percent. In in column P; P - R is the height of the primerthe cold-worked state, the tensile strength may boss above the bottom of the cavity of the case.vary from about 50,000 to about 100,000 pounds This dimension (P - R) is determined entirelyper sq in. Cold work produces plastic de- by the dimensions of the heading mandrel. Toformation which not only increases the tensile allow for wear and recovery of the metal afterstrength, but also increases the yield strength pressing, a rather generous tolerance is usuallywhile decreasing the percent of elongation, allowed. But, because the outside of the headisCold working sets up stresses whose magnitude machined, the tolerance of the head thicknessdepends upen the amount of plastic deforma- may, if necessary, be held quite close. How-tion, these stresses may cause surface cracks ever, 0.01 in. is usually allowed for the smalleror, in the case of thin sections, complete calibers, while as much as 0.05 in. may becracks in the finished cartridge case. The allowed for the larger ones.stresses are relieved ty low-temperature ~'n' 4-102. Flange Thickness affects the seating ofne-tling. the complete round when it is loaded into the

Steel had long been considered as a substitute gun. This thickness is obtained by machining,

for brass in the manufacture of cartridge so that a fairly close tolerance is practicable.

cases; not until World War U, however, did the It rarely exceeds 0.01 in.

shortage of copper and zinc force an accelera- 4-103. Primer Hole. In cases designed for usetion of the development of steel cartridge cases. at chamber pressures in excess of 40,000 psi,

Present specifications (1955) advise the use of a screwed-in primer is used; for pressures

MIL-5-3289, generally in the spheroidized a below 40,000 psi a forced fit is used to hold the

nealed condition. This steel has a carbon con- primer In place.

tent of 0.25 to 0.35 percent. It may contain a 4-104. Thickness at Mouth. In the taper draw-maximum of 0.045 percent phosphorous and ing operations, the walls of the case will thick-0.055 percent sulfur. Steels with lower carbon en; the amount of thickening depending on theor manganese content cannot be properly heat amount of taper: the greater the taper, thetreated. greater the thickening will be. Usually, the

friction of the die will prevent any appreciable

4-100. Base Rupture of Steel Cartridge Cases. increase in the overall length of the case. ThisIt has been found that base rupturing of steel thickening of the wall cannot be directly con-cases at low temperatures is almost always trollod, and the final wall thickness at the mouththe result of small folds or discontinuities depends on (1) thickness of the walls before theproduced on the inside of the base during the taper draw, (2) diameter of the final taper drawheating process. Discontinuities, which under die at the mouth of the case, and (3) recoveryordinary conditions would cause no trouble, may or spring of the walls after leaving the die.cause trouble when the notch sensitivity of the Experience indicates that a tolerance of 0.01steel is increased at lower temperatures. It has in. is necessary for mass production.been found that this increased notch sensitivityat low temperatures is a property of non-heat- The thickening of the mouth that takes placetreated steels. The notch sensitivity of heat- during taper drawing is the primary factortreated steels is relatively unaffected by tem- limiting the amount of necking the case mayperatui e. Frankford Arsenal heat treats the in- undergo. The body of the case is rarely madener section of the base and sidewall of the case more than 1.5 calibers in diameter.at a temperature of 1,650°F, followed by a quenchin brine and a 7507F draw, to prevent these low- 4-105. Chamber Dimensions. Once the car-temperature base ruptures. tridge case has been designed, the gun chamber

DIMENSIONING OF CARTRIDGE CASE AND may readily be laid out by adding the clearance

CHAMBER to the outside dimensions of the cartridge case.The length of the chamber is determined by

4-101. Head Thickness. In table 4-29 the col- adding to the length of the case contained in theumn headed R shows the nominal head thickness chamber (1) the width of the rotating band, andfor certain representative service cartridge (2) the allowable travel necessary for the

4-1.33

i I I I , -

rotating band to engage the rifling. As smooth a chamber to prevent escape of hot gases. Sim-finish as is consistent with production is neces- ilarly, if the build-up of propellant pressure Issary if obturation and extraction difficulties are too slow, there also may be escape of gases.to be avoided.

4-106. Chamber Tapers. In guns using car- If the yield strength of the neck metal is too

tridge cases the taper of the chamber is made low, satisfactory recovery will not take placethe same as that of the cartridge case. In and extraction will be difficult.some chambers, the part that accommodatesthe straight portion of the case is given a Compromise. between the conflicting require-taper of 0.005 in. per in. on diameter. This ment; for extraction and obturation is there-taper has been found to facilitate the extraction fore necessary in specifying the physical prop-of drawn steel cases. In guns using bagged erties of the metal in the neck of the cartridgecharges, the chamber is not tapered. case. Brass cases* (modulus of elasticity,

15,000,000 psi), according to experience, should4-107. Protective Coating must be controlled, have tensile strength at the mouth up to aand tests must be prescribed by the designer maximum of about 55,000 psi. Steel casesof the steel cartridge case to ensure the ability (modulus of elasticity, 30,000,000 psi), accord-of the coating to resist corrosion and abrasion.Thickness of the coating should not exceed ing to experience, may have a Rockwell hard-

0.001 in. ness up to a maximum of B85 at the mouth.This corresponds to ,a tensile strength of

4-108. Nerk of Case and Obturation. Obtura- 82,000 psi.

tion, as well as ease of extraction, tends to 4-109. The Obturating Problem in Howitzers.dictate the physical properties of' the metal at The use of zone c rges in h owitzersc

the neck of the cartridge case. Capability The use of zoned charges in howitzers createsof holding projectile firmly is also important a unique problem in obturation. A cartridgein the case of fixed ammunitions case, designed (and heat-treated) to obturate

successfully when the greatest powder charge

Hot propellant gases must not escape between is used, may not obturate at the lower zone

the walls of the neck of the cartridge case and charge. Two methods have been tried byFrankford Arsenal to eliminate this difficulty.

the walls of the chamber. To prevent escape, The first of these (figure 4-30a) was to use anthe walls of the neck of the case must expand inetdbaplcdnthsrigtotonfoutward and begin to press firmly against the Inverted bead placed in the straight portion Ofouwards ofthechanmbegi teopres feir aginst a- the case at a point slightly below the base ofwalls of the chamber before there is any ap- the shell. It was hoped that this inverted bead

preciable forward movement of the projectile. would at as a th seal andert ef-•This desired expansion is possible because of would act as a labyrinth seal and permit ef-

Thisdesredexpnsin isposibl beaus of fective obturation. Tests of cases modified in

the impact nature of the propellant pressure.

The inertia of the projectile causes the im- this manner revealed that, although obturationmediate initial action of the propellant gases was improved, extraction difficulties were ex-

to stress the base of the projectile and the perienced. The second method involved thete use of two obturating beads in the straightwalls of the case. If the yield strength of the poto o the caser(fig bed The s

metal in the neck of the case is not too high, portion of the case (figure 4-30b). These beadsthis metal in the neck will be strained suf filled up most of the clearance space betweenthe case and the chamber. Successful obtura-ficiently to press firmly against the walls of the techamber during the short interval of time when tion was achieved with this design and no ex-

chamer dringthe horttraction difficulty was experienced.the base of the projectile is elastically de-forming and before the projectile moves for-ward out of the neck of the case.

4-110. Hardness Requirements. Hardness val-If the yield strength of the neck metal is too ues of various parts of the case for certainhigh, the straining of the walls of the case will representative steel cartridge cases are shownlag behind the propellant pressure. In this in table 4-28. In general, it has been foundinstance, the projectile will have begun to 'move by Frankford Arsenal that extraction diffi-out of the case before the walls of the neck are culties Lan be minimized by overall heat treat-pressed firmly enough against the walls of the ing.

4-134

manufacture. Hardness requirement at themouth is mandatory for acceptance.

4-112. Tensile Strength. Brass. Required ten-sile strength of walls of brass cartridge cases

INVERTED at the important sections are given in the/ BEAD specifications for manufacture of brass car-

tridge cases.a. Head. At the head, the minimum tensile

strength varies from 57,000 psi to 60,000 psi,depending upon the particular cartridge case.

b. Mouth. At the mouth, the maximum valuesrange fromi 44,000 psi to 54,000 psi, dependingon the particular cartridge case.

c. Shoulder. At the shoulder, the minimumvalues range from 47,000 psi to 50,000 psi.

d. Body. At the body, the minimum valuesrange from 62,000 psi to 67,000 psi.

A 4-113. Stress-Relief Anneal, Steel Cases. Thefinal taper draw gives the walls their "asdrawn" hardness and sets up stresses in thesteel that, if not relieved, may result in split-ting or rupturing of the cases. These stressesare relieved by a stress-relieving anneal. Thetemperature of the anneal varies from 6000 to

OBTURATING 8000F, depending on the composition of theBEADS steel. Fortunately, the anneal raises the yield

strength and, at the same time, increases theelongation slightly.

WRAPAROUND CARTRIDGE CASES

4-114. Wraparound Steel Cartridge Case. Thewraparound process for forming a steel car-tridge case has been studied along two lines,one a spiral wrap (not too satisfactory) and theother (more successful) a trapezoidal wrap.The spiral-wrapped design employs a strip ofsheet steel wound helically around a mandrel.In the more successful design, a steel sheet inthe shape of a trapezoid is wrapped around a

B mandrel and firmly pressed.Figure 4-30. Obturating beads

A double thickness of metal is usually provided4-111. Elongation. Minimum elongations at the at the neck and a triple thickness at the head.C and D sections (table 4-28) are usually The end ut the case toward the head is spunspecified to assure sufficient ductility to per- over and joined to the head (a seoarate piece).mit expansion without rupture. Experience in-dicates that the minimum elongation in the C The wraparound design is to be preferred forsection should be not less than 6 percent in one cartridge cases that have a relatively smallinch; in the D section, 4 percent in one inch. shoulder taper, that is, whose body diameter

is not much greater than the mouth diameter.Hardness requirements, except at the mouth,are furnished by the designer to the manu- 4-115. Trapezoidal- Wrapped Steel Case. Thisfacturer for the latter's guidance in controlling type of case has several advantages over the

"4-135

-' VI I 111I

S. . . .. . . . r . . .. . . . .. .. I i - r . .. .. I .. . .. . ... . . . .II II . ... II .. I IIIAI

Table 4-28

iran dness requirements, steel cartridge cases

C -j Z2 D DE

A S

RockwellCartridge case Dimension hardness

75mm T6B1 A 21.30 in. max.B 0.05 in. approx. B-92 min.C 3.5 in. approx. C-35 to C-42D 16 in. approx. B-95 to B-102E 1 in. apprjx. B-78 max.ZI* 3/8 in. max.Z2* 1/4 in. max.

76mm T19E1B1 A 22.830 max.B 0.40 in. approx. B-92 min.C 4.5 In. approx. C-35 to C-42D 13 in. approx. B-95 to B-102E 1.3 vi. approx. B-85 max.Z1 * 0.125 in. max.Z2 * 0.25 in. plus 0.25 in.

90mm T24B1 A 23.30 in. max.B 0.40 in. approx. B-95 min.C 6 in. approx. C-36 to C-44D 15 in. approx. B-95 to B-102E 1.2 In. approx. B-85 max.Zl* 0.125 in. max.Z 2 * 0.25 in. plus 0.25 in.

*Z 1 and Z2 represent transition zcne.

drawn case: it may be mad& by using corn- steels with a Rockwell B hardness of 65 to 80.mercial materials; no large-capacity presses Softer steels also have been found to performare required; and te bcdy may be formed by satisfactorily. The minimum percentage elon-conventional pyramid rolls available in corn- gation required is 8 percent, but 15 percent ismercial sheet-metal shops. Extraction diffi- ordinarily specified. The base may be forgedculties and Nbturation difficulties are mini- from steels having a yield stress as low asmized. 30,000 psi, with 35,000 psi the recommended

minimum. Free-machining steels have alsoThe body may be rnIled from 1010 to 1020 been used successfully for manufacture of bases.

4-136

....... .BEST.AVAILABLE COPY

Rigid specifications have not been found neces- neck, length of the base reinforcement, curvesary. All physicals are advisory, and all of chamber slope, and curve of forward slopedimensions other than those directly affecting were plottet4 separately against the caliber offit or intercl-angeability are advisory. For the the projectile for each of the current designs.

' most part, functional tests can be relied upon In each instance, a straight line or curve wasto indicate the acceptability of these cases. fitted to the data by eye. Where a large

amount of dispersion was present in the data,The interior edges of the sheets are ordinarily the slopes were drawn in such a manner as tochamfered so that an extremely sharp bend is favor the conservative values. The equationsnot formed where the sheet overlaps. In order of these curves were then determined, and theto prevent the overlap at the mouth from suggestion was made that future designs couldcausing eccentricity of the projectile in the be based on these equations.case, the upper edges of the trapezoid, whichform the mouth, are scarfed where overlap It is felt by both Picatinny Arsenal and Frank-takes place. Additional information on this type ford Arsenal that these equations may haveof case may be found ir. Section 6. some value in indicating trends. Inspection of

many of the curves, however, reveals that the.4-116. Characteristics of Present Cartridge dispersion of the data is so great as to pre-Case and Chamber Designs. Table 4-29 and clude reasonable extrapolation. In severalfigures 4-31 to 4-47 are taken from a Franklin cases, correlations have been drawn betweenInstitite report.1 The portion of the report projectile diameter and design parameters thatfrom which this material was abstracted was can have no real relationship to the size of thean attempt to extrapolate -the dimensions of projectile. One example of this is the volume

* existing cartridge cases to obtain advisory curve of the case versus the projectile diameter.dimensions for future designs. The volume of the case is determined by the

internal ballistician, and is obtained from aFlange diameter, case diameter at the breech, consideration of the type of propellant to beoutside diametcr at the neck of the case, used, the allowable pressure in the gun, andlength of the case, maximum thickness at the the required muzzle velocity. Given a series

S-. base of the case, thickness of the base flange, of guns with similar muzzle velocities, someI wall thickness of the case near the base, wall correlation with projectile diameter might be* thickness of the case at start of forward slope, expected, and actually "was obtained in this* thickness of the case at throat diameter, out- case. It will be noted, however, that theside diameter at the start of forward slope, greatest deviation from the mean takes placevolume of the case, length of chamber slope, for the three howitzers that have the lowerlength of forward slope, length of the case imuzzle velocities.


1. Cartridge Case and Chamber Design, Report No. 307 Part U, Franklin Institute.

2. Notes on the Design of Solid Drawn Q.F. Cartridge Cases, Technical Report No. R5030-48,Armaments Design Department, Ministry of Supply, Fort Halstead, Kent, December 1946.

-4

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4. X110 - 4

kL-I except for changesM jnoted.Sm astp A

Case Type -A Type- B

NO CALIBERe & Type 7 FNO C LB R Chamber cast A B C C, E IF G H i M N

20MM. M21AI ?1-2-119 A .976 .4w0 .328 .135 .766 .816 - .886 3.732 .250 .360 4.342 .846 .379

37MM, MARK 3 A 71.248 C 1.775 1.60 .63 .549 1.430 1.470 .670 - 4.352 .430 .908 5.69 .77m .32037AN, MARKI IA2

3 AND3 MARK I A281 71-2-73 C 11.735 1.565 .630 .549 13.430 11.473 .670 - 2.922 .120 .598 3.640 .600 .320

4 37MM, M i VMI681 71-2-% C 2.190 1.970 .630 .549 1.430 1.490 .718 5.960 1.28 1.51 85 1.010 .390

5 37110, M17 & M1761 71-2-100 8 7.035 1.970 .630 .549 1 1.430 1.490 .718 1.870 15.960 1.28 1.51 8.75 1.010 .390

13 40MM, M25 71-2-122 B 2.441 2.196 .630 .549 1.541 1.615 780 1.983 -9.74 1.770 .730 12.24 1.378 .600

7 4 , M581 71-2-130 8 2.441 2.196 .630 .5491 1.541 1.615 .750 2.008 9.74 1.770 .730 12.24 1.378 .750

8 57MM, M23A2 71-2-120 C 3.540 3.230 .630 .540 2.229 2.319 .187 14.20 1.950 1.250 17.40 ri 1.250 .490

9 75, M18 & 41881 71-2-71 D 3.426 3.193 .630 .549 2.918 2.998 .787 3.237 ]L504 .590 1.726 13.82 1.811 .49010 75MM, M5AI, TYPE 1-2 71-2-91 D 3.426 3.193 .630 .549 2.958 3.018 787 3.237 7.259 .750 2.681 10.69 1.811 .490

HOWITZER ____ __ 2.913 2.99375MM, WWl~I. TYPET 1- -n - -= 8 .3 .29 .5 .8 1.9 181 .9

I t 7t, SI1HOWITZER 71-2-129 0 3."26 3.143 .630 .49 2.918 2.OM'3 787 3.237 7259 .750 2.681 10.6 1.811 .49%0

2 7BU, Mr6 & M26B1 71-2-123 C 3.566 3.266 .630 .549 2.970 3.086 .787 - 2111 - 1.186 21.30 1.750 .6W

1 3 3 iNCH, MARK 2M2 71-2-95 0 4.270 3.900 .630 .549 2.970 3.00 .820 4.020 21.27 1.000 1.810 23.08 1.780 .450

14 9"a., M19 & M1981 71-2-112 0 5.150 4.700 .630 .549 3.534 3.654 1.000 4.850 17.97 3.50 2.23 23.70 2.200 .700

5 105MM, Mo 71-2-97 0 6.25 5.80 .630 .549 4.115 4.235 .875 .595 24.37 3.75 2.25 30.37 2.51 .790

105M T, M14&M146 1-2-101 C 4.70 4.35 .630 .49 4.143 4.3 .44 .29 - 1.35 14M. 1.77 .5

17 129DM, M24 71-2-U13 0 7.55 7.05 .630 .549 5.434 5.546 1.10 7.20 17.60 12.17 3.03 32.8 2.55 .8W

DIMENSION FORMULA ! 2 ! •FOR - --. . -,. ,

APPARENT PRESENT STO .•Ii C C L

0 .. Z AFIGURE NO. 4- 31 33 -2 43 44 5 45 3

A s BEST AVAILABLE COPY

Table. 4-29Characteristics of present -'artridge case and chamber design

-N

R_

NOTES:

csk I- Toper computed on basic dimensions.)T ICKNESS) V(TICKNES) 2- Max. and min.diameter of rotating

<9 U a 0- a • bond used in computing allowance.

Rotating bond assumed to strikechamber at crest of bevel.

Same as type-A Some as type-Aexcept for changes except for changesnoted. noted.

Type -C Type- D

Ty Cat P" s. Oim.-A Taper-B

.846 3 1 . 2 Cu. In. P•ids Velocity I. Mn. G. Case TaperI846 .378 .233 .098 .118 - .049 .034 .02 5 .02A878 .5359 .950 2.40 23 2850 .AM .00439 _ .06

.77 .320 .160 .082 .079 - .050 .023 .020 .020 .01148 .J188 1.551 9.30 L92 29M 0015 .005 .62 .00571 .00063

.600 .320 .160 -on .079 - .050 .020 .020 .020 .A11 .6841 1.551 5.61 .91 2050 .105 .M .005 .0248 .21071.010 .390 .250 .100 .079 - .055 .032 .030 .030 .0061 .3438 1.930 20.90 L.91 1276 .010 .01.5 .00341 .00341 -

1.010 .39 .250 .100 .079 - .055 I. 3Z .030 .030 .00681 .3438 1.930 20.2 134 1276 .010 M .0 0341 .00341 -

1.378 .1 .380 .240 .079 - .067 .037 .037 .037 .03495 .1452 1.874 31.98 P.C._ 870 .o,5 .01742 .0,_11.378 .750 .24C .240 .079 - .070 .037 .037 .031 .034• 5 .1452 1.,874 31.98 .27 2870 .0175 .0174 .= I1.250 .490 .320 .200 .079 - .070 .045 .045 .045 .03000 .2518 2.810 104.0 J0 295 0,01)

Ull1 A4i0 .315 .115 .079 .229 .057 .040 .040 .040 .0075 .1449 3.083 94.2 12.44 1778 .014 .-O8 .00493 .00487 .0000L.11 .490 .315 .115 .079 .229 .057 .040 .040 .040 .00967 .1427 3.125 97.56 i8L76 7 .014 .008 A12 .00483 .00801

1.811 .490 .315 .115 .079 .229 .057 .040 040 .040 .00967 .1427 3.125 72.56 13.76 705 W512 .0W .00801.1760 1270LM5 .6W0 .380 .225 .079 - .070 .058 - .058 .0W0 - 3.068 149.0 32.8 2800035 .040 .05L78 .450 .320 .150 .079 .280 .0 .055 .A5 .055 .1521 - 212.0 123 2800 .111 11 O!3 .2 .00021Radius

270 • r'

''"

•

.•

.1G5 .02

200 .7o .390 .200 .079 .350 .130 .060 .060 .060 .01 7M .2131 4.40 322.0 2.4 27M .-A5 .003 .= 5 .008515 .00026•.51 .790 .560 .300 .079 .450 .120 .O6 .060 .060 .01672 .3107 5.40 638.0 X277 28 0 .0105 .003 OM .0083 .000291.77 .560 .360 .180 .079 - .0,0 .040 - .040 .00968 - 4.223 191.0 3.. 65 .0105 .003 .0450 .oD44 .0.55 .U .550 .300 .079 .450 .100 .0 .056 .056 .01283 .1120 6.830 1014.5 4M .0612 .0016415 .0002

45 35 36 37 38 39 46 47 40 41

84

I

)n basic dimensions.eter of ro t atingiputing allowance. D_ _E

iumed to strike A 1 C

of bevel

D:t .-A Taper-B _ I m.-C Taper- _ Oim.-E Oim.-F Tu-G Tra !-H

Mu. Mh n. Gun Case Taoer Max. Min. Gun Case A 0 Max. Min. Max. Min. Gn E.AI. Max. Min..00393 .00439 .00046 .26795 .018 .009 .013 .006 .08393

.006 .005 .0062 .A0571 .00063 .007 .002 .05235 .0942 .04185 .019 .011 .0115 .0075 .04206 .261 .093

.0105 .0 .00355 .00248 .00107 .009 .002 .0924 .34205 .24965 MS225 .0115 .0125 .0065 .03615 .532 .290

.010 .015 .00341 .00341 - .0125 .005 .16795 .1718 .00385 .015 .0045 .014 .003 .0757 .1375 .004

.010 .005 .041 .00341 - .0125 .005 16795 .1718 .00385 .115 .0045 .010 .0045 .0757 .1375 .000

1 .01752 .01742 .0001 .0689 .0726 .0037 .0178 .0075 .010 .001 .10325 .044 .024

.01757 .01742 .O1 .0689 .0726 .0m7 .0178 .0075 .010 .001 .10325 .044 .024

.01500 .01500 - .11975 .1259 .00615 .047 .027 .044 .031 .1515 .0602 .0472

• .014 .008 .00493 .00487 .00005 .J138 .0075 .0661 .07245 .00635 .023 .006 .0095 .0045 .06835 .188 .0065

014 .-N .012 .0493 .80 .Am .0025 .600 .07135 .01135 .033 .016 .0195 .0145 .0750 .172 .0075.0L .- O -031 .0048 ._01 .00 -02 - .0880 .02•00_ __ _ _

D00512 .00483 .00801 .0600 5 .1 039 .029 .0750 .157 .013_ _ _ _.0880 .0280 .075 .0 51 .0 _9 ._ __.75 .157_0 1

.00395 .00450 .00055 . . . .-01: .022 .1000 .348 .296

.00 O .00 .01.2n .01260 .00021 .PIG5 .006 .0225 .J5 .0065 .001 .1000 .136 .004

M.009 .003 .0005 .008515 .00026 .014 .0075 .10545 .100 .0006 .0245 .010 .022 .017 .1340 .111 .0168

1 .0105 .003 .00806 .00636 .00029 .01,15 .010 .02027 .022 .00173 .0245 .010 .017 .012 .1675 .170 .042

1 .0105 .003 .00450 .00464 .00033 - - - - .028 .0135 .011 .006 .12625 .125 .013

.00612 .006415 .00029 .05612 .06Nm .00012 .0666

4-139

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4-144

BEST AVAILABLE COPY

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4-145

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CALIBER X (IN.)

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At F ROTATING BAND AND RIFLING DESIGN

ROTATING BAND DESIGN a. The material must have a yield stresssufficiently low. to permit it to be engraved

4-117. Rotating Band. The rotating band is a easily by the rifling and yet high enough toring of easily engraved material, whose pri- prevent fly-off. Ideally, this would require anmary purpose is to engage the rifling in the anisotropic material. An anisotropic rotating-gun tube in order to impart spin to the pro- band material should have a low yield strengthjectile. Materials used for rotating bands in- in the radial direction and a high yield strengthclude gilding meLt., copper, sintered iron, in the tangential if the band is long, in the axialsoft (Armco) iron, nylon, and other plastics. direction if the band is short, or in both axialRotating bands either may be pressed into a and tangerntial directions if the band is of inter-seat machined in the shell body or, in the mediate length.case of the welded overlay type of band, they b. It must be soft enough to obturate ef-may be welded or brazed to the body. When fectively without wearing theguntube excessive-the band is pressed on, the seat is knurled or ly; at the same time, it niust not be so softmachined with wavy grooves to prevent the that particles will adhere to the rifling andband from slipping on the body. The seat may cause excessive metal fouling.be straight-sided or undercut. The undercut c. The material should not be subject toassists in preventing the band froir, flying off age-hardening, nor should its properties bewhen subjected to the centrifugal stresses in- greatly affected by changes in temperature.duced after the projectile leaves thte gun. Theuse of the welded overlay band obviates the 4-121. Rotating Band Design. After selectionneed for concern with either fly-off or slip- of the material, the design of a rotating bandping of the band. may be broken dowv Into the following pro-

-..... cedures.4-118. Function of Rotating Band. In addition 1. Determination of band outside diameter.to its primary function of imparting spin to 2. Determination of band inside diameterthe projectile, the rotating oand is also re- 3. Determination of equivalent width of band!juired (1) to provide obturation; (2) to center 4. Determination of profile of rotating bands,the projectile in the bore in order to limit yaw including cannelures and front and rearof the projectile inside the gun (initial yaw of chamfers, and true widththe projectile as it leaves the muzzle is a func- 5. Check the design for a possibility of fly-tion of the yaw inside the gun); (3) in the case off under centrifugal stresses, which mayof separate-loading ammunition, to hold the dictate the necessity for an undercut bandprojectile in the rammed position when the seat, or the use of welded overlaygun is elevated; (,il to provide a uniform initial 6. Determine location of the rotating band(shot start) pressure at which the projectile with respect to the base of the projectile.will begin its travel through the tube. Thischaracteristic enables consistent performance 4-122. Band Outside Diameter. Experienceof the propelling charge to be obtained. A seems to indicate that a good seal is providedsuccessful rotating band will perform all of if the diameter of the band is made 0.02 inchthese functions adequately in either a new or greater than the diameter of the grooves. How-a worn gun tube. ever, recent experiments i- ` ate that the high

radial band pressure (parag. aph 4-126) that may4-119. Other Methods of Imparting Rotation. be induced as a result of excessive positiveIn sonie special types of ammunition, use has interference between band and groove diameterbeen made of canted fins or jets to provide spin tends to cause rapid wear of the rifling.in lieu of the rotating band and rifling.

During engagement of the band with the rifling,4-120. Properties Required of Materials Used some elastic deformation occurs in the radial,in Rotating Bands. tangential, and axial directions. A properly de-

o 4i,,,_ 4-149 "

-.... . i- ii [- - ___n .. . . d - : . . I I I . . . . . . . .. - ' " i

signed band would utilize the elastic deforma- creases oelow the given value, the radial bandtion to provide continuously a new band surface pressure (paragraph 4-126) rises vpry rapidly,to replace the one that wears away. Thus, if even before the grooves have filled.one could predict the amount of wear that wil'occur, the amount of elastic deformation that 4-124. Determination of Effective Width ofwill exist in the band, and the axial flow of the Band. The effective width of the rotating bandband material, then it would be possible to de- is defined as the bearing area of the band di-sign a band that would obturate perfectly. vided by the average bearing height. The width

selected must be sufficient to ensure that (1)These factors, however, defy theoretical pre- the band will not wear excessively during itsdiction at present. In the absence of the ideal travel through the bore of the gun, (2) the bandsolution, Watertown Arsenal suggests that best will not fail in shear, and (3) the band will notresults might be achieved by designing the band fail ii. bearing.so that the volume of the material in the un-engraved band is just sufficient to flow into and The following procedure is suggested:completely fill the rifling grooves after engrav- 1. Determine the effective band width oning. Such practice could result in poor obtura- the basis of the British wear factor (paragraphtion, and the Watertown Arsenal further suggests 4-125).that a short sealing Up, with a diametergreater 2. Determine the radial band pressure forthan that of the rifling-groove diameter, be inthis width (paragraph 4-126).cluded in the band to provide the necessary ob- 3. Using the radial band pressure and theturation. width determined above, compute the force on

the driving edge of the band (paragraph 4-128).Another practice that shows considerable pro- 4. From the driving edge force and the bandmise is the use of expanding cups attached to and rifling geometry, determine the bearingthe base of the projectile. These cups, which stress (paragraph 4-129) and the shear stressmay be made of metal, rubber, or plastics, (paragraph 4-130). If these stresses are belowexpand into the rifling under the pressure oithe the yield strengths in bearing and in shear ofpropellant gases and provide effective obtura- the material, the width is great enough; iftion. They may be used either as a supplement these stresses are above the appropriate yieldto the rotating band, in which case the cup pro- strengths, choose a greater band width and re-vides obturation and the band provides spin, or peat steps 2 through 4.as a substitute for the rotating band, in which 5. Using the radial band pressure deter-case the cup must perform both functions. ThAs mined for the final band, check to be sure that

-type of rubber cup has been applied experi- excessive stresses are not developed in thementally to several models of canister round shell wall or the gun tube.(see paragraphs 2-266 throegh 2-278) and has 4been found very effective. 4-125. British Wear Factor. The British wear

factor method for computing band width as-

4-123. Determination of Band-Seat Diameter. sumes that wear of the rotating band is pro-

Past practice indicates that the depth of the portional t• the rotational muzzle energy of theband seat should always be greater than the projectile. 1 It is a wholly empirical method and

height of the band above the body or, if pre- requires a value for the wear factor that has

sent, the rear bourrelet of the projectile. Table been previously computed for a rotating bandsfor several repre- for use in a weapon similar to that under de-4-30 lists these dimensions sign. The wear factor (Fw) is defined as

sentative projectiles.Ew-Nhbý

Plasticity theory indicates that the minimum Fthickness ot band material below the lands whereshould be no less than 0.354WP, where Wr is the E = rotational muzzle energy of the pro-width of the land. This will ensure that the en- jectile, ft-tonsgraving pressure, before the grooves are filled, N = number of landswill be no greater than 1/2(2 ÷-T )K, where K is h = groove depththe yield strength, in pure shear, of the band b = groove widthmaterial. As the thickness of band material de- = effective width of band.

4-150 . 9

BEST AVAIBLA.LE COPY

MIN

Table 4-30

Rotating band :haracteristics

Width of Diam- Diam- Diam- Width of'I

Pro- Shape band eter eter eter of band Cazme- Dist.Caliber jectile of width of of band seat lure to base

_......._ band tol. band body seat I

37-mm M51 - 0.74 1.507 1.441 1.320 9.72 none 0.58-0.02 -0.006 -0.008 -0.008 +0.02 +0.02

40-mm Mk 2 • 0.345 1.630 1.547 L45 0.342 1 0.618-0.02 -0.004 -0.005 -0.01 +0.02 +0.015

(to nose)

75-rmm M48 J 0.49 3.011 2.933 2.75 0.47 none 2.26-0.02 -0.006 -0.015 -0.02 +0.02 -0.03

76-mm APC 1.02 3.098 2.980 2.76 1.00 2 0.79M62A1 -0.02 -0.006 -0.01 -0.02 +0.02 -0.02

90-mm M71 - 1.20 3.64 3.520 3.28 1.18 2 2.65-0.02 -0.006 -0 015 -0.02 +0.02 -0.03

105-mm M1 _ 0.81 4.223 4.10 3.94 0.79 none 3.08-0.02 -0.006 -0.02 -0.02 +0.02 -0.03

120-mm M73 _ 2.25 4.980 4.67 4.49 2.29 2 3.53-0.04 -0.006 -0.02 -0.02 +0.04 +0.02

155-1m M101 2.02 6.320 6.07 5.80 1.98 1 3.48-0.04 -0.008 -0.02 --0.02 +0.04 -0.03

8-in. M106 , 2.02 8.254 7.98 7.53 L98 3 6.00-0.04 -0.008 -0.02 -0.02 +0.04 -0.06

240-mm Ml14 ... 2.52 9.820 9.39 9.00 2.48 6.64-0.04 -0.008 -0.02 -0.02 +0.04 -0.06

E = L Mk2 (2 () 2 For most guns, the wear factor should be kept2,000 n d in the range of 20 to 25 ft-toss oer cu. in.; for

where howitzers, it may be as high as 30. These

n z twist of the rifling, calibers per turn values are for gilding metal. Values for otherV = muzzle velocity of the projectile, ft per materials are not available at this time.

secd - caliber of the projectile, ftM = mass of the projectile, lbs 4-126. Theoretical Prediction of Radial Bandk = radius of gyration of the projectile, ft Pressure. An approximate theoretical esti-

(The approximations of paragraph 4-128 mate of the radial band pressure at the instantmay be used to determine k2; the value of ccmplete engraving has been made by Water-of d used must be in feet.) town Arsenal.l

4-151

4.

Case I: Interference Ratio (IR) < 0 (that is, in- wherecomplete obturation after engraving) L = final band width = the width of the band,

with an IR of zero, having the samevolume of band material as the original

3[ rIR 1 band. For instance, "L" can be readily11G - derived if one considers the projectile

to be completely pushed through asmooth-bore cylinder having the same

where inside cross-sectional area at the rifled

Pb = radial band pressure (averaged over tube. As a result, the band materialthe lands and grooves of the rifling) will flow to the rear, increasing its

Y = yield stress of the band material length. The new length is defined as(refer to 'Discussion of Equations" .L."following) t f band thickness = average band diameter

IR = interference ratio after engraving, minus band-seat di-band dia. before engraviwr - aver. bore dia. ameter, all divided by two.

average bore diameter For complete obturation, the band pressure isaverage bore diameter assumed to be due to the pressure required to

fill the grooves, plus additional pressure caus-(The rifling diameter is measured ing the backward flow of the excess band ma-from groove to grtuove of the gun. terial. The bracketed portion of the formula

The average bore diameter may be represents the first effect (see case I) and the

obtained by dividing the entire bore additional term corresponds to the average

area - including grooves - by •,/4 pressure exerted by two rigid platcs squeezing

and taking the square root -of the an ideal plastic material. 3

result.) Discussion of EquationsWL = land width a. Since these equations are derived for anWG = groove width. ideal plastic material, they do not take into ac-

The formula was arrived at from the following count the effects of strain-hardening. In otherconsiderations: the first bracketed factor cor- words, they are applicable to a material that , -

responds to the indentation pressure on the has a flow stress which, at any portion of thetops of the lands, assuming the rifling is a plastic deformation region of the true stress-rigid material pressing into an ideal plastic strain curve, is equal to the yield stress. En-(rotating band) material. 2 The second bracketed gineering materials do not behave in this man-factor averages the pressure acting on the ner. The strain-hardening effect causes thelands over the entire bore surface. The final flow stress, which may be defined as thatbracketed term is inserted to compensate for stress at which plastic flow will take place, tothe flexibility of the gun tube and shell wall increase with increase in strain. If the yieldand incomplete bottoming of the band. It is stress for a nonideal material is used in theseassumed that the band pressure is linear with equations, the band pressure obtained will errrespect to IR up until the time of complete ob- on the low side. This effect may be compen-turation. sated for by choosing as the yield stress the

value of the flow stress for the average strainunder the land. The strain may be computed

Case II: Interference Ratio (IR) - 0 (that is, from consideration of the band and riflingcomplete obturation) geometry. It is equal to the band outside di-

ameter minus the rifling land diameter, alldivided by the band diameter minus the bandseat diameter. The flow stress may then be

[W L found by reference to the true stress-strain3. (W + Wwt curve in compression.

Y L . tb. These formulas should be used with cau-tion until sufficient experimental evidence at-tests to their validity. Several factors, such as

4-152

strain-hardening, strain rate effect, tempera- Values for coefficients of -friction under theture, and effect of gas pressure, have not been conditions experienced during the firing of ataken into account in these approximations. In gun are not available at present. 'Jntil s is-

S, particular, though the formula for band pres- factory values are obtained, the simpler for-sure for IR < 0 was based upon the best infor- mula given in the preceding paragraph may bemation available at the time, current investi- used.gations would appear to indicate that the lastbracketed term should be taken as unity. 2 k2G(t +tan 2li + e 6 r2.

c. These equations apply to an uncannelured R ..... a..a.F.band. Recent investigations indicate that band [hr(tan e - A) + 2Ak2(G tan 0 + I)] N1pressures may be considerably reduced by theuse of cannelures. 4 In effect, if the cannelureis sufficiently wide, so that it will not fill up whereduring engraving, the results obtained will be G = propellant force on the projectileequivalent to those that could be expected if the [maximum pressure (psi) x area ofband were actually made as several smaller the bore, in. 2]bands, rather than merely being dividea by k radius of gyration about the longi-the cannelures. tudinal axis, in.

coefficient of friction between band4-127. Driving Face Force--No Friction. The and riflingforce on tWe driving face of each land of the tOn 9 = tangent of angle made by rifling withengraved rifling may be closely approximated plane perpendicular to borefor a tube with uniform twist rifling by the fol- r = radius of projectile, in.lowing expression. 1 This equation does not h = distance along bore for one com-take into account the effect of Iriction between plete turn of rifling (twistincalibersthe rotating band and the riflirg as the projectile per turn x caliber in in.)passes through the gun. It is, however, quite Fh = force resulting from the radial bandsatisfactory for the range of accuracy present- pressure (radial band pressure xly required in rotating band design. effective band length x band circum-

ference)

,2k2 N number of lands."R = - p The following approximate values k2 may be

used.

where For HVAP projectiles, k2 = U.100d 2

For AP shot, k2 = 0.115d 2

R = driving face force For HE shell, k2 = O.140d2

k = radius of gyration of the pro.jectile about The term k2 G(t • tan B)1/2 in the numeratorn its longitudinal axis reprerents the portion of the force which re-n = n erin t , calrs. psuits from considerarion of the driving face;N = numbew of lands, the term tan 0 Fb(r 2 - k2 ) results from con-

Thedfollow.ng approximate values of k2 may be sideration of the friction acting at the top ofSused. the lands and the bottom of the grooves.

For HVAP projectiles, k2 = 0.100d2

For AP shot, k2 = 0.115d 2 4-129. Bearing Stress. The bearing stressFor HE shell, k2 = 0. 140d2 (Sb) on the driving face of the rotating band is

R4-128. Driving Face Force - With Friction. The Sb = Rhforce on the driving face of each land of the en-graved rifling may be closely approximated for where ý is the effective width of the band (in.)a tube with uniform twist rifling by the follow- and h is the average he~ght of the band land (in.).ing expression, which, in addition to the forcerequired to cause rotation of the projectile, also 4-130. Shear Stress. The shear stress acrosstakes into consideration the force needed to the base of the land of the rotating band isovercome friction on the driving edge and on the Ss Rto-v v t~e land and the bottom of the groove.' 15 b

E •

4-153

..........

where f is the effective width of the band and b self constrains the baid. Special methods haveis the transverse width of We rotating band been used to prevent fly-ofl. One of these,land. which has been ust'1 in connection with plastic

bands that are cast into place on the projectile,4-131. Profile. Table 4-30 illustrates the is to machine ridges iato the seat. Theseshapes of f inish-machined rotating bands used ridges are rolled, so that their tops mushroomon certain representative projectiles. The fol- and provide dovetails, which hold the band inlowing characteristics merit special notice, place. Another is the use of the welded over-

a. Most bands are tapered toward the front lay band, which is applied primarily to veryto match the taper of the forcing cone. thin-walled shell that either are too thin to take

b. In order to allow space for part of the an effectivp seat or that might collapse undermetal displaced by the lands during engraving, the pressure applied in a banding press or "tire-cannelures are provided. The cannelures are setter." Paragraphs 4-134 to 4-140, following,circumferential grooves cut in the band, into deal only with the problem rf calculating for re-which part of the excess metal ahead of th.3 tention of the rotating band by the straight-cannelure may flow. Theoretically, the can- sided and by the undercut band seat.nelure should provide sufficient space to ac-commodate the metal displaced to the rear 4-133. Calculation for Band Retention. 5 Theduring engraving; the purpose is to avoid an following method may he used to determineobjectionable fringe and to lower radial band whether or not a given band will be retaired Inpressure (paragraph .4-126). Actually, the flight. It may also be used to determlne whetherwidth, depth, and profile, of the cannelure are a long band, which calculations indicate will notdetermined empirically or experimentally. As be retained, may be retained by dividing it intoa general .-ule, the depth of a cannelure meas- two shorter bands.ured below the top of the metal immediately toits rear should not be greater than the depth The rotating band Is analyzed as a shell actedof the band metal beneath the cannelure. Can- upon by centrifugal forces. The action of endnelure root diameter should not be less than friction or undercut is considered to imposerifling land diameter, to minimize possibility simple constrzint on the ends of the band. Thisof band flyoff. analysis is then compared to two simpler anal-

c. Approximately the maximum metal dis- yses: one for short bands on the basis of aplaced ahead of a cannelure during engraving simple beam formula; and one for long bands onVEis D2 the basis of a "boiler" formula, which considers

VE -ba Ab1- t the band to be a simple unconstrained shell. A/length parameter (-) is developed, and values

where of v are determined such that the value of 7 may

Dba = maximum band diameter be used to predict whether the simpler beamAb = maximum bore area or boiler formulas may be satisfactorily usedt1 = width of a band, ahead of a cannelure, to determine the retention of the band. Limit-

the volume of which is equal to the ing values of 7, are chosen to peimA caicuia-actual band but which has rectangular tion by either of the simpler methods when thecross section. error introduced by so doing is no greater

than 10 percent.4-132. Band Retention. Band retention refersto thq ability of the rotating band to remain at- 4-134. Suggested Procedure for Calculation.tached to the projectile throughout its flight. 1. Determine geometry of equivalent rotat-During flight, the centrifugal forces caused by ing band for analysis (paragraph 4-135).the rotation of the projectile tend to cause it to 2. Calculate length parameter - (paragraphleave its seat, rupture, and fly off. This tend- 4-136).ency is opposed by the strength properties of 3. If Y is less than 0.63, use the beam anal-the material itself. In addition, the method of ysis (paragraph 4-137).attaching the band to the projectile may aid re- 4. If V is greater than 3.03, use the boilertention. In a projectile that has a nonundercut analy• ,s (paragraph 4-138).seat, the friction at the ends aids retention. In 5. If Y hias an intermediate value, use theone that has an undercut seat, the undercut it- constrained shell analysis (paragraph 4-139).

4-i54

BEST AVAILABLE COPY

6. If calculations indicate that the band will t14 + 4kt1 3t2 - 6kt12t22 + 4ktlt2S + k2t24

not be retained, consideration may be given to H -dividing the band into two shorter bands equiv- (I + k) (t0 + kt2)

r • alent to the single long band. This procedureordinarily will be found effective only foi long 3 r U - 6kT2 + 4kT3 +kT4(y greater than 3.03) or intermediate length U t 4kT - k) ( 4kT) kbands. In any case, the redesigned band should w( + k U + k-Jbe checked. (See paragraph 4-126 for effect whereof this procedure on radial band pressure.) T z i1

4-135. Equivalent Rotating Band Geometry. The t2 = thickness of equivalent band from seat toequivalent rotating band geometry for band re- band land, in.

tention computation may be determined as fol- k a band land width =a i(.)lows: band groove width al i

1. The band will be considered to have been t a band width, in.engraved by the rifling. For the case where k a I (land width equals

2. The outside, band land, radius will be groove width) the value of 6 may be obtainedequal to the radius of the rifling grooves, from the plot at the center of figures 4-48 and

3. The band groove radius will be equal to 4-49. Curves are given for values of 6 rangingthe rifling land diameter, from -0.2 to +0.5447.

4. The inside, band seat, radius will not take 4-137. Beam Analysis. The beam analysis isinto consideration the depth of the band that is made by means of the following equation. Thepenetrated by the knurling on the seat. That is, maximum permissible velocity or minimum per-it will be equal to the radius over the knurling. m i issible yess may bor or -

5. The band width will not take into account ssible yield stress may be solved forfront and rear charmfers. It will be considered /Vn 2 2 (m_• (D_•that the band extends radially from the outer i 44edge of the band seat. where

6. Where the long or intermediate band length V a velocity, fpsanalyses are used, the section of band con- n = rifling twist, calibers per turnsidered will extend from the center of one band OL - longitudinal stress at outer fiber, lbgroove to the center of the next. per in. 2

7. The profile of the rifling will be consid- g a acceleration of gravity, in. per sec 2

ered to be straight-sided in the analysis of the p = density of band material, lb per in.3

intermediate length band. Appropriate stress D - mean band diameter, ir.concentration !actor 0• account for the true a 1/2 (seat diameter + band groove di-fillet radius will be used -,-vb,• calculating the ameter)stress at the root of the band land. t shell diameter

t -band width, In.z quasi-equivalent rotating band thick-

4-136. Calculation of Length Parameter. ness parameter12t1 (1 ut2) t 2(t14 + 4kt13 t2 - 6kt12t2 2 + 4ktlt23 + k 2t24 )

D2 H 2 where (tl + t2) (2t1t2 + kt2 2 - t1 2) (1 + k)

where tI - thickness of equivalent band from seat

t1 f thickness of equivalent band from seat to band grt,-.ve, in.to band groove, in. t2 a thickness of equivalent band from seat

a, = Poisson's ratio (about 0.3 for most to band land, in.materials) a2

D = mean bzlmi diameter, in. k a-) ,/^ (seat diameter + band groove di- a1ameter) a 2 - band land width, in.

z shell diameter a1 - band groove width, In.

4-155

I., net L ATri BETWEEN BEAM AND BOILER THEORY VS. SHELL THEORY F T T T

ae *mt @s-t

0 -- 10 '0

Fo th cas whr ... an setn 4-38 .ole .nls Usngth oieranl

For ~ ~ ~ ~ ~ ~ ~ ~ ~ss th aeweek=Ian etn -3.Bier m nayisum pemisiblte veocityr oral

T tj minimum permissible yield stress may be

4T -6T2 4T3+ T4solved for. The following equation is used.

[1 T + 3T 2 + 4T3 *_~ 14T,4]=T

This analysis will give the solution for initial whryielding of the band. The graph (figure 4-50) whrmay be used to solve this equation in terms of V = velocity, fpsthe following parameters. n = twist of rifling, calibers per turn

aT= tangential stress in material, lb perG a geometry characteristic in. 2

D 2 g = acceleration of gravity, in. per; sec2

I AnAP = density of band material, lb per in.3

= TrinjFigure 4-51 may be used to solve this equation

S = velocity characteristic graphically.

('Atft 4-139. Thin-Walled Theory - Constrained Ends.kn4\ettl The constrained shell analysis assumes that

failure may occur at any one of three areas.QL =material or stress characteristic All of these must be checked. They are:

2'L&'in.\2 1. The band land surface

p= sc 2. The band land-groove fillet

4-156

* -* RELATION BETWEEN BEAM AND BOILER THEORY VS. SHELL THEORYSPECIAL CASE WHERE LA140 WIDTh a GROOVE WIDTH (6-11

-4 -J7

4 Im-

Im"

specialom cas of igre -5

Vf V veoiy p

~~~=44w a ~rlfU~ tist c~1ber pertIr

FCyp 4-49C.. [ elationbetwee bea snoie helly vesssellthero anr (oythspechicnes ofs original4-5

3. The inner surface of the band. equcivaety bhandtr oticimterisi

1.f oraina band, inrfce

Fyy It 134,4 (2\ tj ) tL icline wst, oeqalent band furom=~ 1 Drl 1--Li ett band grodt e, in.1

wher seatnt band iandte, in.2.p B il teso admtral e ...-and land-groove fillet 1/sta daee +bn-re on-e

3. dhe inersityrfband mfatherian, equiaern band to = tidei

g 144 acelraio of grvLy (! pert sec ban Troe in.

"Y1 9 IS k-11 2 5~j t z hickessof euivaentba -dfro

UCTIO4 A-A 4.*.Ve. iM

J(t e1:, tOHt, M kP 1WJ KWA? 1t +4t'4Tr)T £Pi1| +4TT• 9 j R9 k-I. T-~

* *,* I lm (I),l &u IPSS Aiu • yrn plIa..... .....-------- V

wourm ONAM ms"W O

Figure 4-50. Beam analysis

SL shell a2 = band land width, in.SL a L beam a1 = band groove width, in.

a beam a maximum longitudinal stress inbeam having same applicable di- T =t2

mensions as bane t1a shell = maximum longitudinal stress in

rotationally sy-ametric band0 T hoop a maximum tengential stress in ro- V3 =

tationally symmetric band, assum- Vi -

ing no end constraintaT shell a maximum tanger ial stress in ro- 4-140. Position of Band Seat. Positior of the

tationally symmetric band rotating band, and hence the band seat, affectsthe chamber capacity. The location is, there-

Given the value of y (paragraph 4-136), the fore, usually stated with reference to the basevalues of ST and SL may be obtained graphically of the projectile. From the standpoint of ob-from figures 4-48 and 4-49. taining minimum stress in the shell wall, the

rotating band should be located as close to the

1 6kT2 + 4"T3 + base of the shell as possible The position of1 1 tl + 4kT - the rotating band also has an effect upon the

(I + kT) (2T + kT 2- 1) j initial yaw I the shell, as well asupon the drag

1+UT - kT2 + 4kT3 + 24 in flight. All of these factors must be con-(sidered when determining the position of theT) (I + kT2) rotating band. Location is different for (1) flat-

base and (2) boat-tail artillery projectiles and,a2 in both instances, depends on whether the am-

ia munition is (1) fixed, (2) semifixed, or (3)separate loading.

4-158 *qp• . • •, .

4 1 +4-ý,

-1 1 P; I i I

r-il. E: 'H

4 1.1

moo

A I

1 -4- 1 ---- I-

I

aep

......... .....

!Max

FLIT F-

7 7-::

I All

TANGENTIAL STRESSES IN RO G- 13ANDDUE TO CENTRIFUGAL FORCES

USING 8BOILER8 FORMULA Wir aw)j[: K 11

2 0-f g144 1/-?-

Figure 4-51. Boilerformda

4-159

4-141. Flat-Base Pro.ectiles. 4-143. rropertles of Rotating Band Materials.a. Fix.d Ammunition. The rotating band acts a. Gilding Metal:

as the stop for the projectile when it is inserted 1. Composition.into the cartridge cazc. The length of the body Copper 89 to 91 percentbehind the rotating band should be sufficient to Zinc 9 to 11 percentprovide ample bearing surface along the wall of Lead 0.05 percent max.the cartridge case. The location of the band Iron 0.05 percent max.seat usually is from 1/4 to 1/3 of a caliber from Otherthe base. impurities 0.13 percent max.

b. Semifixed and Separate-Loading Ammuni- 2. Mechanical Properties.tion. In these cases the projectile is not pres-sed into the case, and the provision of adequatebearing surface is obviated. The location of the -l-

band seat usually is from 0.1 to 0.2 of a caliber Ten- I gation Rock-

from the base. sile Yield !in 2 in. well Shearstrength strength (per- hard- strength

4-142. Boat-Tail Projectiles. (psi) (psi) cent) ness (psi)a. Fixed Ammunition. As in the case of the

flat-base projectile, sufficient cylindrical sur- 1/2face must be available in front of the boat-tail hard 52,000 45,000 15 B58 35,000to provide a good bearing on the walls of the Ascartridge case. The location of the band seat hot

hotl7l0-1,00 4 F53 28.000usually allows about 1/4 of a caliber of cylin- roll-37,000 10,000 45drical surface between the band seat and the edbeginning of the boat-tail.

* b. Semifixed and Separate-Loading Ammuni-tion. Location of the band seat is usually such b. Copper and Alpha Brasses. Tests per-ais o provide from 0.2 to 0.25 ti a caliber of formed at Frankford ArsenalI yielded the truecylindrical surface between the band seat and stress-natural strain curves shown in figuresthe beginning of the boat-tail. Table 4-30, in 4-52 and 4-53.the column headed "Distance to base," showsthe location of the band seat with reference to Compositions of the materials used are given - -

the base for certain representative projectiles. in table 4-31.

Table 4-31

Material

OFHC Commercial Low CartridgeElement copper bronze brass brass

Cu 99.92 89.39 80.16 70.04Pb < 0.003 (ND) ND ND 0.01Fe < 0.003 0.01 0.01 0.01Zn ... 10.60 19.83 29.93Ni < 0.005 .........Mn < 0.003 (ND) ...... < 0.001Ag < 0.002 ...... < 0.02 (ND)Sn < 0.002 (ND) ...... < 0.01Bi < 0.0005 ...... < 0.0005 (ND)Al < 0.005 (ND) ... ... < 0.01P < 0.005 ... ... ...Sb ... ... ... < 0.005 (ND)Si ... ..... < 0.01,"

ND = none detectedOFHC = oxygen-free high-conductivity

4-160

BEST AVAILABLE COPY

90 s,,o_CURVE MATERIAL GRAIN SIZE (Mtm) CS

IA.R,, RAS.OS OOI CURVE[ MATERIAl. GRAIN SIZE (mullSCARTRIDGE BRASS .O:01o2II orCARIoG[ URASS 040-045

"" - o LOW BRASS .020-.025 t LOW IgASS 035"040o 3 COMdERCIAL BRONZE .045-020 s ro 3 CUR•iACIAL BRONZE .031

* . OF2C COPPER .045 2 4 , OC CO.PER 030-040

to 3.

0 50 0 o

0 0

400

0 V0

w hr

so- 30

0 .08 .16 .24 .32 .40 48 .56 0 .00 if 24 .32 .40 .44 .54NATURAL STRAIN (TOTAL) NATURAL STRAIN (TOTAL)

Figure 4-52. Compression test data for OFHC Figure 4-53. Compression test data for OFHCcopper and three alpha brasses, grain size copper and three alpha brasses, grain size

.. range 0.015 to 0.025 mm range 0.030 to 0.045 mm

"- - c. Sintered Iron. Tests performed by Purdue The iron powder w"s compacted in a double-University to determine the properties of sin- acting die (free-floating), the faces of whichtered iron yielded the curves shown in figures were lubricated with oleic acid and moly-sulfide4-54 through 4-65. The curves in the figures powder. The compacts of densities 4.4 and 5.5include: grams per cc were sintered at 1,100TC for one

Figure No. Title hour, while the compacts of density 6.4 gr:Lvnsper cc were sintered at 1,150°C for one hour,

4-54 through 4-59 True stress-true strain The compacts were unimpregnated.curves in compression

4-60 Variation of modulus of The sintered-iros compacts that were testedelasticity with density were pressed from a hydrogen-reduced mill

scale powder produced by the Pyron Corpora-

4-61 Variation of ultimate tention. The characteristics of this iron powdersile strength with density were as follows.

4-62 Variation of yield point withdensity Apparent Density Specific Density

2.33 grams per cc 0.416 cc per gram4-63 Variation of yield strength

with density Cnmpacting Pressures

4-64 Variation of elongation with Nominai ae,,-iiy (.,a.au, jc"d i4.4 5.5 6.4, ~density .

4-65 Variation of density with Compacting pressure (10.000 psi)final stress in compression 16-17 37-38 67-71

4-161q"•l •

0

000 -- 0/0.

-DENSIT 4.4

I-

2-2 o -LONGITUDINAL STRAIN

e -REDUCTION OF AREA

og J0 .0005 .0010 .0015

LONGITUDINAL TRUE STRAIN AND REDUCTION OF AREA

IN/INFigure 4-54. True stress-true strain curves in compression, density - 4.4

Chemical Analysis Screen Analysis either fail completely or wear to a point atPercent by Percent by which satisfactory accuracy and muzzle velocity

Element weight Mesh weight can no longer be obtained. The complete fail-

C 0.018 on 100 0.34 ure may be caLsed by excessive pressures de-Mn 0.39 pass 100 6.0 veloped iinside the tube as a result of the pre-Si 0.22 on 140 ence of foreign material, the development ofS 0.014 pass 140 23.7 progressive stress cracks, or premature func-0.014 on 200 tioning of the fuze of the projectile. PrematureP 0.012 on 200 functioning may be caused by sudden changesNi 0.07 pass 200 14.7 in rotation of the projectile that result fromMo 0.02 on 270 18.4 worn rifling. Failure by loss of accuracy orCu 0.06 n 325 velocity, which is by far the more commonV nil pass 325 36.5 mode, usually is caused by erosion of the rifling.Fe remainder 4-145. Erosion. Erosion may be defined as the

gradual wearing away of the material cf the boreEROSION OF RIFLING as a result of th3 firing of the weapon. Erosion

takes place throughout the length of the tube,4-144. Failure of the Gun Tube. Failure of the but is most severe in the region of the forcinggun tube may take two forms. The tube may cone (nomenclature of rifling and cartridge

4-162

S•" ' '- . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .

0~

0

T OENSITY-5.5U)

I- I

- - - a-LONGITUDINAL STRAIN

I-O - - - - - - - - - -

0 .0005 .0010 .0015

LONGITUDINAL TRUE STRAIN AND T*RUE REDUCTION OF AREA-IN/IN

Figure 4-55. True stress-true strain curves in compressiox,~ density - 5.5

cases is given In figure 4-66). Figures 4-6T 4-146. Effects of Erosion. Erosion of the ri-and 4-68 illustrate the effect of erosion and fling (wear ol the lands and advancing of theprogressive stress cracking on the 105-mm forcing cone) may have the following effects.howitzer, muzzle velocity 1,550 feet per second, 1. Loss in obturation, resulting in drop Inand on the 76-mm gun MI, muzzle velocity muzzle velocity.3,400 feet per second. Note that erosion is 2. Loss in shot-si. *. i-ressure, resulting inmuch more rapid at the higher muzzle vTelocity. slower burning cii dhe propellant and erraticErosion usually is specified in terms of the ad- internal ballistics.vance of the forcing cone, which is measured by 3. In separate-leading ammunition, which ismeans of a puUl-Gier gage. rammed into place against the forcing cone, ad-

4-16

4-16

:- o4.- LOGTDNLSRI

"-- -- -- -- -- - -- -- -- -- - -- -- -- -- -

10

0

0

~~~~~~OLONGITUDINAL STRAIN ADR.UTO FAE NI

Figure 4-56. True stress-true strain curves in compression, density - 6.4

vance of the forcing cone causes an increase in 4-147. Causes of Erosion. The causes of era-the chamber volume and a corresponding de- sion are (1) the scouring action of the hot pow-crease in the loading density a: the propellant. der gases, and (2) the interaction between theThis affects interior ballistics, gun tube and the rotating band. Factors affect-

4. Wear of the lands may permit a considering the rate of erosion are:able amount of projectile free run. That is, the 1. The type of metal used in the bore of theprojectile may travel for some distance in the guntube before there is obtained a sufficient depth 2. The quantity of propellant useduf engraving of the rotating band to impart spin. 3. The type of propiellant used (combustionThis may result in wiping off of the band lands, temperature, products of combustion)with attendant failure to attain full spin. In ex- 4. The material of the rotating bandtreme cases, sudden erratic imparting of spin .5. The radial band pressuremay cause premature functioning of the fuze. 6. Rate of wear of thp rotating band. (Ex-

5. Excessive wear permits too much clear- cessive "wiping off" of the band lands may per-ance between bourrelet and rifling. This may mit escape of combustion gases, with attendantresult in balloting of the projectile and in ex- scouring of the rifling. This band wear is acessive initial yaw, which in extreme cases can function of the band width.)restilt in tumbling of the projectile. 7. Muzzle velocity

4-164

I -T

a- 0.--------z|

z

2l I I p ' k

40

a 0 0-

ISd 0001- SSU1I.S _ui~

4-165

Ii w

Wd m

lz~ - -

0* p

-j w

4 0-2~

I~~d 001-2NS3u

4-166

BES AVA.-L COPY

- ~ 0

- S t0

0

OLL

2 w

hii

A~z z

in e iI~ 001- SUS .m

4-16

20 -

,o I i ! ,

-4'.3 1/ 15I., I// /-

J I

- -- - 00-TENSIO N --- 40 -COMPRESSION

0 -! 0. 4, 54 5 6 7 a DENSITY-GRAMS PER CC

DENSITY- GRAMS PER .CC

Figure 4-60. Variation of modulus of Figure 4-61. Variation of ultimate tensileelasticity with density strength with density

ui-_ ! /* . -

"I -- t i i i i i IIi "- -.

I8 0

0--- ---- ----- --- II- --.

II

418

2 -

0 CK

&.

Y. I .- TENSIO.N iiL..-4-~-~ '- o ENSION

-. - - - - 0 COMPRESSION

4 5 6 7 465 6DENSITY - G.'CC DNIYGASPRC

Figure 4-62. Variation of/yield point with Figure 4-63. Variation of yield strength.density . Mthdnst

4-168

4 - r / erosion, However, the precise nature of thiseffect is not yet known.

_ RIFLING DESIGN

---- In the design of a new gun and its ammunition,3- .. two important determinations must be made:

-/ (1) profile of rifling, and (2) twist of rifling.

4-149. Profile of Rifling. Design of the profileZ of rifling involves determination of

1. Number of grooves2. Depth of groove3. Width of land

_Z 4. Width of groove

Z 5. Radii, slopes, and chamfers.s sui

z4I.- 4-150. Dimensioning of Rifling. Figure 4-69Z/ shows the method used to dimension rifling.

- - - -- -The four reference circles (bore circle, groovecircle, land base circle, and groove basecircie)are drawn in first. In this figure

a = bore diameter (land diameter)b = groove diameterc = groove chord

0c . . . . d = land chord4 5 6 7 a e = slope of side of land

DENSITY - GRAMS PER CC f = angle of chamfer of land

Figure 4-64. Variation of elongation g = width of chamfer of land

"with density h = radius at root d1 landi = central angle d1 landj = central angle d1 groove.

8. Size and number of unburned propellant The arc intercepted by the groove chord on theparticles, bore eircle is the length of groove. The arc

intercepted by the land chord on the bore circle

4-148. Methods Used to Control Erosion. The is the length of land. The depth cf rifling is themost common method used to combat erosion groove diameter minus the bore diameter.is to use a liner or plating in the tube of thegun. Chromium, or some other material more 4-151. Rifling Standard Forms. The riflingresistant to erosion by the propellant gases than standard forms of drawings 15 OKD 2 and 15steel, is used. Another area that is being in- O 2A (figures 4-70 and 4-71) have been usedvestigated is the development of cool propel- by the Ordnance Department since shortly alterlants, which have less erosive effect than those World War I. The trend in modification af

• in use at present. these forms is toward a deepening of the

grooves on some newer guns. This is beingFrom the standpoint of the rotatir.g band design- done by Franklord Arsenwl, in an effort to re-er, the most important method is the reduction duce excessive erosion caused by the highof the radial band pressure and the supplying radial band pressures resulting from "over-of sufficient band width to withstand the driving- fill" of the grooves. Frankford reports it toedge load without wearing excessively. This have been successful.may be accomplished by designing for minimumor zero interference between band diameter andrifling groove diameter and by the use of can- The design of rifling of semielliptical and ofneluring. It is also known that the type of ma- pseudo-elliptical forms in order to reduceterial used for the bard affects the ratc of 6tress concentrations at the land root fillets

- ' 4-169

I

70 - *- ORIGINAL DENSITY- 4.4 g/cc --

*- ORIGINAL DENSITY-5.5 g/ce

A- ORIGINAL DENSITY-6.4 g/cc

5o0

40,

Z

Z 30 -7-

wz

0 - - -0Z"

S20 f

10 .0,

000,

01r0 10 20 30 40 50 60 70

FINAL COMPRESSIVE STRESS-100 PSIFigure 4-65. Variation of density with final stress in compression

has been contemplated, but no guns with this of the projectile. Most guns and howitzers inform of rifling have been made as yet. army service have uniform twist.

Both advantages and disadvantages have been4-152. Twist of Rifling. Two types of rifling claimed for increasing twist.have been used: (1) uniform twist, and (2) in- a. Advantages.creasing twist (gain twist). Twist usually is 1. Torques on the driving side of thespecified as n, the number of calibers for one lands and on the driving side of the bandcomplete turn of the rifling, and Is determined engraving are supplied more uniformlyby the requirements for the stability in flight throughout the travel of the projectile.

4-170

I(~~~~1WN OFSM .USYI

t~~~aw"LP if "aeqLEN" O "$

£dcaIwior OSLI WST SM as"

ofa AI*LI

,$Ga R 00 SOM LAGLCUERGN

OWAMAW orILLETCEUTUSUW~$a MUZZFGUEF ILIN WEMI

FIGURE AI SMALLG ARSUMLE

FIGrE0ARIDECS

-&M FOW! 4-171QM A-

-- '--i OpLo

orytt'4, t is ,

477

Figure 4-67. Erosion-stress damage, Figure 4-68. Erosion-stress damage,1OJ-mm howitzer M2A1 76-mm gun tube M1

2. Since the torque is applied more uni- contour of the engraved band.formly, the maximum shearing stress, actingto rupture the engraving, is lower. 4-153. Typical Values of Twist. These are

3. Some work has been done on the de- shown in table 4-32 for representative gunssign of guns with zero twist for the first five and howitzers (marked H).inches or so of the rifling, and increasingtwist for the remainder. It is thought thatthis type of design will help eliminate the Table 4-32

shearing of rotating bands by worn tubes inguns using fixed armmunition. In these guns, Vales of twistthe projectile is not rammed, and erosion atthe origin of the rifling leaves an unrifled Twist calibersgap, across which the projectile jumps when Caliber (uniform)

the gun is fired.-The projectile, when it en-counters the rifling in present- designs, is 75-mm MI 1 to 20•76-mam MIAl 1I to 40

subjected to very high rotational accelera- 90-mm M2 1 to 20tion, and, shearing of the band often results. 105-mm H M3 1 to 20b. The Major Disadvantage is that the con- 120-mm M1 1 to 30

tour of the engraving changes as the projectile 155-mm M1 1 to 25moves forward. This results in shearing of the 155-m H M1 1 to 25

metal of the band in the grooves of the rifling. 240-am H M1 1 to 25

The wider the band, the greater the changes of

4-172 - "

BEST AVAILABLE COPY

sary to assure the stability of a given projec-tile, refer to paragraphsq 3-1 through 3-22.

For uniform twist rifling, the slope of the ri-

h fling is constant and is expressed byh tan 9

The developed curve of gain twist rifling usuallytakes the form of the semicubical parabola

"9 \3/22 py

where x represents the travel through the bore,b y represents the distance through which a point

on the outside of the projectile has rotated,and p is a constant. This equation assumeszero twist at the origin of the rifling.

The slope of the rifling at any point may beobtained by differentiating:

&, 30l/2_...tan 0

dx 4p n

where n varies with the distance along the tube.

The rotational velocity of the projectile c atd any point in its travel is

2v tan 0C.

Figure 4-69. Dimensioning of riflingwhere

4-154. Determination of Rifling Twist. Muzzle v = velocity of translation of the projectilevelocity and twist determine the spin, the sole at any point in the bore, fpspurpose of which is to stabilize the projectile 8 = angle of twist of the rifling at the samein flight. If spin rate is too low, the projectile pointis unstable; if too great, the projectile may be = angular velocity of the projectile, radiansoverstable when fired at high angles of quadrant per secondelevation. For a discussion of the twist neces- d = bore diameter, ft.

4-173

*fly I

S ao- ItsI B

s--I~~~ 1!i 5 -E 1

~J. ~~i~VAN-

CHI

A Ei-

4-174

-197

.787 (20MM) RIFLING 3.543 (90MM) RIFLING

NO. OF GROOVES 9 NO. OF GROOVES 32

DEPTH OF GROOVES .015 DEPTH OF GROOVES 04

WIDTH OF GROOVES .205 WIDTH OF GROOVES .1978

WIDTH OF LANDS .068 WIDTH OF LANDS .150

1.573 (40MM) RIFLING \4.5-INCH RIFLING

NO. OF GROOVES 16 NO. OF GROOVES 32

DEPTH OF GROOVES .0225 DEPTH OF GROOVES .037WIDTHa OF GROOVES .220 WIDTH OF GROOVES .2945

WIDTH OF LANDS .069 wIDTH OF LANDS .1473

T.E WIDTHS, SHOWN, FOR LANDS

AND GROOVES ARE NORMAL TO THE AXISOF THE GUN AND ARE ON THE ARC.

ALLOWED VARIATIONS RL THE WIDTH0. LANDS AND GROOVES 16.004. UNLESS

OTHERWISE SPECIFIED.

DHIMENSIONS SHOWN FOR WIDTH OFCHAMFERS ON LANDS ARE MAXIMUM ANDX

MAY VARY FROM THESE OIMENSIONS TO

SHARP CORNER WITHOUT BURRS.O7HRFNISE ECCENTRICITY, BETWEEN BORE

2.244 (5M)RFIGAND OUTSIDE DIAMETER OF RIFLING, ISALLOWED FOR RIFSONG DEPTHS UP TO

NO. OF GROOVES 24 AND INCLUDING L45 AND .0025 FOR

DEPTH OF GROOVES 02 RIFLING DEPTHS OVER .045

WIDTH OF GROOVES 21736

WIDTH OF LANDS .120 TOLERANCES ON RADII IN 8OTTOMOF RIFLING .OIR-.005,.05R-008,OO2R-.0•,.024R-0I.

Ftgure 4-71. Standard rifling forms

4-175


1. Rifling and Rotating Band Design, Report No. WAL 760/410, Watertown Arsenal, Watertown,Mass.

2. Lee, E. H., and B. W. Schaffer, Some Problems of Plastic Flow Arising in the Operation. ofEngraving Bands on Projectiles, Report No. WAL 893/81-84.

3. Nadal, A., "Plasticity," McGraw-Hill, 1931, pp. 221-225.

4. Ross, E. W., Jr., Theoretical Investigation of Identation Pressures on'Rotating Bands, Re-port No. WAL 760/525, Watertown Arsenal, Watertown, Mass.

5. 3luhm, J. I., On the Influence of End Friction of Undercut Angle on the Failure of a RotatingBand Under Centrifugal Forces, Report No. WAL 760/520, Watertown Arsenal, Watertown,Mass.

6. Deformation Characteristics of Copper and Alpha Brasses, Franiford Arsenal Report No.R-1021.

7. Salmassey, 0. K., An Investigation of Properties of Sintered Iron. Purdue University, June1953.

4-176

. .1 1

- !

STRESS IN SHELL

LIST OF SYMBOLS

Symbol Definition unit

A Area of bore of gun sq in.a Linear acceleration ft per sec 2

d Diameter of bore of gun (across lands) in.dl Inside diameter of projectile in.d2 Outside diameter of projectile in.

do Diameter of assumed shear circle in base of shell in.F Maximum force on base of projectile and rotating band lbFT Maximum tangentiaý force on projectile wall lbFW Hoop tension (force) in wall of projectile resulting from

rotation of shell lbF, Taiigential force at section of shell ibfo Setback force lb- Acceleration due to gravity ft per sec2

nI Total depth of filler from nose (head) in.h2 Depth of filler from nose end of cavity to section under

consideration in.I Polar moment of inertia lb-in. 2

Is Polar moment of inertia of metal parts forward of sectionwhen section is at front of rotating band, or rearward ofsection when section is behind rotating band lb-iz. 2

n Twist of rifling calibers per turnP Maximum propellant pressure (usually taken as 1.2 times

max. allowable pressure for gun) lb per sq in.Poh Filler pressure due to setback lb per sq in.POr Filler pressure due to rotation lb per sq in.

Ro i:side radius of projectile in.RI Outside radius of projectile in.r Bourrelet radius in.S Compressive strength of band lb per sq in.ST 1, ST2, etc. Tangential stresses lb per sq in.

SLI, SL 2 , etc. Longitudinal stresses lb per sq in.SR1 SR2, etc. Radial stresses lb per sq in.SSI SS2 etc. Shear stresses lb per sq in.So Static yield stress in tentsion lb per .;q in.SR Combined or resultant stress lb per sq in.T Torque applied to projectile lb-in.tb Base thickness in.V Muzzle velocity ft per secW Total projectile weight lbWS Weight of metal parts forward of section considered lbWf Weight of filler forward of section considered lb

Angular acceleration radians per sec2

Density of metal .n walls of projectile lb per cu in.SDensity of filler charge lb per cu iii.

Angular velocity radians per sec

4-177

-

INTRODUCTION cause the projectile to ballot (move from sideto side) in the bore. If excessive clearance

4-155. Failure of the Shell Under Stress may between bourrelet and bore exists, the ballotingbe s-id to occur when stresses are sufficient forces developed may be sufficient to flattento cause enough deformation of the shell corm- the lands of the rifling. A secondary effect ofponents to prevent proper functioning of the excessive bourrelet clearance *is to induceshell or cause damage to the gun. A certain large values of initial yaw when the projectileamount of deformation can and will take place leaves the gun (see, "i paragraphs 3-23 to 3-4Pwhen the shell is fired. However, if the de- the discussion of initial yaw). Balloting mayformation is not great enough to cause pre- be minimized by designing the shell for mini-mature detonation of the explosive filler, the mum bourrelet clearance. Present practiceshell is considered to be successful, stress- defines minimum bourrelet clearance as 0.002wise at least. This criterion is much less in. plus 0.001 times the caliber in inches, withstringent than that used for machine parts, a minimum of 0.004 in. for 37-mm and smallerwhich allows only elastic deformation. How- projectiles. A tolerance of plus zero minusever, 4t is based on the iact that a shell is 0.005. in. is specified for all projectiles. Thus,designed to be used only once, and hence this projectiles may bIr designed for a maximumlimited amount of permanent deformation may clearance of 0.007 in. pluis 0.031 times thebe permitted. caliber in inches or, for 37-mm and smaller,

0.009 in.

4-156. The Problem of Stress Analysis in the d. In ioading mortar shell there is someshell resolves itself into the following three possibility of damage to the fins as a resultphases. of dropping the projectile into the bore. How-

a. The determination ot the maximum ever, the magnitude of these forces is so smallforces acting on the shell during firing, that compared to those applied by the pressure ofir, of the loading conditions on the shell, in the propellant gases that it can be discounted.the gun. A greater possibility of darnage to mortar shell

b. The determination, for critical points in is that from rough handling and the uneventhe body of the shell, of the principal stresses pressures resulting from turbulence of theresulting from each of these forces,. propellant gases. The effect of both of these

c. The utilization of yield criteria to deter- can be minimized by enclosing the fins in amine if the stress state at critical points of the shroud.shell body is in an elastic or plastic state ofdeformation. 4-158. Forces During Firing. When the gun

is fired the following forces are normally con-

FORCES ACTING ON SHELL sidered in deriving shell stress formulas.a. The force from the pressure of the pro-

4-157. Forces During Loading for Firing. Dur- pellant gases against the base of the projectile,ing loading, the following forces must be con- the rear of the rotating band, and the projectilesidered. wall to the rear of the rotating band.

a. Forces caused by eccentric loading of b. The inertial or setback forces inducedthe shell can cause bending stresses in the in the shell filler and the shell wall by thenose of the shell, which might tend to loosen forward acceleration of the projectile.the bond between the armor-piercing cap and c. The tangential inertia forces in the wallthe body of the APC shell, or between the of the shell arising from the angular accelera-windshield and body of the projectile. tion imparted to the shell by the rifling.

b. Excessively hard or eccentric ramming d. The centrifugal forces inducea in the wallof the separate-loading shell can cause flatten- of the shell and in the filler by the rotationing of the lands near the origin of the rifling, imparted by the rifling.

c. Eccentric ramming may cause cocking of e. A radially compressive force applied atthe proj-ctile in the chamber. If the projectile the seat of the rotating band when the band isis cocked, a transverse moment will be pro- engraved by the rifling in the forcing cone ofduced by the gas pressure when the gun is the gun. A considerable amount of experimentaifired. This moment, together with the forces work must be done before this force can beinduced by the spinning of the projectile, can precisely evaluated. Although it is known to be

4-178

of relatively large magnitude, in computations subparagraph 4-177d). For the purpose ofof total stress on shell it has been disregarded stress analysis it is convenient to compute thewithout apparent bad effect on the design :.rnb- pressures in the charge, rather than the.lem. For further infrmation, see paragraphs forces. This pressure, acting normal to the4-117 through 4-154. walls of the shell, produces both a longitudinal

tensile stress and a tangential, or hoop, stress4-159. Force Resulting from Propillant Gas in the shell walls. The pressure poh at anyPressure. The maximum force (F) on the base section of the shell isof the projectile, the rear of the rotating band,and tho shell wall behind the rotatiag band, isequal to the maximum pressure of the pro- Po = (218)pellant (P) multiplied by the area of the bore g

(A). For design purposes, the maximum pres-sure is usually taken as the maximum rated Combining equations (218) and (215).copper pressure for the projectile.

F (213) poh 2 P (219)

4-160. Setback Forces.a. Settack Forces are caused by the accel- 4-161. Tangential Force. The tangential force,

eration (a) of the Frojectile. induced in the rotating band and transmitted to

F the wall of the shell, is caused by the angulara a - (214) acceleration. This angular acceleration (a)

W/6 may be computed from the linear acceleration,the twist of the rifling, and the diameter of

where, W is the total weight of the projectile the projectile.in pounds, and g is the acceleration of gravityin ft per sec2 . Combining equations (213) and 24ia(214),a nd12) a 24, a (220)

a . -Ag (215)W where n is the rifling twist in calibers per

turn, ... id d is thr caliber of the projectile inb. Setback ef Shell Walls. At any transverse inches.

section of the projectiie the inertia of the massof the metal paits of the projectile ahead of The torque (t), in lb-in., applied to the pro-that Section will exert a compressive force (f') jectile to give the argular acceleration (•) isin the projectile wall.

IT a- (221)',WI g

1=-a (216)g

where I is the polar moment of inertia of the

where W' is the weight of metal forward of the projectile in lb-in. 2 , and T is in lb-in. The

section and a is the common a,.celeration of all tangential force is

parts of the projectile, assumhig the projectileacts as a rigid body. Combining iquations (215) Tand (216) (

f, W Combining equations (222), (221), (220), andfW PA (217) (215).

c. Setback of Filler. The filler charge of a F 48• IPAprojectile is considered to act as a iiquid (see T 48WP (223)

4-1.79

As a simplification, assume Combining equations (226) and (227)

A 4 por 1.23 ( (228)

F T = 1 2 "2 1 p

nW (224) 4-163. Tension .n Wail Resulting from Rota-

tion. The stress in the shell wall, resultingfrom the rotation of the projectile, Is small

since FT is directly proportional to propellant rompare to the srsa ed the seackpresure maimu-FTwilloccr wen ro- compared to the stress caused by the setbackpressure, maximum F. will occur when proof the filler. Therefore, in order t,ý avoid thepellant'pressure is a maximum. This force cope caultnreiedofndses

is of interest primarily in the design of rota- complex calculation required to find stressting bands. For shell design the average force distribution by a thick-cylinder formula, i. ibacting at. For gieln crodection ofthaege s rell i permissible to approximate the stress by con-acting at a given cross section of the shell is sidering the shell to be a thin cylinder. See

pertinent. if in equation (223) (d, 2 + d22)/2 is figure 4-72.

substituted for d2 , we obtain

964,UPAF9 = (225)

nW(d 1 2 + d2 2)

where I' is the. polar moment of inertia of themetal parts forward of the section if it is to thefront of the rotating band, or rearward of thesection if it is behind the rotating band.

4-162. Pressure on Shell Wall Resulting fromRotation of Fiiler. When the filler is regardedas a liquid, the maximum pressure (p0 r) re-suiting from' the rotation of the projectile will VW

occur at Athe periphery of the cylindrical Figure 4-72. Hoop tension force diagramcharge. This pressure will act directly on theinner wall of the shell. Assuming a thin shell, r may be taken as the

mean radius. The elemental mass is then de-8d 12 • 2 fined as

Por ffi (226)144g

where 5 is the density of the filler in lb per dm= rdeLt_ (229)

in. 3 , di is the inside diameter of the shell ininches, w is the angulaY velocity of the shell inradians per second, and g is the acceleration ofgravity in ft per sec 2 . The factor Gi 12 is in- where A is the density of the metal. Consider-

troduced in the denominator in order to convert ing the semicylinder as a free body and equating

g into units of in. per sec 2 . the forces

The angular velocity (w) may be expressed interms of the linear velocity (V) and the twist A Lt 7 s 2of the rifling (n) and the diameter of the pro- 2Fw =. f f 1 r 2c sin 8 djectile (d).

24,7V (227) Lt 2r 2,2nd g

4-180

uRl ( Ro) I d. Tangential Force on Rotating Band.but since r, averae radius, equals kT 2) 2

where R, and Ro are the inner and outer FT 48wIPA (223)radii (in inches) nd2W

aLt .2 12,21pFW a T (R1 + R.) 2 ) n----W1P (224)

substituting the value of 0 in equation (227). e. Tangential Force at Given Section ofShell.

FW -giSL 1 \° 2 nw dXv d12

4 nd /96,I'PA (225)

Lt 2 I2 f. Pressure on Shell Wall Resulting fromg -- (RI + R0)2 ,,2 (Ja) Rotation of Filler.

As expressed originally, g is in in. per sec 2. por- 1.23(-) (--) (228)Expressing g in ft per sec 2

M1A, g. Tension Force in Wall Resulting from

FW = -d2•g (Rl + R) 2 (230)

For steel, za 0.283 lb per in.3. We get FW d2tLt 2 (R1 + Ro)2 (230)

1.04 (Rl + ) 2 2 (Lt) (231) STRESSES RESULTING FROM FORCES

4-165. Signs of Stresses. It is important tonote that the algebraic sign of a stress in-

4-104. Summary of Forces and Pressures Act- dicates whether the stress is compressive or

ing on Projectile During Firing. tensile. It is arbitrary but standard practice toa. Force Resulting from Propellant Gas assien a plus sign to indicate a tensile stressa.esFore. esand a minus sign to denote compressive stress.

Thus, for example, in equation (232) the plusF= PA (213) sign indicates tension and in equation (233) the

minus sign indicates compression. The matterof stress signs becomes especially important

b. Setback of Metal Parts. when the various yield criteria (see paragraphs4-172 to 4-177) are employed.

f'- PA (217) Signs are normally attached only to normal

W stresses acting on an elemental volume of ma-

terial; the signs of the shear stresses usuallyc. Spkck of Filler. are not considered in practice. It should be

conoted that the tangential, radial, and longi-tudinal (axial) stresses herein calculated are

h (h2PA all normal stresses acting perpendicular to theP0 W 219 faces of an elemental volume of she material

441 4..181Sp

Ira .. ... ... ....... ... .. ... ... .. - . ... . . ... . .. . . Ml . ... ... ...... . . . . .. ... ... .... .•-I

at the section under consideration. These d. The total radial stress isstresses, called principal stresses, are the h rmaximum normal stresses possible under the "'o( POgiven loading conditions in the gun--that is, h (235)

such would be the case if the formulas herein SRI -(Poh+ Por)were exact. (See paragraph 4-177.)

e. The radial stress at the inner fiber of4-166. Tangential Stresses. The present prac- the base results from the moment applied bytice of Picatinny Arsenal is to ba.-e the deter- the wall, in the case of a flat base, or fromruination of ,.ress (resulting from internal or the moments applied to the base and the wall,external pressure) in the shell walls upon the in the case of a round base. The pressuresequations developed by LA~n6 for open-ended producing these moments are:cylinders. 1. Pressure resulting from setback of

a. Internal Pressure. Maximum tangential the filler, poh, where h = h.;stress (ST) for this case is 2. Chamber pressure, P;

3. Pressure resulting from rotation ofIR12 + Ro2" the filler, por. Since por is low compared

STI" (poh + por) I (232) to the other pressures (in fact, it is zero.- Ro- / at the center of rotation), and since thestress formulas used are conservative,

b. External Pressure. Maximum tangeritial por usually is disregarded.stress for this case is 212 For a Flat Base the stress SR 2 is

ST2"R - 2\ (233) SR 2 =R 2 p - poh) (236)

c. Stress Resulting from Rotation of Wall.The tension in the shell wall (Fw) resulting where tb is the minimum bAse thickness.from its rotation is For a Round Base (internally), separate equa-

FW 1.04R + Rol 2j\2 tions are used to compute stress resulting1W )Lt (231) from chamber pressure and from filler set-

back.The resultant stress (ST 3 ) is Stress resulting from chamber pressure

FW (SR 3) is 3

( d3 SR3 = P[2(R 1 3 3 11 3) (237)

ST3 = +1.04 1+ (234) Stress resulting from setback pressure

(SR4) is

4-167. Radial Stresses. r+poh 1113 R°3 (238)a. The radial stress in the inner fiber o, - L RI3 - Rj (28

the wall of the shell results from the internalpressure acting on that section.

b. The stress in the walls resulting from The total stress on the base is the sum of thefiller setback SR is two.

SR= -Poh 4-168. Longitudinal Stresses. Longitudinalstress in the shell wall is produced by ihedifference between the setback of the metal

c. The stress in the walls resulting from parts forward of the section under considera-fWller rotation SR is tion, and the filler setback and rotat.'onal

r pressure acting on the base and wall of theSR = s Phr sell to the rear of the section.

4-182

BEST AVAILABLE COPY

Longntudinal stress in the base results from d. Stress in Base Resultinft from Setbackthe filler setback and rotational presstire. Filler. This stress is numerically equal to p0

a. Stress in Shell Wall Resulting from Set- hback of Filler. SL 5 = -Po (243)

SL 1 ih2(Ri 2 Ro 2) R2 e. Stress in Base Resulting from Rotation ofFiller. This stress varies from zero, at the

(vol. filler forward of section) center of rotation, to por at Ru, in accordancewith the equation

This may be writtenSL 6 = - pr (244)

Po Ro h2 ý PA/W 0 )

(RI 2 - R02) -h2(RI2 - Ro 2 ) where R' is the radius of the element under

consideration. Since por is small compared toPOh, and since the element usually considered

((vol. filler forward of section) (239) is at the rotational center, this stress may bedisregarded.

Poh Ro 2 PAWf 4-169. Shear Stresses.

R12 - R02 7,(R,2 - Ro2)W a. In Base. For a flat-bottomed shell withsmall radius fillets, the shear stress on the

area 77dotb should be computed. The pressureb. Stress in Shell Wall Resulting from Rota- producing this shear is the algebraic sum of

tion of Filler. This stress results from the the chamber pressure (p), the filler setbackaverage rotational pressure acting on the base. pressure (poh), and the average filler rotation-The average pressure may be shown to be 1 por. Because it is extremelyequal to 1 o.al pressure j pwBcasitIetrey

e ° Pjr" small compared with the other pressures, the

rr R°2 1 (240) filler rotational pressure usually is omittedSL2= +2 LRI2 So 2j from calculations.

S= (P - poh) ZAQ-....SS, pPh1i Q

Since maximum rotation does not occur until dotbnear the gun muzzle, the stress SL2 is small

in comparison with SLI calculated at peak .. S= (P-poh) 4 0 (245)

pressure. It is therefore expedient to neglect

SL2 in stress calculations. b. AtAny lection of Shell Wall. The tan-c. Stress in Wall Resul~ing from Setback gential force resulting from the angular accel-

of Metal Parts. eration of the 'metal parts forward of the sec-tion if it is in front of the rotating band, or

S W/WPA241) rearward of the section if it is behind theSL3 = (R1

2 Ro 2 ) (41) rotating band, is

A simplification can be arrived at by adding 96,__PA

+ S F'T = nW(d1 2 + d22) (225)

PA(W' + Wf)SL4 -"(R12 - R0

2)w The annular area of the shell wall is

(242)+ POh FRo 2 R2) (d2 2

- d 2 )

-4

i 4-183

The stress produced is a. The inside fiber at the center of the baseb. The inside fiber just under the rear of

r_961rPA ir 4 1the rotating bandSS2 LnW(d2 + d22J L, (d22 - diJl c. The inside fiber just under the ftont of

384pPA (246) the rotating bandS(4d. The inside fiber just to the rear of theSS2 nW(d2 4 - d1 4) bourrele t

e. Shear in the base4-170. Summary of Stress in Shell. Table 4-33 f. Shear at the section just to the rear ofsummarizes the results obtained in paragraphs the rotating band4-166 through 4-169. g. Shear at the section just to the front of

the rotating band4-171. Stresses In Shell. On a new. design, h. Shear at the section just to the rear ofseveral critical elements and sections are the bourrelet. These elements and sectionschosen for stress analysis. If the design checks are shown in table 4-34, along with a tabulationfor these, it is considered good. The elements of the appropriate stresses to be consideredand sections ordinarily used are: at each point.

Table 4-33Summary of stress formulas*

Stress Equationnumber Symbol Formula

Tangential stresses

Internal pressure (232) T +(po h + Por 1. R2 +R2

R,1 _• Ro2

R2

2R2

External pressure (232) +--p (P R 2oh)ST2 2/_2R 02)

Ronalion pressure (233) ST -P 12 2d

Radial stresses

Filler pressure on sidewall (235) SR4 + Po R )

B2

R-18

Flat base (236) AVAIR2 +th

3&

Round base - chamber pressure (237) S -P 3

3 31

Round base - filler pressure (238) 8 R + Po R I ..

R4 2(R 13 - R0

3 )

4-184

'BEST AVAILABLE COPY

Table 4-33

Summary of stress fornmlas* (conS)

Equation

Stress number Symbol Formula

Longitudinal stresses

Filler setbackna pressure -- In wall' (239) SL _2o 21."--n

.. ~~L in'h wl(4) SL (R12. Ro2

R R2

Filler setback pressure - in wall (243) S hr SPoL21 - R-o)

Setback of metal parts forward of element Wl/W PA-in wall (242) 92 _R2

L W"(R -I )

Filler setback pressure - on base (243) p o vs are h

Shear stresses

dShear in base (245) Ss P-P

Acceleratio~n of metal parts - in wall t(246) S ~ 3841 PA

*Tensile stresses are defined as positive; compressive stresses are defined as negative.t Considered expedient to ignore this stress, as it Is relatively small.SIf section is in front of rotating band, use moment of inertia of metal parts forward of section; if sec-

tion is in back of rotating band, use moment of inertia of metal parts rearward of section.

YIELD CRITERIA greatest of the principal shearing stressesreaches the value of shear stress at yielding

4-172. Yield Criteria Theories. The maximum in a simple tension test. According to thisor principal stresses in three mutually or- theory, a material should fail in transversethogonal directions on each element having planes that are inclined 450 to the directionbeen obtained, it is necessary to determine of largest and smallest principal stresses. Ifwhether they produce elastic or plastic de- algebraically S1 is the greatest and S 3 is theformation at the points in question. Several least of the principal stresses, then the maxi-theories to permit this have been advanced. mum shear stress is S -S3 andperma-Three widely used theories are: 2i 1 3, e

1. Maximum shear (Tresca's rule of flow) nent deformation occurs when ISI - S3 1 >So,2. Maximum energy where So is equal to static yield stress in ten-3. Constant distortion (Hencky-Von Mises). sion. Ductile materials, including most metals,

do faii in this manner, but brittle materials4-173. Maximum Shear Theory. This theory behave otherwise. The critical value for yield-siates that in a complex system of stresses ing for a given state of stress given by thispermanent deformation beglnr when the theory differs from that given by tne Von Mises

4-185* V

Table 4-34

Stresses in shell

so S1S7 s,

S2

Stress Type Equation

Si Setback SL5

S2 (flat bottom) Setback (flexural) R2

S2 (round bottom) Setback (flexural SR3 + 8 R4

S3 Hoop of tangential 8 T+ ST 2ST1 2 ST 3

548 S7 10 Radial S

S5 S6 S9 Setback SL4

S8 sll Hoop or tangential ST1 + ST3

Sh 1 Shear at base - thickness t SSI

Shear at any cross section

theory below by 15 percent at most, and is in 4-175. The Constant Distortion or Hencky-Vongeneral smalier. Empirical data plots some- Mises Theory essays to bring the maximumwhere between the values predicted by both energy theory into agreement with the facttheories, that materials can sustain large hydrostatic

pressure without plastic deformation. Thestrain energy associated with volume changes

4-174. Maximum Energy Theory. According to does not produce plastic flow. Therefore, thisthis theory, failure begins to take place when theory states in one form (due to Hencky) that.the energy per unit volume reaches some incipient plastic flow occurs when the straindefinite amount equal to the encrgy per unit energy per unit volume, which changes thevolume at which a bar of the material will shape of a small cube of the material, reachesfail in tension. Results of computations using a critical value, namely, 1/2G (where G is the-this theory, however, are frequently difficult modulus of rigidity of the material). XT is theto correlate with experimental observations. Von Mises yield function defined below.

4-186

Experiments indicate that in general the yield Spoint of pure shear is about 0.6 of the yieldpoint in pure tension for thin specimens, but alimiting value of 0.5 is obtained as the thick-ness of the test specimen is increased. This isin close agreement with values derived fromthe Hencky-Von Mises theory, which gives avalue of l /,. (The maximum shear theoryabove predicts a value of 0.5.) It is commonpractice to use this theory to predict whenplastic flow begins, but there is no objectionto using the maximum shear yield criterionif desired. The Hencky-Von Mises criterion is OS2a more expedient one in the mathematicaldevelopment of plasticity theory.

4-176. Mathemntical Statement of Von Misesi ield Condition. If the principal stresses SI,S 2 , S3 at the point of the material are given, Ewhere tensile stresses have postive signs and Example 1compressive stresses negative signs, thenplastic flow or yielding begins when (form due Given; S1 -40,000 psi

to Von Mises) S2 80,000 psi

I = S12 + S22 + S3 2 S3 50,000 psi

(247) SO = 100,000 psi

.(SIS 2 + S2 S3 + S3S 1) = S02 S02 100 x 108 psi

where So is equal to static yield stress in Von MisesYield Function.tension.

If the value of the expression J on the left, = 812 * 822 + S32 - (SI S2 + S2 S3 + S3 SOcalled the "Von Mises yield function," ob-tained by substituting values for SI, S2, 53,has a value less then So2, then the material is - 16 x 108 + 64 x 108 + 25 x 108still in an elastic state of stress and no yield-ing occurs. This is the state of stress gener- - (-32 x 10 8 + 40 x 108 -20 x 108)ally desired in ordnance projectiles.

In the case of two-dimensional stress, one of = 105 x 108 + 12 x I08the three principal stresses is zero, and thoseterms in the Von Mises yield function contain- = 117x 108 psiing this principal stress drop out. Thus, ifS3 = 0 for initial plastic flow, SI and S2 mustbe such that 117 x 108 > So2; therefore, material is in

plastic stress state.SI2 + S22 - Sl S2 = So2 (248)

The simplicity of the mathematical expression Maximum Shear Criterion Solution.

stating the Hencky-Von Mises yield criteriamakes it unnecessary to use charts and nomc- S2 > S3 >

grams, which are often found in the literature I$2 - S31 = 180,000 - (-40,000)1 = 120,000 > Soon the subject: these graphical methods aremore of academic interest than practical aidsto computation. Therefore, material is in plastic state.

4-187

Sl shell body as an integral unit, will set up shearstress and bending moments at these junctions.

These shear stresses and bending moments,which are caused by the effects of one sectionoi shell on another, are ignored- and assumed(without justification) to be negligible. Ott theother hand, the mathematical treatmeit ofthese additional stresses -or in fact the exactanalysis of shell stresses -is a formridable

S task, analytically and numerically; research on- " S 2 this subject is still in a state of flux.

b. Effect of Base. Presence of the bise ofthe projectile materially increases the strengthof the walls to the rear of the rotating band

S3 through beam action. The shorter the distancefrom the base to the band, the more important

Example 2 this reinforcement factor becomes.c. Maximum Stresses. The forces that pro-

S = -40,000 psi duce the linear acceleration are greatest atthe point of maximum propellant pressure.

S2 = 60,000 psi (See figure 4-73.) This point is well behind theSo = 100,000 psi muzzle. The resultant stresses of these forces

S02 = 100 x I18 psi are greatest at this point. On the other hand,the forces that result from rotational velocity

are greatest at the muzzle. Consequently, atVon Mises Yield Function. this point, the stresses in the projectile result-

ing from these forces are greatest.= Sl 2 22 - S1S2

In the foregoing formulas the propellant pres-= 16 x 108 +;36 x 108 +24 x 108 sure (P) usually is taken as 1.12 times the

maximum allowable pressure for the projectile.= 76 x 108 ps

76 x 108 < So 2 ; therefore, material is indicated VELOCITYto be in elastic stress state. CURVE

Maximum Shear Criterion Solution.

IS2 - SI= 160,000 - (-40,000) = 100,000 S=OS

Therefore, an incipient plastic stress state is

Since empirical data on yielding plots betweenthe Von Mises and maximum shear values, wecan be reasonably assured that the stress stateis an elastic one. i iPRESSR

4-177. Discussion of Formulas and Methods.a. Effect of Free-Body Analysis. It is to be

noted that the Stress formulas uzed herein areralculated by isolating the shell sections and DISTANCE TO MUZZLEtreating them as free bodies. It is thereforeevident that the restraints imposed by joining Figure 4-73. Pressure and velocitycontigguous sections, that is, considering the versus travel

4-188

The linear and angular accelerations are maxi- tributable to (1) propellant pressure, (2) set-mum when P is maximum. The value for , (the back of filler charge, and (3) setback of theangular velocity) is derived from the twist )f walls ahead of the section and its attachedrifling and the muzzle velocity. Using the value parts.of P at maximum pressure and the values de- g. Projectiles with Tapered Backs. Manypendent upon V at muzzle velocity will give mortar shells are made with tapered backsmaximum calculated stresses in excess of and they use no gas check or rotating band.those which would result from using the values The chamber pressure acts, therefore, on alldependent upon V it the point of maximum sections to the rear of the bourrelet. Thispressure. The difference is small and usually produces a longitudinal stress on the taperedis on the side of safety. Therefore, it is not section which must be considered in design.ordinarily objectionable. Consider the portion of such a shell forward

d. Behavior of Filler. The analysis of of a section through the base. At the section,stress in shell assumes that the filler acts as the outer radius is R1 and the inner radius isa liquid, that is, the setback pressure is as- Ro. The bourrelet radius is r, and the pro-sumed to act hydrostatically. This assumption, pellant pressure is P. The pressure acts onwhile it has proved a usable one, has not been the projected area, ?, (r 2 - RI2), forward of thesubstantiated. It is thought, therefore, that the section, and is distributed over the area of thefiller may behave as an anisotropic plastic shell wall, n, (RI 2 - R0

2 ). The stress produced,substance, the rheological properties of which SL 6 , is:have yet to be determined. _ _

e. Weight Distribution. Distribution of metal S(r 2 . R1 2)in the projectile has a substantial effect on its $L 6 = p (Ri 2

- R02 )stability. Any change made in weight distribu- (249)tion in order t:- attain greater strength must be V 2Rchecked to determine the corresponding effect S62 - R=2on stability in flight. R12 -RIR0

f. Fin-Stabilized Projectiles. When a fin-stabilized projectile is fired there is little or The total longitudinal stress at the elementno rotation. The stresses therefore are merely under consideration is therefore:those attributable to the propellant pressureand the setback. Formulas, for these two ef- SL3 + + SL6fects, given in preceding paragraphs, are ap-plicable to the fin-stabilized projectile. It iscustomary to check the stresses in the wal~s (See equations (241) and (242) for SL3 andof the projectile just forward of the fin as- 3sembly. At that point the stresses are at-

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., p1

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REFERENCEV AND BIBLIOGRAPHY

1. Ordnadice Engineering Notebtook, Ammunition Section, Ordnance School.

2. Memorandum Report MR 51, Picatinny Arsenal Tecfr..ical Division, 7 January 1954.

3. Schwartz, Piratinny Arsenal Notes.

4. Tschappat, W. H., "Textbook of Ordnance and Gunneiy," John Wiley & Sons, New York,1917.

5. Symposium on Shell Stresses, Picatinny Arsenal, September 1951.

6. Geldmacher, Little, and Roach, Review . Shell Stress Relationships, Physical ResearchSection Memorandum No. 9, Picatinny.Arsenal, April 1955. a

4

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A J

S&t#• . •t*. *.GVr.M•N RTN 7 ]II 96 t-0• 38)•

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ENGINEERING DESIGN HANDBOOK SERIESListed below are tne Handbooks wlhch have been published or submitted for publication. Handbooks with punlira-

ticn dates prior to I Auglust 196g were piblished as 20-seriei Ordnance Corps pamphlets. AMC Circular 310-338. 19July 1963. redesLgnated those publications as 706-series AMC pamphlets (i.e.. ORD? 20-1 38 was reoesaInated AMCP706-138). All new. reprinted, or revised Handbooks are being published as 706-series AMC pamphlets.

General and Miscellaneous Sub ects Ballistic Missile Series

No. Title No. Itte

106 Element. of Armament Engineertng. Part One. 281(S-RD) Weapon System Efrectivenese (U)Sources of Energy 182 Propulsion and Propellants

107 Elements of Armament Engineering. Part Two, Z83 Ae.odynamicsBallistics 284(C) Trajectories (U)

108 Elements of Armament Engineerirg. Part 86 StructuresThree, Weapon Systems and Components Ballistics Series

110 Experimental Statistics. Section i, Basic Con-cepts and Analysis of Measurement Data 140 Trajectories. Dilferental Effects, and

IIl Experimental Statistics. Section 2. Analysis of Data for ProjectilesEnumerative and Classificatory Data 150 Interior Ballistics of Guns

112 Experimental Statistics. Section 3. Planning 160(S) Elements of Termninal Ballistics. Partand Analysis of Comparative Experiments One. Introduction, ll MMechanism@.

113 Experimental Statistics. Section 4, Special and Vulnerability (U)Topics 161(S) Elements of Terminal Ballistics, Part

114 Experimental Statistics. Section 5, Tables Two, Collectioni and Analysis of Data121 Packaging and Pack Engineering Concerning Targets (U)134 Maintenance Engineering Guide for Ordnance 162(5-RD) Elements of Terminal Ballistics, Part

Design Tlres. App'ication to Missile and135 Inventions. Patents. and Related Matters Space Taores' (U)

(Revised)136 Servomechanism*. Section 1. Theory Carrises and Mounts Series137 Servomechanisms. Section 2. Measurement 340 Carriages and Mounts--General

anid Signal Converters 341 Cradles138 Servomechanismr. Section 3. Amplification 342 Recoil Systems139 Servomechanisms. Section 4, Power Elements 343 Top CarrLaSes

&ad System Design 344 Bottom Carriages

170(C) Armor and Its Application to Vehicles (U) 345 Equiltbrators250 Guns--General (Guns Series) 346 Elevating Mechanisms252 Gun Tubes (Guns Series) 347 Traversing Mechanisms270 Propellant Actuated Devices Military Pyrotechnics Series29)0(C) Warheads--General (U)331 Compensating Elements (Fire Control Series) 186 Part Two. Safety. Procedures and355 The Automotive Assembly (Automotive Series). Glossary

(Revised) 187 Part Three. Properties of Materials

Ammunition and Explosives Series Used in Pyrotechnic Compositions

Surface-to-Air Missile Seriesis Solid Propellant@, Part On*

176(C) Solid Propellamts. Part Two (U) 291 Part One. System Integration177 Properties of Explosives of Military Interest, 292 Part Two, Weapon Control

Section 1 293 Part Three. Computers178(C) Properties of Explosives of Military Interest. 294(5) Part Four, Missile Armament (U)

Section 2 (U) 295(5) Part Five. Countermeasures (U)179 Explosive Trains 296 Part Six. Structures and Power Sources210 Fuses. General and Mechanical 297(5) Part Seven. Sample Problem (U)211(C) Fuzes. Proximity, Electrical, Part One (U) Materials Seri*2174S) Fuses, Proximity, Electrical, Part Two (U)213(5) Fuses. Promnmty. Electrical. Part Three (U) 149 Rubber and Rubber-Like Materials214(S) Fuses, Proximity, Electrical, Part Four (U) 212 Gasket Materials (Nonmetallic)215(C) Fuses. Procimity. Electrical. Part Five (L') 691 Adhesives244 Section I. Artillery Ammunition--General. 692 Guide to Selection of Rubber O-Rings

with Table of Contents, Glossary and 693 Magnesium and Magnesium AlloysIndex (or Series 694 Aluminum and Aluminum Alloys

245(C) Section 2, Design for Terminal Effects (U) 697 Titanium and Titanium Alloys246 Section 3, Design for Control of Flight 698 Copper and Copper Alloys

Characteristics 699 Guide to Specifications for Flentlbe Rnbb~r247 Section 4, Design for Projection Products248 Section 5. Inspection Aspects of Artillery 700 Plastics

Ammunition Design 721 Corrosion and Corrosion Protection of

249 Section 6. Manufacture of Metallic Components Metalsof Artillery Ammunition 722 Glass

*efe Materials geries is being published as Military Handbooks (MAL-HDBK.) which are available to Department at)Defense Agencies from the Naval Supply Depot. 5801 Tabor Avenue, Philadelphia. Pennsylvania 19120.

Documents

AMCP 706-247 Ammunition Series - Section 4 Design for Projection [Clean]