AERODYNAMIC DATA FOR SPINNING PROJECTILES.pdf

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THIS PAGE IS UNCLASSIFIED

REPORT NO. 620/ OCTOBER 1947

AERODYNAMIC DATA FOR SPINNING PROJECTILES H. P. Hitchcock OCT 25I

E

IOrdnance Research &Development Project No. TB3-0824 B3ALLISTIC RESEARCH LABORATORIES

POVIG ABEDEE

ROUDMARYLAND

Ballistic huosearch Laboratories Proving Ground, Maryland

-Aberdeen

14 January 1952 ERRATA SHEET FOR BRL REPORT 620 p. 10, line 3. For "e", read "10". p. 10, par. do

After "459", insert, "532".

p. 11, line 4. Note that a table of p and I/p, "Functions of Stability Factor", is available (BRL File N-II-h6). pp. 11 and 12. The following empirical formulas, which give approximate values of the normal force coefficient and the distance

from the base to the center of Iressure for projectiles with ogiva. and conical heads, should be substituted for those given in the report: -

h

.653 + .0223a - .6139b - .0023c + .2635d + .6476 (1/e),

- .0747 + .0443a,

l.019b + *6032c

+

.2459d + .8083 (1/e).

p. 14, par. h.

After "1408", add "664".

p. 14, bottom.

Add "The axial couple damping factor is a - N/N - KApd4 U/A."

p. 26, last line.

For "MR" read "BRLM 417".

P. 35, par c. After "A.P. T9E4 Tracer" insert "BRL 416". P., 5.

For "M308 (T23) and T23El" read "T23 and M308 (T23E1)".

pp. 56 and 58. For "M308" read "T23", and for "T23EI" read "M308". p.71

-

After "(APO Photo A8392)" insert "Design 3-76J, NDRC Report

A-428". P. 77, par fl

After "Tank Gun MIA2" insert, "T94 and T102", and add the line "76mm Tank Gun T91 -- 25".-

P.

.5, par. f. Add the line "Gun T119 -- 25".

p. 93, par. d.

After "Chem. (WP) M60 M48" insert "BRLM 447".-

p. 140 For "597", read "602", and add the following BRL reports:

-

X120

Maple, C. G., and Synge, J. L. General Equations of Motion for a Projectile with Rotational Symmetry.

491

Sterne, T. E. On Jump due to Bore

503

Goldstine, A. K., and Kelley, J. L.

51 2

Thomas, R. N. Sonie Comments on the Form of the Drag Coefficient at Supersonic Velocities.

567

John, F. Formulae for Computation of Differential Effects for Forward Fire from Aircraft.

591

Hoffleit, D. On the Determination of Yaw from Yaw Cards.

602

Morrey, C. B. Functions.

619

Hitchcock, H. P. Form Factors and Stability of Ammunition for German 3-cm Aircraft Gun MK 103.

628

Synge, J. Lo Initial Effects of Overturning Moment on a Shen Fired with Large Initial Yaw.

658

Karpov, B. 0. The Accuracy of Drag Measurements as a Function of Number and Distribution of Timing Stations.

664

Kent, R. H., and Galbraith, A. S. A Note on the Stability Conditions for Spinning Shell and Rockets.

684

Turetsky, R. Reduction of Spark Range Data.

703

Zaroodny, S. J.

717

Richards, F. Comparative Dispersion and Drag of Spheres and Right Cylinders.

719

Clippinger, R. F., and Gerber, N. Supersonic Flow over Bodies of Revolution.

729 and

Clippinger, R. F., Giese, J. It., and Carter, W. C. Tables of Supersonic Flows About Cone Cylinders.

7.0

Part It Surface Pressure.

p. le.

Clearance. Ballistic Data for Flat Fire.

A Formuila for the Representation of Resistance

On Jump due to Muzzle Disturbances.

Part II:

Complete Flows.

--

After 02930, for *Hicthcock", read "Hitchcock".

p. 142, par. b. Add the following memorandum reportst

347 Hallperin, T. Comparison of Boattail and Square Base. 365 Siljander, d. A. Effects upon the Moment and Drag Coefficient of an Increase in Width of Driving Band.

--

426 Hitchcock, 1f. P.

Ballistics of Caliber 0.60 H.E.I. Bullet T91...

435

Turetsky, R. A.

447

Hitchcock, H. P. Stability of 105-mm Chemical Shell M60.

Cone Cylinder Model E12M3.

456 Hitchcock, H. P. Form Factor and Stability"of A.P.I. Bullet T39 Fired from Shortened Caliber 0.60 Barrels.

464 Zaroodny, S. J., and Sultanoff, M. Ballistic Tests of Cartridge Caliber .50 A.P.I.T., T63. 514

Carter, W. C. Theoretical Supersonic Pressure Distributions on Non-yawing Cone Cylinders with Boattails.

527

Nicolaides, J. D. Projectile.

532

Hitchcock, H. P. Formulas for Normal Force and Center of Pressure of Long Bodies of Revolution, Based on DeMeritte and Darling's Experimental Results.

545

Hitchcock, H. P.

On Estimating the Drag Coefficient of Missiles,

564

Hitchcock, H. P.

Table of Form Factors of Projectiles.

On the Development of a Low Spin Anti-tank

p. 142, par. c.

Add the following miscellaneous reports:

NOTS TM RRB-109

Hall, N. S., Friesen, E. W.,

and Leitmann, G.

Cross-wind Firing of 20-mm Guns. BRL TN 474

Hitchcock, H. P, Projectile T1314.

BRL TN Ui

Krieger, R. H. Supersonic Wind Tunnel Tests of Small Caliber Projectiles: Cal .50 A.P.I. M23, Cal .60 A.P.I. :39,. and 20-mm H.E.I. N97.

BRL TN 392

Patton, R. B. Determination of Drag Functions for 8" Howitzer Shell HE. M106.

p. 2i2, par. d.

After ref. to Fowler's "The Aerodynamics of a Spinning Shell", add "Part II, A222, 227-247 (1922).

Windage Jump of 20-mm Practice

IINCI ASSIFIED &SA

REPORT No. 620

Aerodynamic Data for Spinning Projectiles, P. HITCHCOCK

ORDNANCE RESEARCH AND DEVELOPMENT DIVISION OFFICE CHIEF OF ORDNANCE PROJECT NO. TB3-0824

rTOML947

aopfkqtod-rbruary 1952

ABERDEEN

PROVING

-

GROUND,

C9

MARYLAND

RD,

(vsim

is)

i

70l!l

TABLE OF CONTENTS

Par. 1 2 3 4 5 8 7 8 9 10 11 12 13 14 15 18 17 18 19 20 21 22 23 24 25 26 27 28 29

Title Introduction Nomenclature Formulas Standard Atmospheric conditions at Surface of Earth Calber 0.30 Bullets C ller 0.50 Bullet, Caliber 0.63 Bullets 20 mm projectiles 37 mm projectiles 40 mm projectiles 57 mm projectiles 75 mm projectiles 3-inch projectiles 90 mm projectiles 105 mm projectiles 4.5-inch projectiles 120 mm projectiles 6-inch projectiles 155 mm projectiles 8-inch projectiles 240 mm projectiles Drag of slugs Drag of spheres Point fuzes Drag of typical projectiles List of reports on Aerodynamics of Spinning Projectiles List of Illustrations List of Graphs Index of Projectiles

a, 4 5 9 15 16 21 27 31 38 47 50 58 68 78 85 94 98 98 100 124 126 127 131 132 134 139 143 146 148-

-

-:

WMA,

3

BALLISTIC RESEARCH LABORATORIES REPORT NO. 620 HLtchcock/jmh Aberdeen Proving Ground, Md. 17 October 1946

\A

RODAMIC DATA FOR SPININ -1

PROJECTILES

.L

ABSTRACT

This is a collection of the physical and aerodynamic data of spinning projectilen (excluding spin-stabilized rockets) which have been obtained experimentally In the U.S. during the past decade. Some theoretical and empirical formulas are included. The index classifies the projectiles according to their shape. Most of these data were determined from free fligat, but a few wind tunnel results are included.

b

A

4 1. Introduction a. This report contains the physical and aerodynamic data of spinning projectiles (excluding spin0abilized rockets)which have been obtained experimentally in the United States during the past decade, together with a few of the earlier results. Ballisdc Research Laboratory Report No. 27 on "Resistance Functions of Various Types of Projectiles" gives the data on drag which were obtained from resistance firings and air stream experiments before June 1935. Ballistic Research Laboratory Report No. 30 on "Stability Factors of Projectiles" gives the data which were obtained from stat4lity firings before September 1940 (the first edition was dated December 1935). b. In the present report, the symbols tre listed alphabetically for convenience; they are the ones commonly used in the Laboratory. Some of the formulas which define and connect the physical and aerodynamic quantities are collected for reference purposes: these include several empl-11c;al formulas that can be used for estimating the values of coefficients when no better method of determining them is available. c. The data are arranged in the following manner: ordinary projectiles are grouped according to caliber; then, separate paragraphs are devoted to the drag of slugs, the drag of spheres (included as a simpie basis of comparison), characteristics o! point fuzes, and the drag of typical projectiles. For ordinary projectiles of each caliber, the known data are given In the following order: (1).

A sketch of the projectile, showing the principal dimensions in calibers, and the numbers of

the official drawings. (2). The physical characteristics, Including weight, distance from base to center of gravity, and principal moments of inertia. (3). The drag coefficient and the form factor relative to one of the typical projectiles, with a refer. ence to the report and the method of observation (with a few exceptions, form factors obtained by range firings have been omitted.) (4). The standard stability factor for a given pitch of rifling, the moment coefficient, and a reference to the report. (5). The cross wind force coefficient, which was usually determined from drift firings and taken from the referenced report, and the yawing moment coefficient and Magnus moment coefficient, which were determined from the damping of the yaw in connection with the stability firings. (6). The axial couple coefficient and sl.ir frict!on drag coefficient, which were determined from the observed loss of spin. (7). The pitch of rifling of various guns, In terms of the caliber whose true value is expressed in inches. d. The Mach number

--

the ratio of the velocity of the projectile to the velocity of sound in air -- ,Is

the principal varlable on whi'h the aerodynamic coefficients depend. It Is given whenever both the velocity of the projectile and the temperature of the air are accurately known. Otherwise, only the velocity of the projectile is given. e. The list of reports given herein includes those from which the experimental data were taken, and also some which explain the theory and the methods of performing the tests. The illustrations and graphs

I

contained in the present report are listed. Finally, the index Is convenient when data are desired pertaining to a particular shape of projectile,

2. Nomenclature Symbol

Nomenclature

Unt*

a

Velocity of sound wav.s in air

ft/sec

b

Windage jump coefficient (mil. ft/sec)

c c

Cross wind factor

1

2

c,

1

.

2

ft

Couple factor c"

rad.ft/sec ft

ft .

Damping coefficients

1

ft

c

Damping coefficient

d

Diameter; caliber (inch or mm)

ft

dip d 2

Diameters of bearing -3urfaces (in)

ft

e

2.71828; base of natural logarithms

1

f

Yawing moment damping factor

sec' 2

g

Gravitational acceleration (m/sec )

ft/sec

g

Distance from base to center of gravity

cal

h

Distance from .ase to center of pressure

cal

h

Density factor (m

I

Form factor

1

j

Drift factor

1

k

Retardation coefficient

ft

k

Radius of gyration about transverse axis

cal

m

Mass of projectile (grain or gram)

lb

n

Pitch of rifling; reciprocal of twist

cal

p

Moment of inertia factor; square of radius of gyration about axis of projectile (cal 2

1

Function of stability factor

1

p

I

)

ft

2

o

"I

*These units will produce consistent results. Other common ones are given In.parentheses.

'S

S. Nomeaclature (Cos.) S~blNomenclature

q

Nutatonl frequency

r

factors Function of damping and stability

a

Stability factor

ss

rad/sec sec-1 1

stability factor at the surface of the earth

~tandard

1 sec

t

Time Velocity of projectile relative to air

ft/sec

u

Velocity of projectile relative to gun

ft/sec*

v V

Muzzle velocity

Vr

Recoil velocity

vb

Increase in projectile velocity caused by the blast

ft/sec

w

Velocity of air relative to gun; wind (ml/hr)

ft/sec

w

Angular velocity of axis of projectile (deg/sec)

rad/sec

X

ft/sec ft/sec

ft

ioi ,ontal range (yd or m)

y

Altitude (yd or m)

z

Linear drift (yd or m)

A A

2 or m.lb/n Siacci Altitude function (ft.lb/In 2 lb.in 2 or (gr.in inertia of Axial moment

ft ft 2

)

B

Azimuth (deg) 2 2 (gr.in or lb.in ) Traneverse moment of inertia

B

2 Dragcoefiflent (lb/In /ft); 5.217 x 10"4KD

C

Ballistic coefficient (lb/in )

CL

Drift coefficient

C'DF

Skin friction drag coefficient

D

Angular drift (mil)

D

Drag

DF

Skin friction drag

G

2 Drag function (lb/in /sec)

A

ft 2 lb.ft rad 2 lb.ft

lb/ft2 sec 3/f2 I red lb.ft/sec

2

lb.ft/sec2

sc sec'

2. Nomenclature (Con.)

Symbol

ni

Nomenclature--

G1, etc.

Drag function for Projeitile Type 1, etc.

H

Density as a function of altitude (ratio',

Hw

Yawine moment

I

2 Slaccl Inclination function (lb/In )

J

Magnus moment

K

Magnus force

lb.ft/sec

KA

Axial couple coefficient

1

KD

Drag coefficient; 1916.8 B

1

KDA

Yaw-drag coefficient (deg-2

rad

KDF

Skin friction drag coefficient

1

KH

Yawing moment coefficient

1

KS

Magnus moment coefficient

1

KK

Magnus force coefficient

1

KL

Cross wind force coefficient

1

KM

Moment coefficient

1

KN

Normal force coefficient

1

L

Length of nutational period

ft

L

Cross wind force

lb.ft/aoc

Lb

Bearing length (in)

ft.

M

Moment of air resistance about center of gravity

lb.ft /sec

M

Spin reducing moment

lb.ft 2/se

M

Mach number

1

N

Normal force

lb.ft/sec

N

Spin (rev/sec)

rad/sec

N0

Muzzle spin (rev/sec)

rad/sec

P

Distance, measured along the line of departure, tto a point directly above the projectile (yd)

ft

2 lb.ft /sec

2

1 2 lb.ft /sec

2

2

2

3

2

*'

.-

8

2. Nomenclature (Con.) Symbol

Nomenclature

Unit

Q

Drift function

sec2 /ft 2

Drop of projectile (yd)

ft

R

Total air resistance

lb.ft/sec

R

Reyrolds number

1

S

2 SlacclSpace function (ft.lb/in or m.lb/in )

s'

Surface of projectile, exclusive of base (in )

ft

T

2 Slacci Time function (sec.lb/in )

sec

T

Nutational period

sec

Z

Zenith angle (deg)

rad

a

Maximum yaw (deg)

rad

Minimum yaw (deg) Magnus moment damping factor

rad seec,

Yaw (deg)

rad

Yaw in the bore (deg or min)

rad

0

Angle of inclination of the trajectory (deg or rail)

rad

0

Angle of departure (deg or mil)

rad

X

Cross wind force damping factor

sec

X

Cross wind force factor

lb.ft/sec

Magnus force damping factor (strictly, N X 1 is the damping factor)

I

I I 7

*

p pps U

0Orientation

ft 2

"I 2

lb.ft /sec

Moment factor

ir

2

2

Normal force factor

lb.ft/sec

3.1416; ratio of circumference to diameter

1

3 Air density (l,gr/in

2

,

lb/in , kg/m

3

, etc.)

lb/ft 3 3

Standard air density at the surface of the earth

lb/ft

Air viscosity

lb/ft/sec

of plane of yaw (deg)

rad

Time raLe of change of orientation (deg/sec)

rad/sec

0'

Linear rate of change of orientation (deg/ft)

rad/ft

A

Windage jump (mil)

rad

.

-

-

~

3. Formulas They are explained in the BRL Reports

The following formulas are given without full explanation. whose numbers are given in parentheses (par. 26 lists their ttles). a. Physical characteri:;tIcs: (1)

(X-i13)

For a hollow (or solid) cyjinder of mass m, outside diameter D, Inside diameter d, and length L:

gD=

,L

B A

9BD+d

A =m

2

+m

L=

.

(2) Sim1ar formulas with approxirrate empirical coefficients for caliber 0.30 and 0.50 ball and armor-piercing bullets are: 2 B=0.5A+0.0543 mL

2 A-0.115 md ,

gd=C. 400 L, Here, d is the caliber and L the length of the bullet.

~~L

(3)

Likewise, the approximate empirical formulas for high explosive shells of caliber d and length

are:

. gd=0.375 L,

(4)

B-0.5A+0.0594 mL2

In general, the squares of the radii of gyration, expressed in calibers, are: p = A/rd

b.

A-0.140 md ,

P

2

2

k2.B/md

2

ab: (X-113, 261, 276) 4=-D/m - g sin 0 (Dot denotes time derivative) aich number, M=u/a. and the yaw KD=D/Pd2u2 (A function of the Reynold's number also has a small effect.)

5

Approximately, if the yaw Is not too large, and if KD denotes the drag coefficient for 0 yaw, 0

KD= KDo (I+KD5a '

k - D/mu 2

2

)

KDPd 2 /m

R - (D2+L2 )1/2.

The Magnus force and the yawing force due to yaw-

ing are neglected in this formula. G - D/Pd2u - KD u (In most tables, G - Bu = 5.217 x 104 K u)

In

G/G n (n-

1,2 ...

)

2 C n = m/nd2 (expressed in lb/in unless otherwise stated)

,i n,

,,,

n, ,

, ,

.. , . . i

10 3. Formulas (Con.) Bn " Cn H -

..X -

*h h,

h

1 0.000,045 m- , 0.000,013,716 ft

GH.

GH.. n n

"I

- g (standard trajectory)

y

.-

U

c. S acci Functions: Here, c is an arbitrary constant and U an arbitzary value of the velocity u. The formulas are approximately valid if C (lb/tn2 ) and P (ratio to standard) are constant. The subscript0 denotes initial values. (X-113, 114, 276). S.

Idu~ u

T -

Gu

-

u

cos o (S-S

xM- C

t

, A=

d~f u

u

.Sc-

"fd-, I

gdu2Gu

I-c+

o)

(T - To)

0 2

y-xtan

C o ---..

tanG-tan

°

(AC o)+ (A.A

-C

- sec - 0

( -sc o

-(-

.]

crA - AO

fy-0,sin2

Iox

d. Stability. (X-113, 116, 261, 276, 446, 459). N - P sin S - D sin I + L cos S (normal force) / p d u2 . KDKL

N-

M-Nd(h

-g)-

KM - KN(h c2

a /Bu 2N2

s

2N IfN N

s

a g) -

sin S

a/P d 3u2

=iKM ad3 /8

-

(Here, N is the spin) .2

v2oA 2 fV2

a

fv o

pn d BK MU f

Under standard conditions,

-p p,

u - V,

2

A2

s POn

dBKM

3. Formulas (Con.) The following formulas are approximately valid if the yaw is small, say less than 10s. Neglecting the variation of r radians in orientation during each period of yaw, which usually occurs near the minimum yaw:

0 . I A/Bnd

- AN/2B, '/fp,

Tq -

(1 - l/s)

p

1 2,

L -

/P p

/T - AN/2Bp

sa(T/ r ),(s - 1)

s

V )i/ )2(a- 1)

2

(TO/ (TO/1

2

)s

'

2

Z-

4 2-dld 2(rad), 1 rad 2L

=57.3

deg- 3438 min

The necessary and sufficient condition for stability is that

2 -K

d2 (K

2

d [2 LK.2K..

K

+ 2 (K

Since the right member of this inequality can never exceed 1, it is necessary, though not sufficient, that a

A '

or else negative. The following empirical formulas give approximate values of the normal force coefficient and the distance from the base to the center of pressure for projectiles with ogival heads:'

K N - 0.020 a - 0.748 b + 0.1715 c + 0.540 d - 0.0268 e, h - -0.0135 a + 1.97 b + 0.6276 c + 0.4837 d - 0.0233 e, where a b c d e

is the angle of boat-tail, in degrees, is the length of boat-tail, in calibers, is the length of the cylindrical -art of the body, in calibers, Is the length of the ogival head, in calibers, is the radius of the ogival arc, in calibers.

The following formulas, whose empirical coefficients were poorly determined, pertain to squarebased projectile. with conical heads:* *Some data have been determined recently by free flight in the Aerodynamics Range, but have not yet been published. The above empirical formulas yield approximatelythe same values for KN and h when the ogival radius is moderately long, but give different results for conical or nearly conical heads.

12

S. Formula& (Con.) K

0.575 + 0.25 j,

h - c - 0.51 + 0.30 J, where

C is the length of the cylindrical part of the body, in calibel 3, n calibers. j Is the length of the head, e. Drift: (261, 276) ) sin I (cross wind force) X

L

KL -

/pd2u L2 X /mu - K L pd u/m

.l

Imu2 Kpd 2/m 2

Q-KL/KMU Jr " Q/Or (r- 1, 2....) if Q r is a standard drift function CLr - n/2 r gpj rv - md2n/2 rgAjrVo a -

-

(The subscript Is dropped from

Q CL, G and C)

oLL Approximately, on a nearly horizontal trajectcry, if K - KL/KMCL , BP

N

d(z/K)

df a/K) .z/K

o

Then, since D mz/x (rad), . z/K

D L

(whence K

can be found ifD i observed)

ML

The Magnus force, sin A - muN K-puNd 3KK KK1

sin a,

also has a very small effect on the direction of motion of the center of gravity. f. Damping: (281, 278, 446, 459) w

( 2 +j2 sin' S)1/2 (angular velocity of axis)

KH- 11/ P d4 u (Hw is the yawing moment) f - H/B - K H Pd4u/B KI 1- '1P d uN sin A

y- /AN sin

-KPd4 u/A

13 3.

Formulas (Con.)

The following formulas are approxtrr.dt ely correct along a nearly horlzontal trajectory if the initial minimum yaw Is zero, the retardation coefficient Is constant, the damping factors are proportional to the velocity, and the subscript 0 pertains to x - 0.

2kx, p-(1-/s) a-soe 0 1 1/2 exp( C-a 0(pJ 1/2 -1 80 If a

0 (polp)

1/2 , f+r -.

f+ xp(---

f-

"

+2 2

(-v

)cosh

-

x),

x)

(v x)

x) sinh

and ,C 2 are the maximum yaws at x and x., and 1# 21 is the minimum yaw at 17.

v x2

f

-K

..

,

+27 -2pr,

P f+y

x2 vXl

1

log e

. P2

"

2 . (

..

2-

21) 22)

Usually, but not always, r is approximately 0. The yawing moment ccefficient, determined with projectiles from caliber 0.30 to 37 mm inclusive at velocities from 2000 to 3050 ft/sec, approximately satisfies the relation 1 KH - 0.35 L

5

where L is the length of the priiectile, expressed in calibers. g. Aircraft Gunfire Trajectories: (116, 345) v2 o

U2. 2

0

2 + 2wv o sin Z cos A + w

- w2 (1 - sin2Z cos2A)

/u2

(approximately)

so v 2sS/Pu 2 0 if ss Is the standard stability factor, and p Istheratio of the air density to the standard air density at the surface of the earth

~ .L C

*~p2[

+

KL]

KDPsd2/2m C w+

0

lk

14 3. Fokmulas (Con.) KD62 0

#.

S-S

0

+

-,

P+

I/2 - -(1 ol

-2 pcP

3 -

-e

PCP

dt - 1

ANK L M

t. Spi: (287, 408) No - 21 (Vo+Vr -vb)/nd

~(approximately; °

2

r

the mass of the recoiling partE of the gun) 1i KAd 4 logeN -lOgN

-

-d

here, c Is the mass of the propelling charge, and R is

?f

0

Approximately, on a nearly horizontal trajectory, K logeN

K

- logeN

14 p x

A

" Ms/ 'd 4uN

KDF - DF CDF

, 4 KA

d

DF/ P S' Us

4KAd 2 /S'

The skin friction drag is a function of Reynold s number, R-udP/

w.

The average empirical value of C'DF for ten projectiles is 0.00168. 2 The average value of S'/d for 8 H.E. Shells, excluding the 120 mm Shell M73, is 11.5.

4. Standard Atmospheric Conditions at Surface of Earth

Barometric pressure

750 mm Hg

29.5275 in Hg

Temperature

15' C

59* F

Relative Humidity

78%

78%

Velocity of sound

341.46 m/sec

1120.27 ft/sec

Density

Unit

Log

1.203,4

k /m 3

0.08041

0.075,126,5

lb/ft 3

8.87579 - 10

3

5.63825 - 10

0.000,521,7

lb/in 2 lb/in .ft

0.000,000,301,9

lb.ft2 /in

3.47989 - 10

525.9

gr/ft 3

2.72089

0.304,34

gr/in3 gr/In 2 .ft

9.48335 - 10

0.000,043,48

3.652 43.825

2

gr/In.ft

5

1.71743 - 10

0.56253 1.84171

Note: As explained in the introduction, the sketches of the projectiles on the following pages precede the tabular data pertaining to each caliber.

18

LE.

4.

SAN

ao

0 0

pg

d

pg

p.

4. 'I' -

--

-

.

-

11~

.4

0 I.'

a

a

N

~

I I pg

0

pg

a

a

0%

N

0

SE.

--

I

a

-

a

I'

I a

-

N

-

U

4 0

18

5. Caliber 0.30 Bullets a. Physi-cal Characteristics

Bullet

Drawing

Weight Grains St .- Meas. 172 172

No. of Rds 5

cal. 1.827

A2 gr.in 1.751

B 2 gr.in 16.40

Ball MI

B 10986

Ball M2

B 137545

150

151

5

1.455

1.332

12.i3

A.P. M2

B 138195

164

167

10

1.980

1.855

20.15

Tracer MI

B 16092

150

149

5

2.097

1.777

18.57

Same w/o Tracer

134

2

2.50

1.557

16.68

Average

142

2.30

1.667

17.60

1.44

1.043

9.06

Form Velocity Factor ft/-ec 2

KD

Night Tracer M25* Frangible M22 (T44)00 A.P.L TI5

150

B 7638432

108.5

107

5

157

155

1

* Same contour as Tracer MI **Same contour as Ball M2

b. Drag

Bullet

eor

Ball MI

BRL 276

Ball M2

BRL 276

Observathon Range --

Proj. Type 177" 6

1.13

.132

see graph

Resist.

Ball M2

2740

.107

A.P. M2

BRL 271

Time

5

0.92

2730

.125

Tracer M1

BRL 276

Time & Range

5

0.67

2700

.091

Night Tracer M 25

APG 471.4/490-1

Time

5

0.81

2850

.211

Frane!ble M22 (T44)

FT 0.30AC-U-1

Time

T44

1.11

1360

.202

Frangible M22 (T44) A.P.I. T15

see graph

Resist. APG 471.4/4o2

Time

5

1.08

2790

.146

19

GOEFFICIENT ,

-

-

.

Vs MACH NUMBER T BALL, CAL 030, M

.BULLE

. 3

KD

is.

-'...

/-'

."

ho. 0* -BLLT

A..3

FRANIBLE

DRA

•

a

.*..,*

"-

K -u)

CA00

I-

....

T4

II

-OF

/

4$,L

j

....

AT

F

G

,t

C

DRGDOFFCET -u, L

.e

.,

l.N

...

•'

. I. .6 . " U

tO

u

i .'

T

L,

L,

10 I.

t

20 5. Caliber 0.30 Bullets (Con.) c.

Stability

Pitch of Rifling L

Bullet -

BRL 278

Ball M1

10 inches

No. of Rounds 5

Velocity Mach No. ft/sec T-f 1

S T.815

K M 1.24

7

2872

2.409

1.901

1.05

8

2892

2.571

2.079

0.96

5

2574

3.42

0.51

Ball M2

BRL 278

A.P. M2

BRL 276

10

2750

1.42

1.36

Tracer M1

BRL 276

10

2528

2.80

0.73*

Night Tracer M25

APG 471.4/490-1

2600

2.52

1.12

Frangible M22 (T44)

FT 0.30AC-U-1

1370

1.61

0.89

Frangible M22 (T44)

APG 471.84/238

1280

2.79

--

* This Ls an apparent moment coefficient, computed from the observed stability factor and the average values of the moments of inertia of the bullet with and without the tracer composition. x Fired from a special barrel with an 8-Inch pitch of rifling.

d. Drift and Damping Velocity

K

K

K

Bullet

Report

Ball Ml Ball M2 Tracer Ml Frangible

BPL 278 and 357 BRL 276 and 357 BRL 278 and 357

2856 2770 2734

0.77 0.98 1.07

3.8 2.8 5.4

-0.15 -0.09 -0.22

FT 0.30 AC-U-I

1370

0.98

1.98

-0.06

M22 (T44)

ft/sec

L

H

-

U c

C

C

-

-

21

*11~0%

S

U.. 0

4-

w 'I,.

-

-

-

0

~-

e.

U

-

.4

I

-'i '4

-_____

C.)

-

~I

~l*~

Ij .4 p..4

c.J

g IA 0

0

4.

1 a

.4 0

4 I.

i'4~

0

-~

I'S

C

22

C -

eq

2* 4

0. 4 4

id S

Cd

0. 4 4 0.)

nj

n.j

2 2 ~0

2 2 .n

-

V.

*

ha V.

Sn

0..

o 4

d No

it

2 2

2

~

~it

0.. 0 ~

~

0.. 0

j.JI I L

V

4. N

K

0.)

4 U

~:

hA

en 'a)

M

____

4

~~1~

4

C

j-.

U

U -

C=

C

C

23

-

S. Caliber 0.50 Bullets a. Physical Characteristics DRAWING

BULLET

WEIGHT

NO. OF

GRAINS

RDS.

g

A 2

drT.

B2

2.043

gr-in 21.45

gr.in 244.9

5

1.922

19.71

217.1

Meas. 741

5

Ball MI

B129810

St . 750

A.P. M2

B137655

710

709

698

697

674

674

5

2.269

20.94

246.5

Same w/o tracer

802

5

2.402

19.56

211.9

Ave.

838

2.336

20.25

229.2

Alternate

641

Alternatid B129831

Tracer Ml

635

Headlight Tracer) M21 (TIE1)* )

697

3

2.234

22.04

257.1

A.P.I. M8 x

B7636175

650

653

5

1.823

18.90

179.4

A.P.I., T49

B7640941

501

504

3

1.289

15.28

107.6

614

613

3

1.738

18.52

167.1

513

6

1.618

18.67

114.4

3

1.991

19.17

217.1

A.P.I.T. M20 (T28) A.P.I.T. T63 A.P.T. T38

739

A.P.T. T38EI

870

Inc. Ml

B174991

625

619

Inc. M23(T48)

FB19562

512

495

3

1.466

17.89

161.8

608

3

1.652

19.38

200.6

Inc. T78 * Same contour as Tracer Ml x Same contour as A.P. M2

b. Drag Report

Observation

Proj. Type

Ball Ml

BRL 276

Range and Time

5

A.P. M2

BRL 276

Time

Bullet

Alternate

APG 471.4/206

Tracer MI

BRL 276

Same Alternate

Time Resist

A.P. M2

APG 471.4/206

Form Factor

Velocity ft/sec

KD

0.79

2800

.107

5

0.88

2900

.115

5

0.87

2900

.117

See graph

Range and Time

5

0.77

2800

.104

Time

5

0.825

2800

.111

Time

5

0.81

2800

.109

24 6. Caliber 0.50 Bullets (Corn.)

Bullet

Prol. Type

ReotObservation

Models of 155mm HE Shell) M10l, P1 & P2)

BRL 58"t

Inc. MI

APG 471.4/206

Same Inc. M23(T48)

K-1-9 Mar 45

A.P.I. M8

Form Factor

K D

Resist

See graphs

Time

5

0.86

2950

.115

Time

6

0.92

2950

.099

Time

7

1.28

3460

.118

3460

.120

4450

.102

Resist

See graph

K-1-9 Mar 45

Time

7

Sansd

APC- 41.4/434

Time

A.P.A. T49

Velocity ft/sec

1.29

A.P.I.T. M20(T28)

APG 471.4/434

Time

5

0.80

2900

.107

A.P.T. T38

APG 471.4/434

Time

5

0.87

2700

.119

A.P.T. T38EI

APG 471 .4/434

Time

5

0.81

2900

.109

1

DRAG COEFFICIENT

-

-

VS MACH NUMBER I*0

U LET#

.

., CALO.50 m2

KD

.000

D40

.61

to

.9

L

M

1.6

1*

2.0

2.2

2.4

2.

-BULLET,

DRAG COEFFICIENT Vs MACH NUMBER A.RI.,CAL, 050, me

0 a J4

-

42.65(rd)

-X5+.4~+qx

KD

+

x a 0.0005 V CL54

I dIto IS

12

8

.

M

A

2.

i

s

to4.

is

T DRAG COEFFICET vs MACH NUMBER I CALIBER 0.50 MODELS OF 155 MM H.E. SHELLS -

.140

-

K

I~AU. seat-Ta'. NMI$ Vds

.413

-

- 40J

0

IA

lK

66

mOM

U

0

.4405

.

28

G. Caliber 0.50 Buliets (Con.) c. Stability - Pitch of Rifling: 15 inches Report

Bullet

No. of Rds.

Velocity f

Mach No.

S

K M

Ball MI

BRL 278

4

1982

1.760

1.794

1.15

Ball MI

BRL 278

8

2182

1.960

1.578

1.31

2.293

1.603

1.29

2.801

1.891

1.22

1.87

1.24

Ball MI

BRL 27P

5

2531

Ball M1

SRL 278

4

2929

Ave. A.P. M2

BRL 278

13

3112

2.7-2

2.17

0.97

Tracer M1

BRL 278

4

3000

2.82

2.39

0.86*

Headlight Tracer) ) M21 (TIEI)*

APG 471.511/1113

5

2700

2.59

0.84

A.P.I. M8

BRL M258

10

2930

1.92

1.20

A.P.I. T49

APG 471.4/398-1

3

3400

2.71

0.95

A.P.I.T. M20(T28)

APG 471.4/434

8

2970

2.08

1.15

A.P.I.T. T83

AP

471.4/378-1

14

3400

2.49

1.10

A.P.T. T38E1

APO 471.4/391-1

8

2890

2.58

0.72

Inc. M23

APG 471.4/385-1

8

3400

1.52

1.50

Incendiary T78

APG 471.4,/458-1

8

3000

1.32

1.84

*This is an apparent moment coefficient, computed from the observed stability factor and the average values of the moments of inertia of the bullet with and without the tracer composition. **Same shape as Tracer Mi.

d. Drift and Damping K

Velocity

Bullet Ball MI

Report BRL 276 & 357

ft/sec 2540

KL 0.63

K

j

H 6.0

-0.23

A.P. M2

BRL 278 & 357

2855

0.83

3.2

-0.10

A.P.I. M8

BRL M256

2830

1.84

4.8

-0.145

A.P.I. M8

Memo Mar 44

2936

1.15

Inc. M23

MR

3480

1.44

2.47

-0.036

c27

4

T

4

4

tL

10 a~f*

4.64

-1..-

I0U

BULLET, INCENDIARY, CAL. 0.60, T36, AND T36E2

4671

BULLET, A.P.I., CAL. 0.60, T39 ALL DIMENSIONS IN CALIBERS

29 7. Caliber 0.60 Bullets a. Physical Characteristics A

B

g Cal

gr.in. 2

gr.in. 2 607.2

Weight No. uf

Grains

Bullet

Drawing

Std.

Meas.

Rds.

A.P. TS 4

ALX-H 3-2

1234

5

1.838

50.38

A.P. BU 2

ALX -H 3-42

1192

5

1.867

48.72

b54.5

1.938

48.13

619.8

A.P. BC 3

ALX-H 3-188

1180

same Tracer BC 3

1209

5

1167

2

1099

1

1139

5

1.555

50.15

'80.1

Ball T32 Ball T32E2

B 7637435

1200 1140

1186 1139

5 3

1.885 1.763

49.46 46.9

b35.0 516.2

Inc. T36* Inc. T3E2

3 7640421

1140 1140

1146 1140

5 a

1.554 1.587

51.08 51.18

506.1 492.1

1200

1170

2

767

3

1.520

39.61

292.8

A.P.IT. T6S&*

B 7641008

1050

1043

3

1.843

46.6

491.4

A.P.I. T39

B 7841005

1140

1138

6

1

., 6 5

47.9

490.1

H.E. T19

Inc. T31 Inc. T41

*Formerly called TIE6. **Same contour as A.P.I. T39.

b. Drag Bullet

Report

Observation

Proj. Form Type Factor

Velocity ft/sec

KD

1.255 1.21

3584 3579

j.14 .110

A.P. BC-3 Tracer BC-3

APG 471.4/180-9A APG 471.4/180-9A

Photo Photo

7 7

H.E. T19

K-I-9 Mar 45

Time

7

1.14

3545

.104

Ball T32 Ball T32E2

K-1-9 Mar 45 K-I-9 Mar 45

Time Time

7 7

1.25 1.23

3550 3600

.114 .111

Inc. T36 Inc. T36E2

K-I-9 Mar 45 APG 471.4/478

Time Time

7 7

1.29 1.29

3550 3550

.118 .118

Inc. T31

Photo

7

1.18

3590

.107

A.P.I.T. T60

APG 471.4/180-9A K-I-9 Mar 45

Time

7

1.16

3570

.106

A.P.I. T39

K-I-9 Mar 45

Time

7

1.26

3550

.115

s

!

30 7. Caliber 0.60 Bullets (Con.)

DRAG COEFFICIENT vS MACH NUMBER BULLET, BALL., CAL 0.60, T32

-

~-4.55

-

-•

to.=o .

.... . ....

. ..

..

.

.

Ko

4'

-

. c. Stability

1.1t

1.6

-

W

M

..............

2.4

t.S

-

Wt

.

4.0

Pitch of Rifling: 18 Inches

Bullet

Report

No. of Round6-

Velocity ft/sec.,

S

M

A.P. TS4

BRL 257

6

3100

1.85

A.P. BC-2

BRLM 245

9

3520

1.69

1.18

H.E. T19

BRLM 366

8

3500

1.84

1.32

Ball T32 Ball T32E2

BRLM 305 BRLM 368

4 6

3500 3600

1.85 1,69

1.145 1.17

Inc. Inc. Inc. inc.

T36 T36 T38E2

BRLM 305 BRLM 386 APG 471.4/478

6 6

3600 3460 3600

1.51 1.74 1.53

1.58 1.36 1.59

T41

APG 471.4/6-1

3

4200

1.92

1.37

A.P.I.T. TO0

BRLM 368

6

3550

2.10

1.08

A.P.I. T39

BRLM 366

11

3550

1.79

1.215

1.03

31

4.io 3

2.7Z.-

3.25 R

.46

PROJECTILE, BALL, 20MM ISPANO GUN /A/.

SHOT, A.P., 20MM, M75 ALL DIMENSIONS IN CALIBERS

r~

32

7

9i -

7.

U

33

S S

4%'

~

I

i-I I,.

Id

-

-

4. *6%

q

*

I

I.

ii

4

Ii

2

a a

A.

-

1

4.

3~~~

4.~~~

#4

a

#4 *

S

p.4

4'

-

-.

L~.

'S

34 6. 20mm Projectilea a. Drawings: 75-2-299

Projectile, Ball, Hispano Gun /A/ Projectile, Ball, T4 (same contour as A.P. M75) Shot, Armor-piercing, M75

75-2-308

Shot, Armor-ptering. T9E4

TAM 130

Shot, Armor-piercing, M95 (T9E5)

75-2-333 and 341

Shot, Armor-piercing Incendiary, T21

TAM 480

Shell, High Explosive Incendiary, Mark 1

75-2-300

Shell, High Explosive Incendiary, T18 (same contour as H.E.I. M97)

TAM 22 and 483

Shell, High Explosive, T23 (same contour as H.E.I. M97)

TAM 371

Shell, High Explosive Incendiary, M97

75-2-335

Shell. Incendiary. M96 (T18)

75-2-342 and 334

Shell. Incendiary. T28

TAM 1824

Shell, Incendiary. T35

TAM 1979

Projectile, Practice, M99 (T24) (same contour as Incendiary M96)

75-2-343

Fuze, Percussion, D.A., No. 253, Mark I /A/ Fuze, Point Detonating, M75 (T71E4)

73-1-178 TAM 601

b. Physical Characteristics Projectile

Fuze

Ball (formerly 1935 gr.)

Weight Grains Meas. Std.

No. of Rounds

9 cal

A gr.ln. 2

B gr.in. 2

2000

Ball T4

Plug

2528

5

1.884

190.2

1767

Ball T4

None

2512

5

1.892

190.0

1758

Ball T4

Tracer

2542

2547

5

1.806

190.0

1798

A.P. M75

Tracer

2548

A.P. T9E4

Tracer

2000

2000

5

1.474

154.5

967

A.P. M95 A.P. M95

Tracer wo/tr

2000 1987

3

1.488

148.8

958

A.P.I. T21 A.P.I. T21

Tracer None

2000 1980

7

1.538

150.2

1055

H.E.I. Mk 1

Pero.

2030

1995

5

1.860

184.3

H.E.I. TI (with tracer)

Dummy M75

1900

1965

5

1.719

151.9

1882 1470

H.E. T23

T71E4

2000

2004

5

1.643

185.6

1442

3b 6. 20mm Prolectiles (Con.) Weight Grains Prolectile

Fuze

Std.

H.E.I. M97

M75

2039

Inc. T35 Inc. T28

--

-

Meas.

No. of

g

Rounds

cal

A

B

grAn,

grin.

1200

1186

3

1.074

102.2

415.4

1500

1434

3

1.266

125.0

668,7

Inc. M96

--

1920

1993

5

1.553

155.5

1305

Prac. M99

--

2000

1965

5

1.546

163.1

1388

c. Drag.

Projectile

Fuze

Report

Observation

Proj. Type 1

Form Factor

Velocity ft/sec.

KD

0.98

2820

.207

Ball, 1935 gr.

Tracer

BRL 284

Resist

Ball, T4

Tracer

BRL 515

Time

1

0.96

2530

.212

A.P. M75 A.P. M75

Tracer Tracer

BRL 515 BRL 515

Range Time

6 8

1.71 1.98

2550 2450

.214 .256

A.P. T9E4

Tracer

A.P. M95 A.P. M95

Tracer w/o tr

see graph

Resist BRL 515 K-I 9 Oct 44

Time Time

5 5

1.12 1.15

3000 3000

.149 .153

see graph

Resist

H.E.I. Mk 1

Perc

H.E.I. TI8 (with tracer)

Dummy M75 J

50 BRL 515

Time

5

1.09

2750

.148

H.E. T23

T71E4

BRL 515

Time

5

1.14

2800

.155

Inc. M96

.--

BRL 515

Time

5

1.18

2750

.157

APG 472.5/317-

Range

8

51.28

3200

.127

tl.28

2700

.145

.26

3650

.113

1.26

2700

.102

1.19

2700

.162

Inc. T28

---

1846

APG 471/6-8

Inc. T35 A.P.I. T21

t#

w/o tr

Range

APG 472.5/317-1 Time 1781 J

8 5

* 38

DRAG COEFFICIENT vs MACH NUMB3ER SHOTa A.A. 20M M, T9E4

l-k -.-

.8

- -

0403 #~y I +

.

sd1g3o

u~

At

*

L

ISe

a

la~

&a

m

as

m

L

DRAG COEFFICIENT vAIMACH NUMBER -SHELL, H.E, 20MM, MARK I; FUZE, PERCUSSION, 0.A.,,NO. 253, MARK I/A/ ~

,too

vo K

-

-

.0

to

-

w M $s

-To

t-

-

"

Lt

"

37

8. 20mm Projectiles (Con.) d. Stability

Pitch of Rifling:

25.686 Cal. (Angle 7) No. of

Velocity

Rounds

ft/sec.

3

BRL 515

4

2530

2.89

1.14

Tracer

BRL 515

12

2750

2.78

1.47

wo/tr

APG 472.5/317-1

6

2700

2.28

1.6F,

A.t.. T21

w/o tr

APG 472.5/317-

8

2700

2.52

1.39

H.E.I. Mk 1

Pere

BRL 515

7

2750

2.88

1.16

H.E.I. T18 (with tracer)

Dummy, BRL 515 M75 J

10

2750

2.91

0.89

H.E. T23

T71E4

BRL 515

9

2800

2.85

1.09

8

2750

2.80

1.09

3000

3.07

Projectile

Fuze

Ball T4

Tracer

A.P. TOE4 A.P. T95 (M95)

Report

18211 1821 J

Inc. M96

--

BRL 515

Inc. T28

--

AG

Inc. T35

--

APG 471/6-8

3

2600

2.4

Prac. M99

--

BRL 515

6

2750

2.61

472.5/317-1 1848J

M

1.20

The caliber of the 20mm gun is 0.787 inches

e. Drift and Damping V elocity ft/sec,

KKK KL

KH

BRL 515 BRL 515

2483 2483

2.50* 2.50*

4.8 2.7

-. 10 +.02

Tracer Perc.

BRL 515 BRL 515

2530 2830

2.50* 1.12

3.7

-. 12

T71E4

BRL 515

2800

1.27

1.56

-. 005

Projectile

Fuze

Ball T4 Ball T4

none Tracer

A.P. M75 H.E.I. Mk 1 H.E. T23

Report

*This value was determined with the A.P. Shot M75 and assumed to be the same for the Ball Projectile T4; but it Is probably too high.

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