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UNCLASSIFIED

U.D.C. No.621.455.018 : 551.510.53

LTechnical Note No. G.1.291

December, 1953

2- ROYAL AMMAT ESTABLIS&U,ENT, F.V-,3OUGH

The Limitations of Upper-ftmosphere osearch Vehiclesf Powered by Current British Solid-Fuel Rockets

by

D. G. King-Hole, V:.A.

AL

SUIZRY

Two rocket motors were selected as typical of current British boostand sustainer motors respectively, and the minimum. amounts of fin structure,etc., needed to convert them into aerodynamically stable vehicles wereadded. The performance of these single-stage vehicles in vertical climbsfrom sea level was evaluated by numerical integration. The maximum altitudeattained was 120,000 ft, which is not much above the economical limit forballoons. If current rockets are to be of value in upper-atmosphereresearch, therefore, they must either be used in a two-stage arrangement,or be launched well above sea level, perhaps from a balloon or mountaintop. Alternatively, a new solid fuel rocket motor witl, a long burningtime and high length/diameter ratio could be designed specifically for thepurpose of high-altitude research - this is probably the best approach.

DISTRIBUTION STATEMENT AApproved for Public Release

Distribution Unlimited

UNCL.ASSIIED

UNCLASSIFIED

,Tech. Note No. G.W.291

LIST OF CONTENTS

Page

1 Introduction 3

2 Properties of the rocket motors selected 3

3 Stability 4

3.1 General 4

3.2 Effect of altering the weight of the nose cone 4

4 Calculation of 11eight and drag 5

5 hesults 5

6 Conclusions

References 7

Advance Distribution 7

Detachable Abstract Cards -

LIST OF TABLES

T able

Assumed characteristics of rocket motors I

Weights and performances of vehicles A, B and C II

LIST OF ILLUSTRATIONS

Fig.

Sketches of Vehicles A and C 1

Variation of Vehicle Empty Weight and Drag with Nose Weight 2

Variation of the Drag of Vehicles of Fig. I with Mach Numberand Altitude 3

Variation of the Velocity and Altitude of the Vehicles with Time 4

Variation of the Velocity of the Vehicles with Jatitude 5

2Variation of 'Potential .ltitudc', y + v with time on atual

2gTrajectories and in Vacuo 6

icceleration of the Vehicles as a Function of Time 7

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Tech. Tote No. G. '.291

I Introduction

An Anglo-Amerioan conference was held at Oxford in August 1953,under the auspices of the Gassiot Committee of thc Royal Society, todiscuss the use of rockets for upper-atmosphere research. The visitingspeakers' accounts of the extensive American work on this subject duringthe last few years served to emphasize the meagreness of the effort beingdevoted to it in Britain. The Gassiot Committee therefore wished to knowwhether any of the rocket motors now in production for G.71. projects wouldbe of value for upper-atmosphere research. Balloons arc likely to remainthe cheapest method of carrying instruments up to about 'iO0,O00 ft altitude,and a rocket vehicle would prove useful if it could cover the altituderange 100,000 to 200,000 ft.

This note gives an indication of the altitudes which might beattained by the simplest type of rocket, a single-stage vehicle with asolid-fuel motor and fixed stabilizing fins, launched at sea level.Typical vehicles are sketched in Fig.l.

2 Properties of the rocket motors selected

Two possible solid-fuel motors are considered here: thoso are basedon the i: ayfly boost motor and the sustainer motor for a surface-to-airmissile project"', and may be regardcd as typical examples of current boostand sustainor motors respectively. The assumed characteristics of themotors arc; listed in Table I.

TABLE I

Assumed Characteristics of Rocket 11otors

iayfly type Sustainer

Thrust (at sea level) lb 18,000 3,400

Burning time sec 3 30

Total impulse lb-sec 54,000 102,000

Propellant specific impulse sec 210 170

Propellant weight lb 257 600

Total motor weight lb 401 850

Propellant/total weight ratio 0.64 0.71

Overall S.I. total impulse sec 135 120

total motor weight

Diameter inches 10 18

Length (excluding exit nozzle) inches 112 66

The final design of this motor is not yet decided, and the assumed

performance figures are therefore drastically rounded off.

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Tech. Notc 11o. G. ,.291

3 Stability

3.1 General

Since the altitude attained by the vehicle is quite sensitive tochanges in empty weight and drag, it is of the utmost importance toensure that the additional structure needed to transform the basic rocketmotor into an aerodynamically stable missile should create as little extradrag and weight as possible. But since cost per flight is the index ofmerit in an upper-atmosphere research vehicle, the means of stabilizationmust be cheap mad simple. Here the two obvious methods of improvingstability were used - weighting the nose and adding fixed fins at therear. The variation uf fin size with nose weight was investigated and thenose weight which appoared to be t optimum' was chosen.

The fin lift coefficient decreases as 11ach number increases, whilethe body lift coefficient tends to increase slightly; so the criticalspeed for stability is the maxini.m speed and the critical moment is justafter all-burnt". If' the flight Mach number is increased far enough fin-stabilization becomes impracticable because the fin lift coefficient isso small that adding fins at the rear moves back the centre of gravitymore than the centre of pressure (provided the fins ore not ridiculouslylarge). This effect is already beginning to assume importance in thevehicles discussed here, which reach -1,ach numbers of up to 4.5, and itproves advantageous, up to a point, to add ballast in the nose rather thanfins at the rear, i.e. to shift forward the C.G. rather than move thec.p. aIt.

3.2 Effect of alter.te weisht of the nose cone

Fig.2 shows ho: the empty weight and drag of vehicles carrying nopayload vary with nose weight. 2educing either drag or empty weight willincrease the max imm altitude attainable, and1 it is to be expected thatthe weight w,ill have a relatively more powerful effect than the drag. Onthe basis of this general argument the optinmun value of nose weight willbe near the value givin rinimm empty weight, but rather higher becausean increase i the nose weight decreases the fin size and hence the drag.The values chosen for the nose wcight, which are marked on Fig.2, were60 lb for vehicle (wi 0_th the boost motor) and 80 lb for vehicle C (withthe sustaincr motor). Though thes, vehicles, which are sketched in Fig.1,carry no payload, the additional weight of a payload of 20-50 lb can invehicle 0 be comoensated by the removal of ballast from the nose, sinceadequate volume is availablc; in vchicle A however extra volume would beneeded (see section 5).

Although the nose weiEhts were chosen somewhat arbitrarily anapproximate analytical method for determining maximum altitude basod onthe computed trajcctori cs) showed -, hat the values chosen were very nearthe optima.

In makinp the stability oulculations a static margin of 6" wasallowed, but since it w:s,-, of course necessary to guess the maximum speedof the vehicle beforc the numerical integrations were carried out, thestatic morgins of the vehicels at their actual maximum speeds differsomewhat from 6". The ostimatud positions of centre of gravity and centre

After, not before, because deceleration h a destabilizing effect, fora given stability margin. Jot vanes, which cease to act at all-burnt, cantherefore do nothing to alloviatu the stability problems. At the highestEach numbers a diverging tail cone of circular cross-section - a flaredskirt - would probably be more efficient than fins in providing stability.

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Toch. Note Yo. G....291

of pressure at maximum speed are indicated in Fig.l. The methods rooom-

mended in the G.*2. Aero Handbookl were used in calculating the lift-curve

slopes d2L for the fins. It was assumd that thu body dl incrasedda da

with hiach number up to H 3 as indicated in the Handbook, and remainedconstant for 11 > 3, in accordance with ref.2. No allowance was mado forflexure of the vehicle, i.e. the fin efficiency was taken as 10Q,.

4 Calculation of drag and weight

The apex angle of the nose cone wuas taken as 200 and tht fins wereassumed to be of cropped delta form, rith 300 leading-edge swecpback, netaspect ratio 1.5 and thickness/chord ratio 0.03. The drag was calculatedby the methods of ref. 1, and a 5,: addition was made to allow for holes,aerials, etc. The variation of drag with 1,ach nuber for the vehiclessketched in Fig.1 is shovn in Fig.3.

The weight of fins and attachments was taken as 5 lb/sq ft of netfin plan area. The minimum weight of the nose cone and attachments was

taken as 6 lb/sq ft of surface area for the vehicles vrith boost motors

and 3-5 lb/sq ft for the vehicle with the sustainer motor, which encountersnch less severe heating.

5 Results

The vehicles A and C sketched in Fig. 1 carry no payload. The nose

cone of vehicle C, which has a volume of 2.5 cu. ft, should be able to

accommodate a payload of up to about 50 lb, and the results for vehicle C

therefore apply, as a first approximation, whether or not a payload is

carried. Extra volume must be provided however if vehicle A is to carry

a 50 lb payload, and separate calculations have therefore been made for

such a vehicle, which is labelled B.

The performances of vehicles A, B and C in vertical climbs have boon

calculated by numerical integration of the equation of motion. Table II

gives weight breakdowns for the three vehicles, together with their maximum

altitudes and velocities.

TABLE IIhights and Performance of Vehicles A, B and c

Vehicle: A B C

X,otor (see Table I) iayfly type 'Iayfly type Sustainer

Payload lb 0 50 80Nose weight (excluding payload) lb 60 39* )Weight of fins lb 32 40 70

Veight of motor case lb 144 144 250

Empty weight of vehicle lb 23_36 273 00Propellant weight lb 257 257 oOO

Initial weight of vehicle lb 9 r 1000

Length 152"186" 137"

Diameter i0" 1 o" 18"

1.,aximum velocity (at all-burnt) ft/sec 4530 4070 2610

Altitude at all-burnt ft 6100 5600 36,800

Kaximum altitude ft 119,400 94,000 99,500

*The nose section of vehicle B consists of a nose cone plus a cylindrical

section nearly 3 ft long. The volLume allowance for the 50 lb payload was

2 cu. ft.

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Tech, _1'Totc _i'o. .9

The velocitius, altitudes and accelerations of the throe vehicleson vcrtical-climb trajectories are showrn ini Figs.4-7. Fig.4 gives thevariation of velocity v and altitude y with time, and these resultsarc rcplotted in 1,ig.5 to show directly how velocity varies with altitude.The 'potcntial altitude' y + v2 , ic. the altitude the vehicle would

2greach if drag ceased at time t, is plotted against t in Fig. 6 , and comr-pared with its value in vacuo, i.e. if there were no dxag from t = 0onwards. Fig. 6 shows tiaat the altitudes actually attained by the vehiclesaro less than one third of the altitudes they would roach Li vacuo. Largeincreases in altitude would therefore be obtained if the drag were drasti-cally reduced, e.g. by launching at high altitude. -Tig-7 shm.rs thelongitudinal accelerations of the vehicles as functions of time.

it 'Al be seen from Figs.4-7 that vehicles A and B reach a .muchgreater speed than vehicle C, but at such low altitudes that the largdrag quickly reduces it. The velocity-time variation of vcnicle Cmuch more favourablu and it is somewhat disappointing to find that itsperfori-ance is inferior. The reason is that its small length/diaotorratio increases the body drag and, indirectly via the stability, the findrag. Vehicle C would have an all-burnt velocity of 5020 ft/scc ingravity-free airless space; the loss in velocity due to gravity is 970ft/sec, and the loss due to drag is 1450 ft/sec. Thus if tho drag worehalved the all-burnt velocity might be increased by about 251u and thepotential altitude at all-burnt by about 50,.. The loss in potentialaltitude after all-burnt would also be smaller and the maximum altitudeattained might be approximately doubled. (It is not however a generalrule that halving the drag doubles the altitude: this could never occurif the altitude oriLinally attained were more than half the potentialaltitude in vacuo.).

It is apparent therefore that a sustainer rocket motor designcdspecifically for the uppor-atmos-hcre research role could propel vehiclesto altitudes much greater than 100,000 ft, even if its specific impulseand charge/weight ratio wcru no better than those of current motors. Amore detailed investigation woula be necessary before attempting to specifythe desirable characteristics of such a motcr. Prom the somewhat inadequateevidence in this note it would seem likely that a burning time of 15-20 secand a length/diameter ratio of about 1,, might be called for, and this mightinvolve the use of a modified cigarctte-burning charge.

6 Conclusions

A single-stage vehicle pmiered by an existing boost or sustainermotor, launched at sea level and having conventional forms of aerodynamicstabilization, is not likely to attain altitudes very much in excess of100,00 ft when carrying a payload of 20-50 lb. Such a vehicle if it wereto be of value would therefore have to be launched from a high mountain ora balloon; alternatively, of course, a two-stage configuration could beused. These possible improvements would however increase the cost andcomplication.

The present rocket motors, because they were designed for verydifferent purposes, are somewhat inefficient for upper-atmosphere research;but a new solid-fuel rocket capable of pmroring a useful ground-launchedvehicle could probably be designed if required.

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Tech. Note No. G.'7.291

iLUNTCES

No. Title, etc.

I Handbook of Supersonic Acrodynamic Data .pplicable to Guided WeaponDesign.R.Z.. Guided ?1apons Dept., giandbook/l.

2 Long-Rango Surface-to-Surface Rocket Vehicles. jreliminaryInvestigations and Results: Aerodynamics.Project Rand, ?eOport RA 15065 (Karch 1948).

Attached: Drgs. G.!/P/4862 to 4868Detachable Abstract Cards

Advance Distribution:

IL.0.S. HeadquLarters

Chief ScientistCGIML

PDG r - 70JO/r.7 (R)TPAS/TIB - 90

R.A.E.

Direct orDD(E)DD(A)RPD -3AeroArmGMtTI" - 2

Library

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Q.W/P. 462SECRET T-N. rA zi

F IG. L.(a b)WEIC;HTS LB

60 LB. NOSE NOSE CONE 60FINS, ETC. 3MOTOR CASE 144PROPELLANT t.57.JALL- UP WEr%HT14931

MAYFLY DIMENSIONS, ETC,MOTOR. LENrqTK 152,

BODY DIAMETER 100SCALE FIN SPAN 374

C-I AT ALLPBURKIT NET PLAN AREA 0F3Z.F

FEET ESIAE ErE~ ONE PAIR OF FINSPRESSURE AT M, 4.4 MAX .VELOCITY 4530 FT/SM

MAX. ALTITUDE 119,400 FT

d) VEHICLE A, WITH MAYFLY MOTOR & ZERO PAYLOAD.-

WEIGMTS LBNOSE come. 80FINSI ETC.- 70

80 LB NOSE MOTOR CASE tsor2QAL& PROPELLANT. 1600O F I ET zALL-UPWEIGKT 1400

DIMENSIONS. ETC.SU5TAINER LENG;TM 137'MOTOR BODY DIAMETER IB"

FIN SPAN 55"o.0 CA . AT ALL- BURNT NET PLAN AREAOF9S-T0-ESTIMATED CENTRE OF ONE PAIR OF FINS

PRESSURE AT Mu Z.7 MAKNVELOCITY Z610 FT15C.MAK .ALTITUDE 99,500 FT

()VEHICLE 'C', WITH SUISTAINER MOTOR &ZERO PAYLOAD.

FIG I (aab) SKETCHES OF VEHICLES A AND C.

P.4803T.k W.QW. ZSI.

Z60 FIG .( b

zs PT EMPTY EIGHT

OF

40VEHICLE LB.

'4 CHOSEN YALUEOF NOSE WEIGHKT

RELATIVE -

DRAr: ATM-3 AT

SSEA- LEVEL AN,___ __________

MINIMUMPRACTICABLENOSE WVEIGHT

0 zo 4060so10WEIGMT OF NOSE CONE L.B.

4O(a) VEHICLE WITH MAYFLY MOTOR.

1 10EMPTY WEICIHT

OF

40VEHICLE L.B.

390 _W_AQHT AT__ ALL-_ BURNT____

ALL-UP WEIGiHT -SGOOLB

RELATIVE -COSNVAUDRAr; AT OF NOSE VqEI*Mv 3 AT

1-I SEA-LEYEL _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

1.0

PRACTICABLENOSE WEIGHT

zo 40 60 10WEIGHT OF NOSE CONE L.

(b) VEHICLE WITH SUSTAINER MOTOR.

FIG.2 (a&b) VARIATION OF VEHICLE EMPTYWEIGHT AND DRAG WITH NOSE WEIGHT .

.A.W/P.46648.OOQ00 T.N. W. Z91.

FIG-3.. = - ATMOSPHERIC PRESSURE AT ALTITUDE

ATMOSPHERIC PRESSURE AT SEA-LEVEL

6,0,.

5,0 _________-VEHICL.E C

DRAG LB

OF FIC-i, I.3.00

* 0 4__ _ _-S

FLICNT MACA N112 M.

FIG.3.VARIATION OF THE DRAG OF VEHICLESOF FIGI. WITH MACH NUMBER & ALTITUDE.

G.W IP.4865.SECRET. T.N. G-W.?.Z91

FIG. 4.

KEY.VEHICLE A - MAYFLY MOTOR, NO PAYLOAD.

13- MAYFLY MOTOR, 50L5 PAYLOAD.-SUSTAINER MOTOR, NO PAYLOAD

TRAJECTORY - VERTICAL CLIMB

4,600 lzo=0

4,400 - 10,000

4,000 1 00,000

31600 ___ ___ 90,000

3,ZQO 1000

Z'800' /-0 07qO0VELOCITY ALTITUDE(rT/SEr-) CFT)

Z,400 - 0,000

2,00 50,000

1,600 40,000

[,zoo 30,000

Soo Z0,000

400 ~,0

00 10 zo 30 40 so 60 70 s0 90 100

TIME - SECOND$

FIG.4. VARIATION OF THE VELOCITY & ALTITUDEOF THE VEHICLES WITH TIME.

kk

SECRET. T.N W .Qw. Z9 .

____ ___ ____ ___ ___FIG . 5.

KEY.VE1HICLE A - MAYFLY MOTORI NO PAYLOAD

5 - MAYFLY MOTOR, SOLB PAYLOADG - SUSTAINER MOTORV NO PAYLOAD

TRAJECTORY - VERTICAL CLIMB.

A

TEVHCE WIHALTITUDE.

P. 4067. SIEDPOTENTIAL ' *r.IT.N.S.F[ED

AL"ITUDE' F.I FIG. 6.VEHICLE A.

VEHICLE C _

IIII

-ON ACTUAL

Yz ALTITUDE AT TIME tIY VELOCITY AT TIME t

_____ _____ ____ SEE FIG-.I. FOR SKETCDHES1

O0F VEHICLES A AND CI I

SIN VACUO, DURING BURNIN

I ON ACTUA

WHERE IMUD MASS AT TIME t

_____ _____ We INITIAL MASS,I z-SPECIFIC IMPULSE.

I SE I_- K' .

VEHICLK A

VEHI1CLE'CM-A-

0i" 3- 40 so r.0 78 so 90 100TIME t SECONDS.

6 I t

FIG-6. VARIATION OF 'POTENTIAL ALTITUDE,9+t9IWITH TIME ON -ACTUAL TRAJECTORIES

AND IN VACUO UUNCLASSIFIED

G.W/P. 4868

UNCLASSIFIED FIG,7.

e~oLONQITU3DINAL IKEY TIME To MAx.ACCELERATION IALTITUJDE

CLI-1IA- M4AYFLY M OTOR,NO PAYLOAD , St SEC. - 08B-MAYFLY MOTOR, 501.5. PAYLOAD 71 SEC.IC -SUSTAINER MOTOR, NO PAYVLOAD 9O SEC.

Z000 ~TRAJECTORY- VERTICAL CLIMB. 60

FT/SEC' 50

1500 _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ oI LOWITUDIW4AL

ACCELERATICI 0IALL-BURNT.

F i 4900 1ALL- aBURNT 59

-I9

I zo4SD6

__4j

-zoo - 69

-300

-- l0g

FIG.7. ACCELERATION OF THE VEHICLES AS AFUNCTION OF TIME.

UNCLASSIFIED