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AIRCRAF ARAMENt FORl

140V 02 1995 Alft-TO-GROUN1M OPERATIONS,

MVIST

tDec Iass ify n OADR* Authori.y; DoD 5200.1-R, Para 4~-600b W I 7 I

LC)

* Vista EnOrd, Report 121,

88 4 15 50 f

SECRET

SECURITY INF 'ORMATION.~ 15'Now40A , i ~9fA

II

.DIscLAIMIR NOTI-cK

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"V"R 121

SECRET

SEURITY IOIUF ATION

AMQCArr ARK&NNT FOR hIR-T0-OaOUND OPERtATIONS

PRiOJECT VISTA

CArIUM INSTITE OF TCHNOLOIU

Pasadena, California

November 30, 1951

This docuint contains information affectingthe National Defense of the United Stateswithin the meaning of the Espionage Act, 50U. S. C., 31 and 32. Its transmission or thereftlation of its contents in any mamoer toan unauthorised person is prohibited by law.

q2Copy No. V of I copiesin Seriesj68Wpags.

SECRET

"SIOt Y INFORMATION

54AA 68205"1'

SECRET VER 121

c-s

Foreword

List of Tables ii

List of Figures iii

Introduction iv

Text 1

References 33

Accession *ow

MTIS QWA1DTIO TABUnannounce4d

3ut1-ioat ur---------

DistwlbuiitLO/

Avallabutiyt sod"a•D IILYI floI!_ ... ..

DIst

SECRET

SECES T VER 121

IThis report was prepared by R. N. Stevens of the CO:nell Aeronautical

Laboratories during his a&ssociation with Project Vie..a during the summr

and fall of 1951. It represents the opinions of the author and may not

in detail reflect the viewpoints of Project, Vista.

B. H. Sage

-1.-

SJX

SECRET VER 121

LIST OF TABLES

Table I. Ralease Error Control Requirements.

s•RaTAi i i

SECR.ET VER 121

List of Figures

1. Effect of gravity upon trajectory of a projectile in a vacuum.

2. Assumptions for rango error.

3- Comparison of app-oxixate and exactAY 9gIn.

4 b a. Effect of uncertainties as to point of release on dispersion ofbombs.

b. Effect of uncertainties as to point of release on dispersion ofbo~m.

c. Effect of release error on cy*

a. Effect of range upon hit probability per square foot of targetarea.

b. ProbabiliUty of hit per square foot of target area as a functionof range.

c. Effect of range upon hit probability per square foot of targetarea.

d. Effect of range upon hit probability per square foot of target* are*.

6. a. Effect of velocity of projectile relative to aircraft upon hitprobability per square foot of target.

b. Effect of velocity of projectile relative to aircraft upon hitprobability per square foot of target.

7. Effect of release error on cx"

a. Effect of slant range upon rounds required per hit for a specifiedtarget area.

b. Effect of slant range upon rounds required per hit for a specifiedtarget area.

c. Number of rounds required per hit as a function of range.

8. Effect of burnt velocity of rocket upon ratio of weight of warheadto that of total armawmet sysates,

S9. Effect of wuszle velocity of gun projectile upon ratio of weightof warhead to that of total armament system.

-iii-

AM~E

SECET VER 121

"List of Figures (cont.)

10. Effect of muzzle velocity of projectiles from recoilless gunsupon ratio of weight of warhead to that of total armament system.

11*. Reciprocal of aircraft armamnt logistic factor as function ofrocket burnt velocity.

U. b. Reciprocal of aircraft ordnance logistic factor as functionof rocket burnt velocity.

12. a. Reciprocal of aircraft armament logistic factor as a function ofgun muzzle velocity.

b. Reciprocal of aircraft armament logistic factor as a function ofgun aUZsle velocity.

13. a. Reciprocal of aircraft arnament logistic factor as a function ofgun nuzzle velocity.

b. Reciprocal of aircraft armament logistic factor as a function of

muszle velocity of projectile from recoilless gun.

14. a. EHfect of slant range upon airplane armarent logistic factor.

b. Airplane armament logistic factor as a function of range.

c. Airplane armament logistic factor as a functiou of range.

a

SECRET VER 121

7 AIRCRAFT ARMAMENT FOR AIh-TO-(HOUND OPERATIONS

INTRODUCTION

Of late, extensive and valuable studies have been made of the

aircraft weapons systems in their undisputed, but not necessarily most

productive role, air-to-air combat. Comparatively little attention has

been given to their other domains of usefulness, in particular, that of

tactical air-to-ground operations.

A comprehensive and detailed study of this operation is beyond

the scope of this project. However, it is believed necessary to identify

sufficiently well the Loverning physical phenomena that substantial bases

are provided for recommendations either for further studies or specific

actions.

In particular, this report will be concerned with aircraft

anmament, the anmunition and propellant system carried aboard the airplane.

However, the other parts of the system, the tarpet, the tactical situation,

the airplane, the fire control system, the navigation system, and the general

logistics of the operation will be considered wherever the characteristics

of the armament cannot be considered independently. Soecifically, this

report will

1. Submit a measure of aircraft armament effectiveness, Ik

2. Examine systems and tactical paraieters of which Ik is a

function, and indicate methods of mjaifldzing rk

3. Compare Ik's of various aircri ft armwient systems

4. Recommend specific actions toward obtaininC the maximum air-

craft armament effectiveness

-iv- ;

SECRET

•.• :• • :•,• '• "• " •' ~ r!• • •! , . •,• • .••- II" l.• • •w "•' "• • i . ....• P n • 'P ' " ...... • :.:,.> .•,,..,• • :.,.,...•,' ...... "•" •:.:,•,...:,', '• •;.;.,:. OF

KEU VER 121

A Measure of Aircraft Armament Effectivezess

It is subm.itted without argum~n-t that an adequate measure of

aircraft armament effectiveness will be the ratio of the number of

kils obtained against specified targets to the weight of the

armament installation which must be curried by the aircraft to obtain

those kills. Symbolically

T MaIhr = 14fl N 11 -N(L&1 kLh~)-IPhi 1 JPh t ((K/h) IT WR T

W0: Weight of armnaent systmexr inatalUt ion

wh Weight of warhead per round

Wh Total weight of warhead in W0

4 )Uumber of rounds of amuunition in W0

I~kTNumber of kills obtained against target, T,, in WOfrk T Prb ilyofil erodaaittrgtT

h(k/IT Probability of kill per hout against target, T

j w Single-shot probability of hit per round against target., T

The affectiveneva index equals the product of the probability of

hit per rouad,. the probability of kill per hit per pound of warhead,,

and then ratio of the total weight of warhead to the total 't.aight of

armamen~t system installation.

In other ft&Ord reporta., the inverse of the product of hit

probabili.V. and tbh, ratio of total warhead weight to ordnance

Wtyete. weight has been called the ortia~nce logistic factor,, L. We

shlul adopt the sam tbrminology, but since ixA this case we are

4--

SREOM VmR 121

considering In W onlyv part of the ordnance systen weight (ignorinzg

the airplane weighit) we shall say that:

uhare 2

Lu The aircraft armawnt logistic factor

For the relationship between. L and L.see'(9).

Ezamination of Parameters

P(NjI)- ProbabilitZ of-kill per hit pr unit warbsai weight.

Vh

The parameter PW ) is principally a function of the fype of

target,, the ty.of warhead,, the striking velocity., the striking

attitude., and the type of fuzing. For simplic-ityj, it will be anssumd

that comparatively this parameter is invariant among a11 aircraft

armament propellant systems capable of delivering equal warhead

Lwi ucino w paaetr. hici in turn aefnto

of anyvaiibes eclla toth operation,, an follows:

I P. L.:Probability of hit noer round awainat. target- T. -1 a function

of$gR :Slat range from point of release to target

T UT (AT~xT~yT) ~'Target (area,, shape,, normal to trajectory)

-2-

is *A

VPR 121

V- Dispersions of round due to aUl causes other than rolsas.

err along the night line

SDispersion of round due to release errors along the eight

1lime, in twu a function of:

R a Slant range from point of release to target

Van Airplane velocity at release

Vr - Velocity of round

9 a Airplane dive angle at release

ai s3 Release errors along sight line, in ranges diveoangle,

and airplane spetd

$ Wb/ATo

The ratio of total warhead weight to the ordna ea systm weight

is a fimeti! of the ratios of round, gun, inatallatioa and control

Waight to 14be wraig•t of the warhead per round (WR , Wg a Wi , We )

Wh h Whh

vbich Az ti a" V•lctona of variables peculiar to the operation a

foli'ma 2

C la.tia of tomd vaight, to warhead weight,, a function of:1

~ W~oit~rof rowai

Dh of rwOf l

U tio of gu (or propalllu• 3tyem) weight to varbhead weight,

a fwwt~ioa of 2

-3-

+.•1 '" 'l ... .+•• '. +' 1+1'' + "' ,+ 1 '' 1'+ '+++"+'+ P '+< • : +', 1 "+. . " +1 '++ "1 d ... + '+ '' ''.+++ , •+ 1b L++:" ++ ': • '+ . . 1+1 T. .. . + 1

UIa 321

Vr x Velocity of round

Dh - Caliber of roimd

I U mber of v=mg

% Number of rounds

rg 9 Rate of fire

.4 a ype of guns

Rkatio of installation xeight to warhad weight & fmcticm of:

Wz a Weight of gm~

Dh a Caliber of round

ug limber of guns

Number of round

rg R-ate of fire•

Gi T •Tpe of guns

fI a Type of Ita3atiMo

W Ratio of control weight to warhead weight# a ftmoti of ratesof cbano of th fudamental variables as well as of the

variables.

There ure other fundametal variables and relationships than the.

listed above. lHomwer, it is believed that enough have been recopdjad

for fairly accurate genera couparison of aircraft armanmt systems,

yet the number has been kept sufficiently low that fairly simple analytic

xpressions my be derived.

Thus we say:

Ph f (R, Ts rip g- (Us T a' Vr., 9

¶EM

SECRET VER 121

~w '/s~WhIk = K/d 1

It will be observed that f and g are functions of common variables.

Theretore, Ph and Wh/Wo cannot be treated independently in maximixing

LW.

An xpression for Ph

Assume a rectangular target of width, w, and length, 1, (normal

to the target). Assume that the dispersion of the weapons system may

be represented by a linear standard deviation of 3 in y (width) and

q-IR in x (length), where V and T an measured in mils.

Then:

For values of " up to 1.0, the following relation

/• ''.•0Y q /e -"s•

does not introduce errors greater than 15%, the error decreasing with

decreasing values of 1,/2- R."• r..Thu for: L- " .V.-

with errors not greater than 35%.

-5-SECRET

SECRET VER 121

If it is assumed that the number of rounds required per hit is

equal to the reciprocal of the single-shot hit probability, to the

nearest higher integer,

for values of R 1.0, the maximum error will not be greater than

50%, and this error will be greatest for the least number of rounds re-

qulred (1-6 required by approximation as against 3 required by exact

expression f-r L. = --/ ( .99).

Inasmuch as for the taeta and ranges with which we are most con-

cerned, - 4e 1.0, it is considered that the following expression

for hit probability is a satisfactory approximation.

.. k. e- I

In the above expression, the variables which are not fundamntal

ame V 7and . X is a function of both (T and V-g, while

J7- is primarily a function only of 7i as defined above. It will be

y

assumed that for each type of aircraft armament -is a constant, the

value averaged from firing tests. However, as defined above,

s0 that T- 4I~

With the above assumption:

A1-

-6-a ~ EATRVV" ;

SECREPT vEi 121

It may be shown that for a vacuum trajectory (see Figure 1) the9.

trajectory drop nay be expressed as:

R

where:

Trajectory drop (ft./ft.)

Trajectory drop (ft.)

R = Slant range (ft.)

Vaw Average velocity of projectile (ft./sec.) over slant range, R.

Angla of airplane flight path to horizontal at time of firing.

Va = Airplane velocity at time of firing.

And~

L Vc~j(See Figure 2)

If itisumdta

S-7-

SK2ECT

------

SECRET VER 121

and that these release errors are the principal ones not included in O,

then, - Vq- •÷ Cr -A6,-S R V

R Va, Z i •_L VIZ. V4 VJ m~

- ~+~-

Assume for a moment that Vav may be chosen arbitrarily, independent of

R , V a , a n d e, t h e n : 7 A 7

9 c g-( R + ( u .

and ... ..T

Here we observe that if V'i is small relative to Q"g' (sayv 3; - )

and - - I P Ph increases linearly with Atincreases as the square of Vav

increases as the reciprocal of the cube of the

range

increases as the reciprocals of 9ri and i•-increases as the reciprocal of cos e

If, on the other hand -i is large relative to Ug (say 7T.' 3O5 ),

and P , Ph increases linearly with At

increases as the reciprocal of the square ofthe range

increasev as the recinrocals of V-. and 1 -

Now,, is also a function of ray so without further exploration of

their relationship, the variation of Ik with Va cannot be stated. However,

; is not a function of the other variables except as Vav is aWe

function of theo, so that for our assumption of an arbitrary Va, the

-8-

SECRET

SECRET VEB 121

variations of I with AT, ', e' 9 "- and are generallyk gel

the same as those of Ph,

It should be observed that ratie has a very significant effect on

Ph and Ik L _ ('2.-(2-

Therefore, training and equipment plans should consider the vry

conviderable gains to be obtained by firing at short range. (For

example, although aircraft armor to protect against small-arma anti-

aircraft fire and fragment damage would increase W,, the reduction in

safe firing range resulting trom its installation might well increase

Ph sufficiently to result in higher Ik's for the armored airplanes.)

For a particular weapon, where Vav may not be independent of R,

Va, and E , the same general trends follow, modified as indicated in

the above expreasion for 7-9.

The above analysis has been based upon an approximation for the pro-

jectile trajectory. The error8 introduced by this ap .,oximation should

be explored. First it is necessary to obtain expressions for the average

velocities and their derivatives for the various weapons. These follow:

For bombs:10 V, >R V~ i f oooý ! .

For rockets:

_R R..- 9-

"..r..

SECET VER 121

Thant

For bombs: AR R . \O.

Vaz V4,.'2V

For rockets: __6 v~t s

(V -

For guns:

V4. (vO. C\4w) (a+vw6

Teassuin that the errors are indeymndenitt

For rombes:

For gunset:

L&L RV Gt;L j +VbýK 40R-

+-a-.-"L2; SECRExTxl

SECRET VR 121

For bombs:

For rockets:

For guns:SV \2z)'-,2.

'igure 4 plots 7-, versus a1 -=-.•5) for various values

of &, Vb, and V. corresponding to existng bombs, rockets., and guns.

For rockets and bomba, Va was set -qual 500 ft./sec.; for guns, V. uas

set equal to zero. Actual values of 17-9 as taken fron trajectory Table

I are shown for comarison. It will be observed that 'he calculated

rocket deviations correspond quite well to the actual, the errors ranging

from 2 to 7 percent high for the bomb, 2 to 12 percent low for the 50 Aa,

14 to 26 percent low for the 50 HVAR, and 8 to 13 percent low for the gun.

These errors are, in most cases, no greater than those ihich must result

from asamptions for (-i. It appears then that trends shown by the ap-

proximate analytic expressions derived above will be generally correct

and that the absolute values will not be greatly in error.

L7j has been defined as dispersions due to all causs other than

release e- ror along the sight line. These would include free flight

Sballistic dispersions, dispersions caused by mechanical and aerodynamic

disturbances, sighting error&, alignment errors and azimuth errors.

~~L I .:.W- I

-11-E

SECRET VER 121

It will be assumed that these errors are circular. The values given

below are for the linear componentA (ý= =7 0. 70707iJ). The free

flight ballistic dispersions have been given in other EngOrd reports

(2,3,4,5) and are approximately:

3-4 mils - Bombs (Existing bombs with modified fin assemblies andproposed new farilry of boibs)

3-7 ,ils - -cketr (Air-fired, fin-stalillzed)

1-3 mile - Ouns (Air-fired)

There have been no satisfactcryr isolatiouis of the other dispersicmns

contained in 'Q-i Theivfure, for the reir•Andnr of this analysis two

assumptions as to its value will 1-c mude. The :rirst (lower limit) will

be that ITh is equal to the ballAstic dispersioi, alonoe, valite to be:

4 mils - Bomas

4 vii - Rockets

2 nils - Guns

The second (upper lindt) will be that Krj is equal to dispersions general-

yIly fouind in firing tests corrected for •'y. These values are approximately

(6).

9 mile - Bomba

9 midls - Rockets

5 mils - Ouns

Release Error Control Requireiments

With the aid of the above equations aid numbers it is possible to

approximate the values within which AN R, 4 V, and 41 & must be main-

tained in order that dispersion along- the sight line, V-,, will approach

its minimum practical limit. Since

the ziinimum limit will be 7-iT, with gk R, AV, A E) all equal to zero.

-12-

... .. . •"".. . .. . . . . . -- •...•ii . t - - m: 1

SECRET 9VE 121

However, it will be assumed that a minimum limit below which further

expenditure of effort to reduce release errors would be impractical

will be:

Then for bombs and rockets:z

For guml t . ls(i.a4ml)5ml

S3.3 milse• 5 mils) =6 mas

Then using the approximate equation for <r-:.....

R Z

~4 ý

Using the above equation, the maximlm allowable value of may

approximated. Then it is necessary to assign maximum allowable value to

,and 4%RFirst it will be assumed that there are maximum limits wit.in which

these errors can be controlled by even a very simple fire control system

Li (fixed sight, standard releaso range, trained pilot). & R is probably

the most difficult error to estimate or control; 4 Va somewhat less dif-

ficult; and • 0 is the least difficult. Experiences of trajied gunnery

pilots, firing with fixed saghta indicate that these errors can be held

within thin folJowisnW maxiwm= liuits:

-13-SECRET

I

SECRET VE 121

R 0.5R •Va- 50ft./sc. 5°

It will be assumed that no errors greater than these will be

permitted. Then the necessary reductions below these limits to satisfy

the above equation will be determined. The distribution of errors will

be such that when all the allowable naximum errors are below the simply

controllable maximum limits,

Va

With these assumptions, the maximAs allowable values have been computed

OF for a range of Vav's from 500 to 3000 ft./sec., H 2 3000 and 6000 feet,

e9 - 20P and•60o, 70 z 2, 5, and 9 ai and Va N 500 ft.le. The

results are presented in Table I. A generalized mumary of the results

is given below, for i mils.

oRnge Allowable Errors

BMAtI V&Vaa

G)uns (Via 1500 ft./si~c.) 6000 0.15 0.1 53000 0.3 0.1 50

Rocketa .Rockets (VA 1000 ft./soc.) 600 0.35 0.1 50

3000 0.15 0o5

Rockets (500 Vi 1000 ft./sec.) 6000 0.02 0.02 203o00 .o05 o.o0 50

Boabs 6000 0.005 0.003 103000 0.01 0.006 10

Therefore, if the effect of gravity drop is to be reduced to a mininum

practical limit, range error must be controlled within limits from x <

C.005 for bombs to .-. 0.15 for guns. Velocity and range error

effects, for errors below those controllable by fairly simple systems,

are negligible, except in the case of bombing.

Figures 4a through 4e show the effects of release error on for

SECIT

SECREn VER 121

various weapons at various ranfes and release angles.

Ph

Finally then, the following expressions are derived for Ph'

For bombs: ~I

or rockets: V

rr C .q - - 4(

For rockes:( R L4

1-_- + 1-54;

Figurs 5a through 5d show the values of"'--P for various wsa~nD,

AT,• ~~d~i.e• angles, and the l1iAting values of 2-i, plotted as a function of

Frckets, and Vm for guns. The .arked increase of hit probability with

decreasing ran•.e will be noted in Figure 5. It will be noted that no

*+ significant iDmprover~nets in rocket hit probabilities will be made until

reductions in inherent dispersions are accomnplished. Roweer, improvmentu

in bombing fire control above those assurned will result in significant

iuprovmewnta in bombing hit probabilities. Figure 6 indlicateB that as

A L3EC

SREMT M 121

* long as firs control errors remain large,, burnit or muzzle velocities

should be kept iiigh to improve bit probabilities. As fi-re control

errors are reduved, velocities may be correspondingly reduce&. It in

obvious, that with perfect fire control, 'velocity will have no effect

on hit probability. Similarly as long as inherent dispersions are high,

burnt or mu: ale velocities may remain relatively low. As inberent dis-

persions are reduced, velocities should be increased to improve bit

probabilities.

In Figure 5* the hit probabilities obt~iiiawd in Air Proving around

tests with 50 WVAR rockats, using the A-IC)I night with varying degrees

of sewIti Ity has been shown (7). R~anges were un~certain, betweien. 2500

and 3500 feet. Results were In remuarkable agre;snt with those bypeths-

usied with the use of the foregoing approximatimons

Based on the data of Figure 5# Figure 7 shows the number of rovuiads

required per hit (subject to the errors inherent in use of the approximate

formsula) wm a function of range and target area for guns,, rockets,, and

bombs and for the combinations of waxium range errors and inherent dlis-

persiona and miniau range errors and inherent dispercions. The saximmis

may be considered as approximating present aystams, the miriium~s as the

limit of inherent improvemsnt. Three target areas have been chosen, 200

sq. ft. (approximately that of' a tank, side on)., 2000 sq, ft. (a pill-

box or artillery emplacement) and 20,000 sq. ft. (troop vehicles ot supply

coucentration).

*1 ~In analyzing these data, let us consider that a i'vcimu of 8 rounds

per hit are desired. Then the following table indicat'so tha maxima ranges

in feet at which the various weapons may be used.

-16-SMaz

q1SNCRET VER 121

Target Area Guns ___Rockets BombsPma.~ent Improved P..ip .Imp.

_______ Errors

20sq. ft. R 3000 ft. R < 6000 R <l150 R '3000 R-clOGO R' 1502000 sq. ft. R '6000 R< 6000 40h00 R--60OO0 R-2000 R-l350

20,000 sq. ft. H-6ouo H --6000 R 6000 R-:6000 R-4500 R-,6000

On the basis of hit probabilities above, with npecilicatioris aE so-

tablished, guns should be used for the 200 sq. ft. tarret, bom~bs should

not be used, and extrezuely close mranges aire necessary with rockets.

Either guns or rockets migpht be used aegaitst the intermediate area target,

but close ranges are necersary wi th bomhr. Guns, rockets, or bombs might

be used against, the 20,000 sq. ft. target.

Wh-Ratio of Total. 'lha0Wiht to ArmawoenL. Syswwu Weirlit

The total warhead weight cai-ried by' Uma a~irplwie:

The total armament system 'weight:

RR

Wg NWJwhere:

WO=Armnament system weight

4i Total warhead weight

2R Total round weightL

Wi=Total installation weight

We =Total f'ire control weight

Wg =Total gun weight

NR = Number of rounds

Hg9 Number of guns

-17-SECRET

SECRET VER 121

wh = Warhead weight per rounid

vR = Round weight

Wg Gun weight

So: Wh

11- N~ VVW11 "h NRWh N~wi

In other EngOrd reports (2, 3, 4, 5, 9) exPressions have been derived

for ŽWR - and \/i as functions of round diameter, rate of fire,Wh Wh

velocity of round, and subsidiary parameters characteristic of the type

of weapon. However, there are no such exprassions derived forNR Wh

Therefore, in this report, it will be considered that comparable fire

control systems are provided for all weapons (weapons will be compared

for the same release errors), W. will be included in the basic airplane

weight, and the term eliminated from the above expression.

Bombs

For bombs, gun weight is zero, and the installation weight per rouhd

varies roughly linearly with the weight or' tLe round. Thits

and from (2), W 4, . o

Wh

(considering warhead weight to be the total bomb weight minus the stabilizing

system weight)

So that:

SHCRET

SECRET VE 121

Rockets

As for bombs, gun weight is zero, and the installztion weight per

round varies roughly linearly with the weight of the round. Thus

w5

'I Wh

and from (3),

W1 (/ , */ 0--"-:~C M 0• .- P' l,))

!um Motor diameter, inches

4 *Vb = Burnt velocity, relative to launcher, ft./sec.

W*= :Ratio of rocket motor w~.ight (burnt) to propellant weight.

Then:

S÷I<.K

6- +

o+ 5.0Vb V4) Vb 4 z•-O

wp 6?00

Fcr simplicity, say

•, Nj Wh

And that

4% P

-19-SECRET

,Himl$

3" M .•r.T VER 121

Then: OO-Vb

- 850 -- 0.7 Vb /

1 0. Vb (o-1 ( ?t

These values are plotted in Figure 8. Actual values are shown for

comparison. Good agreement is shown between the estiiwted and actual

values for the older rockets but probably will be approached as develop-

ment continues. It will be noted that decreases markedly withwo

increasing Vb-

Standard Guns

From (L,5):

wh -- h"t

where

VZ Z Muzzle velocity, ft./sec.

Dh = Projectile diameter, inches

r = Rate of' fire., rounds per minute

"h -

ŽY9 .W

so that:

• Dh' x ID

V't Lj3 q j~ q,9 I +-. oLT 4 4

For example, let us consider two classes of guns, a small caliber, high

cyclic rate gun (say 20 mm., 650 rpm) and a large caliber, low cyclic rate

gun (say 75 nim., 10 nm). Then

-20-SECRET

• •,CRET VE 121

. 6

•Wo ' 3+ PI

V~LJ~5!75I3 xdINR

Values are plotted in Figure 9, and compared against actual values.

Good agreement is found. Again, it is found that --- decreasesWo

markedly with increasing m=zsle velocity. It will be noted that anuwber of rounds por gun has a significant effect on -- the

WO

larger number of rounds per gun giving higher ratiox. This would

be expected until the total weight of the rounds are equal to or greater

than the total veight of the gun. Also, inspection of the above equations

reveals that for the same muszle velocities and rounds per gun, increases

in rates of fire decreases WhWO

Recoilless Guns

From (5 and 8):

- .> 16- (exiating designs) (o nldnlA/h 4. S x 0 6V 4\4n (proposed future designs) automatic feed)

WP 2.9 ' (57-105 m. euns)

For an automatic feed mechanism, we shall assume (based on the

standard gun) W --. K--. . o,/5-E, ,--7

(existing design)-21-

SECRET VER 121

-0' v- 55

* U~h~J(proposed new design)

Then:

,:L :_" -v•.. (existing design)

-Výýx 1'F5 + os5i-.- 1 (proposed new design)

wa _ _ V 1.5 q

f -Weight of automatic feed mechanism

wc Weight of care of round

The installation weight should be between those for rockets and

atandard guns, say

N WhThen:

Wh (existing guns)

.. (prcposed guns)

Let us now consider a large caliber, low cyclic rate gun (say

75 =., 10 rpm). Then

(i--(exsting guns)

T,+V, 1 , -'Eproposed guns)

Values are plotted in Figure 10. The same trend of marked de-

crease of with increase in Vm is found as with guns. The: WO

-22-SECH9T

SECRET VER 121

sipnificance of the number of rcmnds per gun will apain be noted.

Gun-Launched Rockets

Inasmuch as pn-launched rockets (or closed-breech rocket launchers)

are still in early development stages, there are little statistical data

against which empirical relationships describing the family can be checked.

In general, it would appear that the weight of the launcher must be in-

creased over that for the pure rocket as a function of the rate of fire

and velocity upon leaving the launcher, as in the case of Ians. The

ratio of rocket warhead weipht to round weight would be expected to be

lebs than for the pure rocket because of the necessity for strengthening

the case to withstand the higher initial accelerations. Ther fore, the

over-all W.ft for the gun-launched rocket would be l6os than for the

pure rocket. Counterbalancing this, however, is the increase in accuracy,,

the dispersions approaching those of guns.

For the T131 rocket, used with the T11OE2 launcher

wh '. lb. .

wg a 300 lb. (launcher, mapazine, and feed weight)

wR = 10.7 lb.

V% a 2500 ft./sec.

NU w 25

Ngr 650 rPm

Assiming an installation wight equal to 0.5 wg

This compares with the values of 0.11 found for tne pure rockets,

"(light case), 0.038 for a standard gun with the same performance, or

0.095 for a recoilless gun with the same performance.

Comparison of '-- for Various WeaponsWb

Of the veapons described, the bomb has the highest value of -Wa

-23-SECR•T

SECRET VER 123.

because no propellant, or structure to resist the supporting f~orces is

neces3sary. The rocket (except for t~he closed breech launched rocket)

requires a comiparatively large amount of propellant, but relatively

little structure. The recoilleso gun recpiires less propellant than

the rock-at, but more structure. The gun requires evenl less propellant,

but even more structure. This will be noted in the cornpariz-an of warhiead

.1 weight to round wieiphts where the rocket has the lowest ratio of the) three.,

the recoilless Fun an inte?-sdiate ratio., anJ) the v-un the lowest ratio.

Therefore, at spzae number of rounds per gun, the - ~ratios of the

three weapons should be the same., that weapon requirin,,o the. greatest

structural weieht requiring the most rowids per pun. These numbers are

tabulated below,. the nambera corresponding to the number of rounds per

tgun which must be carried to give an equ~a to that of a rocket,

i~~.the gun muzzle velocities being equal to the rocket's burnt velocity.

An intertiediate velocity of 1500 feet per second was chosen for this

comparison.

Projectile Diameter1 Number of Roundis per Gun Required at

10 rpm600 Ma

1 nh235 550

2 inch 145 34j5 Standard guns

5 inch 90 215

I inch

inch My 5 Recoilless Guns

5; inch 5 4

A similar table basad on the number of rounds per k~un required to

equal the of the T131 rocket and launch'~r, 21175 projectile, 650Q

rpma, 25; rounds per launcher and 2500 feet per second burnt, velocity is

-214-

SZCRET

MSCRT VER 121

* ~gi'ven below.

Pro~iectile Dianeter Number of rounds per g=n required at

M75 105taridard G n

2~7~ 70Recoilless Gun

$ A-Ml' IVValue3_of L, Thom Aircraft Arnasuernt Logistic, Factor for Various Weoapons.

As previously defined, the aircraft armament lovistic factor is

the product of the reciprocal of the probability of hit and the ratio

of total weight of armiataent systeM; carried to total w aight of warhead

carried. Thus:

Lw W(gun) or burnt (rocket) veloc~ities. Their variations as functions of

ve1lociLy have been individually discussed in previous sections.* The

over-all variaticnL will be ciiscuased balow.

For bcmZ* in u essen~tially fixaid. Thaerefore l/Lw, varies

linearly wi th the probability of hit. Relat~ive values of the product

of LW anrd the tart area are given in the fol±'awirg table:

* .t 0.1 9502,5074v,000000

0522,0004900 1750ODO 39O0,0O

SPURCIT

2 smm vu in

Rockets

The variation of 1/LAT for rockets as a function of range, , l

burnt velocity and range release error is plotted in Figure 1). It

will be noted that 1/L. reaches a maximum (Lw reaches a minimin) within

the velocity range of the rocket. As might be exected, the optima

velocity is somewhat lower for small release errors than for high; sox*-

what lower for large inherent dispersions than for small; and somewhat

lower for short ranges than for long. The best compromise velocities

(weighted toward firing at long ranges), appear to be approximately

1000 feet per hiecond for the older (higher case weight) rockets, and

1600 feet per second for the newer (low case weight) rockets. Both

values are s81 mwvat lower than those found in existing designs. Rela-

tive values of the product of LwAT are abom below:

R --- __ 3000 6000 feet

1049 14 9 ails

0.1 2600 11,000 13o0O 52,500Older rockets

0.5 5350 155,00 43,500 95,000

0.1 1650 9100 8150 35,9500Never rockets

0.5 26S0 9800 18,5wo 50,00o

Standard Guns

The Vayiatmon of i/L-- A.,- for standard Pimn a a function of _ranvge.

q-i muzzle velocity, and range release error are plotted for two guns

is (a wmull caliber high cyclic rate, and a large caliber, low cyclic rate

gun,, for various numbers of rounds per gun) in Figure 12. There, optiwim

velocities are also shown to be lower than standard design, approximately

7 -26-'4 -- o. ~ f

SECFT VW 121

1700 feet per second for both types. The trends of variation of

optimum velxcity with release error, inherent dispersions, and range

are the same as with rockets. Relative values of the product of

Lw AT are shown below.

____~~~L LAT _ _ _ _ _

R -0 3000 6000 feet

2 5 2 5 mils

0.1 785 4550 4ooo 20,000 200 roundsper =un

0. 1700 6650 12,000 33,500 Samallcaliber

0.1 600 3500 3250 15,000 400 rounds high cyclicper gun rate

0.5 1200 4750 9500 23,500

0.1 1550 14,000 fl,500 30,000 10 roundsper gun

0.5 4650 15,5oo 35,500 85,00o L0* caliber

0.1 1250 7050 6150 29,500 20 rounds low ivlicper fnm rat.0.5 2550 9250 2o,pooo 51,5oO

It will be noted that for corresponding inherent disperwions, in

the ranges of rounds per gun shown, the logistic factor for guns is

higher than for the newer rockets (effectiveness per pound of instal-

lation weight is lower). This was indicated in the comparison givenWh

in tlhe section discussing T Th& lower limiting values for guns

than for rockets are due to the lower range of dispersions.

Recoilless Guns

The variation of 1/Lw AT for recoilless guns, as a function of range,

A j., musze velocity and range release error are plotted in Figure 13

for two gun designs, one corresponding to existing, practice, und a

-27-SECIM

SEC•IT VER 121

lighter one corresponding to proposed new designs, both taken as a

large caliber, low cyclic rate weapon. The optimum velocity is shown

tc, be approximately 1200 feet per second (weighted touard the longer

range firing), for present desipn and approximately 1400 feet per second

for the now design. The trends of variation of optimum ve ocity with

release error, inherent dispersions, and range are the same as with

rockets and standard gwuw. Relative values of the product of Lw and

the target area, for thu above velocities are showi below:

A~_________ Liv AT___

- 3000 6000 feet

-P2 5 mile

0.1 1150 3330 7350 28,000 10 roundsper gun

0.5 3300 9100 41.,500 111,000 PresentIDesigns

0.1800 230 510 18,00 20 roundsper gi0.5 2300 6600 18,o00o 49o000

2300 ~ ~per Suni:;, o.5 2300 6650 18,ooo 45, •oo Nov1O Designs

0.1 68 3600 3900 16,000 20 rounzn

0.# .5 1 750 5400o l3a500o 26,500

"It will bo noted that for recoilless guns, as with at&ndard guns,

in th ranges of rounds per gun shown, for corresporndig inh erent dia-

persions, the logistic factor is higher than for the newar rockets, as

was indicated in the -L comparison. The lower limiting values for

S.recoilless guns than for rockets are due to the lowbr range of dispersions.

However, the logistic factors for large caliber low cyclic rate recoil-

less guns are smaller than those for correspondini standard guns under

-28-

SECRET

SECRFT VER 121

comparable conditions.

Gun-Launched Rockets

The logistic factor for gun-launched rockets can be confidently

determined only at the design velocity of the exiat.ing weapon, the T131

at 2500 feet per second. Assuaing its dispersions to be in the same

range as guns, the relative values of the product of Lw AT are given

below.

LwAT

2 5 2 5

0.1 1300 7800 5650 329o00

L0.5 1 1950 1 _855 1 1250 4 20500

Thete values are higher than for the recoilless gun (20 rounds per

gun) at its best velocity. However, a reduction in the velocity of the

T131 would reduce. the lolistic factors, until, at the stme volocity the

comparison would be approxinaitely the same as given in the section on

, since the aare. inherent dispersions were asasued both for theWe>

recoilless gun and the gun-launched rocket.

Comparison of Weapons on the Basis of LI.

SFitna- 14 shows the values of LW versus rnpe for the following

weapons, againnt three target areas. 200, 2000, and 20,000 square ftoet.

•+:.:i1. Boz~b

2. Rocket - Light case, 1600 ft./sec.

3. Recoilless Guns, Large caliber, 1400 ft./sec.

a. 10 rprA, 10 rounds per gnn

b. 650 rpm, 20 rounds per gun

-29-SECRET

SECTET VER 121

4. Standard Guns, 1700 ft./sec.

a. Large caliber, 10 rpm, 10 rounds per gun

b. Small caliber, 650 rTm, 600 rounds per gun

5. Gun-Launched Rocket T131, 2500 ft./sec., 650 rpm, 25 rounds per•':I gun

No emal caliber recoilless Cuns are included., since previous examnina-

tion of logistic factors has indicated thpir relative inferiority to

other weapons. No high cyclic rate large caliber standard guns are in-

cluded because of the practical difficulties associated with their design

and installation, and their relative inferiority in Lw. The projectile

velocities are the optimum indicated in the previous sections, except

for the Tl31, whose design velocity was taken.

The target areas, as stated previously, were selected to roughly

correspond to the following tactical targets.

200 sq. ft. - Tank, or transport on rail or road

2000 sq. ft. - Pill box, artillery emplacement, or bridge abutment

20,000 sq. ft. - Troop vehicles or supply concentration

In general, the trends follow those shown in the hit probability

section, emphasizing the Vreatmr weight of the hit probability term in

the logistic factor. For the 200 sq. ft. targets at the longer ranges,

the better guns have lower logistic factors than rockets, and rockets

have lower logistic i'actors than bombs. For the 2000 sq. ft. targets,

the rockets are generally comparable with guns, but better than bombs.

For the 20,000 sq. ft. targets, rockets are better than most guns, but

at short ranges or low errors and dispersions, hot-ibs are better than

all. Above 20,,000 feet bombs will be best.

The effect of ranpe is aiain emphasized, particularly against small

-30-SECRET

SECRET VER 121

targets. Against tanks, effactiveness in gained only by firing at short

ranges, no matter what the weapon.

There are some rather important supplements to the conclusions

reached in the section on hit probabilities when the weight characteristics

of the weapon are considered. The gain in effectiveness from the use

of guns over rockets against small targets is not nearly as marked be-

cause of the greater weight ratios of the guns. However, the effective-

ness of all weapons is so low against small targets that even the small

gains in effectiveness made possible by the use of guns should be utilized,

since it may make the difference between failure and success of a sortie.

Among the various I-uns or gun-launched rocwýts, the small caliber,

high cyclic rate, large number of rounds per gun standard pun is superior

against all areas. It also has a good logistic factor compared with

rockets or bombs. The large caliber standard gun, however, is the least

effective of the guns. Between these two lie the gun-launched rocket

and the recoilless puns. The gun-launchod rocket, for comparable rates

of fire and rounds per gun, appears somewhat superior to the recoilless

rifle at the longer ranges, higher dispersions, and smaller areas, The

two are nearly equal at the shorter ranges, lower dispersions and larger

targets.

Examination of Effectiveness Index of Various Weapons

The previous se.tion compared weapons on the basis of logistic

factor. However, the results must be modified by the influence of

•-2))T, the remaining terui in the effectiveness index. There are

not sufficient effectiveness data to quantitize the effectiveness index

in detail. However, the relative index of the different weapons may be

examined qualitatively.

-31-SECRET

SECRET 1 121

Against small targets, the small caliber high cyclic rate gun

has the moot generally favorable logistic factor. However,( P ,Aý1 ')) forSfor

this weapon is essentially sero, when used against armored targets. The

low cyclic rate recoilless rifle, or gun-launched rocket, which can de-

liver larger caliber and weight projectiles would have the best effective-

- -. ness index against tanks. The small caliber, high cyclic rate guns would

have the best effectiveness index against convoys or trains of vehicles

and troops.

Against the intermediate sized targets, unarmored or of light

structure, the small caliber gun still shows the best effectiveness

index. Against heavy structures, guns or rockets would show approximate-

ly equal effectiveness indices, but the lower accelerations of the rocket

would enable the more efficient use of a greater number of warheads.

Against targets of 20,000 square foot area and greater, bombs have

generally the highest effectiveness index, except where penetration

must be accomplishud by the kinetic energy of the round rather than by

explosive effects.

4-I

-32-SECRET

SEMM VER 121

1. *Trajectories of Aircraft Rockete' 0SRD Report 2540., CIT-UBC 35..January,, 1946. (Restricted)

2. OPhysical Characteristics of Aircra~ft Bcab". Vista Na*Wr Report119, California Institute of Tecbnologys Decembe-r. L951. (Secret,)

3.6 *P)byuca1 Characteristicae of ALLvr.Jt Roolast", Vista M%)g'4repa220% calufwiau tntitute of Teckmology, Decmbea', 1951. (Secwt)

4~. oWeapong Sumary of Aircreft Gunsm, Vista tr'erOrd Report 115,, Califor-nia Institute of Technoio&70 December, 1951. k'Jontfident1.al)

(Secret)

7. *Report of the TAC Air Ground Tests with the A-1 Rocket Sight*,, AirWeapons Researlch Center,, University of Chicago, Julyj, 1951.

8. *Characteristics of Standard Recoilless Guns"~, Vista XngOrd Report108, California institute of Technology,, Decemaber, 1951. (Confiden-tial)

9. "The Ordnance Logistic Factor of the Airplane as a "ir Power DeliverySysteu',, Vista Ing0rd He ort 122, California Institute of Technology,,December., 1951. (Secret)

-33-SECRET

SECRET

SECRET VER 121

TABLM I

RELEASE ERROR CONTROL REQUIRENTW*

2 m.le ;'•= 5 mile CL = 9 Milova, AR/R WV/Va 49(?) •R• AV/Va &eG) &R,/R 4V/Va &0()

500 0.0021 0.0011 0.33 0.005.3 0.0027 0.84 0.0095 0.0048 1.51oo0 o0.o084 0.o84 1.3 0.021 0,021 3.2 0.0o1 0.041 501500 0.019 0.029 3.0 0.o04 0.081 5.0 0.13 o.1 5.02000 0.035 0.070 5.0 0.13 0.1 5.0 0.26 0.1 5.02500 0.076 o.1 5.0 0.22 0.1 5.0 o.1a 0.1 5.03000 0.12 0.1 5.0 0.32 0.1 5.0 0.5 0.1 5.0

e= 600

500 0.0040 0.0020 0.13 0.0099 0.0050 0.32 0.018 0.009 0.601o00 o.o16 0.016 0.053 0.040 0.040 1.3 0.071 0.071 2.3.1500 0.036 0.048 1.2 0.098 0.1 3.2 0.22 0.1 5.02000 0.069 0.1 2.3 0.22 0.1 5.0 0.47 0.1 5.o2500 0.12 0.1 4.0 0.40 0.1 5.0 0.5 0.1 5,03000 0.17 0.1 5.0 0.5 0.1 5.0 0.5 0.1 5.0

R = 3000'Va = 500 ft./aec.S= 200

500 0.0042 0.0021 0.65 0.011 0.006 1-7 0.019 0.010 3.01000 0.017 0.017 2.7 o.o46 o.o46 5.0 0.090 0.090 5.01500 0.041 0.062 5.0 0.15 0.1 5.0 0.28 0.1 5.o2000 0.10 0.31 5.0 0.29 0.1 5.0 0.5 0.1 5.02500 0.18 0.1 5.0 0.35 0.1 5.0 0.5 0.1 5.03000 0.26 0.1 5.0 0.5 0.1 5.0 0.5 0.1 5.0

SI e =600S500 0.0079 0.0040O 0.26 0.020 0.010 0.66 0.036 0.018 1.2

100IOC 0.031' 0.031 1.0 0.079 0.079 2.6 o.16 0.1 5.0

ou 0. 3 .00 .-r, 01 -0I... 2000 0.15 001 5.0 o.5 0.1 5.0 o.5 0.1 5.0

2500 0.30 0.1 5.0 0.5 0.1 5.0 0.5 0.1 5.03000 o.47 0.1 5.0 0.5 0.1 5.0 0.5 0.1 5.0

B•elow 0.5, -z = o.1, 6e= 5.0

SECRET

SECRET

.9.oVE

-v0-t~ Cos e

R *VAV -t SLANT RANGE (i)(VAv DEFINED AS EQUAL TO( R-

A M u ýt2 COSe ~RCoSe -TRAJECTORY DROP (tM2 2 VAV2

E (MILS) - R CO050 - TRAJECTORY DROP (MILS)R 2 VAVt

I *TIME OF FLIGHT FROM RELEASE POINT TO GROUND (SEC.)

4M0 e ANGLE OF RELEASE

V 0 *SPEED OF RELEASE (FPS)

* FIGURE 1. EFFECT OF GRAVITY UPON TRAJECTORY OFA PROJECTILE IN A VACUUM

SECRET

SECRET

"E0

AE0 EO

ASSUME SIGHT SETS DEFLECTION ANGLE E0 AT Ro BUT RANGE INFORMATION ISUNCERTAIN WITHIN RI =RO+AR>R 0 -Ro-AR-R 2

TOTAL DISPERSION AT TARGET (MIL) -AEOAE 0 2 -AE 0 1 =( ER2- / -(EoRI-'7 1 )P'o Ro

-EOR 2 -E2R 1-;R +E1 R1 - RAg-EZ)R,(E1 -E0 )Ro Ro

E(R -A [ R)(Eo-2) t (Ro E0 AR)(EI -Eo)

RoE ,- E + ýL [(E, •) (• - )Ro I-E)-(o-E)

BUT (E.-Eo) CONST ,,R - Eo-E2)

SO, L Eo E1 -E 2

THE LOCATION OF THE MEAN CENTER OF IMPACT (MIL) i -COUST(-k-2)ASSUME THIS CORRECTION IS INSERTED IN EO) KNOWING RANGE OF --

) RO

THEN INCREMENT OF LINEAR ERROR FROM MEAN (MIL) ± El-E 2

ASSUME R = Et-E CONST. (AR) 22

FIGURE 2. ASSUMPTIONS FOR RANGE ERROR

SECRET

SECRET

W a: 6(l)W OW 0

a: >

0 - >

-j 0 o

*_d 00

Not0(0 Iz

IL-

IL. 0

Cia

0 LO

SECRET

SECRET

BOMBS200 ____ Vo 500 FPS. ZO5

ax-L vct5OF.PS.aG5* -a~xuaoVa. A0 L~eo 00

o a,*9MILS C30ri-4MILS__4

160R6OOT

R0 300___R_60

807

640

120

0 20

FIUE48EFC0F NETITE ST

ARASECRET

SECRET

5IN AR ROCKETVo.-500 FPSI

___Vbw708 FPS.I__Tb 4O.91 SEC.~

O-ux &uCL*.50FPS.,% 9e-50

0 10.M LS 0-i-4!L

40

R 3000 FT. -0FT

30

rr'X

20 - __

10 ,- - ~ ~-_ _ _ _

FIGURE 4B. EFFEC OF UNETAITET

POIN 00 RELAS ON DISERSIOOF3Oo

aERE

SECRET

5"10 HVAR ROCKET

Vo6-5 0 0 FPS.V601361 FPS. -_ _

0. O 8 8 SF-C.

15 0-y :,VA, 5O ER AO*5 0

0 Tt- 9MIL ~O~4PvtR*3000FEET e*200 R 6 000 FEETT

10O

'5

R 3000 FEET R w6000 FEET

10 - _

0.2 0.3 0.4 0.2 0.3 0.4

*AR ARR R

FIGURE 4C. EFFECT OF RELEASE ERROR ON Gy-

SECRET

SECRET

.010

.009R

V4R - 500 FPS..008 0 - 00 DIVE ANGLE

.7 - 600 DIVE ANGLE

NO GRAVITY DROP

.006

-P.F3 GUN -2500MRS.AT a ,2MILS.

.005

.004

.003 NO GRAVITY DROP -

ai-4 MILS.

,002 ! ' ROCKETSa,- 4 MILS. 25

-- --... . -- - -"-SQ.FT

.001 .2 3o r-.PS.--- v7 " .25

BOMBS3 P".25

Oiw4 MILSO. Af-2000SQ.FT. -177 --'-t --"- -" -- , - • . .

0 2000 4000 6000 8000SLANT RANGE, FEET

FIGURE 5A. EFFECT OF RANGE, UPON HITPROBABILITY PER SQUAREFOOT OF' TARGET AREA

SECRET

"SECRET

0.0022 RVA 500 FPS-o 0o DIVE ANGLE

0.0020 n__- -- N =

0.0018

0.0016

GUN0.0014 -0L"5 MIL NO GRAVITY DROP

VM-2500 FPS 0"r 5 MIL PN.25

AT- 2 0 0 SQ.FT

0L~ 0.0012 -- --- --- _

0 .00 10 ........-...

0.0008

0..00. NO GRAVITY

ROCKETS0,0 06 "-,C o, w 9 MIL-• - I..

0.0004 01-9MIL _ __.

V~ m1367 FPS. 1367 FPS.~-EXP2350 EPS. RANGE

0.0002 -BOMBS -- ...... -- PNNO.2OrU 9•MIL b-70 8 FPS ATm2OOO SQ.FT

- 2-20,000 S Q. FT

1000 2000 3000 4000 5000 600L '00 8000

SLANT RANGE- FEET

FIGURE 5B. PROBABILITY OF HIT PER SQUARE FOOT OF TARGET AREAAS A FUNCTION OF RANGE

SECRET

--- ,, - in,•- n.-- .'nr•• t ,• l • . p 1 ir! •°lll tl' =! 1•11

SECRET

.011---

____ ___ ___ __ AR

.010 -R

VA - 500 FPS.

- ~ a 00 DIVE ANGLE _

.009 -3 0 60 0 DIVE ANGLEGUN

Cr .2 MILS rNO GRAVITY DROP _____

.008 VC25rFS a 2 MILS -___-

.007

.006__ _

1. AT

.005 __________-

.004-ROCKETS(Iia4 MILS V NO GRAVITY DROP

.003 O~4 MI LS

.002 PS

.001 FPS.

l i i0 0 L F P . 20 0 __ __ __ __ __ __ _

BOMBS PH '-25u4L~a t :41, AT z20O00SQ. FT.

1000 2000 3000 4000 5000 6000 7000 8000 9000

SLANT RANGE, FEET.

FIGURE 5 ac-EFFECT OF RANGE UPON HIT PROBABILITY PER SQUAREFOOT OF TARGET' AREA.

SECRET

A ARM

SECRET

.0022

.0020

R 5

.0018 GN - __ __ _ VA =500 FPS.

CFI 5 MI LS0 =O0DiVE ANGLE250 MIS. LS M 0 6d'DIVE ANGLE

0016

.0014

PiPH= .25.0012A - - 200 SQ. FT.

PH NO GPA,/ITY DROP

AT .010ROCKETS0 5ML

0'js9MILS

.0008 - __

U,3=708FPS.Va 1376 /-NO GRAVITY DROP

FP~s\ -.=9MILS.___ __

.0006 __

~V523 50 FPS..0004

PH.25.0002 BOMBS m T 2 00 S.T

c9MLSAT. 20000 SQ..FT.

2000 3000 4000 5000 6000 7000 8000 9000 10000

SLANT RANGE,FEET

FIGURE 5al- EFFECT OF RANGE UPON HIT PROBABILITY PER SQUAREFOOT OF TARGET AREA.

SECRET

SECRET

.0012

.0010

R.0000FT

o~.0009

I-. RZ.3000 FT.

o .0007 - 0-4MILS ze 30u__

0_0 V

.0006 5

a 500005S

0 1._SEC

M -f

cy .0003 +- - l5SE.

CL .04 0jý1 K9 R600T

.000 R300OFT R*GOOOFT.

AR..

R RRco~~. 000 VILSIL

c0r.9.6OOT

00010 00 5020VBU BRNT VLOCIT,30 FT/C.

FOOT OFTARGET

0001RER

1K,9 IL

* SECRET

.0045 i2R30.F

.0040 - _ __

e* 300

o 00301

LL

'.0025

a.02 R 00FTy/A I Lu.IO 2 MILS, 6C0FT.

II.0020 R 5MLR*0FT

2 ýL 001 Cri ~5M ILS, R a6000F17.0R

5 g w.5 (..-5 MILS, R-m3OOOFT-

cri (Y(,0,0T 2,R60 T

.00105 R

yeo ri5 ,11R- OOFT 250 0 0 20 00 30RAMZL -EOIY 6000SET.

SQUARE0 FOOT OFTRE

VAMUZS ELCRETYF.S

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2700 FPS. MUZZLE VELOCITY GUN

_____ VA - 500 F PS.___

Vm - 2700 P S.~~V'50FP46-50

Gx- AVAu.O 50 PS.

0 M- ZoMIL 1 13:OMt2MIL -

0-2006 ~ R ___ R3000_FEET R__ -_ R6O000 FEET0

6 -0

R=3000 FEET R -6000 FEET

6 _ _ _ _ _ _ _ _ _ _ _0

0.2 0.3 0.4 0.2 0.3 0.4

AR A RR Rl

FIGURE 7. EFFECT OF RELEASE ERROR ON Crx

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-1 ---------. PS

Vi.100 6 300

___ 200_ _ _

s0o SQ.FT.TARGET

80Rw IB. B

w ___ 2MILSGUNS70

00

0

x 50 o BOMB Au- 700EPS.ROCKET RW5 0B

o1360 EPS.ROCKET 9M ILS {ROCKETS

z

10

2000 &+vvv 4000 6000

SLANT RANGE (FEET)

FIGURE 7A. EFFECT OF SLANT RANGE UPONROUNDS RF.QUIRED PER HIT FORA SPECIFIED TARGET AREA

SEC-RET

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II10 IJ-

Va, 500 F.PS. 2000 R4VG. SQ.FT. 1 .5

Va, I TARGET ,bOMBS -

&350 9 M'" LROCIKETS

S90 1 10 _ _ "MILS GUNSz/

AR6L 80 '' .BOMBS

-

w4MILS LROCKETS0`2 MILS GUNS

. 70 S

0 B0MBS* 700ERS.ROCKET

60 r- 160 6EPS.ROCKET -

cr A 2500EPS.GUN

0cr 50w

z 40

30 -

S...TI I iiI

2000 4000 6000 2000 4000 6000SLANT RANGE (FEET)

FIGURE 7 B. EFFECT OF SLA,NT RANGE UPONROUNDS REQUIRED PER HIT FORA SPECIFIED TARGET AREA

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110

20O0

100 SQ. FT.VA 500 FP. S. TARGEIAVA 0. 1.tVA

0 e =300X' AE)= 50

a: 80 - A -_o.-1 t0.5R R R

a. 4MIL fBOMBS 9 MIL fBOMBSa ( .MIROCKET = (ROCKETS-a: 70 2 M --S2 MIL(GUNS 5 MIL GUNSw o 0W60 i

0 BOMBS, 700 F R S. ROCKET

Z 50 1260 RP.S. ROCKETA 2500 F. RS. GUN

0

LL4O00

13 0

20

100

o __ __i.__ _o __.__- __ _ __

2000 3000 4000 5000 6000 2000 3000 4000 5000 6000SLANT RANGE FEET

FIGURE 7C. NUMBER OF ROUNDS REQUIRED PER HIT AS AFUNCTION OF RANGE - TARGET AREA 20,000

SQUARE FEET

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0

0

LL wU

Lii __

0~c- >L a )

4w 4Q)

>.f) ~W

-r) L W) L

04-~1 - IL.

0w

'0-X oLLW

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.8

GUNS

020MM 75 MMF 100OIMF NRI [3200 10

6~QQ ING L 400 20

wo 20MMI GUN,650RPM.

75MM GUN, 10 RPM..4

.3 -_ _ _

.2

L.V1000 1500 2000 2500 3000 3500 4000

%VMu MUZZLE VELOCITY, FPS.

FIGURE 9-EFFECT OF MUZZLE VELOCITY OF GUN PROJECTILEUPON RATIO OF WEIGHT OF WARHEAD TO0 THAT OF

I TOTAL ARMAMENT SYSTEM.

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.6 RECOILLESS GUNS

75 MM -10 RPM..5 . -- -

.4

PROPOSED NEW GUNS

.3

wHWO_

o- 5

.4,

PRESENT GUNS

500 1000 1500 2000 2500 3000 3500

VMw MUZZLE VELOCITY, FPS.

FIGURE 10- EFFECT OF MUZZLE VELOCITY OF PROJECTILESFROM RECOILLESS GUNS UPON RATIO OF WEIGHTOF WARHEAD TO THAT OF TOTAL ARMAMENT SYSTEM.

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.0001lR=65000FT.AVA A

.000 14 IAz50FS.1 69-500F~ -___ 4 MILS

.000000Lwwr

.00040

.0003 VA -50F

.00002

'00002

FATO AS A FUCINOROKT UNEOIY

SECRE

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.00018

.00014 R .1 ROCKETSOj-4MILS R=6000 FT.

.00010 L VA

R=9MILS VA=500 FPS.0i 4MIl tA6•50

00006=300

IL," ,AR x 5R W

.00002

I

LwAT A.

.0005 1i C=4MILS-7I /R•3OOOFT.iARR 5 AVA"a I

4MILS "-A.0004 -AO=50

VA •500 FPS.

W3u 3.0.0003 P,

R W9~3gis 9MI SVRWM

.0002

.0001Tia9MIL

0 500 1000 1500 2000 2500 3000

VB3- BURNT VELOCITY, FT./SEC.

FIGURE II b - RECIPROCAL OF AIRCRAFT ORDNANCE LOGISTICFACTOR AS A FUNCTION OF ROCKET BURNT VELOCITY.

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HIGH CYCEIC RATIE -- SMALL CALIBER GUNS

R -6000 FEET R-00FE

0.0003 R -* 0.5 A-.

0.0002

0.0 A___ 00__ __

ML

Ol=S5MI r --___

Rm3000 FEET R v3000 FEET

0.0016 '& - -0.45 _AR0VA 0500 FPS'

0-014Q -300- _

VAMI

0.0012 69 50MM

RATE OF FIRE-650R.PM.0-100 ROUNDS PER GUN ___

0.0010 -0-2OOROUNDS PER GUN

0.00048

0ri -2 MIL

0.00041.0_____________ __

0.0002 5 MIL ___

2000 2500 2000 2500Vil MUZZLE VELOCITY FEET SECOND

FIGURE 12A. RECIPROCAL OF AIRCRAFT ARMAMENT LOGISTIC FACTOR AS A

FUNCTION OF GUN MUZZLE VELOCITY

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LOW CYCLIC RATE LARGE CALIBER GUNIS

R - 6,000 FEET K.6000 FEET

AR 0 ARR 0.R 0.5tr. RR

2 MIL

* 0.0001

CrL -2 MIL WL bIOll -5 MII _ __ _ __ _ _ _

0.0009R - 3000 FEET R 3000 FEET

0.0008 R 0. 5 -R

VA '500 F.RS.10.0007 e .3Q00--___

AVA*VA2MI

0.000t6 &e .50

DH *i75 MM.RATE OF FIRE -10 R.R M.

0.0005 0 -5 ROUNDS PER GUN --

a =10 ROUNDS PER GUN0 -15 ROUNDS PER GUN

00004 A = 20 ROUNDS PER GUN _

0.0000

0.0002

2000 2500 2000 2500

Vm MUZZLE VELOCITY FEET/SECOND

FI4GURE 12B. RECIPROCAL OF AIRCRAFT ARMAMENT LOGISTICFACTOR AS A FUNCTION OF GUN MUZZLE VELOCITY

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LOW CYCLIC RATE-LARGE CALIBER RECOILLESS GUNS-PRESENT DESIGN

R 6000 FE ET R =000 FE ET

0.0002 -,"R-0-.

0.00015 T 1

, *(, ~'0.000100

13oo s - ---- ---

1$ 4c~5Mi-0

R 3000 FEET R =3000 FEET0.0012 - A 051R=.

9RVA = 500 F PS.

0.0010 6e =300 ___

tAe =500.0008 ~DH = 75M.M.

RATE OF F IRE 10 R.P. M.

0 5 ROUNDS PER GUN0.000 t3 0 ROUNDS PER GUN

*15 ROUNDS PER GUN ýA 20 ROUNDS PE-R GUN

0.0004 o

0 1000 L50 2000 250L0 50 00 20

VM -MUZZLE VELOCITY - FEET/SECOND

FIGURE 13A. RECIPROCAL OF AIRCRAFT ARMAMENT LOGISTICFACTOR AS A FUNCTION OF GUN MUZZLEV ELO CIT Y

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... .......

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LOW CYCLIC RATE -- LARGE CALIBER

RECOILLESS GUNS -NEW DESIGNS.

.0003 Rh00T A__3__

.0002

.0001

2MILS ___ __ ___

5MILS R-3000FT., Rm6000FT.I-_ ARR

LWAT RR

.0014 ^

0e 50D.E U

.0010 8 00RS.E U

0 15 RDS. PER GUN

.0 A2RDS PER GUN

2 MILSS

.0002-071m

SMILS----

1000 1500 2000 2500 1000 1500 2000 ;!boo

V'ms MUZZLE VELOCITY FT./SEC._

FIGURE 13 B. RECIPROCAL OF AIRCRAFT ARMAMENThLOGISTIC, FACTOR AS A FUNCTION OF'MUZZLE VELOCITY OF PROJECTILE FROMRECOILLESS GUN

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111

4- T -2

100~~ 4MILS~'~s

Ae:0 j~MILS GUN-" 200

90 0 BOMB.

.FP.RECOILLESS GUN.

LARGE CALIBER,

L. 6010 ADS. PER GUN.4 aFP. RCOLLSSD GUN,

LAG CALIBER,

702 D.PER GUN.______

50 -70 FSO PS. TI3IGUN,

401 RPM.R

Go_ 10 FPS._ STD.L GUNS

50 7,l2500 PS. T311GU

404

SIIL

TARGET ROCKET00SQ.-~ I /4

SLANET RANCA =200 SQFT

FIGURE 14A.EFFECT OF SLANT RAK,(E UPON AIRPLANE ARMAMENT

LOGISTIC FACTOR.

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11o -R-O 0. R-0.5 - __

4MIL fBoMBS 2000 9MIL !BROMBSiROCKETS SQ. FT. orL 9 ROCKETS

GUNS TARGET GUNS10oo 2 MIL T 131 EA MIL(T131

VA *500FR.S.

90 AVAVA0.G -300

80 Ao5

I-BOMB I70-2-1600 FPRS. ROCKET70 3-1400 FPS. LARGE

CAL1I3ER REC'.OILLESSGUN, IORPM,

60 - 10 RDS. PER GUN~ 60 4-1400 FPS. LARGE

CALIBER RECOILLESSGUN, 650 R.P.M.

r' ~~~~~ 20 RDS. PER GUN __ _ _ _ _ __ _ _ _ _ _

50 -5-100 FP.S. STD. GUNLARGE CALIBER, 1O RAMito R.DS. PER GUN

40-6-IT00FP.RS. STD, GUN --

40 SMALL CALIBER650 R.RM.600 RDS. PER GUN

30 7-2500 FP S. T 131GUN -LAUNCHEDROCKET

20

3000 4000 5000 3000 4000 5000

9SLANT RANGE-FEET

FIGURE 14B. AIRPLANE ARMAMENT LOGISTIC FACTOR AS A FUNCTIONOF RANGE TARGET AREA *2000 SQUARE FEET

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11

HO AR-- *0-.I - . - 0,5

(BOMBS (BOMBS100 - 4 MIL .ROCKETS - CrL MIL IROCKETS

2MIL UNS 5 MIL GUNSiT3 ý ,5 I T 1:31

1 120,000VA -500 EPS. SQ.FTAVA TARGEIVA0. AREA

80 -- -300

G-BOmB70 - 3-1600 F.P.S, ROCKET

A- 1400 FPS, LARGECALIBER RECOILLESSGUN, 10 R.PM.

60 - 0 ROUNDS PER GUN-: V- 1400 FPS, LARGE

-.J CALIBER RECOILLESSGUN, 659 R.P.M

, 50 20 ROUNDS PER GUN _

-1"700 FRS, STD, GUNLARGE CALIBER, IOFRPM.10 ROUNDS PER GUN

40 .1700 FPS STD. GUNSMALL CALIBER 650RPN600 ROUNDS PiR GUN

0 2500 FPS. T131 GUN-"30 LAUNCHED ROCKET

20

10 -

3000 4000 5000 3000 4000 5000

SLANT RANGE- FEET

FIGURE 140. AIRPLANE ARMAMENT LOGISTIC FACTOR AS A FUNCTIONOF RANGE

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