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AERODYNAMIC CHARACTERISTICS FROM MACH 0.22 TO 4.65 OF A TWO-STAGE ROCKET VEHICLE HAVING A N UNUSUAL NOSE SHAPE

by John T. SzlttZes

LungZey Reseurch Center LungZey Stution, Humpton, Vu.

N A T I O N A L AERONAUTICS A N D SPACE k D M I N I S T R A T I O N WASHINGTON, D. C. NOVEMBER 1 9 6 4

https://ntrs.nasa.gov/search.jsp?R=19650000798 2020-01-06T02:06:56+00:00Z

TECH LIBRARY KAFB, NM

i ii I ill I I I I I ii ii iiiii iini iii I i MI iiii uii 0354353

AERODYNAMIC CHARACTERISTICS FROM MACH 0.22 TO 4.65 OF A

TWO-STAGE ROCKET VEHICLE HAVING AN UNUSUAL NOSE SHAPE

By John T. Suttles

Langley Resea rch Center Langley Station, Hampton, Va.

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION ~

For sale by the Off ice of Technical Services, Deportment of Commerce, Washington, D.C. 20230 -- Price $1.50

AERODYNAMIC CHARACTERISTICS FROM MACH 0.22 TO 4.65 OF A

TWO-STAGE ROCKEZ VEHICLE HAVING AN UNUSUAL NOSE SHAPE

By John T. Su t t l e s Langley Research Center '

SUMMARY

An invest igat ion has been conducted i n various wind-tunnel f a c i l i t i e s a t the Langley Research Center t o determine the aerodynamic charac te r i s t ics of a two-stage rocket vehicle having an unusual nose shape. This unusual nose consists of a blunted cone followed by a square body segment which terminates i n a conical f l a r e . Four f a i r ings a re located near t he conical nose and on the f l a t surfaces of t he square body segment. The tests were conducted f o r subsonic, transonic, and supersonic Mach numbers. The angle of a t tack w a s varied from about -2O t o 9 5 O f o r the subsonic t e s t s and the angles of a t t ack and s ides l ip were varied from about - 8 O t o 8' f o r the transonic and supersonic t e s t s .

moments, and centers of pressure with Mach number, angle of a t tack , and angle of s ides l ip . The e f f ec t s of two auxi l ia ry rocket motors attached t o the f i r s t stage w e r e invest igated a t subsonic, transonic, and supersonic speeds. They w e r e found t o cause very small changes i n s t a b i l i t y l e v e l but increased the a x i a l force by up t o 16 percent. The e f f ec t s of t he four f a i r ings a t t he nose were investigated a t supersonic speeds. The f a i r ings were found t o produce a small decrease i n the s t a b i l i t y l e v e l and an increase i n drag of up t o 13 percent. Data fo r t he configuration without auxi l ia ry rockets and f i n s w e r e obtained a t supersonic speeds so t h a t t he f i n and body contributions t o t h e aerodynamics could be determined. The r e su l t s of a comparison of estimated and measured f i n and body aerodynamic charac te r i s t ics indicated t h a t reasonable estimates could be made of the e f f ec t of t he f i n s on the s t a t i c s t a b i l i t y and axial-force charac te r i s t ics . By assuming a simplified shape f o r t he body, reasonable estimates were made f o r the body contribution t o t h e s t a t i c s t a b i l i t y ; however, t h i s assumption led t o estimates of the a x i a l force which were considerably lower than t h e measured values.

R e s u l t s are presented showing the var ia t ion of t he aerodynamic forces,

INTRODUCTION

The National Aeronautics and Space Administration has undertaken a general program t o evaluate various rocket-vehicle control-system concepts. One such control system i n conjunction with a two-stage rocket vehicle has been described i n reference 1. The vehicle consis ts of two stages with a spacecraft compartment mounted a t t he forward end of t he second stage. Housed within t h i s spacecraft

compartment is the control system which is used to stabilize and control the second stage. The second stage with its spacecraft compartment is placed in a near space environment by the fin-stabilized first stage which does not utilize a control system. A prerequisite to the study of the dynamics of such a rocket vehicle is the determination of the aerodynamic characteristics of the configuration.

The configuration of the spacecraft compartment of the vehicle described in reference 1 has an unusual shape because of the requirements for housing the par- ticular control system used.’ This shape consists of a blunted, conical nose followed by the main body of the spacecraft which has a square cross section. On each of the flat surfaces of this section is a fairing which is used to protect vulnerable portions of the control system during atmospheric flight. Because of the design of the control system, the fairings are asymmetrically located. The square section then joins a conical flare which terminates in the cylindrical diameter of the second stage. This configuration is very unusual and an analyt- ical analysis of the aerodynamic effects of the shape would be difficult if not impossible to obtain.

Wind-tunnel tests were therefore-conducted at the Langley Research Center to determine the aerodynamic characteristics of the two-stage research rocket vehicle described in reference 1. These data are needed for use in simulations of the dynamics of the vehicle and for determining structural loads. For vehicles such as that being considered, three specific problem areas require the use of accurate aerodynamic data. Subsonic high-angle-of-attack data are necessary for use in a wind-compensation procedure prior to launch. required since the vehicle being studied does not utilize a control system during the exit or first-stage boost phase. Transonic force and moment data are necessary since the maximum aerodynamic loading most often occurs in this speed range. The static stability of fin-stabilized rocket vehicles often is a mini- mum at high supersonic speeds. Supersonic data are therefore required to be sure that the vehicle being studied possesses sufficient static stability for the uncontrolled portion of the flight.

This procedure is

The data presented herein are results of tests of a 0.10-scale model of the vehicle at subsonic, transonic, and supersonic Mach numbers. For the subsonic tests the angle of attack was varied from approximately -2O to 9 5 O at zero angle of sideslip. The transonic and supersonic tests were conducted for angles of attack and sideslip from about -80 to 8 O . centers of pressure were determined for the basic vehicle configuration. The effect on the vehicle aerodynamics of two auxiliary booster rockets attached to the first stage was investigated for subsonic, transonic, and supersonic Mach numbers. supersonic speeds. Data for the basic configuration without auxiliary rockets and fins were obtained at supersonic speeds so that the fin and body contributions to the aerodynamics could be determined. Estimates were made of the effect on the aerodynamic characteristics of the fins and the body. In order to make these estimates, a simplified body shape was assumed. These data are compared with the measured fin and body contributions.

Aerodynamic forces, moments, and

The effect of the four fairings near the nose was investigated at

2

I

SYMBOLS

The coefficients of forces and moments are referred to the body-axis system. (See fig. 1.) Aerodynamic moments presented are referenced to a moment center located 21.60 inches back of the model theoretical nose apex as shown in figure 2. Coefficients are based on the first-stage body diameter of 3.10 inches and a corresponding area of 0.0524 square foot.

Axial force axial-force coefficient, ss

axial-force coefficient at an angle of attack of 00

Rolling moment rolling-moment coefficient, qSd

Pitching moment clsd

pitching-moment coefficient,

slope of pitching-moment curve through an angle of attack of Oo

Normal force normal-force coefficient, ss

slope o f ndrmal-force curve through an angle of attack of Oo

Yawing moment yawing-moment coefficient, qSd

slope of yawing-moment curve through an angle of sideslip of Oo

Side force qs

side-force coefficient,

slope of side-force curve through an angle of sideslip of 00

diameter of first stage of test configuration, in.

free-stream Mach number

free-stream dynamic pressure, lb/sq ft

radius of nose, in.

cross-sectional area of first stage of test configuration, sq ft

0

3

I l1111lll1111l1111l1 II II I I I I I l l

center-of-pressure location i n p i tch plane, body diameters forward a of model base

center-of-pressure location i n yaw plane, body diameters forward of model base B

location of balance center, body diameters forward of model base Xmc d -

U angle of a t tack of model center l i ne , deg

P angle of s ides l ip of model center l i n e , deg

* A incremental change due t o presence of fa i r ings or auxi l iary rockets

APPARATUS AND TESTS

Model

Model de t a i l s and dimensions a re presented i n the drawings shown i n f ig - The model i s a 0.10-scale model of ure 2 Eind i n the photographs of figure 3 .

the research vehicle described i n reference 1. The basic configuration consists of a f i r s t stage composed of a f in-s tab i l ized booster with two auxi l iary rockets t o give additional take-off acceleration and a second stage composed of a rocket motor with a spacecraft compartment mounted on i t s forward end. A control sys- t e m i s housed i n t h i s compartment and i s used t o maintain s t a b i l i t y and provide control f o r the second stage a f t e r separation from the uncontrolled f i r s t - s t age booster.

The first stage i s equipped with a cruciform arrangement of modified double- The f i n panels wedge f i n panels, one of which i s shown i n d e t a i l i n f igure 2(b) .

had an aspect r a t i o of 1.5, a leading-edge sweep of 18O24' and represented full- scale panels of 12 square f ee t . The model w a s mounted i n the tunnel so t h a t the planes formed by the f i n panels made an angle of 45' with the p i tch and yaw axes. The f i r s t - s t age auxi l iary rocket motors, shown mounted on the vehicle i n f i g - ure 2(a), a r e shown i n d e t a i l i n f igure 2(b) . The control rocket fa i r ings on the spacecraft compartment, shown on the model i n f igure 2(a) , a re used t o pro- t e c t the exposed ends of the control rockets through the period of high aerodynamic heating and dynamic pressure encountered during ascent. fa i r ings and the protruding ends of the control sockets a r e i l l u s t r a t e d i n f ig - ure 2(c) . The model t es ted was constructed so t h a t the configuration with and without the fa i r ings , f i n s , and auxi l iary rockets could be simulated. Other features simulated on the model such as t h e wiring tunnels and separation band a re i l l u s t r a t e d i n figure 2(.a) and may be seen i n the photographs of figure 3 .

Details of t he

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Tests and Procedure

Subsonic tes t s . - The subsonic t e s t s were conducted i n the Langley 300-MPH 7- by 10-foot tunnel a t a Mach number of 0.22. The Reynolds number per foot w a s maintained a t 1.53 X 106 and the angle of a t tack w a s varied from -20 t o 9 5 O a t zero angle of s ides l ip . Results f o r these tests are presented f o r t he basic configuration, the basic configuration a t a 4 5 O roll angle, and the basic con- f igurat ion with the auxi l ia ry rockets removed. (clockwise when viewed from rear), t he f i n panels w e r e a l ined with the p i tch and yaw axes and t h e auxi l ia ry rockets l a y i n a plane making a 4 5 O angle with the p i tch and yaw axes.

With t h e model ro l led 45O

Transonic t e s t s . - The transonic tests were conducted i n the Langley 8-foot transonic pressure tunnel f o r Mach numbers of 0.60, 0.80, 0.90, 0.95, and 1.03. The angle of a t tack w a s varied from approximately -80 t o 8 O a t zero angle of s ides l ip and the angle of s ides l ip was var ied from about -80 t o 8 O a t zero angle of a t tack. 1.35 X 106 for these tests. configuration and t h e basic configuration with the auxi l ia ry rockets removed. Because of t he low Reynolds number these tests were conducted with a t r ans i t i on s t r i p located 1.50 inches from the nose-cone theo re t i ca l apex. A s t r i p 0.10 inch wide and composed of no. 60 carborundum grains set i n a p l a s t i c adhesive w a s used.

The Reynolds number per foot was maintained a t approximately Two model configurations were tes ted, t he basic

Supe-rsonic tests.- The supersonic tests w e r e conducted i n the high-speed section of the Langley Unitary Plan wind tunnel. basic configuration with auxi l ia ry rockets removed, and the basic configuration with control rocket f a i r ings removed were t e s t ed a t Mach numbers of 2.30, 2.96, 3.96, and 4.65. rockets and f i n s removed) w a s t e s t e d a t these Mach numbers. the Reynolds number per foot w a s maintained a t about 2.8 x 106 and the angle of a t t ack was varied from approximately -80 t o 80 a t zero angle of s ides l ip and the angle of s ides l ip was var ied from about -80 t o 8O a t zero angle of a t tack.

The basic configuration, t he

I n addition, the body alone (basic configuration with auxi l ia ry During a l l t e s t s

Measurements

I n a l l tests reported herein, aerodynamic forces and moments w e r e determined by means of a six-component e l e c t r i c a l strain-gage balance housed within the body of t h e model. The balance, i n tu rn , was r i g i d l y fastened t o a s t ing support. Because of balance component malfunctions, data were not obtained from the side- force component a t some negative s ides l ip angles a t transonic speeds and from the normal-force and pitching-moment components a t some of the l a rge r negative angles of a t tack a t supersonic speeds.

Corrections

The data presented herein f o r a l l tests have been adjusted t o correspond t o the condition of free-stream s t a t i c pressure ac t ing a t t he model base and i n the balance chamber.

5

For t he subsonic and transonic tests, the e f f ec t s of subsonic boundary interference i n the test section were considered negl igible and no corrections f o r t h i s e f f ec t have been applied. For the transonic tests, data are not presented f o r Mach numbers a t which supersonic boundary-reflected disturbances would be expected t o a f f e c t t he results. speed range are not presented a t Mach numbers above 1.03. photographs of t he flow over t h e nose are presented f o r Mach numbers up t o 1.20.

For this reason data i n t h e transonic However, schl ieren

I n the transonic and supersonic tests, angles of a t t ack were corrected f o r average tunnel flow angular i ty and f o r t he def lect ion of the model and s t i n g support as a r e s u l t of aerodynamic loads.

It w i l l be noted t h a t t he normal forces and pi tching moments and the side forces and yawing moments do not pass through zero a t zero angles of a t t ack and s ides l ip , respectively. This result indicates tha t there w a s a model misalinement or e r ro r i n determining t h e e f fec t ive angles of a t t ack and s ides l ip s ince the e f fec t ive aerodynamic shape i s symmetrical i n t h e p i t ch and yaw planes. These charac te r i s t ics were not corrected f o r t h e bias i n the data; however, t he slopes o r aerodynamic der ivat ives discussed herein are not azfected. of-pressure data a re a f fec ted and spec ia l care w a s taken i n computing these data so a s not t o present erroneous var ia t ions with angle of a t tack and s ides l ip . These calculations were made f o r the p i t ch data by cross p lo t t i ng the normal force against t he pi tching moment a t angles of a t tack . A curve w a s faired through the data and t h i s curve w a s sh i f t ed so t h a t it passed through the or igin. The centers of pressure were then computed f o r points on t h i s curve and p lo t t ed against t he corresponding angle of a t tack. The centers of pressure were computed from the following equation:

The center-

Calculations were made f o r the yaw data i n t h e same manner by using the following equation :

Since data from faired curves were used i n these computations, symbols are not used when presenting t h e center-of-pressure data.

Accuracy

The estimated accuracieE of t he measured coeff ic ients , based on instrument ca l ibra t ion and data repea tab i l i ty , are within t h e following l i m i t s :

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

Subsonic : M = 0.22

C N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . k0.2

C m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . k0.2

CA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . k0.02

c ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . k0.05

Transonic : M = 0.60 M = 1.03

c m . . . . . . . . . . . . . . . . . . . . . . . . . k O .11 ko .07 cy . . . . . . . . . . . . . . . . . . . . . . . . . ko .19 kO.1 Cn . . . . . . . . . . . . . . . . . . . . . . . . . ko .19 k O . 1 C A . . . . . . . . . . . . . . . . . . . . . . . . . kO.014 *O .009

c1 . . . . . . . . . . . . . . . . . . . . . . . . . ko .09 20.05

C N . . . . . . . . . . . . . . . . . . . . . . . . . k0.2 20.14

Supersonic : M = 2.3 M = 4.65

C m . . . . . . . . . . . . . . . . . . . . . . . . . a . 0 2 a.04

C n . . . . . . . . . . . . . . . . . . . . . . . . . a .02 k0.04

C N . . . . . . . . . . . . . . . . . . . . . . . . . ko .03 ko .06

cy . . . . . . . . . . . . . . . . . . . . . . . . . *O -03 31.06

C A . . . . . . . . . . . . . . . . . . . . . . . . . kO.0075 . k O .015 c 2 . . . . . . . . . . . . . . . . . . . . . . . . . . ko.005 k O . 0 1

The l i m i t s for the subsonic coeff ic ients ( M = 0.22) apply t o the low-angle- Accuracies a t higher angles a re not def in i te and there- of-attack range (k l5O) .

fore these data should be used t o es tabl ish trends only. Model angle of a t tack and angle of s ides l ip a re estimated t o be accurate with k0.lo.

PRESENTATION OF RESULTS

The results presented i n t h i s report a re f o r a vehicle which has an unusual nose configuration. This f ac t should be kept i n mind i n drawing conclusions from the r e su l t s or i n comparing the r e su l t s with data f o r s imilar configura- t ions. been used i n some of the f igures and care should be taken i n select ing the proper zero axis f o r each curve. The f igures presenting the r e su l t s of this investigation a re as follows:

I n order t o f a c i l i t a t e presentation of the data, staggered scales have

Figure 4

s ides l ip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Subsonic aerodynamic charac te r i s t ics a t angles of a t tack . . . . . . . . Transonic aerodynamic charac te r i s t ics a t angles of a t tack and

7

Supersonic aerodynamic charac te r i s t ics a t angles of a t tack

Effect of Mach number and configuration on zero angle-of-attack and angle-of-sideslip aerodynamic charac te r i s t ics . . . . . . . . . . . . .

Effect of configuration asymmetries on the Mach number var ia t ion of the zero angle-of-attack and angle-of-sideslip aerodynamic charac te r i s t ics . . . . . . . . . . . . . . . . . . . . . . . . . . . and body i l l u s t r a t i n g the e f f ec t of the unusual nose shape . . . . . .

and s ides l ip . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Comparison of the estimated and measured aerodynamics f o r t he f i n s

Figure

6

7

8

9

DISCUSSION OF RESULTS

Subsonic Data

The subsonic data a r e presented i n f igure 4. Data f o r a l l the configura- t ions tes ted indicate t h a t CEJ and Cm vary l i nea r ly with angle of a t tack up t o about 15' with s igni f icant nonlinear e f f ec t s occurring a t the higher angles. For the angle range i n which CN and Cm vary l i nea r ly with angle of a t tack, r?) does not vary. A t the high angles of a t tack r?) s h i f t s forward by

a U

a s ignif icant amount. The general trend i n CA var ia t ion i s a decrease a s the angle of a t tack i s increased. The small values of C2 measured near zero angle of a t tack a re close t o the accuracy l i m i t of these data. The spikes occurring i n the C z data a t high angles a re not r e l i ab le data. (See section e n t i t l e d Accuracy. ") 11

The e f f ec t s of the auxi l iary rockets on the subsonic data a re very small except a t high angles of a t tack. A t the high angles the auxi l iary rockets

(?)a increase the magnitude of CN and Cm and cause a rearward s h i f t i n

so tha t the s t a b i l i t y i s increased. They cause a small increase i n CA a t the

low angles of a t tack.

The e f fec ts of ro l l i ng the basic configuration 45O a re a l so small a t low angles of a t tack. A t the high angles the magnitude of Cm i s reduced and

(7) i s sh i f ted forward so t h a t the s t a t i c s t a b i l i t y i s reduced. In addition,

there a re s ignif icant values of C2 t o the asymmetry created by the auxi l iary rockets a t this r o l l angle.

U

a t the high angles which a re probably due

8

Transonic Data

The basic transonic data are presented i n f igures 5(a) t o 5(h) . Schlieren

CN photographs of the flow f i e l d over the nose sect ion a t transonic Mach numbers a re presented i n f igure 5 ( i ) . The range of angles of a t tack over which and Cm vary l inear ly , approximately +4O, i s smaller than t h a t f o r t he subsonic data. The presence of t he auxi l ia ry rockets does not s ign i f icant ly a f f e c t t he l i n e a r i t y of CN and Cm. A s mentioned i n the section on "Corrections," t he b i a s i n the data i s not important; it i s the slope of these curves which i s of

significance. The computed values of f+) are constant i n t h e range of

angles where CN and Cm vary l inear ly . I n t h e range of nonlinear var ia t ions

of CN and &, there i s a t rend toward a forward s h i f t i n - . The var ia-

t i o n of as the angle i s increased from zero. A notable exception i s the e r r a t i c var ia- t i ons a t a Mach number of 0.95 f o r both the basic configuration and t h i s configurat ion with the auxi l ia ry rockets removed. This condition i s probably caused by an unsteady flow f i e l d a t t he unusually shaped nose. The schlieren photographs of f igure 5 ( i ) show the changing shock-wave pat terns on the nose a t these Mach numbers. The e f f e c t of t he auxi l ia ry rockets i s t o increase CA and angle of-attack var ia t ions seem t o have l i t t l e e f f ec t on t h i s axial-force increment. The r o l l i n g moments measured were very small and could have been caused by a s l i g h t misalinement of t he f i r s t - s t age f ins . Such an e f f ec t w i l l be shown i n the discussion of t he supersonic data. The d i rec t iona l s t a t i c s t a b i l i t y char-

a c t e r i s t i c s Cy, Cn, and r2)p show the same charac te r i s t ic var ia t ions with

angle of s ides l ip a s t he longi tudinal data show with angle of a t tack.

U

(T) U CA with angle of a t t ack i n general i s smooth with a decrease i n CA

Supersonic Data

The basic supersonic data a re presented i n f igures 6(a) t o 6( 3 ) . Schlieren photographs of the flow over the e n t i r e vehicle a t supersonic speeds are shown i n f igure 6 (k ) . The var ia t ions of CN and Cm with angle of a t t ack are l i n e a r through a range of about S O only. The e f f ec t s of t he auxi l ia ry rockets and control rocket f a i r ings are small a t low angles of a t tack. The data a t t he higher angles, however, do ind ica te t h a t t he auxi l ia ry rockets measurably increase the magnitude of CN and Cm and the f a i r ings decrease the magnitude

of Cm. The computed values of r+)u are constant a t low angles with forward

s h i f t s i n rT)u a t the higher angles of a t tack.

9

The body alone, t h a t i s , the basic configuration with both the f i n s and auxi l iary rockets removed, was a l so t e s t ed a t supersonic speeds. f i g . 6 (d) . ) The var ia t ions of CN and Cm with angle of a t tack f o r the body- alone configuration has a small l i nea r i ty range of only +lo or l e s s . The re la -

(See

t i v e l y large var ia t ions of r?) with angle of a t tack fo r the body-alone con- a

f igurat ion i s fur ther indication of the nonlinear character of these data.

There were no s ignif icant var ia t ions of CA with angle of a t tack f o r the configurations t e s t ed a t supersonic speeds. The small values of C z f o r the configurations with f i n s and the disappearance of these moments f o r the body- alone configuration i s evidence of a smallmisalinement of the f i n s on the model.

The direct ional s t a b i l i t y data have the same character-

i s t i c var ia t ions with angle of s ides l ip a s did the longitudinal data with angle of a t tack.

Effect of Mach Number on Zero Angle of Attack

and Sideslip Character is t ics

Presented i n f igures 7(a) t o 7(g) a re the aerodynamic derivatives, centers of pressure, and axial-force coeff ic ients a t zero angle of a t tack o r s ides l ip f o r the t e s t Mach number range. These data a re shown f o r the basic configura- t ion, the basic configuration with the auxi l iary rockets removed, the basic con- f igurat ion with the control rocket fa i r ings removed, and f o r the basic configura t ion with the f i n s and auxi l iary rockets removed. The r e su l t s indicate t h a t the auxi l iary rockets have only s m a l l e f fec ts ( l e s s than 10 percent) on CN~'

C%, and (T) . This small e f fec t , however, does indicate t h a t the auxil- G O

i a ry rockets decrease the f i n effectiveness a t subsonic and transonic Mach nun- bers posi t ive &%). However, a t the high supersonic Mach numbers the auxil-

i a ry rockets increase the f i n effectiveness. l i g i b l e e f f ec t ( 5 percent o r l e s s ) on the direct ional s t a b i l i t y character is t ics

( The auxi l iary rockets had a neg-

I \

The auxi l iary rockets increased CA,O by between 12 and 16 percent except i n the drag-rise region where the increase was about 6 percent. e f fec ts due t o the presence of the auxi l iary rockets are presented i n f igure 7(h) f o r the longitudinal s t a b i l i t y and axial-force charac te r i s t ics and i n f igure 7 ( i ) f o r the direct ional s t a b i l i t y character is t ics .

The incremental

10

The e f f ec t s of the control rocket f a i r ings were only investigated a t supersonic Mach numbers. The presence of t he f a i r ings w a s found t o cause a de f in i t e decrease i n the s t a t i c longi tudinal and d i rec t iona l s t a b i l i t y leve ls (pos i t ive E, and negative X n p , respect ively) . The changes i n s t a b i l i t y leve ls w e r e

associated with very small changes i n

i n r+)Go and r?) . The presence of the control rocket f a i r ings caused

an increase i n C A , ~ t he highest supersonic Mach number.

and Cy but de f in i t e forward s h i f t s cNa P

p=0 of about 6 percent a t t he lowest and about 13 percent a t

The benef ic ia l s t a b i l i t y e f f ec t s of the f i n s and the associated drag penalty may a l so be obtained f romthe data i n figures 7(a) t o 7 ( g ) . determined by comparing t h e configuration without auxi l ia ry rockets with the configuration without auxi l ia ry rockets and f i n s (body alone) . used i n a subsequent f igure t o compare estimated f i n and body contributions with the measured e f f ec t s a t supersonic Mach numbers.

The f i n e f f ec t s are

These data a re

Effect of Configuration Asymmetries on Zero Angle of Attack

and Sides l ip Character is t ics

Since the control rocket f a i r ings on the s ides are forward of those on the top and bottom, there i s an aerodynamic asymmetry between the longi tudinal and d i rec t iona l s t a b i l i t y planes. This asymmetry, however, i s ins igni f icant compared with the asymmetry a r i s ing from t h e f a c t t h a t the two auxi l ia ry rockets are fastened t o the s ides of the f i rs t stage. (See f i g . 2 ( a ) . ) With t h e aux- i l iary rockets located i n t h i s manner they increase the planform area of t he 'basic configuration with respect t o the longitudinal s t a b i l i t y but create no change i n the planform area a f fec t ing t h e d i rec t iona l s t a b i l i t y . I n order t o invest igate t h i s asymmetry, the longi tudinal and d i rec t iona l s t a b i l i t y data f o r the basic configuration a r e compared i n f igure 8. Also, a t the lowest t e s t Mach number the s t a b i l i t y data f o r the basic configuration a t a 4 5 O roll angle a re presented t o i l l u s t r a t e the e f f ec t of t he asymmetry due t o the auxi l ia ry rockets for t h i s configuration.

For subsonic, transonic, and supersonic Mach numbers up t o about M = 2.50, t he basic configuration has a higher s t a t i c d i rec t iona l s t a b i l i t y than longitu- d ina l s t a b i l i t y . A t higher Mach numbers the basic configuration i s more s ta t i - c a l l y stable i n the longi tudinal plane. The data near zero angle of a t t ack f o r t he 4 5 O roll angle ind ica te a small increase i n s t a b i l i t y over t h a t of t he basic configuration.

11

Comparisons of the Estimated and Measured

Aerodynamic Characteri s t i c s

It i s of i n t e r e s t t o determine the accuracy which may be obtained by using preliminary design methods f o r estimating the aerodynamic charac te r i s t ics of the configuration. Estimates were therefore made of the aerodynamic character- i s t i c s of the fin-body combination (basic configuration with auxi l iary rockets removed). It was previously pointed out t h a t an analyt ic determination of the aerodynamic e f f ec t s of the unusual nose on the configuration t e s t ed would be d i f f i c u l t i f not impossible t o obtain; therefore, a more conventional, blunted cone-cylinder body shape which approximates the ac tua l shape was assumed. The assumed shape was a 15' half-angle blunted cone (radius of 0.35 inch) which terminated i n the 3.1-inch diameter of the second-stage cylinder. i n f ig . g (a ) . )

(See sketches

The method t2)a f o r the

erences 2 and 3

of reference 2 was employed f o r the determination of Cna and

fin-body combination.

fo r the f i n contribution and from references 2 and 4 f o r the

Theoretical data were obtained from ref -

body contribution.

The ax ia l force C A , ~ was determined by summing the CA,O of the compo-

nents. and the separation band ( f i g . 2 ( a ) ) and the skin-fr ic t ion drag were included. The pressure drag of the nose was obtained from experimental data of reference 5 and theore t ica l data of reference 6. The pressure drag of the separation band was obtained from experimental data i n reference 7. The skin-fr ic t ion drag was computed by the method of reference 8. drag of the modified double-wedge p ro f i l e and skin-fr ic t ion drag were considered. Pressure drag fo r the p ro f i l e was neglected a t subsonic speeds, estimated from data i n reference 9 a t transonic speeds, and computed from l inear theory a t supersonic speeds. The skin f r i c t i o n was again computed by the method of r e f - erence 8.

For the body contribution the pressure drag of the blunted conical nose

For the f i n contribution the pressure

Comparisons of the estimated aerodynamic charac te r i s t ics with w i n d - t m e l measurements of t h e charac te r i s t ics a re presented i n figures 9(a) t o 9 (c ) . Wind-tunnel data a re presented fo r the fin-body combination f o r the en t i r e Mach number range and f o r the body-alone configuration a t supersonic speeds only. The f i n e f f ec t s a t supersonic speeds were deduced from these data and a re a l so presented. Estimates of the aerodynamic charac te r i s t ics for the f i n , body, and fin-body combination a re presented f o r the Mach number range of in te res t . The

f i n contribution includes interference e f f ec t s f o r CN and r?) but does

not include interference e f f ec t s for

a a C A , ~ .

The comparison of the estimated C N ~ with wind-tunnel measurements i s shown i n f igure 9(a) . The estimated r e su l t s f o r a l l Mach numbers agree with the

12

measured results within t h e f10 percent accuracy range associated with the method of reference 2. The estimates a t subsonic and transonic speeds are i n general about 10 percent higher than the measured data. bers t he estimates are i n very good agreement with the measured data.

A t supersonic Mach num- The com-

parison f o r t he center of pressure t+)a i s shown i n figure g(b) . The accu-

racy range quoted i n reference 2 f o r the estimates, i n terms of body

diameters of t he present configuration, i s kO.31. The results indicate an e s t i -

mated r?) of as much as 0.8 diameter a f t of t he measured data a t subsonic

Mach numbers. This difference between estimated and measured data decreases with Mach number and becomes constant a t about 0.3 diameter f o r transonic and

U

supersonic Mach numbers. The results of t he comparison f o r t he s t a b i l i t y data

(c.. and t2)a) indica te t h a t , except f o r tT)a a t subsonic speeds, the

estimates agree with measured data within the specif ied accuracy l i m i t s . The assumption of a simplified body shape therefore resu l ted i n a reasonable pre- d ic t ion of the s t a t i c s t a b i l i t y of the fin-body configuration.

The r e su l t s f o r t he a x i a l force CA,O a r e presented i n figure g (c ) . There

i s good agreement between the estimated and measured data f o r the fin-body combination a t subsonic and transonic speeds and very poor agreement a t supersonic speeds. The f i n data a t supersonic speeds indicate estimates which are somewhat l o w pa r t i cu la r ly a t t h e higher Mach numbers. This r e s u l t i s t o be expected since f in- interference e f f ec t s were not included i n the estimates and there was some bluntness a t t he f i n leading edge which was not accounted f o r i n the ax ia l - force estimations. The estimated data f o r the body alone a t supersonic speeds a r e considerably lower than the measured data. The differences i n these data a re as much as 35 percent ( M = 2.30). The results of t h e comparison therefore ind ica te t h a t t h e assumption of the simplified body i s inadequate f o r predict ing t h e a x i a l force of the fin-body configuration.

CONCLUSIONS

A n invest igat ion has been conducted i n various wind-tunnel f a c i l i t i e s a t t he Langley Research Center t o determine the aerodynamic charac te r i s t ics of a 0.10-scale model of a two-stage rocket vehicle. The aerodynamic charac te r i s t ics of t he model w e r e obtained f o r subsonic, transonic, and supersonic Mach numbers. The effects of two auxi l ia ry rockets attached t o the sides of t h e first s tage were determined a t subsonic, transonic, and supersonic speeds. The e f f ec t s of four control rocket f a i r ings a t t h e nose w e r e determined f o r supersonic speeds. The body-alone configuration w a s a l so t e s t ed a t supersonic Mach numbers so that t h e f i n and body contributions could be determined. I n addition t o providing

aerodynamic data f o r t ra jec tory simulations and the determination of aerodynamic loads, t h i s invest igat ion indicated the following conclusions:

1. The presence of t he auxi l ia ry rockets on the s ides of the model caused small (less than 10 percent) changes i n the s t a t i c longi tudinal s t a b i l i t y l e v e l near zero angle of a t t ack a t a l l Mach numbers. A t subsonic speeds and high angles of a t t ack t h e rockets caused s igni f icant increases i n the s t a b i l i t y leve l . The e f f ec t s of t he auxi l ia ry rockets on the d i rec t iona l s t a b i l i t y l e v e l near zero angle of s ides l ip were negligible.

2. The aerodynamic asymmetry i n t h e roll plane resu l t ing from the auxi l ia ry rockets causes the aerodynamic charac te r i s t ics t o vary with roll angle. For example, near zero angle of a t tack and s ides l ip t h e longi tudinal s t a b i l i t y (corresponds t o Oo roll angle) i s up t o 10 percent lower than the d i rec t iona l sta- b i l i t y (corresponds t o 900 roll angle) a t Mach numbers up t o about 2.5 and t h e longitudinal s t a b i l i t y i s as much a s 20 percent higher than the d i rec t iona l s t a - b i l i t y a t higher Mach numbers. A t subsonic speeds a 4 5 O roll r e su l t s i n a small increase i n s t a b i l i t y near zero angle of a t tack . A t high angles of a t tack the 4 5 O roll angle r e s u l t s i n a s ign i f icant decrease i n s t a b i l i t y leve l .

3 . The presence of the auxi l ia ry rockets caused an increase i n a x i a l force of between 12 and 16 percent except i n the drag rise region where the increase was about 6 percent.

4. The presence of the control rocket f a i r ings resu l ted i n a decrease i n s t a t i c longitudinal and d i rec t iona l s t a b i l i t i e s of up t o 15 percent a t supersonic speeds.

5. The f a i r ings caused an increase i n axial force of up t o 13 percent a t t he supersonic t es t Mach numbers.

6. The r e su l t s of a comparison of estimated and measured f i n and body aerodynamic charac te r i s t ics indicated t h a t reasonable estimates could be made of the e f f ec t of the f i n s on the s t a t i c s t a b i l i t y and axial-force charac te r i s t ics . By assuming a simplified shape f o r the body, reasonable estimates were made f o r t he body contribution t o the s t a t i c s t a b i l i t y ; however, t h i s assumption leads t o estimates of the a x i a l force which were considerably lower than the measured values .

Langley Research Center, National Aeronautics and Space Administration,

Langley Station, Hampton, Va., July 20, 1964.

14

REFl3RENCES

1. Young, A. Thomas, and Harris, Jack E.: A n Analog Study of a Rotating-Solid- Rocket Control System and I t s Application t o Att i tude Control of a Space- Vehicle Upper Stage. NASA TN D-2366, 1964.

2. P i t t s , W i l l i a m C . , Nielsen, Jack N. , and Kaattari , George E. : Lif t and Center of Pressure of Wing-Body-Tail Combinations a t Subsonic, Transonic, and Supersonic Speeds. NACA Rep. 1307, 1957.

3. DeYoung, John, and Harper, Charles W.: Theoretical Symmetric Span Loading NACA Rep. 921, a t Subsonic Speeds f o r Wings Having Arbitrary Plan Form.

1948.

4. Syvertson, Clarence A. , and Dennis, David H.: A Second-Order Shock-Expansion Method Applicable t o Bodies of Revolution Near Zero L i f t . 1957. (Supersedes NACA TN 3527.)

NACA Rep. 1328,

5. Geudtner, W. J . , Jr.: Sharp and Blunted Cone Force Coeff ic ients and Centers of Pressure From Wind Tunnel Tests a t Mach Numbers From 0.50 t o 4.06. Rep. No. ZA-7-017, Convair/Astronautics, June 16, 1955.

6. Staff of t he Computing Section, Center of Analysis (Under Direction of Zdengk Kopal) : No. 3 (NOrd Contract No. 9169), M.I.T., 1947.

Tables of Supersonic Flow Around Yawing Cones. Tech. Rep.

7. Hoerner, Sighard F.: Fluid-Dynamic Drag. Publ. by the author (148 Busteed Drive, Midland Park, N . J . ) , 1958.

8. Chin, S. S.: Missile Configuration Design. McGraw-Hill Book Co., Inc., c .1961.

9. Spre i te r , John R . : On the Application of Transonic Similar i ty Rules t o Wings of F in i t e Span. NACA Rep. 1153, 1953. (Supersedes NACA TN 2726.)

E7 i Relat ive

Top view u I/

X -I c

wind--==-

t Z

. - .

y/

Side view

Figure 1.- Body-axis system. Arrows indicate pos i t ive direct ions.

n i i o

(a) Sketch of basic configuration. Circled numbers indicate s ta t ion i n inches.

Figure 2.- Details and dimensions of model tes ted. All dimensions a r e i n inches unless otherwise noted.

1,236

__c_

Sect ion A-A - I .698 I

Fin pane

8.991-

+ S e c t i o n B - B

First-stage aux i l iary rocke t motor

(b) Sketch of f i n panel and f i r s t - s t a g e aux i l i a ry rocket motor.

Figure 2.- Continued.

18

0.369 Cone E l l i p s e

0.165 R

0.550 1 8 O

1 kI0

I

Control-roc ket f a r i ng

0.600

b- +---0.7 0 0

I I10.175 -0. 274

0,275

Con trol-roc ket h e ad cop

(c) Sketch of control-rocket fairing and control-rocket headcap.

Figure 2.- Concluded.

pi- &?

(a) -sic configuration. L-62-6675

(b) Closeup of nose sec t ion with control-rocket f a i r i n g s removed.

Figure 3. - Photographs of model t e s t ed .

L-62-7993

CN

30

0 Basic conf igura t ion

0 Auxiliary rockets removed [)ri)

20

10

0

- 10 -10 0 10 20 30 40 50 60 70 ao 90 100

a,deg

20

0

-20

-40

-60-

-80

-100 -10 0 10 20 30 40 50 60 70 80 90 100

( a ) E f fec t of aux i l i a ry rockets on CN and C,.

Figure 4.- Subsonic aerodynamic c h a r a c t e r i s t i c s of bas ic configuration with t h e e f f e c t of a w d l i a r y rocke ts and roll or ien ta t lon . M = 0.22; p Oo.

21

Data computed Experimental d a t a from f a i r e d curves

0 Basic conf igura t ion - Basic conf igura t ion

Auxi l ia ry rocke ts removed - - A u x i l i a r y r o c k e t s removed

Base 0

2

(3). 4

30 40 50 60 70 80 90 100 6 -10 0 10 20

1 ’

‘ A

-1

1

c L O

30 40 50 60 70 80 90 10 0 0 10 20

(b) Effec t of auxi l iary rockets on e); CA, and CZ.


22

30

20

10

0

-10


0 Basic conf igura t ion r o l l e d 4: (b)

-1 0 0 1 0 20 30 40 50 60 70 ao 90 10 0

a,deg

20

0

-20

- 40

- 60

- ao

- 100 -10 0 10 20 30 40 50 60 70 ao 90 100

a,deg

( c ) E f f e c t of r o l l o r ien ta t ion on CN and Cm.


23

Experimental d a t a D a t a computed from f a i r e d curves

0 Basic c o n f i g u r a t i o n - Basic c o n f i g u r a t i o n

0 Basic c o n f i g u r a t i o n r o l l e d 45' -- Basic c o n f l g u r a t l o n r o l l e d 45

Base 0

2

(%,a

4

G

1 1T -

0 1 0 20 30 40 50 60 70 ao 90 -10

a, deg

100

-10 0 10 20 30 40 50 60 70

(d) Effec t of r o l l o r ien ta t ion on b)a~ CAY and


ao 90 100

24

4.0

3.0

2 .O

O M

O M

-1 .o

-2.0

-3.0

-4.0

0 Basic configuration

0 Auxiliary rockets removed [

-8 -6 -4 -2 0 2 4 6 8

a, deg

(a) cN; p c 0'.

Figure 5.-. Transonic aerodynamic characteristics of basic configuration and effect of auxiliary rockets.

25

20

15

10

5

0

0

0

0

0

-5

-1 0

-15

-20 -8 -6 -4 -2 0 2 4 6 8

a, deg

(b) C,; p 2= Oo.


26

Data computed irom fa ired curves

- Basic configuration Q -- Auxiliary rockets removed

0 Base 0

2

4

Base o

2

4

Base o

2

4

Base 0

2

4 -8 -6 -4 -2 0 2 4 6 8

( c ) r?) ; p = oo. a


27

0 -sic configuration 0 Auxiliary rockets removed

0.6

0.4

0.2

0.6

0.4

0.2

0.8 C A

0.6

' I 1 0.8 I I

1.0

1.4

1.2

1.0

-6 -4 -2 0 2 4 6 8 -8

a,deg


28

0 %sic configuration

0 Auxiliary rockets removed 0

1

0

-1

1

0

-1

1

0

-1 -8 -6 -4 -2 0 2 4 6 8

a,deg

(e) CZ; p = o0.


I II

CY

4

3

2

1

0

0

0

0

0

-1

-2

-3

-4 -8 -6 -4 -2 0 2 4 6 8

p9-g

(f) c y j a = 00.

Figure 5 . - Continued.

20

15

10

5

0

0

0

kd 0 Basic configuration

0

0

- 5

-10

-15

-20 -8 -6 -4 -2 0 2 4 6 8

P,deg

(9) cn; a== 00.


D a t a computed from fa i red curves

- Basic configuration

---- Auxiliary rockets removed

Base 0

2

4

Base 0

2

4

Base o

2

4

Base 0

2

4

Base 0

2

4 0 2 4 6 8 -8 -6 -4 -2

P,deg


32

0"; M 10.90

a -0"; M =0.80

a = O o , M.0.95

a m O D ; M10.85

a z o " ; M = l . I O a m o o i M = I 20

L-64-4751 (i) Schlieren photographs of t ransonic f l o w over nose sect ion.


33


0 Control-mcket f a i r i n g s removed

0 Auxiliarj rocke ts removed

2.0

1.5

1.0

0.5

-0.5

-1.0

-1.5

-2 .o

-8 -6 -4 -2 0 2 4 6 8

a,deg

CN of bas ic configuration and e f f e c t on control-rocket f a i r i n g s and aux i l i a ry rockets. p = 00.

Figure 6.- Supersonic aerodynamic cha rac t e r i s t i c s of bas ic configuration and body alone (with f a i r i n g s ) with the e f f e c t of control-rocket f a i r i n g s and aux i l i a ry rockets.

34


I7 6ontrol-rocket 10

8

6

4

0

Cm

0

0

-2

-4

-6

-8 -9 -6 -4 -2 0 2 4 6 8

a, deg

of basic configuration and effect of control-rocket fairings and auxiliary I f3 iJ oo.


:ockets.

35

Data computed from f a i r e d curves

Control-rocket f a i r ings removed

Basic configuration

-3

I .

--

2

4

6

( c ) t?) of bas ic configuration and e f f e c t of control-rocket f a i r i n g s and aux i l i a ry rockets. a

p = 00.


.5

0

0

0

-.5

- - 1 2

a ' 12

diameLers --- - - 12 forward of base

-8 -6 -4 -2 0 2 4 6 8

a,deg

(a) CN, Cm, and tq) of body-alone configuration (with fairings). p Oo.


a

37

l l l l l l I I1 I1 I 111ll111111l111l1ll1111ll11l1ll1111l1l11

0 Control-rocket


0 Auxiliary rockets removed A Body alone

0.8

0.6

CA 0.4

0.8

0.6

0.4

0.2

0.6

0.4

0.2 -9 -6 -4 -2 0 2 4 6 8

a, deg

( e ) CA of bas ic configuration with e f f ec t of control-rocket f a i r i n g s , aux i l i a ry rockets, and CA of body alone (with f a i r i n g s ) . p = 00. .


0 % s i c configuration

0 Control-rocket f a i r i n g s removed

0 Auxil iary rockets removed

A Body alone (wi th f a i r i n g s )

0 0 (0)

.4

0

- . 4

.4

0

- .4

.4

0

-.4

.4

0

-.4 -a -6 -4 -2 0 2 4 6 8

(P) C z of bas i c configuration with e f f e c t of control-rocket f a i r i n g s , aux i l i a ry rockets, and C i of body alone (with f a i r i n g s ) . p = Oo.

Figure 6 . - Continued.

39

11111 111 Ill11

CY

^ ^ i2.U

1.5

1.0

0.5

0

0

0

0

-0.5

-1.0

-1.5

-2 .o


0 Control-rocket fairings removed

0 Auxiliary rockets removed

-8 -6 -4 -2 0 2 4 6 8

(g) Cy of basic configuration with effect of control-rocket fairings and auxiliary rockets. a =


40

'n

10

8

6

4

0

-2

- 4

-6

-8 -8 -6 - 4 -2 0 2 4 6 8

(h) Cn of bas ic configuration and e f f e c t of control-rocket f a i r i n g s and auxiliary rockets. a ZJ O0.


41

Data computed from f a i r ed curves

(a) Basic configuration

-- Control-rocket fa i r ings removed (a Auxiliary rockets removed

Base 0

2

4

6

-a -6 -4 -2 0 2 4 6 8

P.deg

(i) t?) of bas ic configuration and e f f e c t of control-rocket f a i r i n g s and aux i l i a ry rockets.

a = oO.


P

42

5

CY

-5

d iame te r s forward ----12 of base

-8 -6 -4 -2 0 2 4 6 8

P, deg

( j ) Cy, Cn, and r2)p of body-alone configuration (with f a i r i n g s ) . a = Oo.


43

a = O o i M.2.30 (I cooi M = 2.96

a n 0": M = 3.96 a = O o ; M.4.65

(k ) Schl ieren photographs of supersonic flow over complete model.


44

. . 0 &sic configuration

.8

.7

.5

.3

.2

.1

0 1 2 3 4 5

Figure 7.- Effect of Mach number, auxiliary rockets, and control-rocket fairings on zero angle of attack and sideslip characteristics of basic configuration. Characteristics of body alone are also shown.

0 1

I ' 0 % s i c configuration

0 Auxiliary rockets removed

0 Control-rocket fairings removed

A Body alone (with fa ir ings) (0)

3

!&ch number


46

4 5

Base 0

Data computed from fa i red curves

&sic configuration a Auxiliary rockets removed

- Control-rocket f a i r ings removed a - -- Body alone (with fairings) (0)

--

0 0

2

4

6

10

12

14

16 0 1 2 3

Mach number 4 5

l id


CYp,

1 deg

-.a

- .7

-.5

- .4

- .3

- .2

-.l

1 2 3 4 5 0

Mach number

(dl cyp.


i

i

0 1 2 3 Mach number

(e) Cnp-


4 5

Data computed from f a i r e d curves

Basic configurat ion

Auxiliary rockets removed --- (a) --- - Control-rocket f a i r i n g s removed

Body alone (with f a i r i n g s ) (0) --- Bas e

=O

Mach number

T

Figure 7. - Continued.

‘A, 0

V Mach number

( 9 ) cA,O*


I

.04

%, O

- e 0 4

.2

A, 0 AC

.1

1 2 3 4 5 0

Mach number

(h) ~ C N ~ , A@)a=oo, &A,O due t o adding auxi l ia ry rockets t o fin-body combination.


E E .4 0 E

A(??) p=o O

y .-.4 4 0 1 2 3 4 5 w

Mach number

( 1 ) MYp and due to adding auxi l iary rockets t o fin-body combination.


ul w

cKl or

-CYp

1 aeg

.8

.7

.s

.4

.3

.2

.1

0 1 2 3

Mach number

4 5

(a) Force derivative.

Figure 8. - Effect of configuration asymmetries on aerodynamic characteristics of basic configuration.

or

cnP 1

%

0 1 2 3

Mach number

(b) Moment derivative.


4 5

Base

or

IO 0 1 2 3

Mach number 4 5

( c ) Center of pressure.


Estimated data Experimental data

Fin-body combination 0 Fin-body data

(including carry-over effects)

Body contribution (simple cone-cylinder a s A Body-alone data

-- -- Fin contribution Fin data ( obtained from f in-body and body-alone data)

(0) shown below) (with fai r ings as shown . below)

C a

0.35 R L 0.35 R

0 1 2 3

Mach number

4 5

( a ) CNa.

Figure 9.- Comparison of estimated data with measured f i n and body contributions t o aerodynamics.

0

2

4

6

E

10

12

14

1 6

0

Data computed from Estimated data f a i r e d experimental curves

- Fin-body combination 0 Fin-body da ta

---- Fin cont r ibu t ion 0 Fin da ta (obtained from fin-body and

Body cont r ibu t ion body alone d a t a )

‘as shown in fgg. 9?a)1 A Bod,-alone d a t a . (0) simple cone-c l i n d r

1 2 3 4

Mach number

(b) r3) . a

4

5


s rn

+. W m J1

7 w v) [v 0

1.8

1.2

1.0

'A,O

0.8

0.6

0.4

0.2

(

Estimated data Experimental d a t a

0 Fin-body data - Fin-body combination

-_ - - Fin contr ibut ion \ I I \ I 0 Fin d a t a

(obtained from fin-body

( c ) cA,O.


aerodynamic characteristics from mach 0.22 to 4.65 of a ... · i aerodynamic characteristics from...

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