]/ec.l~ss·,f,ed J-lo-'1-r. .

OFFIC f: Of SCI E. NTI fiC MENT

NATIONAL DE. FEN0E R.E..SEAR.CH COMM JTTE'.E.

DIVISION SIX-~tCTlON G.l

'w'ATE~ TUNNEL TEST..S OF THE.

15CM.GERMAN SPINNER. ROCKET.

THE HIGH ,SPEED WATER TUNNEL CALifORNIA JN~TlTUTE OF TECHNOLOGY

PA~ADE.NA,CALJF'ORNlA.

SECTION Ne.G.t-sr-2o7-'332.

t1ML R.E.P. N9 ND 2.3.

CONFIDENTIAL

(CONFIDENTIAL)

Office of Scientific Research and Development National Defense Research Committee

Division Six - Seotion 6.1

YlA.TER TUNNEL TESTS

OF THE

15 C:M •. GERMAN SPINNER ROCKET

·by

Robert T• JO,:lapp

Official Investigator

The High Speed water Tunnel at the

California Institute of Technology HYdraulic Machinery Laboratory

pasadena, california

Section No. 6.1-ar-207-932

HML Rep. No. ND-23

cONf\OENI\1\L

November 11, 1943

., G)

1---"

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1.6or-[t.z(;]l

7.86 [;21.5]

f 'I;"

-~·p~>~ luJI

[2. 72] . .099 m tf OF RING OF 26 .JETS AU~£/)

AT 14° WIT# Af'o..IECTILE ;1/X/S

-.- ·t=r= I I -

' ' ~ ~ 1 - ~R oR o)r:-, ~ ..... ----c!'l- - t\~ -

"1\9. f\j l(j CENTeR oF / -...: 'f. LJ LJ GPAVITY I I..:.J

I

!---'*--- 2. 7 7 [7.57]

-----+-------.5 5<1- 1 1 Jrr~:.t] [1.5:;.5]-<1.09 .. "" 3'.83 ll .

@-.97] [!D.~8]

NOTE- PROTOTYPE DIMENSIONS

A!.?e Sf/OWN IN BRAC!<ETS

II. · L " AL.aANI:Nil" -1(. • 1:. CO. , N. Y .-&GI. U. a . PAT.O,JO.

i~23a·~--------------------------------~ ~-~

PHySICAL 0AT,I/ rOR PRoroTYPE

W'r c 61 !6&i:e. WtrHour PRQPEUENT

= 75.3 /bs :!:z WfrH WOP&-LL£NT

If = IJJ<IA L tV/OMEN'T CT- IN'ERTII'/

= 0 .0625 SLIIGS • Ft Z

B = TR/fNSvEK!>c Ma--rENT oF /N&RT//1

'"- /,06 SLU6S -FT2.

HYDRAULIC MACHINERY LABORATORY CALIFORNIA INSTITUTE OF TECHNOLOGY

P'ASADENA, CAUFOI'INIA

L:vMt :N5!0VS FOR 15 CM.

GERMAN SPINN£12 ROCKET

DR /IC_i_ o/~LSCALE

CH CRA 1'1~h"IND-5Z9 -U

AP'

0 0 z ,., -0

):= r

'

CONFIDENTIAL -1-

MEMORANDUM ON WATER TUNNEL TESTS OF THE

15 CM. GERMAN SPINNER ROCKET

This memorandum covers water Tunnel Tests of the 15 em. German Spinner Rocket. The tests were made at the request of the Ballistic Research Laboratory of the Aberdeen Proving Ground. A photograph of the 2" diameter model used for the tests is shown in Figure 2. _ overall dimensions of the model and dimensions and physical data for the full-scale projectile are shown'in Figure 1.

·1 I 1 I . .t_! f 'S L Ji 1~ 1;

· Figure 2

2" Diameter Model of the

16 em. Gel"lllaD. Spinner Rocket

This rocket has a velocity somewhat above the sonic and is spin stabilized. As seen in Figure 1, the propulsive jets are located in the enlarged section just art of the center of gravity and are aligned at 14 • with the axis of the rocket. The tangential component of the jet reaction spins the projectile and thus pro­vides the required stability. The results of the water Tunnel tests, ·which were made without spin, are valid for flight in water or in air at velocities below about 760 feet per seoond. For flight in air at velocities near or above sonic 1 the results are not directly applicable.

curves showing the variation of the drag, cross force, and moment coefficients with yaw angle, and of center-of-pressure eccentricity with yaw angle are shown in Figure 3. Definitions of terms and coefficients used in this figure are given at the end of this memorandum. The data in Figure 3 have been corrected fer support interference effects. ·

These curves show that the rocket as tested is unstable. The destabili~ing moment coefficient, CM' and the negative center-of­pressure eccentricity, e, both show that the center of pressure lies ahead of the center of gravity. Furthermore, the increasing values of e from -o.24 at 1/2• yaw to -0.46 at a• yaw show that

ONFlDENTlAL

I-0,12. ZV)

llJ· u ~ 0.10 0 \-z=> 0 0.08 \DCO 2<t N ~ O,C6 __j r a.:JU 0.04-~ ...... 1-u_' (/)UJ 0.02. uJ oG

\.J 0

0.6

A o.s \J

...., 0,4 u.:

UJ 0 0.3 \.)

\9 0.2 <t

Ci 0 - 0 .1

0

- 2- CONF\DENTif\L

/ v

u u ...,.

1L:

-1-/ v:M /

v

v ~ v

Cc l----::::: - ~

~ ---~ _,?.

0.4 lLl 0 u

C,3 l1.l 0

0 ,2 Ol ,0 J..

0. ~ ~ VJ

8 0 u

0 z 4 ~ 8 YAW A NGL E ; ~.r; DE::GK.EE. S

I I

j

" I ""' -

" ~ CD

I ~ h._ e

i :

i I

I I I I --

l--

0

-0.1 Q)

>--'"' - 0 .2. l­

u ~ r­z I.L..l u u

-0.3

-0,4

\lJ 0:

-0.5

0 2 4 ~ -O. G., U

8 YAW A N.Gl E 1 fr D '-G Pc: r.:: .::: \ - ) 1 ) l- . -• -- ~--u

L = 3.0 ! f-T.

L = 1.73 f T. cg

FIG. 3.

15 em. GERMAN SPINNER ROCI<ET

RUNS I 4 Z OC.T. \6 ; 1943

H IGH s PE.ED W-'\T ~R Tu NN'E-'­ATTHt::..

CA LI FOR N IA JNST\\UTE.

OF TECHNOLOGY

CON -N SHEET ND 23-1580-L

~ONFIDENTIAL -:s--

the rocket becomes more unstable as the yaw angle increases from zero. These results are normal since the rocket is stabilized by spinning, and, hence, has no tail fins or rings as stabilizers. The drag coefficient is 0.25 at zero yaw and increases to Oo35 at 8° yaw. The cross foroe coeffioient .increases approximately linearly with yaw at a rate· of 0.025 per degree.

It is interesting to. note that the above characteristics are roughly similar to those that have been measured for simple cylin­drical projectiles with either ogive or hemispherical noses and square trailing ends. For example, a cylinder with hemispherical nose six calibers lang (note that rocket is 6.86 calibers long) has a drag coefficient of 0.276 at zero yaw, and increases to 0.40 at s•. The eccentricity varies :from -o.33 at zero yaw to -0.39 at 8 •. The reason for this a :1milari ty lies in the fact that both the present Spinner Rocket and the simpler "bullets" ba.ve the same general cylindrical shape with rounded nose and blunt, trail­ing end. Of course, as the velocity of s O'lmd is approached or exceeded, these statements no longer apply since nose shape then becomes of paramount importance. It can be said, as a first approximation, that for simple bullet shaped bodies traveling at subsonic speeds, the afterbody and tail shapes largely determine the aerodynamic forces, whereas for supersonic speeds, the nose shape is the predominating influence.

A1J. interesting. indirect measure of the deviation of the sub­sonic characteristics ·from those at supersonic velocities can be obtained by making use of the spiDning stability criterion and the propulsive nozzle alignment angle •

• According to Hayes, the condition for stable motion of' a spinning projectile is

(1)

or

where

*

2 A. • axial moment of inertia in slugs-ft

N • spin in radians per sec 2

B • transverse moment of inertia in slugs-ft

"Elements of ordnance• by Col. ThaD&s J• Hayes, 111ley, 1938 page 4:17

CONf\DE.N1\AL

L;Ul'tlllJC.t~ tanL-

/'- • moment f'actor in foot-lbs per radian of yaw

For projectiles spun by rooket jets the stability requirement oan be written in terms of the angle which the jet center line makes with the projectile axis. This is accomplished as followaa The relations between hlpulse of the jets and the resulting linear and angular momen tuma can be written

(F cos 0)t • mV

'l't • (F aiD e)rt • .A1f

or el:l:ainating t between the two expre.ssions

H • mvr tan e A

where

(2}

V • maxhltlll velocity reached by rocket in feet per second

F • jet reaction in lba

t • burning time of propellant in seconds

• • mass of projectile in slugs

'1' • torque exerted by jets about projectile axis in lb-ft

r • radius to center line of jet ring in ft

e - jet alignment -.ngle

It the value tor the spin velocity, N, given by thia equation is substituted in the stability relation (l) above and the resulting relation rearr-.nged, the f'ollowing expression tor the required jet angle is obtaineda

l/2

tone> k{ 2Br>Ayf ~} (3)

ID this equation e and Cv/'11 are the va.riablea, all other quanti ties

being constant f'or a given projectile. If values of Cll/'ljl from the

ater Tunnel testa are used to evaluate e, an angle of approxi­lll&.tely s• is obta:i.ned as the minimum jet angle for stability at subsonic· velocities. Since, as equation (2} shows, N varies directly with tan E>, the actual jet angle of' 1~• shows that the

2 2 stability coefficient, A 'N , has a value of about 6.6:5 instead of 4B.fL

the minimum of' l. .Although a part of this large excess is un­doubtedly needed to provide the desired "stiffness" to the rocket, it is probable that this high value indicates that, at supersonic velocities, the destabilizing aerodynamic moment coefficient is considerably greater than it is at subsonic apeeds. CO \DE T\Al

CONF\DENT\AL -5-

Definitions of terms, symbols, and coefficients used on curve slieets

D • drag foroe in lbs

C • cross foroe in lbs

)( • moment in foot-lba about a transverse axis through the center of gravity

c.p.~ center of pressure. The point in the axis of the pro­jectile at which the resultant of all foroes acting on the model is applied.

• • center-of-pressure eooentrici~. The distance between the center of pressure (c.p.) and the center of gravity (e.G.) expressed as a fraction of the projectile length

p • density of water (or air) in slugs per cu ft

V • relative velocity between water (or air) and projectile in feet per s eoond

• area in square feet of the maximum cross section normal to the projectile axis

L • overall length of the projectile in feet

CD • drag coefficient _____ D ____ _

PfAn CC • cross foroe coefficient

c ---.....;. .. 2 __ _

p t "n c

11 • moment coefficient