c 0 frfCE Of' .SCIENTIFIC Q.ESEAQCH ~DEVELOPMENT

NATIONAL DEFENSE. R.:ESEARCH COMMITTEE. DJVJ.SION 51 X- :>ECTlON E>.l

FORCE TE5Tj OF CONCRETE PRACTICE BOMB:S

MJBAZ PRACTICE BOMB AN-M43 G.P. 500LB. BOMB AN-M56 L.C. 4000 LB. BOMB

HYDRODYNAMICS L' C ,f: CALIFORNIA fitSHT,_'TE GF If_ -

PASADE~A

PUBLICATION NO. 5

THE HIGH ~PEED \.lATER. TUNNEL CALJP012.NJA JN~TlTUTE OF TECHNOLOGrY.

PA.SADENA.CALIPOR.NIA

~ECTION Ne<:..t-.sr Zo7-lZ.4~

LABORAT012..Y N2 ND-32 c COPY NS!I43

66~[ I f)E NT I AI

OFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT NATIONAL DEFENSE RESEARCH COMMITTEE

DIVISION SIX -SECTION 6.1

FORCE TESTS

OF

CONCRETE PRACTICE BOMBS M38A2 PRACTICE BOMB

AN-M43 G.P. 500 LB. BOMB AN-M56 L~C. 4000 LB. BOMB

ROBERT T. KNAPP

OFFICIAL INVESTIGATOR

THE HIGH SPEED WATER TUNNEL AT THE

CALIFORNIA INSTITUTE OF TECHNOLOGY HYDRODYNAMICS LABORATORY

PASADENA, CALIFORNIA

Section No 6 i sr207 - 2245

Labo ratory No ND-- 32

August i4, i945

This docuaent contains inforaation affecting the national defense of the United States wlthin the aeaning of the Espionage Act, oO u.s.c., 31 and 32 , as aaended. The transaission or the revelation-of its contents in any aanner to an

Report Prepared by Robert M Peabody Hydraulic Engineer

C1) N F I A EffD:tj;

•

CONFIDENTIAL

TABLE OF CONTENTS

Sec t i o n P a g e

INTRODUCTION 1

SUMMARY AND CONCLUSIONS 2

DESCRIPTION OF BOMBS AND MODELS 3

TEST PROCEDURE - FORCE TESTS 4

EFFECT OF ASYMMElRY 7

CONCRETE PRACTICE BOMBS 9

M38A2 - 100 LB. PRACTICE BOMB 14

AN-M43 G.P. 500 LB. BOMB 16

AN-M56 L.C. 4000 LB. BOMB 18

COMPARISON WITH TESTS AT WRIGHT FIELD WIND TUNNEL 20

APPE ND IX

CONFIDENTIAL

INTRODUCTION

FORCE TESTS

OF

CONCRE~E PRACTICE BOMBS M38A2 PRACTICE BQMBS

AN~43 G P 500 LB . BOMB AN -M56 L C. 4000 LB BOMB

This report covers model tests in the High Speed Water Tunnel and Polarized •Light Flume of the Hydrodynamics •Laboratory at the California Institute of Techn ology on the following aircraft bombs for use against land targets and surface targets on water

Concrete Practice Bombs

(a) with large fin box tail,

(b) with sma 11 fin box tail

(c) with drum type to i 1

M38A2 Prac t ice Bomb

AN-M4") G p 500 lb Bomb

AN- M56 •L c 40<Xl lb Bomb

The tests were authorized under Project OD 99 .

Tests were made on two- inch diameter models in the High Speed Water Tunnel to determine the hydrodynamic forces (drag ~ cross force ,- and moment) under steady state conditions No tests were made to determine the damping forces The test results apply only t o velocit i es below the velocity of sound

Tests were made 1n the Polarized •Light Flume to give a visual indication of the streamline patterns in steady flight

A comparison is made of the results of the Water Tunnel test s with tests previously made on models of the same bombs at th P Wright Field Wind Tunnel ( i )

C1) "Aerodyna~ic Tests of Finned Projectiles Performed in tbP Twenty Foot Wind Tunnel at Wright Field" by A. C Charters and J. L . Xelley , Report No . 471 , 16 June 1944 , Ordnance F esearch Center Project No 3986

CONFIDENTIAL -2-

SUMMARY AND CONCLUSIONS

Table I showsJ for comparison the principal hydrodynamic characteistics shown by the tests

TABLE

COMPARISON OF HYDRODYNAM IC CHARACTERISTICS

Concrete Practice Bombs M38A7 :i.OC lb Proct Bo'Tlb

AN-M43 AN M56 •Large Small Drum GP •LC

Box Ta1l Box Tail Toil 500 lb 40CXl lb CPCA-i CPCA 2 CPCA-3

Drag coefficientJ CD

At zero yow

At :!:.6° yow

Cross force coefficientJ CC

0 7..85

0 31.5

Cc per degreeJ 0 to +1. 0 yaw -o 062

Cc at +6° yow 0 450

0 7.50 0 240

c 305 0 290

0 065 0 050

0 460 0 335

Bomb Bomb

0 270 0 220 0 287

0 295 0 260 0 325

0 055 0 060 0 056

0 440 0 380 0 355

Moment coefficient J CM

CM per degree , 0 to+{ 0

CM at +6° yow

-0 008 -0 006 -0 009 -0 008 -0 009 -0 005

-0 085 -0 08i -0 058 0 074 ·-0 065 -0 04:1

Center of pressure eccen­tricityJ e at +6° yaw -0 1.89 -0 1.76 -0 1.73 -0 1.68 -0 i7i -0 ii5

Reyno l ds number x 1.06

Model in water at 32 ft/sec

Prototype in air at 600 ft/sec

2 4

1.2 1.2

2 8 2 9 2 0

1.4 1.4 1.8

The comparison is with the box tails so oriented that the sides of the fin box are at 45 degrees with the yaw piane

Of the three concrete practice bombs that with the drum type tail (CPCA No 3) showed the greatest static stability near zero yaw and also showed a somewhat lower drag than the others If t he shroud of t ·he drum-type tail could be slightly increased in diameter it is believed thatstill greater stability would result

The M38A2 Practice Bomb has characteristics closely com­parable to the concre t e practice bombs with box tails ·

The AN-M56 4000 lb Bomb shows cons1derably higher drag and less static Rtability than the An M43 500 lb Bomb The higher drag can be attributed to the steep slope of the afterbody of the 4000 lb Bomb and the lower stabi~ity to the location of the

CONFI DENTIAL

i 7

35

-:)-

box tail so close t o the afterbody that it l ies directly in the afterbody wake (see Figure 20).

All of the models vibrated at a speed of 32 f t /sec in t he water tunnel. The vibration caused fai l ure of the tail supports an each of the concrete practice bomb models. The vibration was particularly severe on the model of the 4000 lb. bomb. At :)2 ft/sec the fin reinforcing struts on the model failedJ a n d at 55 ft/sec one side of the box tail col l apsed.

Drag measurements at velocities hiqher than 32 ft/sec were unsatisfactory on account of the vibration.

Failure of the models does notJ of course J indicate corres ­ponding failures on the prototype bombs. HoweverJ the failures do show that forces of considerable magnitude act on the tails of

the bombs at high velocities.

Comparison with the tests prAviously made in the Wr1ght field Wind Tunnel on prototype size models of the Concrete Practice BombsJ the 500 lb . BombJ and the 4000 lb. Bomb showed close agree­ment for the SCO lb. and 4COO lb. Bombs.

DESCRIPT ION OF BOMBS AND MODELS

Figure 1 showsJ to the same scaleJ the outlines of the proto­type bombs. The principal dimensions of the prototypes and models are given in Table II.

TABLE I I

PRINCIPAL PROTOTYPE DIMENSIONS

Concrete Practice Bombs M38A2 AN-M43 AN- M56 Large Small Drum 100 lb GP LC

Box Tail Box To i 1 Tail Freet. 500 lb 4COO lb CFCA-1 CPCA-2 CPCA-3 Bomb Bomb Bomb

Maximum diameterJ in. 8 8 8 p 14 34

Cve ra 11 1engthJ in. 38.5C 38.5C 45.50 47 . so 58.14 H6.06

Body lengthJ in. 30.10 30.10 30.iC 40. 66 48 . 33 96 .i 2

Afterbody taper J deg. iC. 3 iC . 3 10.3 i 5. 7 24 3C from long . axis

Side of fin boxJ in . 6 .oc 4.75 8(dia) 6.0C 7.60 22.56

Max. span of finsJ in. ii .00 H.OO 8(dia) iC. 77 18.94 47.62

Weigh t J pounds 103.25 103.25 104 iOC 508 4200

Nose tip to C.G.J in . 14 75 14.75 iS. 50 18.15 24 . 00 49.20

Seale rat i oJ prototype 4 : i 4:1 4 :i 4:1 7: 1 i 7 :i to model

CONFIDENTIAL

CON FIDENTIAL -4-

Details of t he projectiles covered by this report will be found on t he following reference draw1ngs

Conc r ete Practice Bombs Concrete Products Co of America Drawings B6 B7 , B8

~8A2 Practice Bomb U S Ordnance Department Drawing 82 -0 - 23

AN-M43 G. P , 500 lb Bomb

u s Ordnance D;apartmen t Drawing 82 -0-27

AN-MS6 11, G 4000 lb Bomb u. s Ordnance Department Drawing 82 -0 - 55

The noses of the concrete pract1ce bombs and the M38A2 Prac-­tice Bomb are identical and approximate very closely a i 28 cali . ber x 56 degree spherogive The nose of the 500 lb Bomb is a compound ogive of i . 26 caliber followed by a radius of 0 76 coli ber ~ a nd t erminating in a blunt nose tip The nose of the 4000 lb BoFb is an ogive of 0 94 caliber terminating in a conical end of 88° included angle and w1th a blunt nose tip

All of the models are two inches in diameter and as to external dimensions are accu -ate scale reproductions of the proto types except that nose and tail fuzes are omitted The models are made of b r ass or bronze and stainless steel

TEST PROCECURE - FORCE TESTS

The hydrodynamic characteristics determined by the model tes t s are expressed in t erms of drag . cross force , a n d moment coefficiPnts calculated from the observ~d forces and moments The symbol3 and definitions of the coefficients are given in the appendix

For the force and moment measurements the model is mounted on a shielded spindle in the working section of the water tunnel The spindle , to which the model is rigidly attached is extended outside the working section and connected to balances which meas ­ure the forces and moments The shield which surrounds the mount ­ing spindle in the working section is streamlined and extends from the bottom of the working section to w1thin a few t h ousandths of an inch of the model ~ thus protecting the spindle from the tunnel flow To compensate for interference between the shield and the mode 1. each s e r i e s of t e s t s ; s rep e a t e d w i t h a n i rna g e s h i e 1 d extending from the top of the working section to the same clear ­ance from the model as the spindle shield The i mage shield is a mirror duplicate of the spindle shield

A tare or shield interference correct1on i s then applied in accordance with standard wind tunnel practice as follows

F = F 0 - (Fw · · F 0

)

CONF IDENT IAL

CONFIDENTIAL -5-

SMALL FIN BOX

"RACTICE BOMB

AN-M56-LC 4000 POUND BCHB

M - M M M - M • M M M M I 0 5 10 15 20 25 30 35 40 <16 !10 55 60

SCALE, INCHES

FIG. l- OUTLINE DRAWINGS OF AIRCRAFT BOMBS

CONFIDEHTIAL

COHF I DENT! AL -6-

" 20

~ 18 (/)

\ 0 z

16 ~ \P :r

1\ 0

14 z .\ -...,: a:

12 0

\) (l. (l. ::::>

10 (/)

.\ 1-::::>

f-·- 8 0 -- ~ f..-- ~

\:> ID t--<I

\ 6 1-

.\) z UJ ~

4 0

~ ::!!

2

-~ YAW, , DEGREES -12 -10 -8 -6 - 4 !'--... 0 2 4 6 8 10 12

;..;, ~ -2 •'\P

-4 ~ I \~

··-

TAIL ORIENTATION ~ -6 2 f\ -8

\~ -

- 0 FIN I IS UP -10

-· FIN 2 IS UP (AFTER- -12 \ BCDY ROTATED 180°) \p

-14

F\ ~ 16

\ -18

' -20

" FIG. 2- EFFECT OF AS YMMETRY ON MOMENT

CONF I DEtn I AL

CONFIDENT IAL - 7-

where

F the corrected force or moment

F 0 = the measured force or moment with the spindle shield only

F = w the measured force or moment with both the spindle and image shield

EFFECT OF ASYMMETRY

None of the bombs is completely symmetrical about any plane through the longitudinal axis The asymmetry is due mainly to the construction of the tails, also to the effect of; the supporting lugs and to accidental asymmetry in construct1ion The result of asymmetry is that the curveg of cross force and moment vs yaw do n o t pa s s t h r o u g h z e r o a t z e r o y a w T h i s. e f f e c t i s t y p i c a 1 1 y illustrated by F1gure 2 1n wh1ch the observed moments in inch­pounds (after shield interference correct 1on J are shown for a range of positive and negative yaws and for orientations of the bomb tail i80° apart w1th respect to the yaw plane If so to speak J the asymmetry itself wer\3. symmetrical the two sets of points for opposite orientations.would be expected to give moment ­yaw curves passing on opposite sides of and about equidistant from the intersection of the coordinate axes As can be seen from the figure , th1s is not the case The smooth curve of the figure is drawn through moment values which are, the average of the values given by the two i80° apart orientations To approximate the moment curve of a completely symmetrical bomb the portion of the averaged curve for negative yaws and positive moments is replotted for corresponding positive yaws and negative moments and averaged w1th the curve already plotted for positive ya.ws The resulting curve passes through the intersection of the coordinate axes and values obtained from this curve were used in calculating the coef­ficients

All of the models tested showed the effect of asymmetry to a g reater or less degree The asymmetry Indicated in Figure 2 1s f or the Concrete Pract1ce Bomb w1th the large f1n box tail (CPCA No . i) w\ich appeared to have a greater degree of asymmetry than any of the other models

The force and moment coefficients for all of the models tested were calculated from force and moment curves faired and averaged by the procedure above outlined The resulting coef ­ficient curves therefore represent the characteristics of a c ompletely symmetrical projectile

CON FI DENTIAL

CONFIDENTIAL

CONFIDENTIAL

·-8-

FIG. 3- MODEL~ CONCRETE PRACTICE BOMB, CPCA NO. 1

(LARGE FIN BOX )

FIG. 4- MODEL OF CONCRETE PRACTICE BCMB, CPCA NO. 2

(SMALL FIN BOX )

-9-

FIG. 5- MODEL OF CONCRETE PRACTICE BOMB, CPCA NO. 3

( DRUM TYPE )

CONCRETE PRACTICE BOMBS

CONFIDENTIAL

The Concrete Practice Bombs were designed by the Concrete Products Company of America. The bodies of the three bonbs are identical) formed of solid concrete) the variation being in the construction of the tails) which are fabricated from steel plates.

fig~res 3J 4J and 5 are photographs o f the three models.

The CPCA No. i and No. 2 Tails are identical except for the dimensions of the square) open-ended box which forms the princi­pal part of the tail. Cn the CPCA No. i Tail this box is 6 inches x 6 inches, and on the CPCA No. 2 Tail it is 4-3 / 4 inches x 4-3 / 4 inches. Cn both tails there are fins extending ~utward from the corners of the box.

The CPCA No. 3 Tail is called the "drum type". The tail is a cylindrical shroud ring supported from the afterbody on four U-shaped steel members. The shroud ring or drum is the same diameter as the cylindrical body of the bombJ and the length o f the ring is equal to the diameter. The CPCA No. 3 Tail extends seven inches farther aft than the other two.

r.nNI= I ni=NT I jJ

CONFIDENTIAL

1.00

0.90

0.80

uv • 0 .70

'2 ... G ~ 0 .60

8 0.50

"' u

~ 1).40

IR 0 0.30 IE u

0.20

!L .L

~lc~ CPCA NO. ~

f' L f L_

I VcPC• N0. 3

.t. L 1/ v

I v ...,....

- i O-

NO .I

0.18

0 . 14

a u

,: t::

0.12

0 .10

i 0.08 ell

~ 0.06

~ 0.04

u a 0 .02

t 0

.

_L

/

/ L v

/

v /

l FINL ~ss ' fTERBI pov

v J I

~ ~ ... ' YAW ANGLE OEGf EES

.. u

0.10

0 ~ -.-,;;;; .£SS FTER91 )m

v .-

2 4 6 8 10 12 YAW ANGLE, DEGREES

!i". 30 !;;;:::::;=:F---::t-:=::=f'c~t-;;:;;\t;"--j ... ~ 0. 20 t----ir----:::::.:;::1;=-:::-:;;t;:;;;;;--alr;=~.-----1 ... 8 ~ 0 .10

IE a

0

C. 50

0 .40

0.30

0 .20

0.10

• 5

0

~-0.10

B - 0 .20 A: ti

-0.30

2

/ lFI

/

r-._.s. PCA ' r--- ....... r--~

4 6 8 10 12

~-""

LESS AFTER poot

J~ I

0. 2

CP ~N,S ~-- ::--CP< A NQ I

i5 G-0.02

!.0.04 I' '2 ... 2 -0.06

'i .... ,

1\ CPCA NO. ~

i l{\ " Cl'cA NC 1'.. -O.OS

~' ' CPCA NO.I -

~ '

-0. 10

-0.12

~

~

' .1,). 14

-0.18

-0.18

-0.2 0

-0.2 2

CPCA NO. I IS LARGE FIN BOX TAIL

CPCA NO. 2 IS SMALL Fl~ BOX TAIL •

CPCA NO. 3 IS DRUM TYPE TAIL

BOX TAIL ORIENTATION -<> (YAW PLANE HORIZONTAL)

F IG, 6- CONCRE TE PR ACTICE BOMBS

tOMP ARISON OF FORCE AND MOMENT COEFFIC IENTS

CONFI DENTIAL

" ....

l1 \\

CONFIDENTIAL -U..-

Fiqure 6 shows a comparison of the draq, cross forceJ and moment coefficients of the three ePeA tails, and also shows the coefficie ·nts of the finless afterbody.

The significant differences between the three tails appear to be the following:

0

-0.10

-0.20

i . T h e d r a g i s h i g h e s t f o r t h e 1 a r g e f i n b o x t a i 1 ( e PeA No. i). The drum-type tail (ePeA No. 3) has the lowest drag, but only slightly less than the small fin box tail (ePeA No.2). For all three bombs the drag in­creases with yaw.

2. ~he cross force is almost the same at all yaws for the large and small fin box tails, and is considerably less for the drum-type tail than for the box tails.

3. The static stability at small yaws (less than 3°)is greater for the drum-type tail than for the box tails, a measured by the center-of-pressure eccentricity curves and the slope of the moment coefficient curve. At yaws greater than about 3°, the box-type tails show a greater restoring moment.

4. The finless afterbody, as would be expected, is stati­cally unstable.

YAW, Vf , DEGREES 2 4 6 8 10 12

.. -0.30

The coefficiacnt curves of the finless afterbody offer a means of locating the resultant of the forces acting on the fins alone. Let eeH and eMH denote the cross force and moment coef­ficients of the finless af­terbody. ee and eM are the cross force and moment coef­ficients of the bomb with fins. Then (ee- eeHl and ,eM - GMH) represent the croes force and moment coef­ficients of the fins alone (including forces developed by interference between body a n d f i n s ) • Om i t t i J\ g t h e effect of drag, which is negligible at small yaws, the location on the projectile axis of the resultant of the fin force is

II

0: -0.40 ()

~ ~ CPCA NO. 2

-0.50 ~ 0

z -0.60 0 t= ~ -0.70 0 ..J

-0.80

::::::: ::::-'C"PCA NO. I -~ --/

A NQ 3

/ -0.90

F IG. 7- CONCRETE PRACTICE BOMBS LOCATION OF RESULTANT OF FIN FORCES AFT OF C.G. 1 AS FUNCTION OF YAW

eM eMH e =-=---=-

F ee eeH

where

COHFIDENTlAL

COMf\OEM'TlAL -i2-

CPCA NO I

38.!1"

20" --1 .,

CPCA NO. Z

34.~· ----!--.!

CG CP ----

CPCA NO. 3

FIG. 8- CONCRETE PRACTICE BOMBS LOCATIO~ OF C~NTERS OF PRESSURE OF BODY AND FINS

TOGETHER (cP) AND OF FINS ALONE (CP FINS) AT 3° YAW

eF is the distance between the center of gravity and the location of the fin force resultant expressed as a fraction of the pro­jectile lengths. The location of the resultant of the forces on the fins alone has been computed in the above manner for ~he three variations of the Concrete Practice Bomb and shown on Figure 7.

Figure 8 shows~ to scale~ the three concrete practice bombs~ with the location of the center of gravity~ the location., at 3° yaw., of the resultant normal force due to cross force and drag on the bomb as a whole (CP)~ and the resultant normal force due to the fins alone (fin CP).

It is to be noted that the fin CP is considerably farther aft on the drum-type tail than on either of the box tails~ al­though~ as shown by Figure 6J the static restoring moment at 3° yaw is nearly the same for all three bombs. Observation in the Polarized Light Flume offers a clue to the difference in behavior of the box-type and drum type tails. The fluid 1n the flume has asymmetrical physical and optical properties which permit obser­vation of the flow lines when viewed through polarizing plates. The velocities in the light flume are below the range of the water tunnel tests and the pattern can be considered only qualitative. rigures 9 ar.d iC show the flow pattern around the box.-t ype and drum type tails. From Figure iC it can be seen that the shroud r i n g o f t he d rum; t y p e t a i 1 ( C PCA No . 3 ) i s v e r y c 1 o s e t o t he eddies formed in the wake of the rather blunt afterbody. The fins

CONFIDENTIAL

CONFIDENTIAL -13-

YAW = 0°

FIG. 9- FLOW PATTERNS AT 0° AND 10° YAW AROUND AFTERBODY AND TAIL CONCRETE PRACTICE BOMB CPCA NO. 2

(SMALL FIN BOX)

=======----------

018~~~

I .tO

1.10

LOO

o.to

0.1 0

u• 0

0

0.10

0 .10

YAW = 0°

FIG. 10- FLOW PATTERNS AT 0° AND 10° YAW AROUND AFTERBODY AND FINS CONCRETE PRACTICE BOMB CPCA NO. 3

(DRUM TYPE)

!J II

TAIL J ~ T4 L II

~ w

..... · 004

i ·0 .10

E .....

I~-· •

1"'-1'\

1\ \ TAIL t:l

~ T -Q- ~

~ __\..\

I/ - \1\ . Q.tl

5 ~ - Qll

J /

.....

/ 4 I I 10 II

..... • . • .... YAW, , ~[£5 'tltlll, . ~

r---

t.:"~:~ TAIL ¢- k--" ~

FIG. 11 - CONCRETE PRACTICE BOMB CPCA NO. 1: EFFECT OF TAIL

ORIENTATION

1\\ \

..

which project from the cor­ners of the box tails have n span greater than the shroud ring of the drum tail and extend into the almost undisturbed fluid. The cross force due to the previously undisturbed fluid acting on the wider fins probably accounts for the greater cross force (see Figure 6) on the bombs with the box tails •

Figure ii shows the effect of the orientation of the box tail of CPCA No. i on the force and mo­ment coefficients. The effect is seen to be neg­ligible except at large yaws. The same negligible effect was observed in tests of the CPCA No. 2 and No. ~.

r.nlllr: I nJ:"WT I AI

-i1-

FIG. 12- MODEL OF M38A2- 100 LB. PRACTICE BOMB

M38A2 - 100 LB. PRACTICE BOMB

This is a bomb with sheet metal body designed for sand load­ing to weight at point of use.

It is furnished with a sheet metal box tail, welded to the afterbody.

Figure i and Table II give the outline and principal dimen­sions. Figure i2 shows two views of t~e model. The nose profile is the same as on the Concrete Practice Bombs. The box tail has approximately the same dimensions as the tail of the CPCA No. i Concrete Practice Bomb.

Figure i3 shows the drag, cross force, and moment coaf­ficients for the M38A2 Bomb with the tail in two positions rela­tive to the yaw plane.

Figure i4 shov.·s the flow pattern around :he 'lfterbody and tail of the M38A2 Bomb. It shows the same characteristi~s as Figure 9 for the CPCA No.2 tail.

0 .80

0.70

c:J'o.60

l 0.50

i 0.40

~ I§ 0.30 ...

0.10

0

0.40

• u !i0.30

Ill

~ t 0.20

8 i 0.10

0

-iS-

~ I w TAL-(

jv J.'f TA LJ(

;f ) ~

/ v

0

.J-o.o

~ : -0.06

1-

~-ODe it 8-0.10 1-

;-0.12

-0.14

-0.16

"' " TAIL -<

CONFIDENTIAL

~ ~ ~

~TAl ~):(

\ ' i\

' 2 4 6 8 10 12 2 4 6 8 10 12

TAIL

YAW, T , DEGREES

ll:i

-

v-/' ~

TAIL 4-

., 0

~ ~-0.10 a:: 1-

~-0.20 .... ~

c,;-0.30

-......_

F IG. 13- M38 A2 PRACTICE BOMB

FORCE AND MOMENT COEFFI C IENTS

YAW, "¥ , DEGREES

TAl

~ TAIL

F IG, 14- FL OW PATTERN S AT 0° AND 10° YAW AR OU ND AFTERBODY

AND FINS OF M38A2 PRACTI CE BOMB

-¢-

):(

CONFIDENTIAL

COMFIOEHTIAL -i6-

F I G. 15 -MODEL OF AN-M43 G.P. 500 LB. BOMB

AN-M43 G.P. 500 LB . BOMB

This is a general purpose demolition bomb with cylindrical body. ogive nose. and box type tail.

Figure i and Table II give the outline and principal dimen­sions . and photographs of the model are shown in Figure iS.

Figure i6 shows the drag. cross force, and ficients with the tail in two positions relative to The tai l orientation has no effect on the drag. slightly more stable (statically) at small yaws plane is at 4S degrees to the sides of the fin box.

moment coef­the yaw plane.

The bomb is when the yaw

Figure i7 shows the flow pattern around the afterbody and tail of the SOC lb. Bomb. The same general flow characteri~tics are indicated on the M38A2 Bomb (see Figure i4). except that due t o the steeper afterbody taper, there is slightly more separation along the afterbody just ahead of the tail. This is particularly noticeable in the flow pattern at iC degrees yaw.

CONFIDENT IAL

o.ao

..,aro (.)

~ 0.60

"' G iE "' 0 .50 8 ~ 0 .40

~ (I) 0.30 g 5 0.20

0.10

0

0 .40

...: z 0 .30

"' G 1&: ~ 0.20 (.)

(l) 0.10 <(

15 0

v

CONFIDENTIAL - 1.7-

J TAIL ~ 7 J.

/ TAIL }:X

I /

/

• (.)

0

.-0.02 ci u ~-0.04

; c

-0.06 ~ "' ~ -0.08 ... ~ -0.10 ~ ;

' TAIL

~ t( ~A L~

~,

'\ \.

" v i - 0 .12

-0.14

2 4 6 8 10 12 -0.16 2 4 6 8 10 YAW, 'Yf, DEGREES YAW, -yr , DEGREIES

0

TA L n ~ --,....... TAIL ..,. -~ 0-0.10

I -0.20 - T IL "(>

TA L lt --fil Q;

c.) -0.30

FIG. 16 AN-M43 G. P. 500 BB. BOMB

FORCE AND MOMENT C OEF~ICIENTS

YAW = 0 °

FIG. 17 FLOW PATTERNS AT 0° AND 10° YAW ARCUND AFTERB ODY

AND FINS OF AN-M43 G.P. 500 LB. BOMB

12

CONFIDE.,TIAL

CONFlDEMTIAL -i8-

FIG. 18- MODEL OF AN-M56 L.C. 4000 LB. BOMB

AN- M56 L. C. 4000 LB . BOMB

This bomb is a light case demolition bomb, with ogive nose, cylindrical body, and a box tail similar in design to the AN-M43 SOC lb . Bomb and the M38A2 Practice Bomb, except that braces are privided to stiffen the fin box and the fins.

Figure i8 shows two photographic views of the model. The fin braces are clearly indicated.

l'igure i9 shows the drag, cross force, and moment coef­ficients of the 4000 lb. Bomb with the tail in two positions rela t ive to the yaw plane. The orientation of the tail has no appreciable effect on the drag. The moment and cross force, how­ever , are affected very noticeably by the tail position in such a way that the static stability is considerably less when the sides of t he fin box are at 45 degrees to t•he yaw plane . This effect is t he opposite from that observed in the other box-tail bombs , and the reason is not apparent, either from the behavior during the force tests or from observation in the Polarized Light Flume.

Fiyure 20 shows the flow pattern around the of t~rbody and tail. Due to the sharp taper of the afterbody, ther3• is a wide zon e of separation and eddying flow around the afterbody extend­ing into the interior of the fin box. The bluntness of the after­body probably accounts for the higher drag of this model and also its lower stability as measured by the moment coefficient.

CON FIDENTIAL

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CONFIDENTIAL

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FIG . 19- AN-M56 L.C. 4000 LB. BOMB

FORCE AND MOMENT COEFFICIENTS

' .. '-

YAW

FIG. 20- FLOW PATTERNS AT 0° AND 10° YAW AROUND AFTERB ODY

AND FINS OF AN-M56 L.C. 4000 LB. BOMB

12

CONFIDEHTIAL

CONFI DENTIAL -20-

COMPAR ISON WITH TESTS AT WRIGHT FIELD WIND TUNNEL

Tests of the bombs covered by this report were conducted at the Wright Field Win~ Tunnel . in June, i944(i) The models tested were of prototype size . The shielding system was almost th e same as that used in the water tunnel , and the same method was used in correcting for shield interference

The notation used in the Wright Field report is different from that used in this report

In the Wright Field report , the following expressions were used for the dimensionless fo"rce and moment coefficients :

Drag coefficient , K0

•Lift (cross force) coefficient . ~L

Moment coefficient . KM

where

d diameter of bomb

U = free stream velocity

D 2

p d u

2 2 p d u

M 3 2

p d u

Comparing the above notat i on with the notation in the appendix to this report , it is seen that to convert the Wright Field notation to the water tunnel notation, the following transformations are necessary :

"In order to compare the ~right Field coefficient curves with the curves resulting from the water Tunnel tests , the Wright Field curves were first corrected for asymmetry, then replotted and £aired to represent completely symmetrical projectiles The re­sulting comparisons are shown in Figures 2i to 25 for the Concret e Practice Bombs, the 500 lb Bomb . and the 4000 lb Bomb The comparisons are for the same orientation of the tails with respect to the yaw plane

For the Conc rete Practice Bombs the drag shown by the Water Tunnel tests is, near zero yaw. some 50% higher than shown by the

CO NFI DENTIAL

CONFIDENT IAL -2i-

Wright Field tests. The cross force compares reasonably well for all three of the concrete bombs. The moment coefficie n tsJ except for the bomb with the CPCA No. tailJ do notcompare at all closely . The erratic variation of moment near Z8ro yawJ shown by the Wright Field testsJ could not be reproduced in the Water Tunnel. Cn Page 5 of the Wright Field report the authors state that the re­sults obtained on the iCC lb. bombs were notentirely satisfactory .

For the SOC lb. Bomb and the 400C lb . Bomb the Wright Field tests and the Water Tunnel tests show coefficients that compare quite closely. The drag coefficients are slightly higher in the Water TunnelJ but the moment and cross force coefficientsJ par­ticularly at small yawsJ compare very well.

The Reynolds numbers for the full size models tested in the wind tunnel are fr om three t o twenty times the Reynolds numbers for the small models tested in the water tunnel. The comparison of the Reyn o lds numbers is shown in Table I. The drag coeffi­cients measured in the water tunnel are about twice as ~igh as have been measured at the same R~ynolds number in tests of ~ore fully streamlined shap3S of approximately equal dimensions and surface areas. This would indicate thatJ for the bombs J form drag predominates and only a small decrease in drag could be expected even with a large increase in Reynolds number .

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F IG. 21- COMPAR ISO N OF WATER TUNNEL AND WRIGHT FIELD WINO TUNNEL TE STS

Concrete Practice Bomb with CPCA No . i (Large Fin Box) Tail

CONFIDENliAL

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CONFIDENTIAL

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F IG. 22- COMPARISON OF WATER TUNNEL AND WRIGHT FIELD WINO TUNNEL TESTS

Concrete Practice Bomb with CPCA No . 2 (Small Fin Box) Tail

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AN-M56 L.C. qOOO LB . BOMB

COHFIDEMTIAL

CONF IDENTIAL

CONFIDENTIAL

APPENDIX

DEFINITIONS

YAW ANGLE, ~

The angle , in a horizontal planeJ which the axis of the pro­jectile makes with the direction of motion Looking down on the projectile, yaw angles in a clockwise direction are positive (+) and in a counterclockwise dire~iion negative (-)

PITCH ANGLE, a

The angle _ in a vertical plane, wh1ch the axis of the pro­jectile makes with the direction of motion Pitch angles are positive (+) when the nose is up and negative r-J when the nose is down

LIFT, L

The force , in pounds exerted on the projectile normal to the direction of motion and in a vertical plane The lift is positive (+) when acting upward and negative r-J when acting downward

CROSS FORCE, C

"The force . in pounds exerted on the projectile normal to the direction of motion and 1n a hor1zontal plane "The cross force is positive when acting in the same direction as the displacement of the projectile nose for a pos1tive yaw angle 1 e to an observer fac1ng in the direction of travel a positive cross force acts to the right

DR AG, D

The force 1n pounds . exerted on the proJeCtile parallel with the directi o n of mo tion The drag 1s positive when acting in a

' direction opposite to the direction of motion

MOMENT. M

The torque in foot pounds, tending to rotate the projectile a b out a tra n sverse ax1~ Y0~1n0 mo ment D ten01 ng t o ro totG th ~

projectile In a cloc kwi s e direction (when looking down on the pro ­Jectile ) are positive (+) , and those tending to cause c ounter­clockwise rotation are negative (-) Pitching moments tending t o rotate the projectile in a clockwise direction (when looking at the projectile from the port side) are positive (+), a~d those tending to cause counterclockwise rotation are negative ( - )

r.nNFIOFNTIAL

CONFIDENTIAL - b-

In accordance with this sign convention a moment has a de­stabiliz.ing effect when it has th.e same sign as the yaw angle or pitch angle and a stabilizing effect when the moment and yaw or pitch angle have opposite signs

NORMAL COMPONENT, N

The sum of the components of the drag and cross force (or lift) acting normal to the axis of the projectile . The value of the normal component . is given by the following .

N = D sin ~ + C cos ~ (i)

or

N D sin a + •L cos a (1 a)

in which

N Normal component in lbs

D Drag in lbs

c Cross force in lbs

•L •Li ft force in lbs

~ Yaw angle in degrees

a = Pitch angle in degrees

CENTER OF PRESSURE , CP

The point in the axis of the projectile at which the resul­tant of all forces acting on the projectile is applied

CENTER OF PRESSURE FCCENTR'C ' Tv. e

The distance between the center of pressure (CP) and the center of gravity (CG) expressed as a decimal fraction of the length (1) of the projectile The center -o f - pressure eccentricity is derived as follows

1n whicn

e

1

leg

l cp

CONFI DENTIAL

e i Meg : N

Center-of pressure eccen+~icity

•Length of proJectile in feet

Distance from nose of projectile to CG in feet

Distance from nose of projectile to CP in feet

( 2)

CONF IDENT IAL -c-

COEFFIC 1 ENTS

The force and moment coefficients used are derived as follows

Drag coefficient D c =-----

D v2 p- AD

2

Cross force coefficient/ CC c

•L c;L v2

•Lift coefficient ,

p 2 . AD

Moment coefficient M

eM -2

p v ADl 2

in WhlCh

D Measured drag force in lbs

C Measured cross force in lbs

•L Measur ed lift force in l bs

p Density of the fluid in slugs /cu ft = w/g

w SpecifiQ weight of the fluid 1n lbs/cu ft

g =·Acceleration of gravity in ft/sec 2

( 3)

( 4)

(5)

(6)

AD= Area in sq ft at the maximum cross section of the pro jectile taken normal to the geomet -i c ax1s of the pro Jectile

V - Mean relative velocity between the water and the pro jectile in ft/sec

M Moment, in foot -pounds measured about any part 1cular point on the geometric ax1s of the pTOJec1ile

1 - Overall length of the pToJectlle in feet

CONFIDENTIAL

CON FI DENT IAL -d-

RUDDER EFFECT

The total increase or decrease 1n moment coefficient at a given yaw or pitch angle resulting from a given rudder sett1ng This increase or decrease in moment coefficient is measured from the moment coefficient curve for neutral rudder setting

REYNOLDS NUMBER

In comparing hydraul1c systems involving only friction and inertia forces a factor called Reyn~lds number lS of great utility This is defined as follows

R =

in which

lV v

R Reynolds number

1 Overall length of projectile , feet

V Veloc1ty of projectile feet per sec

(7)

v Kinematic v1scosity of the flu1d sq ft per sec

p Mass density of the fluid in slugs per cu ft

~ = Absolute viscosity in pound seconds per sq ft

Two geometrically similar systems are also dynamically sim1 lar when they have the same ·value or Reynolds number For the same fluid in both cases a model with small linear dimensions must be used with correspond1ngly large velocities It is also possible to compare two cases with widely d1ffering fluids pro vided 1 and V are properly chosen to give the same value of R

CAV I TAT I ON PARAMETER

In the analysis of cav1tat1on phenomena the cav1tat1on parameter has been found very useful Th1s 1s def1ned as fo.lows

K ( 8)

1n which

K =Cavitation parameter

pL= Absolute pressure in the undisturbed l1quid lbs/sq ft

p 8 = Vapor pressure corresponding to the water temperature , lbs/sq ft

V Velocity of the project1le, ft/sec

CONF IDEMTJAL

CONFID ENTIAL -e-

p mass density of the fluid in slugs per cu ft w/g

w weight of the fluid in lbs per cu ft

g =acce l eration of gravity

Note tha t any homogeneous tation of th i s parameter this parameter i n terms of

set of units can be used in the compu Thus it is often convenient to express the head i e

K = 1'\L -- hB

(9)

where

t:L= Submeraence plus the barometric head , ft of water

hB= Pressure 1n t he bubbl e ft of water

It will be seen t hat the nume rator of both expressions is simply the net pressure act1ng to co llapse the cavity or bubble The de nom i na t or ·is the velocity pressure Since the entire variation in pressure around the moving body is a result of the velocity it may be cons idered that the velocrty head is a measure of the pres sure available to open up a cavrta tion void From t h is point of vrew the cavitation parameter is s1mply the ratio of the pres·sure available t o collapse t he bubble to the pressure available to open it 1f t h e K for incipien t cav1tati on is considered , it can be interpreted to mean the maxrmum reduction in pressure on the sur­fac"' of t h e body mPnsured in terms of the veloci t y head Thu s rf a body starts to cavitate at the cavitation parameter of one rt means that the lowest pressure at any point on t he body is one vglo~ity head below that of the undisturbed fl u id

The shape and size of the cavitation bubbles for a specif ic proiPctilP ore functio n s o i. the cavita tion parameter Tf f'p ;c­

tf11:<>n to rPplP<;Pnt the> Ot1S r- pq<;nTP w1ihin thp hnhhle in'lh'nd oi thP vnpcn pT"' 'lS1JJ<=> n1 t h<=> wnter as 1n noTmnl i nve s t igation"' th~"

vnlue o f K obtained by t hP abovP formula will he npplicnble to an ai r bubble In other words thP behav1or of the bubble will be th e same whether the bubble is duP t o cavitati o n the injection of e xhaus t gas or the entrainment of air at the time of laun c hing

The covitation paromPter for incipiE>nt cavi tation has thP "Ymho l K

1

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-f-

disturbance Dynamic couples and forces including either positive or negative damping are not obtained If t he hydrodyna~i c moments are restoring the projectile, then it is said to b e stat i c a lly stable, if nonrestoring, statically unstable In t he discussion of static stability the actual motion following a perturbation is not considered at all. In fact, the projectile may oscillate con­tinuously about an equilibrium position without remaining in it . In this case it would be stat1cally stab le , but would have zero damping and hence, be dynamically unstable With negative damping a projectile would oscillate w1th continually increasing amplitude following an 1nitial perturbation even though it were statically stable. Equil i brium IS obta1ned 1f the sum of the hydrodynamic, buoyant, and propulsive moments equal zero . In general, propul­sive thrusts act through the center of gravity of the projectile so only the f.r s t two I tems ore 1mportant .

If a projec t i le i s rotating from its equilibrium position so as to Increase I ts yaw angle positively, +he moment coe f ficient must increase negatively (according to the s i gn convention odor­ted) in order that it be sta t ical l y stal5le . Therefore, for p ro­jectiles without controls or w1th f ixed control surfaces, a nega­tive slope of the curve of mo me nt coefficient vs yaw gives static stability and a positive slope gives instability For a p ro­jectile without controls, statiC stability IS necessary for a successful fl igh~ unless stability is obta ined by spinning as in the case of rifle shells For a project ile with controls, s tabil­izing moment s can be obtained by adjusting the control surfaces, and the slope of the moment coefficient, as obtained with fixect rudder position, need n o t give s tatic s tability where buoyancy either acts at the center of gravity or can be neglected, equil­ibrium is obtained when the hydrodynamic moment coe f ficient equals zero. For symmetrical prcje ct i les this occurs at zero yaw angle, i.e., when the projectile axis is parallel to thQ t~ jectory. For nonsymmetrical projectiles, such as a torpedo wr[e

1n the rudders are not neutral~ the moment is not Z~'>ro at ZPro yaw but vanishes ct somE. dPf i ni te on-; 1 1" of at tncJ,. '/here buoyancy annot be neglected Pquil ibrium is obtained whPn c .. = - '>uoynnc,' nnd the aYis of the

pr0jecti le i s at some angle wit ~ thl" trajectory.

·' F or symmetrical p~ojectile~ t~P degree of stability,or in­stability can be obtained from t he center-of ~ressure curves . If the center of pressur~: fall!" be h1nd tl.P center of g ravity , o re­s torin g moment e xists giving static stabilit y. If tbe center of pressure falls ah~ad of :thA center of grovi.ty, t he moment is non­restoring, and the projectile 11•ill be statically unstable . The degree of stabil ity or I ns tabilit y is indicated approximately by the distance betwePn the center of gravity and the center of pressure In general, for nonsymme trical projectiles, the cross ~o rce or lift is not zero when the noment vanishe s so that ·the ce nter of pressure curve i s not sy~~e tr ica l and the simple rules just stated cannot be used to de t e rn ine'whethe r or not the pro­jecti l e will be stable In such cases careful interpreta~ion of the moment curves is a more sa t isfac tory method of determining stabil ity relationship

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