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FROMDistribution authorized to U.S. Gov't.agencies only; Test and Evaluation; 14 Dec1973. Other requests shall be referred toNaval Weapons Center, China Lake, CA

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USNWC ltr, 14 May 1975

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-•NWC TP 5607

I

i-

SEffect of Projectile Nose Shape on

Ballistic Limit Velocity, Residual

Velocity, and Ricochet Obliquityby

Thomas W. Ipson

Rooney F Recht

William A Schmeling

Denver Research Insltute

for the

Weapons Development Depaitment

191974 /

Naval Weapons Center( ;-CHINA L, \K CAL" ORNIA u DECEMBER 1973

istribut- nf nIrltei to US Governmr nt agencies oniy test ,Jd erIaijj!,i,-n 14 C'-- -mber 1973. Other requests for

this r-;ouirtIn IliUSt be referred to the Naval Weapons Center

NWC Technical Publication 5607

Published by ................... Weapons Development DepartmentM anuscript ................................. 40/MS 73-1 23Collation ............... Cover. 23 leaves, DD Form 1473. abstract cardsI:irst printing .............................. 215 unnumbered copiesSecurity classification ............................. UNCLASSIFIED

Naval Weapons CenterAt4 ACTMITY OF THE NAVAL MATERIAL COMMANDPaul E, Pugh. RADM. USN ..................................... CommanderLeroy Riggs ..................................... Technial Director (Acting)

FOREWORD

The Chief of Naval Material Command (CNM) assigned to a group ofNavy laboratories a program on Soviet ship vulnerability, one of theselaboratories was the Naval Weapons Center (NWC), China Lake. Calif. As apart of the Soviet Ship Vulnerability Program (SSVP), a series of technologyhomework work unit plans were conducted. This program on effect of noseshape on penetration by a projectile was one of these technology homeworkprograms conducted at NWC and tinder contract at the Denver ResearchInstitute.

The work on this task was accomplished by the Denver Researchinstitute under Contract No. NOOI23-69-C-1970. This work unit was fundedby CNM through Naval Air Systems Command AirTaskA-350-532!/O08B/3F32-353-50l.

This report has been reviewed for technical accuracy by M. H. Keith andis released at the working level for information only.

Released by Under authority ofM. M. ROGERS, Head F. H. KNEMEYER, Ml,.ad (Acting)Weapons Systems Analysis Division Weapons Development Department13 December 1973

iii

NWC TP 5607

ABSTRACT

Target vulnerability analyses consider ballistic penetrators whichhave various nose shapes. Nose shape often undtrgoes changes duringthe target penetration process due to deformation. It is importantthat the effects of nose shape upon ballistic perforation dynamics beknown and accounted for in vulnerability analyses. An experimentalfiring program was conducted in which rigid penetrators having threedifferent nose shapes were fired against steel plate. Experimtentaldata generated concerned ballistic limit velocity, residual velocity,and ricochet obliquity. Experimental data were compared with predictionsof analytic models. The prediction models were modified to reflect theresults of experiments.

iv

NWC TP 5607

THE EFFECT OF PROJECTILE NOSE SHAPE UPONBALLISTIC LIMIT VELOCITY, RESIDUAL

VELOCITY, AND RICOCHET OBLIQUITY

Contract Number N00123-72-C-0267

Prepared for

Weapons Development DepartmentNaval Weapons Center

China Lake, California

February 1973

Denver Research Instituteof the

University of Denver

APPROVFD BY: PREPARED BY:

Rex E. Paulsen, Head Tom W. Ipson f

Mechanical Sciences Division Research Engineer

Rodney F./AechtSenior Research Engineer

William A. Schmeling /Research Engineer

V

NWC TI' 5b07

NOMENCLATURE

a Exponential coefficitnt, dimensionless

RH Cofiin In 50 equation; - T fn6 1 ft/sec

BHN Plate hardness, Brinell hardness number

b Exponent in empirical V50 equation, dimensionless

C Coefficient in empirical V5 0 equation, ft/sec

CA Coefficient in V50 equation; (0.0396. Kp 1/2; for steelplate - 0.000305), dimensionless g I

d Projectile diameter, inch

e Base for natural logarithms, dimensionless

E Young's Modulus of plate material, lb/in2

Ep Young's Modulus of projectile material, lb/in2

Ee Maximum elastic energy in projectile, In-lb

f Dynamic sliding coefficient of friction ( 0.01), dimensionless;Also used to denote "function of:

g Gravitational constant (386), in/sec 2

hdc Parameter, descriptive of false nose formed on projectile,dimensionless

K Plate material bulk modulus, lb/in2 ; also used in ricochetmodel as a constant of portionalitv, dimensionless

L Effective length of projectile, inch

fn Natural logarithm, dimensionless

14p Projectile weight, lb

vi

NWC TP 5607

'1 Weight of plate plug, lb

n The fraction (V50n - V5Onb)/(V5Ons - V5 0 nb) at a ac,dimensionless; also used as empirical co.-tant in ricochetmodel, dimensionless

Rc Projectile hardness, Rockwell C scale

T Plate thickness, inch

V Projectile impact velocity, ft/sec

Vh Ricochet velocity component parallel to plate surface, ft/sec

.V Ricochet velocity component normal to plate surface, ft/secn

V Residual velocity, ft/secr

V50 Ballistic limit velocity, ft/sec

V:on Ballistic limit velocity at normal incidence, ft/sec.On

(V5on)b V5 0 n for blunt rigid projectiles, ft/sec

(V50n) V 50n for sharp rigid projectiles, ft/sec

W Projectile weight (same as ,p ), lb

W1 Weight of equivalent projectile, lb

y Deviation from (V5 0o)s, ft/sec

z Deviation from (V"50n)b' ft/sec

z z - .- , dimensionlessm m j1+ 2

I Half angle of projectile conical nose (effective conical halfangle of non-conical nose), deg

( Value of a which divides nose angles into sharper and blunterc categories, deg

Total deflection of impact surface due to penetration andflexure, inch

Ac (V 9 0n)s - (V5on)b at a - ac' ft/sec

9 Impact obliquity, measured with respect to plate normal, deg

vii

NVC.: TIP 50:07 ..... . ........

0 r Ricochet obliqultv, metasured with respect to plate normal, degr

0 Specific weight of plate material, lbtin3

Pp Specific weight of projectile material, lb/in'

0 Static tensile strength of plate material, lb/in2

0 Compressive '!timate strength of projectile material, lb/in2

1 Static compressive shear strength of plate material, ib/in 2

viii

NWC TP 560)

CONTENTS

Introduction ....................................................... 1

Experimental Results and Comparison with Model Predictions ......... 2Experimental Procedure ........................................ 2

Firing Setup ................................................ 2Projectile Characteristics ............................... 2Tsrget Plate Material .................................... 3Ballistic Limit Velocity Determination ................... 3Ricochet Obliquity ........................................ 3

Experimental Results .......................................... 4Ballistic Limit Velocity ................................. 4Residual Velocity ........................................ 9Ricochet Obliquity ....................................... 12

Comparisons of Experimental Data and Predictionsof Analytical Model ......................................... 15

3allistic Limit Velocity ................................. 15Residual Velocity ........................................ 24Ricochet Obliquity ....................................... 27

Summary ............................................................ 34

References ......................................................... 35

ix

NWC TP 5607

INTRODUCTION

There exists a need for a knowledge of the effects of nose shap.upon the ballistic perforation characteristics of projectiles. Vulner-ability analyses concerned with missile warheads, bombs, penetratingtype projectiles, and projectiles which change nose shape duringperforation due to crushing or fracture must consider the effects ofnose shape upon ballistic limit velocities, residual velocity, andricochet angles. Current perforation prediction models analyticali"define the role of nose shape in ballistic perforation. Data forcorrelating these analytical definitions is sparse. It was the objec-tive of this research effort to experimentally examine the effects ofnose shape upon ballistic perforation and to compare the data thusgenerated witb predictions of the analytical model. Based upon thesecomparisons, modifications to the models would then be made to improvepredictive capabilities where necessary.

A 300-round firing program was conducted in which rigid steelprojectiles having three different nose shapes were fired at threethicknesses of steel plate. ObliquiLies of 0, 30, and 60 deg wereinvestigated. The data generated concerned ballistic limit velocities,residual veloc:ities, and ricochet angles.

Experimental results were compxred with predictions of analyticalmodels. Predictive methods for ballistic limit velocities were modifiedto account for unexpectedly dramatic effects of projectile hardness.These modified methods produce excellent correlations of ballisticlimit velocity and residual velocity data. A model for prediction ofricochet obliquity was developed.

Reported herein is a description of the experimental procedureemployed during the firing program, a presentation of the experimentalresults, and comparisons between predictions of analytical models andexperimeatal data.

NWC TP 5607

EXPERIMENTAL RESULTS AND COMPARISONWITH MODEL PREDICTIONS

EXPERIMENTAL PROCEDURE

Firing Setup

Special 50-caliber steel projectiles were fired from a standardMann Test Barrel having a 15-inch twist. The velocity was controlled bythe amount and type of powder used. The projectiles were spin-stabilizedby means of an integral gas seal and rotation band machined on theprojectiles. Yaw cards were emplyed to monitor projectile stability atimpact. Only data for stable (zero :yaw) projectiles were recorded.Initial (impact) and residual (post perforation) velocity measurementswere accomplished by systems of contact switches and chronographs.

Projectile Characteristics

Caliber 0.50 projectiles were machined from 4340 steel and heat-treated to a hardness of Rockwell C 50 to 55. The weight of all testprojectiles was intended to be 410 grains. Due to miscalculations, theinitial batch of projectiles produced were 445 grains. These were usedin initial test series. All other test projectiles weighed 410 grains.Projectiles having three different nose shapes were used in the firingprogram--two conical-point and one blunt (flat) ended. The conicalpoints were of 30 and 60 deg interior balf angles (m). Figure I is aphotograph of the three test projectiles.

FIG. I. 'rest Projectiles 0.50 Caliber, 410 Grains, 4340 Steel Heat-Treated to aHardness of Rc 53;Conical Nose Half-Angle (Left to Right) 30, 60, and 90 Deg.

2

NWC TP 5607

Target Plate Material

The plate material used in the test program was 4130 steel with ahardness of 220 and 260 HIMN. Plate thicknesses used were 0.125, 0.250,and 0.375 inch. Eight-inch square plates were fiLmly clamped into thetarget assembly.

Itllistic ILimil Velocity leterminalion

The ballistic" limit velority (V50)--defined ir this study as theimpact velocity for which there is a 0.5 probability that a projectilewill have zero residual velocity--was determined by using the six-shotballistic limit velocity procedure. Firing was conducted until threecomplete and three incomplete perforations were obtained within avelocity spread of 100 ft/sec or 10% of the ballistic limit velocity(whichever was lower). These six velocities were then averaged toobtain the ballistic limit velocirty. A complete perforation was definedas occurring when the rroiectlle completely passed through the plate(had some measure of residual velocity). This V5O corresponds veryclosely to the Navy Criteria Ballistic Limit Velocity. Figure 2 illus-trates a typical set of V50 testing data. During thelfiring, if acomplete perforation was obtain-d, the next test was conducted at alower velocity; if an incomplete perforation was obtained, then thefollowing test was fired at a higher velocity. This practice (withinthe limits of producing the desired velocity changes by means of smallchanges in propellent loads) insured staying within the zone of mixedresults once it was found.

Ricochet Obiqluity

Limited ricochet tests were fired with the three test projectilesagainst 0.250-inch-thick 4130 steel plate at 30 deg obliquity. Theinitial velocity was measured by the previously mentioned method. Theangle of ricochet (defined in the same manner as obliquity; i.e., withrespect to the plate normal) was determined from impacts upon woodenwitness targets. The projectile would ricochet off the target plateinto the wooden witnesF target, leaving an impact impression. Fromthe geometry of the plate configuration and the wooden witness target,the ricochet angles were easily measured by noting the location of theimpression made by the ricocheting projectile. The ricochet trajectorywas essentially in the same plane as the obliquity angle.

3

NWt: TI S...; ._ __ _ ___.. .

COMPL.ETEPENETRATION 0 * OS

INCOMPLETE 0 0 000 0 0

PENETRATION

ISIX) am 70 MG

V. VELOCITY, FTISEC

FIG. 2. Typical Ballistic Limit Velocity Data; 410-Grain, 4340 Steel Projectile (Re53), Conical Nose Half-Angle of 30 Deg; 0.1 25-Inch-Thick 4130 Steel (230 BHN)Plate, 0-Deg Obliquity.

EXPERIMENTAL RESU LTS

Important ballistic perforation parameters which the projectilenose shape may influence are ballistic limit velocity, residual velocity,and angle of ricochet. The results of the experimental investigation ofthese parameters as functions of projectile nose shape are presented inthe following.

Ballistic Limit Velocit)

Ballistic limit velocities were determined for fourteen impactconditions involving various combinations of projectile nose shapes,plate thicknesses, and obliquities. Table 1 lists the ballistic limitvelocity results of these tests. The projectile nose shape is describedin ter-s of nose half-angle, (a). Recall that this angle is the interiorhalf angle of the conical point. A small angle corresponds to a sharppoint, a larger angle to a blunter conical nose. An (ca) o1 90 deg isthe flat-faced projectile.

NWC TP 5607

TABLE I. Experimental Ballistic Limit Velocities Determined for

Rigid Steel Projectiles and 4130 Steel (230 BHN) Plate.

T, inches O, deg W, grains a, deg V50 , ft/see V5 0 n/cos 0

0.125 0 410 30 6920.125 0 410 60 7170.125 0 410 90 651 -0.125 30 410 30 782 (798)0.125 30 410 60 787 (827)0.125 30 410 90 - (750)0.125 60 410 30 1410 (1385)0.125 60 410 60 -

0.125 60 410 90 -

0.250 0 445 30 1290 (1 -0.250 0 450 60 901 -0.250 0 410 90 893 -0.250 30 410 30 1422 (1490)0.250 30 450 60 1232 (1040)0.250 30 410 90 - -0.250 60 410 30 - -0.250 60 445 60 2218 (1800)0.250 60 410 90 - -

0.375 0 410 30 15360.375 0 410 60 11930.375 0 410 90 1297 -

Figure 3 presents normal (O-deg obliquity) ballistic limit velocitydata as a function of projectile nose half-angle for three thicknesses(T) of 4130 steel plate--0.125, 0.250, and 0.375 inch. Seven of thenine data points represent 410-grain projectiles. The two data pointsfor the tests with 30- and 60-deg a against 0.250-inch plate wereobtained with 445-grain projectiles. The dashed lines indicate thetrend of the data. The trend line for the 0.250-inch thickness isdrawn above the two data points for the 445-grain projectiles. Asindicated by the data on Fig. 3, against the thin (0.125-inch) plate,the effect of nose shape is very slight; the ballistic limit velocitiesietermined for nose half-angles of 30, 60, and 90 deg show a maximum

difference of 66 ft/sec. Against the thicker plates (0.250 and0.375 inch), the data indicates a higher ballistic limit velocity fora nose half-angle of 30 deg as compared to that obtained for half anglesof 60 and 90 deg. Little difference is noted between the data obtainedfor projectiles characterized by 60- and 90-deg aose half-angles.

5

KUC TP 5607

eorWp

0.I,X.-,•445 fares

€,)

I,-

5--. ,-.. .

lowT .2506"

0- - - - - L- - -

0

PROJECTILE NOSE HALF-ANGLE. 0. DEGREES

FIG. 3. Experimental Results; Ballistic Limit Velocity as a Function of Projectile, Nose

Half-Angles (30. 60, and 90 Deg) Against 4130 Steel (230 BHN) Plate of 0.125-,

0.250-, and 0.375-Inch Thickness, 0 Dcg Obliquity. Dashed Lines Show Data Trend.

Figure 4 compares ballistic limit velocity/nose-shape data obtained

against 0.125-inch thick steel plate at obliquity with data obtained at

normal incidence. This figure contains data points for the a - 30 deg

projectile fired at 30 and 60 deg obliquity and for the a - 60 deg

projectile fired at 30 deg obliquity. The dashed lines labeled 30 and

60 deg obliquity were obtained by multiplying the 0-deg obliquity data

trend line by the secant of the obliquity angle. The oblique data

points correlate very well with these lines. This illustrates that for

projectiles with various nose shapes, the ballistic limit velocity at

obliquity can be closely approximated by multiplying the normal ballistic

limit velocity by the secant of the obliquiy angle. This procedure

also works well for ogival armor penetrating projectiles and blunt

fragments (Ref. 1).

6

"_ _ _ _ _NWC TP 5607

Obb~quity

0 0*

20D 0 O0*

S|VSoN) sec 0JJ

(9.600- O - 3

.J-J

0

00 30D oo0

PROJECTILE NOSE HALF-ANGLE, a. DEGREES

FIG. 4. Experimental Results at Obliquity; Ballistic Limit Velocity as a Function ofProjectile Nose Half-Angle; Comparison of Oblique Data With Normal Data; 0.125-Inch4130 Steel (230 BHN) Plate, 0-. 30-, and 60-Deg Obliquities.

The ballistic limit velocity values experimentally determined forthe a = 90 deg test projectiles were much lower than were anticipated.Previous research efforts (Ref. 2) with blunt elongated fragments hadshown analytical equations (Ref. 3) for blunt-nosed projectiles to bevery accurate in predicting ballistic limit velocities. The ballisticlimit velocity dat3 obtained for the a - 90 deg projectiles were wellbelow those predicted by these equations. It became obvious frominspection of impacts and perforations made in the target plates thatprojectile rigidity had to be playing a major role in the differencesbeing produced. The rigid (Rc 53), blunt (a - 90 deg) projectiles usedin this research effort produced clean, square-bottomed impressions inthe target plates at sublimit velocities. At velocities above theballistic limit, plate perforations had the appearance of machined-likeholes. Softer (Rc - 30) non-rigid fragments, for which the predictiveequations were derived, deform upon impact and expend much more energyin projectile and plate deformation. To prove that the difference inexperimenta] ballistic limit veiocitiub d5 z•v.pared with predictions

7

NWC TP 5607

was attributable entirely to projectile rigidity, a test series using* - 90 deg, 410-grain projectiles having a hardness of Rc 30 was con-

ducted against 0.250-inch steel plate at 0 deg obliquity. This testseries produced a ballistic limit velocity of 1,698 ft/sec. The ballis-tic limit velocity determined for the Rc 53 fragment under exactly thesame conditions was 893 ft/sec. Figure 5 illustrates the physicaldifference in the plate and projectile deformations associat-ed withimpacts and perforations by the two types of projectiles. The projec-tiles shown in the photograph are ones recovered after impacting atvelocities just below the ballistic limit velocity. Note the amount ofdeformation experienced by the soft (Rc 30) projectile. The rigid(Rc 53) projectiles exhibited no deformation during any of the testsconducted during this research effort. Compare the plate deformationsfor both the incomplete and the complete perforatiois. The rigid pro-Jectile, by not deforming, maintains a concentrated shear stressgradient for promoting plugging. The non-rigid projectile, as itdeforms, becomes a much less efficient penetrator and thereby must havea much higher impact velocity to achieve perforation.

30Rc 53Rc 4m III

FIG. 5. Effect of Penetrator Harness on Projectile and Plate Dctformation at VelocitiesJust Below and Above the BaiUstic Limit Velocity.

8

NWC TP 5607

The stated objective of this project was to study the effects ofnose shape upon the ballistic perforation behavior of rigid projectiles.The startling VS0 results obtained for rigid flat-nosed projectilesnecessitated modifications to the theoretically developed equations forpredicting ballistic limit velocities for rigid prcjectiles with bluntnose shapes. Prior to this experimental investigationz, most data avail-able pertaining to blunt nose shapes concerned projectiles of a nominalhardness of 30 Rc. Consequently, eftorts to account for nose shaperelied upon data for rigid.arnor-piercing projectiles at the sharp endof the nose-shape spectrum and data for blunt, non-rigid fragments atthe other end of the spectrum. Modifications of the analytical predic-tive methods for rigid penetrators of various nose shapes are discussedin the next section, Comparisons of Experimental Data and Predictions ofAnalytical Model (p. 15).

Residual Veloci[)

Measurements of residual velocity were made for four of the fourteentest conditions investigated. Figures are included herein which presentprojectile residual velocity data as a function of impact velocity.Also plotted on these figures are the prediction curves of the residualvelocity equation (Ref. 1 and 3) for penetrating-type projectiles.This equation (which applies to standard armor-piercing projectiles) hasthe form:

r 2 2r -V 0 (i)~

Equation 1 applies to projectiles which perforate plates by displacingplate material radially rather than by driving a plug from the plate.

For the latter perforation mode (blunt projectiles), the applicable formof the DRI residual velocity equation includes terms which account forthe momentum of the material ejected from the plate. For the bluntprojectiles (high valueg of the nose half-angle, a), the DRI residualvelocity equation is:

v2 2 (2)V /27_ V50

r=

1 +

p

where

MS is weight of the plate plug material, lb

Mpis weight of the projectile, lb.

9

NWC TP 5607 i

For flat-ended (,1 = 90 deg) projectiles, Ms is very closely estimated bythe weight of the plate material which" lies in the path of the perforat-ing projectile, or: 2!

M = prd 2T (3)s 4 cos 6

Note that Eq. 2 reduced to Eq. I when the Ms term is zero. As the nosehalf-angle, cx, becomes larger (a projectile becomes blunter), thereshoul.d be a transition from the penetration mode to the plugging modewhen perforating relatively thin platec. The specific objective of the

residual velocity experiments was to examine the relationship betweenMs and nose shape with respect to accurate residual velocity prediction.Residual velocity data are presented with the predictions of Eq. 1 (MSassumed to be zero) for comparison purposes.

Figure 6 displays residual velocity data obtained with the sharppointed 4 10-grain, a = 30 deg projectile against 0.125-inch thick 4130steel plate at 0 deg obliquity. Also plotted on this figure is theresidual velocity prediction curve of Eq. 1. The value used for the V50value is that determined experimentally for this impact configuration.Figure 6 shows very good agreement between the experimental residualvelocity data and the prediction curve of Eq. 1. Correlation with Eq. 1indicates that there is very little influence of plate material (Ms)upon the residual velocity for this impact conditInn.

'I>L

0

0

dl "1000i- v. *Iv2 _(69212

0 200 3000 4000IMPACT VELOCITY, V, PTISEC

FIG. 6. Residual Velocity as a Function of Impact Velocity;0.125-Inch 4130 Steel Plate (230 BHN); 410-Grain. a =30-Deg Rigid Projectile (53 Rc), 0-Deg Obliquity.

10

NWC TP 5607

Figure 7 presents residual velocity data for the same projectilebut against thicker plate (0.250 inch). These data show good agreementwith the prediction curve of Eq. 1 at the lower values of residual veloc-ity. The deta point at an impact velocity just less than 3,000 ft/secis well below the prediction curve. This may indicate that at thehigher velocities even a relatively sharp nose does plug out some platemater ial.

.2000,

1000-

0

0 1000 -300 3000 4000IMPACT VELOCITY. V, FT/9EC

FIG. 7. Residual Velocity as a Function of Impact Velocity;0.250-Inch 4130 Steel Plate (230 BI-N)-. 410-Grain, a30-Dcg Rigid Projectile (53 Rc), 0-Deg Obliquity.

Residual velocity data for the blunter (aL - 60 deg) projectile isshown in Fig. 8. The target plate is 0.125-inch 4130 steel at 0 degobliquity. These data also show very good correlpt~ioii with predictionof Eq. 1. Plate plugs were recovered from the projectile trap. Figure 9shows a photograph of a typical plate plug recovered from residualvelocity test series with the (oL - 60 deg) projectile and 0.125-inch and0.250-inch target plates. On Fig. 8, the prediction of Eq. 2 (whichconsiders the plate plug) is also shown (dashed curve). The ratio ofthe plate plug mass to the projectile mass (M5/Mp) is small (0.113) withthis thin plate, and Eq. 2 predicts only slightly lower residual velocityLhan Eq. 1. The effect of the plate plug mass upon residual velocity iswell illustrated by the data obtained with the a~ - 60 deg) projectileand the 0.250-inch plate. Figure 10 presents these data together withthe residual velocity predictions of both Eq. 1 and 2. As nay be seen,the experimental data agrees with the prediction of Eq. 2, as it should.

NWC Tl' 5b07

/,

//

0 D0o 2000 3000 4000

IMPACT VELOCITY- V, FI/SEC

FIG. 8. Residual Velocity as a Function of Impact Velocity;0. 1 25-1nch 4130 Steel Plate (230 BHtN); 410-Grain, a=

60-Deg Rigid Projectile (53 Rc), O-Deg Obliquity.

ileii experimental investigation of the effect of nose shape upon

perforation mode and associated effect upon residual velocity has shownthat, in the range of plate thickness studied, the vi = 30 dcg) projec-tile tended to perforate without producing a plate plug and that the(,x = 60 deg) projectile acted in the same manner as a flat-endedprojectile and perforated by the plate plagging process. Allowancesfor nose shape when predicting residual velocity are discussed indetail in the next section, Comparisons of Experimental Data and Predic-tions of Analytical Model.

Ricochet Obliquity

Angles of ricochet associated with an impact obliquity of 30 degwere measured in test firings involving 0.250-inch 4130 steel targetplate and each of the three test projectiles (a = 30, 60, and 90 deg).Figure 11 presents the ricochet obliquity (Or) data obtained as afunction of impact velocity. Ricochet obliquity is measured withrespect to the plate normal as is impact obliquity. The data for each

of the three projectiles is differentiated by means of the symbols

employed. Note that the ricochet obliquity is large (the ricochetdirection is nearly parallel to the surface of the target plate) at lowimpact velocities. At higher velocities (as the ballistic limit veloc-

ities are approached), the ricochet angle decreases. This occurs asthe result of plate deformation (flexure and surface penetration); the

proiectile is deflected upward while escaping the impact impression.

12

•WC TP 5607

IwO -

FIG. 9. Conical Nosed Rigid Projectile (a 60 Deg) and Typical Plate Plugs from0.125-Inch (Left) and 0.250-Inch (Right) 4130 Steel (230 BHN) Plate; O-DegObliquity.

0-

0 1000 2OW 3 W00IMPbACT VELOCITY, V, FT/AIC

FIG. 10. Residual Velocity as a Function of Impact Velocity;0.250-Inch 4130 Steel Plate (230 BHN); 410-Grain, a ='60-Deg Rigid Projectile (53 Rc), 0-Deg Obliquity.

13

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NWC TP 5607

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U 0

0 4

UU

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i20

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50' 0

& 300

W -

•,200 400 600 800 | 000 0200

IMPACT VELOCITY, V, FT/SEC

FIG, 1 1. Ricoche't Obliquity Angle Data as a Function of Impact Velocity; Rigid 4340Steel (53 Rc) Projectiles of 30-, 60-, and 90-Deg Nose Half-Angles (a) RicochetingFrom 0.2 50-Inch 4130 Steel Plate (230 BHN); 30-Deg Obliquity.-

014

MOM=1

NWC TP 5607

ligure 12 is a plot of the r1cuthet angle data as a function of theratio of impact velocity to tile individual ballistic limit velocity ofthe particular projectile involved. Plotting in this manner tends togroup the data and hbtter illutstrates tile manner in which the ricochetangle changes with impact velocity. Data in Fig. 11 and 12 do notdisplay any distinctive differences in ricochet angle due to differencesin nose shape. For rigid projectiles, it would appear from the resultsof this study that the angle of ricochet can be considered as beingindependent of nose sha-2. Although this study was limited to oneimpact obliquitv and one plate thickness, if the influence of nose shapeupon ricochet angle was significant, this effect should have beenevident in these experimental results.

COMPARISONS OF EXPERIMENTAL DATA ANDPREDICTIONS OF" ANALYTICAL MO[DEL

In 1970, the Surface Target Vulnerability Program, JTCG/ME (throughthe Naval Weapons Center, China Lake), supported a research program atthe University of Denver Research Institute (DRI). Its objective wasto develop a suitable multiple plate perforation model which could beused to predict the penetration of large-caliber piojectiles, guidedmissile warheads, and bombs into ship structures (Ref. 3). This model Iincorporates methods for considering various projectile parameters suchas nose shape. This present experimental investigation was performedto obtain data which could be used to improve prediction capabilitiesof the ship penetration model (SPM) as related to nose shape. Theprediction models for ballistic limit velocity, residual velocity, andricochet obliquity were modified. These models are discussed.

Ballistic Limit Velocity

Predictions of the ship penetration model were inaccurate whencompared with the experimental ballistic limit velocity data generatedin this program. This inaccuracy is attributable to the dramaticinfluence that projectile deformation exerts upon ballistic limitvelocity. In the original penetration model for rigid penetrators, thesubmodel which considered variations in nose shape was based upon con-siderations of data for arnor-piercing projectiles (representative ofsharp penetrators) and fragment-simulating projectiles (representativeof flat-ended or blunt penetrators). Armor-piercing projectiles have ahardness of 63 Rc. Since there was an absence of data for rigid, flat-ended projectiles, fragment simulator data was used. It was felt thatthe hardness of these projectiles (29-31 Rc) was sufficient to representrigid projectile,; for the small values of T/d (plate thicknecs/penetratordiameter) typical during ship penetration. The results of this study.'illustrate th, strong influence which penetrator deformation exerts uponthe ballistic limit velocity of steel plates (see previous discussionrclatcd tc Fig. 5). It has bec, slowr that rigid prujeLtileq., Lu be

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0 02 04 05 0.8 1.0

V50

FIG. 12. Ricochet Obliquity Angle Data as a Function of Normalized Impact Velocity;Rigid 4130 Steel (53 Rc) Projectiles of 30-, 60-, and 90-Deg Nose Half-Angles (a)Ricocheting From 0.250-Inch 4130 Steel Platt; (230 BHN)ý 30-Deg Obliquity.

0160

NWC TP 5607

considei ed as suich, must truly remain rigid (exhibit almost no impactdeformation) and that there can he a dramatic increase in ballisticlimit velocity as projectile hardness decreases.

Based upon the results of the tests with the Flat-ended (C - 90 deg)projectiles, the ship penetration model was modified. In Fig. 13, thenine circular data points are the same as presented in Fig. 3. Thethree triangular points do r t represent firing data, but are interpre-tations of experimental data curves for monobloc projectiles (Ref. 4).They apply to 0.50-caliber, 410-grain rigid projectiles having standardarmor-piercing ogives (equivalent to a conical nose having a nose half-angle of 14.5 deg; Ref. 3). The three dashed curves shown on Fig. 13are the predictions of the ship penetration model for "sharp" rigidprojectiles. This equation (DPI Sharp ProjectIle Equation) is:

T 2 5 (CA) (W/d) B (50n) siT . .d .(V ) - - n 1 + - (4)

sina. + fcosa 50n s sincA B

3000a

2500

/""• DRI Sharp

2000 Projectile Equotion

2000 (1c /•- • • • -

1500 Least Squares Dato FitT/d> / •I• -- 0.75

1000 - - 050

500& 4P (Equivalent at:14.5*)

* Conical Nose

0 I 1 1 I I 1

0 10 20 30 40 s0 60 70 80 90

a, DFGREES

FIG. 13. Correlation of Ballistic Limit Velocity Data as a Function of Projectile NoseShape; Rigid Steel Projectiles (53 Rc): Steel Plate (230 BHN).

17

NWti IT.'b)____________

AN :: ncreaý-i, the projectile nose geometry changes from "sharp"to "'blunt." Ohviouslv (t rem comparing the prediction of Eq. 4 with thedat. po its), the tranl ition from "sharp" to "blunt" starts somewherebetween .t .= 15 deg and x = 30 deg, and is essenti[allv complete befcre.1 = 60 deg (i.e., the experimental results at Lt = 60 deg are essentiallythe same as at ,1 i 90 deg). The three values shown ik Fig. 13 for uC.(the critical nose half-angle) were determined as outlined in the shipptenet rat ion final report (Ref. 3) (and in the following discussion), and.are' esLimate.s of the boktndarv between "snarpncss" and "bluntnes" (i.e.,the appearance of plug,'ging during perforation). The three solid curvesin Fig. 13 represent the model developed to predict (VSO)n as a functionof nose shape as characterized by u. Following is a brief descriptionof the model. (Th, model will be presented In dctail subsequently.)

1. For ý- 15 deg, Eq. 4 for sharp penctrators is used to predict

S otr I', deg - ., - xcc' a computed val'ie of the parameter y (aliInear functiun of ii - 15 deg) is subtracted from the rolutlon

of Eq. 4 to predict (VSO)n.

3. For -A, ,x 901 deg. a cori~puted value of tile parameter z (anr

exponentLiil itl('t ,,n ti t tt - -t,) is added to th-, (%'50n) valucfor fla;t-ended projcectiles to predict (VU0n)

4 I01 r - 90 deg a;, equation of the followl 'g form is used to

pred ict (V5 0n)

(\-fn " (W/dI)"i(I/d)h (5)

whtern a, h, and C aret constants which depend upon platepropI'rt itt. and project ile character 1nti vs.,

:,t- thI .t at'. h loe!tSL fd valuei (Fig. 13). there I .1.trv little changeiii ' )n with nose Hhtapi. lata for lower l/d valuteis are hard to ubtnindite t.o the low vw lo Itties Involved,; sli'e It was d(enonn t rated that(V%'5),I, Is inFn4v ti4 lvt, to chlangen' in (i at T/d a 0.25, 1L was nut. neceb-Sarv tO perform such low velocity experiments.

Th, data plott(d on I Ig. I J pertain to h'/d valtues of 0.25, 0.50and () . .5. RI w I! proj v'c t Il es4 wht ch t re charac Le r I zed by I ow u vaI uetutt-nd to pen'trate by punhlnhg materin] aside so an to produce a hl!.. andart, referred to asi "sharp."' Rig d project l14-is which are cLharacteritzedby high -t vwlt,'. tend to push niterlat ahetad it m ts toT produice a i platepht ig dtirlng iptrforiatlIto and arv referred to nit "b'int ." Armor-pler,'lug

p'roje.c' lien ur, "'dtunrp" and fliit-cnd,.d p Ler t i,.•s are "hliunt;'" pr'joc-.tIlIt' liiving 1 vaUiivte itt b'etween rtaln a[ir lihiLtt'tl ('f "''hip''" anid"h. itblun " ,ro~lt'rt I It, to varvy rg, (Jed gre''m

IM

NWC TP 5607

E".quation 4 pertains to projectiles which can be classified as"sharp." As was stated, Eq. 4 was used to generate the three curves(dashed above cr - 15 deg) which rise from left to right on Fig. 13. TheA:' (sharp proiectile data, triangular symbols) fall on these curves, butthe data at az - '30 deg fall below the three curves indicating that theassocinted projectiles already exhibit some attribute.- of "Lluntness."Obviously, the projectiles possessing nose half-angles of 60 deg arebehavin8 essentially as "blunt" proje-tiles. (Plate plugs produced by(t - 60-deg and ca - 90-deg projectiles are quite similar in appearance;see Fig. 9.) The three dashed curves associated with the circular datapoints are least squares fits to the data for the three T/d values.

A prLdiction model would compute (VsG)ln for "sharp" projectilesidsing Eq. 4, and would compute (V5o)n values for blunt penetia,:rs usingan equation applicable to Cu - 90 eeg. It would accomplish a tranbtilonbetween the "flharp" and "h!unt" predictions for C. values between 15 and90 degrees. The following approach was used to develop the '¶odel fcrrigid projectiles which provides the nrediction represented by hne solidcurves in Fig. 13.

Shar 2 .ro.jetjles. For : < 15 deg, Eq. 4 is used.

Flat-rlnded Projectiles. For ca - 90 deg and T/d < 1, the followingform correlates data pertaining to flat-ended rigid projectiles:

wr 50 -.C (W/d 3)a (T/d) b (5)

whe re

W - wegUhL ol projectile, 11)

d - diameter .,f prnjectile, in.

T - plate thicko'If4, in.

C, a, and b are ,.-nstants which vary wiLh plat.-! naterial and

projectile characteristirs.

Above T/d - 1, the projectile is forced to penetrate to considerabledepth before driving a plug from the plate and the (Vso)n is higher thanthat predicted by l'q. 5. For L/d - 2 and 4130 steel plate heat-treatedto 230 B1IN the followInp equation applies to the above conditions for

- 90 deg:

"(V50) n 930 ( /d% 0.b) 1475 (T/d) 0 " 1 (6)W/d /

39L.A

NWC TP 5607

Deterajinatiun of the Critical Nose Italf-Angle, cic. A criticalvalue of the nose half-angle (i.e., ac) which serves to separate"sharpness" from "bluntness" can be determined by considering that during

penetration a flat-ended penetrator picks up a false nose (a physical

fact when penetrating thick plates) made up of plate material which

redefines the nose shape. Then, as outlined in Ref. 2, the projectilecan h'e represented by a sharp projectile with a nose half-angle, ac, aweight, W!, equal to the weight of the original projectile plus thefalse nose, and a velocity V1 which is (W/Wl)(V 5 0 n)--thereby conservingmomentum: (V50n) is the limit velocity of the orij,'nil projectile. Theplate thickness in the representation Is taken to be 11 which is lessthan T due to the transfer of plate material to the projectile. Giventhis sharp projectile and thinner plate representation, Eq. 4 can beused with Eq. 6 to establish a relationship between ac and T/d for givenvalues of CA, B, and f. That is, since (V50)n for the representativeprojectile must be equal to that of the actual flat-ended projectile.Eq. 6 can be substituted into Eq. 4 for (V50)n for wherein T is replaced

by T1 , CA is replaced by (W1 /W)CA, (Vs0)n is replaced by (W/Wl)(V50)n,and a is replaced by ac.

W1I (7/d + T 1/d)W- I + -o (7)

W 4 (W/d3)

vhere o is specific weight of plate material, lb/in3 .

If hdc is defined as being:

h 1 (8)dc 2 tan ýi,

and if T/d > hdc, then

hdc 9

Tl/d - T/d 3 (9)

otherwise

(hd - T/d) 3

Tl/d - T/d - (hd/ 3 ) + dc -Y-----3(10)dc 3 h 3dc

Making the previously mentioned substitutions Into Eq. 4, thefollowing equaLion results:

20

raNWC TP 5607

32.5(CA)(W /W)(W/d)(T /d= (V (-((1 (sin a + f cos (L d)n (W5W0)

B Zn + ((V5 0 ) sin a

sin a (W I/W)B (1

Substitution of Eq. 7, 9, and 10 into Eq. 11 results in the 'aforementionedrelationship between ac and T/d which can be resolved by iteration, bothwith respect to the variables and the conditions pertaining to Eq. 9 and10. T'urves of ac versus T/d for various values of B (or plate hardness,BHN, dhich is directly related to B) can be constructed so that ac valuescan be determined rapidly. The ac values applying to the three T/dvalues used in this experimental program are shown on Fig. 13. Figure 14shows the Ac versus T/d rlationship computed for the 230 BHN, homo-geiieous steel plate used.

BLUNT PROJECTILES (az90*)

.V 7 PSEUE -BLUNT

U7 PROJECTILES (acs-a <90') "

60O

X. 50,

_ 40 ROLLEO HOAOGENEOUS STEEL PLATE

SdJ.'l; 230t- 30SPSEUDO - SHARP '

20o- PROJECTILES (15*<(a< a)

F SHARP PROJECTILES WI 5 150')

0 L , j , j . . . .. I-L _ I . . . .

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 '.2 1.3 1.4 1,5 1.6 1.7 1.8 19 2.0

T/d

FIG. 14. Computed Critical Nose Half-Angle (a) as a Function of T/d for RolledHomogeneous Steel Plate (230 BHN).

21

NWC IT 9607 _-

The Transition from "Shar'p to "Blunt." The change from "sharp" to"blunt" as ci increases, would not be expected to take place suddenly atsome value, ixi; it would be expected to be transitional. Further, the:,hnve Iro,,Jurt tot ,:omputi.M tic merely provides a reasonable estimateof the boundary between "sharpness" and "bluntness." Figure 13 suggeststhat (V50)n values will begin to deviate from the "sharp" curve generatedby Eq. 4 as x becomes larger than 15 deg. As values become larger than(1c, plugging should develop rapidly. Consequently, the transitionsuggested by Fig. 13 is proposed as being representative of observationsand expected behavior. Figure 15 illustrates the transitional modelwhich utilizes the ballistic limit velocity predictions for sharp(o5On)s and blunt ('5On)b projectiles.

AC

- ac

a :150 Cc

FIG. 15. Model for Predicting Transitional Values of Ballistic Limit Velocity.

For values which lie between 15 deg and ac, the value for (V50)ncomputed by Eq. 4 is diminished by an amount (y) to obtain a transi-tional value for (V50)n. For values exceeding cxc, the (V50)n value fora flat-ended projectile is increased by z to obtain a transitional valueof (V50)n. The parameter Ac represents the difference betweer the(V50)n value computed by Eq. 4 at a = ac and the (V50)n value computedfor a flat-ended projectile (Eq. 5); thus (nAc) represents the value ofz at .x - cxc and (1 - n) Ac represents the value of y at cc - c (where n

has some value between 0 and 1). Obviously, n is I at a - 15 deg and0 at a = 90 deg. If y is assumed to be linear with c%, then

y (1 - (n) i/cx - 15 deg (12)CC- 15 deg

22

NWC TP 5607

It z is assumed to decrease exponentially with ca, then

z - n A e C (13)

Letting a = 0.1 is appropriate with respect to the data plotted onFig. 13. I

The dastied curves representing least squares fits of Fig. 13 (theirvalues at C% cic) can be used to determine a relationship for n as afunction of ac. These three values are plotted along with two otherknown values on Fig. 16. The curve on Fig. 16 represents the followingequation:

n 0.0001480(cc - 15 deg) 2 - 0.0 2 4 4(0tc - 15 deg) + 1 (14)

10

09

08 •

07

0641

705

0.4 FIG. 16. Relationship Between

0.3 Parameter (0) and Critical NoseHalf-Angle (a.).

02

0.0 10 20 0 40 50 60 70 80 90

ac

For "Semi-Sharp" Projectiles, 15 Deg < c,_S ".. As indicated above,the (V50)n fur semi-sharp projectiles is computed an follows.

a -15 deg (5(V50)r - (Vs 0 ) - (1 - n) Ac 15 deg (15)

where (V5On)s is (V50)n as computed using Eq. 4 and Ac is the differencebetween (V5On)s as computed by Eq. 4 (at a %c) less (VSOn)b as computedby Eq. 6 (a - 90 deg).

23

4

NWC TP 5607

For "Semi-Blunt" Projectiles, fl,. a ' 90 beg. As indicated above,(ie (V5 0 )11 for semi-hunt projectiles is computed as follows:

(V 50) = (V5on)b + n e-0.1 (it ( C (16)

where (VsOn)b is the (V5 0 )n as computed using Eq. 6.

Application and Limitations of the (Vso)n Prediction Model. Thesolid curves On Fig. 13 were generated using the prediction model out-lined above. In Its present form, the model applies to rigid projectileswhich are characterlz,ýd by projectile length-to-diameter ratio equalto 2. It is limited to T/d values less than 1.0 and to steel platescharacterized by 15W.1 equal to 230. It can be used for projectiles havingother (L/d) vaiues and plates with different characteristics simply byreplacing Eq. 6 by the appropriate equation for flat-ended projectilesand using this new equation with Eq. 4 to compute ac& values as describedabove. Also the limitation of T/d can be lifted If Eq. 6 is replaced byan equation valid fvr '/d values above 1.0.

Residual Velocity

tn the previouh section, Experimontcal Results, residual velocitydata generated during the experimental firing program were presented ingraphical form, (Fig. 6. 7, 8, and 10) and compared with the predictionof Eq. I using the experimental value of (150)n. Equations I and 2predict residual velocity; the applicablility of one or the other isdependent upon the comparison between A and ac. For "sharp" penetrators('t - 'Ac)j, Eq. 1 applies. For "blunt" penetrators (a ', ac) Eq. 2 applies.Figures 17, 18, 19, and 20 compare residual velocity data with the pre-diction ot 9.q. I or 2, whichever applies. The (Vso)n values used insolutiont of these equations are those predicted by the previouslydiscussed model and shown on Fig. 13.

tFigure 17 presents residual velocity data for the a - 30-deg pro-jectile against 0.125-inch thick 4130 steel plate at 0 deg obliquity.The critical nose half-angle (ac) predicted for this impact condition isequal to 53 deg (see Fig. 13). Since (ri) is less than (ac) , Eq. 1applies to the residual velocity prediction. The projectile is assumedto he behaving as a "semi-sharp" penetrator and perforating the platewithout formation of a plate plug. Figure 17 shows excellent agreementbetween the experimental data and the curve predicted by Eq. I.

2-4

NWC TP 5607

UJ

w

0

Prdcto ooI I .|51ohTic!13 tel 30BN

00

LU

-J

4E I

UEQ

0'000 2000 3000 40D0

IMPACT VELOCITY, V, FT/SEC

FIG. 1 7. Correlation Between Residual Velocity Data andPrediction of Eq. 1; 0. 125-Inch-Thick 4130 Steel (230 BHN)Plate; 4 1 O-Grain, a = 30-Deg Rigid Projectile.

Figure 18 presents the residual velocity data for the (ai 30 deg)

projectile perforating 0.250-inch-thick 4130 steel plate at 0 degobliquity; occ for this condition is equal to 33 deg. Since a is againless than ac, Eq. 1 applies to the residual velocity prediction. Asseen on the figure, the higher velocity test data lie below the predic-tion curve. These data points suggest that the plate may be pluggingand the momentum of the plate plug detracting from the residual velocityof the projectile. However, the two lower velocity data points (thedata point at an impact velocity of 1,725 ft/sec should be ignored sinceit appears to be an anomaly) correlate well with the prediction curve.The fact that the predicted critical nose half-angle (33 deg) is soclose to the actual projectile nose half-angle (30 deg) suggests that

the projectile may be borderline between "sharp" and "blunt" behaviorand is performing as a sharp penetrator at the lower perforationvelocities, but is plugging the test plate at the higher velocities.

25

S..... •'• '• • • ....... I ........ IT• .......I ... •-"7 '"• "" 1

r

NWC TP 5607

3000 F

0 I 0U.

I> to I

I-

-J

LL

Eq

00

_J

0

ol- - _____.______________

0 1000 2000 3000 4000

IMPACT VELOCITY, V, FT/SEC

FIG, 18. Correlation Between Residual Velocity Data andPrediction of Eq. I; 0.250-Inch-Thick 4130 Steel (230 BHN)Plate; 410-Grain, a = 30-Deg Rigid Projectile.

Figure 19 compares data with Eq. 2; in this case the critical nosehalf-angle (53 deg) is less than the nose half-angle of the projectile(60 deg). The plate is 0.125-inch-thick 4130 steel. The data plotslightly above the prediction curve of Eq. 2, showing very good agree-

ment with the prediction curve.

Figure 20 again compares data with the prediction curve of Eq. 2.For this test condition (0.250-inch-thick 4130 steel plate, cL = 60 deg),the predicted critical nose half-angle (33 deg) is well below the pro-jectile nose half-angle. There is no doubt that this projectile is

behaving as a "blunt" penetrator as illustrated by the correlationbetween the Eq. 2 prediction and the data. The prediction of Eq. 1 forthese data would be 20% higher than the Eq. 2 curve shown in Fig. 20.

26

WoSulI

Wcc 20 0

U-

0

_-J

0 o0 IBM 3000 4000

IMPACT VELOCITY, V, FT/SEC

FIG. 19. Correlation Between Residual Velocity Data andPrediction of Eq. 2; 0.125-Inch-Thick 4130 Steel (230 BHN)Plate; 410-Grain, a = 60-Deg Rigid Projectile.

Ricochet Obliquity

The ricochet model incorporated within the Ship Penetration Model(Ref. 3) provided an average value for the ricochet obliquity angle( 0 r) The ricochet obliquity data are represented in Fig. 21. As dis-cussed previously, the effect of projectile nose shape upon ricochetangle as depicted by these data does not appear to be systematic,deviations appearing to be chargeable to experimental scatter. For thetest condition pertaining to the data in Fig. 21, the ship penetrationmodel ricochet obliquity model predicts a ricochet obliquity of 66 deg,independent of impact velocity. This predicted value depicts a goodaverage of experimental results, but does not define the observabletrend of the data wherein the ricochet obliquity appears to approachthe impact obliquity as the impact ,elocity approaches the ballisticlimit velocity.

27

NWC•T P 5607 .__ _ __

3000

3OO0 0

4 2000 1tL

>I

o ..10 0 /"J

Eq 2

2 000LU ~UI

0 1 I00 0O00 200 3000 4000

IMPACT VELOCITY, V, FT/SEC

FIG. 20. Correlation Between Residual Velocity Data andPrediction of Eq. 2; 0.250-Inch-Thick 4130 Steel (230 BHN)Plate: 410-Grain, a = 60-Deg Rigid Projectile.

The following ricochet model was developed for rigid projectilesand steel plate based upon experimental observations of this and pre-vious work (Ref. 5), and the physics of the ricochet problem. Thismodel incorporates means for including the effects of penetrator defor-mation--not a consideration herein.

As long as the impacted surface remains undeformed and rigid,ricochet dynamics are relatively easy to predict. The maximum elasticenergy which can be stored within a penetrator is equal to

2E = 1 _ (in-lb) (17)

e 2 p E

28

NWC TP 5607

A

70

Lii.

-l•50o

so

00

40'

20

a

A30.

10. 90'O

0 200 400 6000 800 1000 1200

IMPACT VELOCITY, V, FT/SEC

FIG. 2 1. Correlation Between Ricochet Obliquity Data and Eq. 25 ; 30-Deg Obliquity.

29

NWC -I' 5607

whltre

L-= speciIic weight of pLf)etrator material, Ib/in 3

, p = compressive ultimate strength of penetrator material, psi

Ep = Young's modulus of penetrator material, psi.

In such a ricochet situation the velocity component, Vh, parallel to thesurface changes very little. The normal component, Vn, is defeated,

elastic response of the penetrator being responsihle for the normalcomponent of the rebound veUocity. Using this model, the two componentsof the ricochet velocitv become

Sh si•;n (ft/sec) (18)

V = - (ft/sec) (19)n 12 -f

whe re

- impact obliquitV, deg

g acceleration of gravity, 386 in/sez2

The tangent of the-minimum (corresponding to maximum elastic energy)

ricochet obliquity angle, Or, is then

12 /WT g V sin 6

tan V = /V = (20)tn•r 11 n 0

According to this equation, a steel penetrator characterized by C--

150,000 psi which impacts a rigid surface at an obliquity of 45 deg,and at 200, 500, and 1,000 ft/sec, will exhibit corresponding minimumricochet obliquities (measured with respect to the plate normal) of 59,77, and 83 deg. The softer the penetratur the more rapidly er approaches90 deg. Since the entire projectile will not be stressed to the ultimatestress, rebound will be less and er values will be higher. The rightside of Eq. 20 can be multiplied by a proportionality factor, J, to

account for this, and an appropriate value can be determined fromexperiments.

Surface deformation will act to decrease ricochet obliquities by

presenting a ramp to the parallel (with respect to the plate surface)motion, which will reduce the parallel component of ricochet velocity

and increase the normal componert. Surfaces are deformed in two ways,surfqre penetration and by plate flexure. I.etting 6 he the total

deflection due to penetration and flexure, dimensional analysis leadsto the following functional relationship for a non-deforming penetrator:

3

NWC TP 5607

c/d -f T/d, --P- V cs 2' (21)

d 3 V •

The total normalized deflection, 6/d, will be the sum of the deflectionsdue to penetration and flexure. Studies of the respouse of waveguideto ballistic impact have shown that the permanent flexural deflection islinear with respect to velocity below the ballistic limit velocity(Ref. 6). Further, th 4Ls flexural deflection appears to be inverselyproportional to the square root of the normalized thickness, T/d.Cratering (penetration) studies have shown that crater volume is approx-imately proportional to the impact energy; thus, deflection due topenetration is approximately proportional to the cube root of thekinetic energy. Measurements of flexure and penetration near theballistic limit at normal incidence during these experiments (at T/d =0.5) indicated that the flexural component was over twice as large.Penetration by a deforming penetrator will be related to its deformeddiameter, D. These considerations lead to the following equatiun fordeflection:

O/ (M /d 3)ý12V) 2cos 2' 1/3 [(M /d 3)(12V )2 os 261/

= . + 0.29 -p (22)

where K is an empirical constant of proportionality placed on the leftside of the equation for convenience.

If Eq. 20 (modified by the proportionality conatant, J, mentionedpreviously) defines the ricochet obliquity angle for a penetrator Impact-ing a rigid plate, the following equation would be expected to define thericochet obliquity for a penetrator impacting a non-rigid plate:

tan 0 1 S + f (23)r i3

Using the data presented on Fig. 11 to plot f[(6/d)/KJ versus (6/d)/KEq. 23 was found to take the following form (which applies where(6/d)/K > n/K):

tan er =p -. expm K (24)

where in and n are empirical constants. When (5/d)/K < n/K the exponentialterm is replaced bv 1.0.

I31

A

N%:( 11

I t hi d, t .1 ))ll~ttI-d on F I I I Oil fol l owl ng valIuies of paramieters

It)X 1); 43 0)5 in.;

0.," 11, In ; 1, 10 deg.

. 271M,000) pwl; 1-:1, ii) x 106' pw.; IDid z I

Va uIhicievl. ioulq . 211 and 2.1 becone

d~ V ~7. + . Y . ( '(26)

I. 1)11i Ia 26 k I~b wii~toLvu d 1:ii~ 1x; 25~ for (;J/d)/K. If *i*4, mn 3.6,,ind. n/K 21.i, the' curv(* HtI''Wo Ol FI g. -2] resrit) I ; lielIow 415 ft/gec ,I

'id)3/ 2.0 -Ind thu iiXponon t-I i]l Lerm Ii Eq . 25 1w 1 .0. The predictionurve of 1.41. Z")a 4rtklitt(*!i wucl wi th tht expIeritnen~al d(tt~. Figure 22

ig A al) Ai at Lhr pred Ic ti laki :rviL.~ of E~q. 25 for valrious val ues ofImpact ob Iiqlisi I . Th is f IgMorc %IIOWs L1w predict tuns of the ricochlet'i'd'i for tht lit. :%pa ofI,~ th Lost dn' :i Ovh'wii In Fitz. 21. IcII IIH lu~r~iteP tht. vfect 1 of ImplAct, Obliquitytv upn i rCochet obhliquity,

Tilt- P~rowartlI ,i;. ILv crolq t outn, .1, is i overicily related to the ratioof OW Ihat .ini I Cl usttic onergv wh ich appears In Lilt' projectilie to themay~inti mm will(),l conilid ippv.air ; .1 s 4 Is prohnb ly a good value for anyrlcrchvi Psit nat ion iconcerulI ug *'1 Kolid tilt-cl project!ice. The constant mn

yI)vr- iho rate aif den a,,' of thu e xponential1, and there Is no redson 10bL1l] IvC thit i0, v3lor wouild he different. for difforeI)L materials. The,unotant ilK it, the Value of ('Idt) 1K Whi-rc plate deflection (deformation

aind I I exurv) hegl~ L O ;n fiW I L ho r icoc'et obl iqu ity . Though K isd~l!YI',.II~H, lhOr IN. nlo Jus-tifi~lt iton for prce~tmirng that it will he

the sarih for allI rlIcucine I impact!o (it probahbly vnrlv.- with the ML rengib,I'inn k --odu iius, and ienmis t of t no plao) . kir then , the' coef ficient 0.2Iin 1'(. 2 ! re late,.; to the experiment,, duscr ihad he-re in which involvedrigid proIc(t uie. While the model appears to be capaithi of general;lipjl lIcat ion to ricochet. predIctI'OnS, additional data will have to beannal yzed to dOvI.'rn Iint how thec empfIr Ical cons tanti varY.

_ NWC TP 5607

0 60

70"

"rj

60, 0

J 400'

30

20

10,

20

0 'I . , I I I

0 200 400 600 800 1000 1200

IMPACT VELOCITY, V, FT/SEC

FIG. 22. Ricochet Obliquity as a Function of Impact Velocity as Predicted by Eq. 25.

33

NWC TP 5607

SUMMARY

Nose shape of rigid penetrators affects ballistic limit velocity

and residual velocity as regards the penetration of steel plates. Nose

shape has little effect upon ricochet obliquity. The variation in

ballistic limit velocity with change in nose shape is not large. Rigid

projectiles can be categorized in behavior as "sharp" or "blunt." The

classification of a given nose-shaped projectilo as to mode of behavior

Js accomplished by comparing the equivalent conical nose half-angle to

the critical nose half--angle. The critical nose half-angle is predict-

able by analytical methods. Blunt-nosed rigid penetrators behave quite

differently from non-rigid penetrators. Based upon the experimental

data generated in this program for rigid blunt penetrators, predictionmodels were successfully modified to provide means of accurately pre-

dicting ballistic limit velocity and residual velocity for rigid pro-

jectiles having various nose shapes. A model was developed for predicting

ricochet obliquity for rigid projectiles and steel plate.

3 4

NWC TP 5607

REFERENCES

1. Naval Weapons Center. Transformation of Terminal Ballistic ThreatDefinitions into Vital Component Malfunction Predictions, byR. F. Recht, T. W. Ipson, and E. Wittrock, Denver Research Institute.China Lake, Calif., NWC, May 1969. (NWC TP 4871, publicationLNCLASSIFIED.)

2. -------- Terminal Ballistics of Elongated Fragments, by T. W. Ipson,and W. A. Schmeling, Denver Research Institute. China Lake, Calif.,NWC, December 1972. (NWC TP 5449, publication UNCLASSIFIED.)

3. -------- Ballistic Penetration of Ship Slructure, Final Report (U),by R. F. Recht, Denver Research Institute. China Lake, Calif., NWC,September 1972. (NWC TP 5419, publication CONFIDENTIAL.)

4. Naval Proving Grounds. The Construction of Plate Penetration Chartsor Tables, by A. V. Hershey. Dahlgren, Virginia, NPG, May 1955.(NPG Report 1120, publication UNCLASSIFIED.)

5. Denver Research Institute, University of Denver. The Dynamics ofTerminal Ballistics (U), by R. F. Recht and T. W. Ipson. Denver,Colorado, DRI, February 1962. (Final RepolL, Contract DA-23-072-ORD-1302, for Army Tank Automative Center; DDC File No. AD-274-128 andAD-328-796; UNCLASSIFIED Report and CONFIDENTIAL Appendix.)

6. Naval Weapons Center. Characteristics of the Deformation ofBallistically Impacted Waveguide, by T. W. Ipson and W. A. Schmeling,Denver Research Institute. China Lake, Calif., NWC, February 1972.(NWC TP 5328, publication UNCLASSIFIED.)

35

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38

UNCLASSIFIEDDOCUMENT CONTROL DATA R & 0

S.-nnI,, tt, . Ii, on rifIe. tod. T jt .rM I. ..d.,'de.,,,':... nolaI,,, n .t I,, *-(-ed .. "r thile v- -l11r -p-rI m I .-- #ed)

I~~~0 At".�a'N. T1 (7tl IS,'Ft 11A1,0.

Denver Research Institute UNkLASSIFIEDUniversity of Denver 2, GROUP

Denver, ColoradoI SREORT -11 I

Effect of Projectile Nose Shape on Ballistic Limit Velocity, Residual Velocity,and Ricochet Obliquity

4 LI¢CRIP"IVE NOTES(TVp* oivcpott and I-u1rC1tn dlte@)

5A. ?.OrS 'Frar n•.n. IiddF, - Inl. ' Il... t ne a

Thomas W. IpsonRodney F. RechtWilliam A. Schmeling

6 REPORT OATE I.. TOTAL NO OF -AGCES | NO OF REVS

December 1973 38 6*S CON-AC OR GRANT NO 90. ORIGINATOR'S REPORT NU"VERI(S

N00123-69-C-1970.. RolC I N NWC TP 5607

AirTask A-350-53211008B/3F32-353-501C. st OTt- AR REPORT NO1S,1 (Any ort numbr. oher may be sixgfnod

thIn• 1.001)

d

ItOISTA.G.i.0, '.-TEITN7

Distribution limited to U. S. Government agencies only; test and evaluation;14 December 1973, Other requests for this document must be referred to the NavalWeapons Center.t1 •UP• E ENM TAR' NOTIE 12 SPONSORING .. 1U 1 At1. m. T,

Naval Weapons CenterChina Lake, Calif. 93555

Target vulnerability analyses consider ballistic penetrators which have variousnose shapes. Nose shape often undergoes changes during the target penetrationprocess due to deformation. It is important that the effects of nose shape uponballistic perforation dynamics be known and accounted for in vulnerability analyses.An experimental firing program was conducted in which rigid penetraturs having threedifferent nose shapes were fired against steel plate. Experimental data generatedconcerned ballistic limit velocity, residual velocity, and ricochet obliquity.Experimental data were compared with predictions of analytic models. The predictionmodels were modified to reflect the results of experiments.

I~ .... I AIfDD,' 0 1473 UN A USSIFIED

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Terminal ballisticsExperimental dataNose shapeBallistic limit velocityResidual velocityRicochet obliqultyShip penetration miodelVulnerability analysisBallistic prediction models

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3 Defense Intelligence Agency"DI-7, COL A. Belmont (1)DI-7E, MAJ N. L. Leone (1)Technical Library (1)

1 Center for Naval Analyses, University of Rochester, Arlington, Va.1 Falcon Research & Development Company, Albuquerque, New Mexico1 Falcon Research & Development Company, Baltimore, Md.I Falcon Research & Development Company, Denver, Colo.1 Honeywell Inc., Systems & Research Division, Minneapolis, Minn.

(C. R. Hargreaves)2 Institute for Defense Analyses, Arlington, Va.

Research & Engineering Division (1)Technical Library (1)

2 Remote Area Conflict Information Center, Battelle Memorial Institute,Columbus, Ohio

I Rockwell International Corporation, Los Angeles, Calif. (W. L. Jackson)1 The Boeing Company, Seattle, Wash. (R. G. Blaisdell)3 University of Denver, Denver Research Institute, Denver, Colo.

T. W. Ipson (1)) R. F. Recht (1)

W. A. Schmeling (1)

7