N A S A C O N T R A C T O R

R E P O R T

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pr: U

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LOAN COPY: RETURN 78 AFWL (DOUE)

KIRTLAND AFB, N. k

EXPERIMENTAL VERIFICATION OF LOW SONIC. BOOM CONFIGURATION

by Antonio Few& Hnai-Cbu. Waug,

Prepared by NEW YORK UNIVERSITY Bronx, N.Y. 1045 3

for

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. JUNE 1972

https://ntrs.nasa.gov/search.jsp?R=19720022357 2020-06-28T16:17:15+00:00Z

TECH LIBRARY KAFB, NM

1. Report No. I NASA CR-2070 I 2. Government Accession NQ. I 3. Recipient's C a t a l o g No.

4. Title and Subtitle

EXPERIMENTAL VERIFICATION OF LOW SONIC BOOM CONFIGURATION

I 5. Report Date

June 1972 6. Performing Organization Code

7. Author(s) 8. Performing Organization Report No.

Antonio Ferri, Huai-Chu Wang,and Hans Sorensen NYU-AA-71-19 10. Work Unit No.

9. Performing Organization Name and Address A. Ferri & H . C. Wang New York University, Bronx, NYC 10453

H. Sorensen, Aeronautical Institute of Sweden, Broma, Sweden

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration Washington, D. C. 20546

15. Supplementary Notes

11. Contract or Grant No.

NGL-33-016-119 13. Type of Report and Period Covered

Contractor Report 14. Sponsoring Agency Code

RAA

16. Abstract

A configuration designed to produce near field signature has been tested at M = 2.71

and the results are analyzed, by taking in account three-dimensional and second order

effects. The configuration has an equivdent total area distribution that corresponds

to an airplane flying at 60,000 ft. having a weight of 460,000 lbs. and 300 ft length.

A maximm overpressure of 0.95 lb/ft2 has been obtained experimentally. The

experimental results agree well with the analysis. The investigation indicates

that the three-dimensional effects are very important when the measurements in wind

tunnels are taken at small distances from the airplane.

17. Key-Words (Suggested by Authoris) i ~

"" ~ ~~~ ""

18. Distribution Statement

Sonic boom measurements or near field configurations at M = 2.7. Unclassified - Unlimited

.~ ~~-~ 19. Security Classif. (of this report)

$3.00 22. Rice' 21. NO. of Pages 20. Security Classif. (of this page)

Unclassified Unclassified

For sale by the National Technical Information Service, Springfield, Virginia 22151

CONTENTS

1.

I1 D

111.

I V 0

V.

V I 0

V I 1 0

V I 1 1 . I X . X.

X I 0

I n t r o d u c t i o n . o . o . . . . o o . . . . . . . . . . . . .

Definit ion of the Problem . . . . Experimental Techniques . . . . . . . . . Description of the Model . . . . P o s s i b i l i t y of Obtaining Information on the Rear Shock

from Wind Tunnel Tests . . . . . . Results of the Analysis . . . . . Review of the Experimental Data . . . . . . Correct ions Introduced on the and J u s t i f i c a t i o n

for the Correc t ions e . . Description of the Method of Analysis Used . . . Application of the Method to the Present Experiments . Conclusions O . O . . . O O O . O O . . . . O O O O . O .

Page

1

3

8

10

13

14

16

16

18

2 1

24

References . . . . . . . e . . . . 27

iii

LIST OF FIWRES

FIGURE

1

2

3

4

5a

5b

6

7

8

9

10

11

12

13

14a

14b

14c

- psge

Schematical view of test se t -up 30

Schematical indicat ion of geometr ical parameters of the experiment 31

Design of yaw probe 32

Design of airplane configuration 33 Model design ;k Airplane configurat ion corresponding to the area d i s t r i b u t i o n of t he model of Fig. 4 35 Var ia t ion o f to ta l equiva len t area due t o t h e j e t exhaust of an engine as a func t ion of d i s t ance from t h e e x i t of t he j e t 36 Equivalent area d i s t r i b u t i o n 37

Sonic boom s igna tu re L = 300 f t , h = 60,000 f t , w = 460,000 lb , M = 2.70 var iab le p ressure program

Sonic boom s igna ture cons tan t p ressure program Kp = K = 1017 l b s / f t 2

p60,000 'SL

Perturbat ion of the area d i s t r ibu t ion cu rve M = 2.70, w = 460,000, h = 60,000 ) L = 300

Sonic boom s igna ture cor responding to area curve B of Fig. 10

Sonic boom s igna tu re a t M = 2.718,L = 300 f t , h = 60,000 f t , W1= 430,000 lb, (CL = 0.055) W2 = 516,000 l b , (CL= 0.066)

Variat ion of equivalent area d i s t r ibu t ion co r re spond ing t o curve c of Fig. 12

Experimental values of c as funct ion of d i s t ance a t several meridian planes r / L = 0 . 2 7 1 , ~ = 2.6O

Continued

0

Continued

V

14 d

14 e

14 f

14g

15a

15b

15 c

16a

16b

16c

16d

16e

16f

17a

17b

17c

18

19

2 Oa

2 Ob

2 oc

Continued

Continued

Continued

Continued

Experimental values of 0 a s f u n c t i o n o f d i s t a n c e a t s e v e r a l m e r id i an p lanes

Continued

continued

Experimental values of E as func t ion of d i s t a n c e at several meridian planes r/L = 0.558, a = 2 . 6 O

Continued

0

Continued

Continued

Continued

Con t inu ed

Experimental values of 0 as funct ion of d i s tance a t several meridian planes

Continued

Continued

D i s t r i b u t i o n of dev ia t ion ang le at T; = 0.271, Cn= 0.055 (a = 2 . 6 O ) , for d i f f e ren t l ong i tud iua la loca t ions of the mode 1

r

Continued

Continued

47

48

49

53

51

52

53

63

64

65

66

67

2 Od

2 Oe

20f

2og

2 la

2 l b

2 I C

22a

22b

22c

22d

22e

22 f

22 g

2 3a

2 3b

2 3c

24a

24b

2 5a

25b

26

27

Continued

Continued

Continued

Continued

Experimental values of 0 as funct ion of d i s tance a t s e v e r a l m e r i d i a n p lanes

Continued

Continued

Experimental values of e as func t ion o f d i s t ance a t s eve ra l m e r id i an p lanes

Continued

Continued

Continued

Continued

Continued

Continued

Experimental values of 0 as func t ion of d i s t a n c e a t s e v e r a l meridian planes, a = 3.2O, '/Lo = 0.558

Continued

Continued

Schlieren photographs a t = 2.6 , 8 = o Schlieren photographs a t = 2.6 , Q = goo

Schlieren photographs a t a = 3.2 , 8 = 0

Schlieren photographs a t a = 3.2 , e = 90'

Determination of region of i n t e r f e r e n c e between probe and shock

P r e s s u r e d i s t r i b u t i o n on a hemisphere, Mo= 4 .6 i n t e rac t ing with a shock tha t def lec ts the f low of 5. Arrow ind ica t e s point a t which disturbance meets model Surface

0 0

0

0 0

0

vii

28.

29

30

31

32

33

34

35

36

37

38

39

40

41

Dis t r ibu t ion of c: at . r / L = 0.558, a = 2.6O, 0 = 0

Comparison between experimental and calculated values

Comparison between experimental and calculated values

Double values of F (y) for cone cyl inder

Distr ibut ion of F funct ion as function of y corresponding

to curve 1 of Fig. 28

F(y) used in the analysis corresponding to curve 1 of

Fig. 28, a = 2.6', r / L = 0,558

Sonic boom s igna tu re a t r / L = 200, fo r L = 300 ft and L = 0.555,

var i ab le dens i ty program (Curve 2 of Fig. 28)

Sonic boom s igna ture (cons tan t p ressure) at r / L = 200 Rp = 1017

0 0 0

l b /€t2

Comparison of sonic 600nz sigrratures €or several types of

analyses r / L = 200

Measurements of deviatcan angle of SST model a t r / L = 0.271,

% = 0.055, a = 2.6 a t s e v e r a l p o s i t i o n s

Sonic boom s i g n a t u r e for a = 2.6 , $ = 0.055 a t r/Lo = 208 from

data at r / L = 0.271, I(p = 1017 B/ft

Assumed d i s t r i b u t i o n of e at r/L = 0.558 = 0.066, (r. = 3.2O

F(y) curve for a = 3.2" from data a t r h = 0.558

Sonic boom s i g n a t u r e f o r (x = 3.2O, 5, = .066, r / L = 200

Kp= 1017 l b / f t

0

0

0

2 0

0

0

2

91

92

93

94

95

96

97

98

99

10 1

102

103

104

v i i i

EXPERIMENTAL VERIFICATION OF LOW SONIC BOOM CONFIGURATION

Antonio Ferri t and Huai-Chu Wang tt

New York Universi ty

Bronx, New York 10453

and

Hans S orens en

A e r o n a u t i c a l I n s t i t u t e o f Sweden

ttt

I. Tntroduction

Airplanes f lying a t supersonic speed produce "sonic booms" on the

ground. Sonic boom r e f l e c t e d on the ground i s f e l t by people as a "s tar t -

l ing no ise ," and the present levels and shapes of the overpressures are

highly object ionable . The sonic boom is unavoidable for vehicles having

l i f t and c ru i s ing i n ho r i zon ta l f l i gh t . The re fo re , t he d i r ec t ion t o fo l low

i n o r d e r t o a t t e m p t t o minimize the unacceptabili ty on the p a r t of the

people is to decrease the main source of annoyance which is largely con-

nected with the presence of shock waves.

The r e s u l t s o f an ana ly t i ca l and experimental invest igat ion are p r e -

sented and discussed herein, and have been performed in o rder to de te rmine

conf igura t ions tha t p resent a reduct ion of shock wave s t rengths wi th respec t

t o va lues produced in p resent conf igura t ions , and t o v a l i d a t e r e s u l t s o f

t Director, Aerospace Laboratory, and Astor Professor of Aerospace Sciences tf Research S c i e n t i s t ttt Head of the Tr i sonic Tunnel , Aeronaut ica l Ins t i tu te o f Sweden

approximate analysis by means of experimental resul ts . The i n v e s t i g a t i o n a l s o

is usefu l for deve loping sa t i s fac tory p red ic t ion methods .

The inves t iga t ion ind ica ted tha t the ana lys i s and exper iments are i n

good agreement, and that sonic booms having the f i rs t shock s t rength o f the

order of 1 l b / f t as predicted by the ana lys i s a r e measu red i n t he expe r i -

ments. The i n v e s t i g a t i o n i n d i c a t e s some o f t h e d i f f i c u l t i e s e n c o u n t e r e d i n

ex t r apo la t ing nea r f i e ld da t a a t l a rge d i s t ances . The experiments have been

performed a t t he Aeronau t i ca l Resea rch In s t i t u t e o f Sweden, by the research

2

group directed by Professor M. Landahl and D r . G . Drougge, and have been

performed by using a new experimental technique developed by the group

based on the higher order analysis developed by M. Landahl, I . L . Ryhming,

and o the r s . The model has been designed by a research group a t t h e Aero-

space Laboratory of New York Universi ty , as a pa r t o f ar, inves t iga t ion on

low boom configurat ions. 3 y 4 The la t te r group a lso performed the analysis of

1

2

the expe r imen ta l r e su l t s desc r ibed i n t h i s r epor t . The work has been carried

out under two NASA Grants: (1) NGR 52-120-001, assigned t o the Aeronaut ical

Research Ins t i tu te o f Sweden; and (2) Grant NGL 33-016-119, assigned t o New

York Universi ty . The experiments have been performed by H. Sorensen of the

Aeronau t i ca l In s t i t u t e o f Sweden. The analyses have been performed by a

team under the direct ion of Professors Fe r r i and Ting, which includes besides

the authors , Mrs. F. Kung, Messrs. M. S i c l a r i and A . Agnone. This repor t

d i scussee the resu l t s cor responding to an angle o f a t tack c lose to the

se l ec t ed f l i gh t cond i t ions fo r t he SST, and a t ano the r s l i gh t ly h ighe r ang le

of a t tack .

2

11. Def in i t ion o f the Problem_

Predic t ion of sonic boom s igna tu res a t la rge d i s tances from t h e a i r p l a n e

is based mainly on the Whitham.second order The a i r c r a f t is

represented by a d is t r ibu t ion of mul t ipo les and l i f t ing e lements der ived from

the a i rp lane ' s geometry on the basis of l inear ized supersonic theory. The

asymptot ic solut ion i s expressed in terms of the c r o s s - s e c t i o n a l a r e a d i s t r i -

bution. S(xg) is a funct ion of the dis tance x and azimuthal angle F) of an

equivalent body of revolut ion, and an equiva len t c ross -sec t iona l area t h a t

r e p r e s e n t s a n e q u i v a l e n t l i n e a r l i f t d i s t r i b u t i o n . The pres su re va r i a t ions

produced by a veh ic l e a r e s t rong ly non l inea r nea r t he veh ic l e ; however, t he

nonl inear effects decrease rapidly moving away from the a i rplane. Therefore ,

a t some f i n i t e d i s t a n c e from the a i rp lane sur face , l inear theory i s general ly

v a l i d l o c a l l y . Then the only nonl inear effects to be considered are the

e f f e c t s r e l a t e d t o t h e v a r i a t i o n of the speed of sound t h a t when combined

wi th the loca l var ia t ion o f ve loc i ty o f f lu id p roduces d i s tor t ions o f the

s igna l w i th r e spec t t o l i nea r Mach waves. This second order effect is

cumulative and therefore must be considered when propagat ion of dis tur-

bances a t a la rge d i s tance is inves t iga t ed . The whitham theory takes into

account these effects and p e r m i t s us to determine the propagation of waves

from a region where the disturbances produced by the veh ic l e a r e a l r eady

s u f f i c i e n t l y s m a l l , s o tha t l i nea r t heo ry app l i e s .

The a n a l y s i s p e r m i t s u s t o ex t end t he s igna l produced by t h e a i r p l a n e t o

reg ions fa r from the a i rp lane , p rovided tha t the d i s turbance produced by the

a i r p l a n e i s known i n a region where such disturbances are a l ready small.

The analyt ical determinat ion of such dis turbances is ex t r eme ly d i f f i cu l t ,

3

espec ia l ly a t high Mach numbers. The l inear theory that is the most adapt-

able type of analysis avai lable for three-dimensional f low, cannot be used

for the purpose of re la t ing the shape of the a i rp lane to the s igna ture p ro-

duced in the near f ie ld , because i t neglec ts h igher o rder e f fec ts bo th in

the def in i t ion o f the loca l in tens i ty o f the s igna l , and i n t h e decay and

shape of the wave propagation.

Experimental methods, where the wind tunnels are used as analog machines

to de f ine t he s igna l s a t some dis tance from the veh ic l e , open a promising

way to so lve t h i s problem because they do not have the l imitations of the

l inear ized theory. ” lo’ l1 Such approaches, however, have other limitations

that only recently have been recognized.12 The most direct approach for

e l iminat ing many of the uncertaint ies due to the s implif icat ions introduced

in the ana lys i s to de te rmine the ac tua l s igna ture o f an a i rp lane a t some

dis tance from the a i rp l ane , i s t o measure the complete signature experi-

mentally. A t Mach numbers on the order of 2 t o 3 , the dis turbances produced

by good L/D configurat ions a t dis tances of the order of a few body lengths

from the model are extremely small; therefore , l inear theory appl ies here .

The experimental approach proposed by NASA’, and used extensively for sonic

boom determination, has been to build a model and to determine experimentally

the dis turbances produced a t some dis tance from the a i rp l ane and then extra-

po la te the measured s igna l t o t he r equ i r ed he igh t of f l i g h t by means o f the

Whitham theory. The concept is s u r e l y v a l i d , and therefore p resents one of

the most d i r e c t ways of obtaining accurate information. However, it has been

shown12 that in applying the concept that more attention should be given to

the type of measurements performed, and to t he i n t e rp re t a t ion o f t he expe r i -

mental data, before such methods can give comple t e ly s a t i s f ac to ry r e su l t s fo r

configurations producing weak sonic boom s igna tures as requi red for future

a i rp lanes . One of the bas i c s imp l i f i ca t ions of the Whitham theory is that

a t la rge d i s tances from the body, t h e d e t a i l s of the spanwise dis t r ibut ion of

the sources of disturbances are not important provided that the span of the

veh ic l e is very sma 11 wi th respec t to the d i s tance cons idered . Then, t h e

airplane can be subst i tuted by an equiva len t ax ia l ly synunetric body i n any

of the meridional planes around the axis of the body considered. This

approximation has been introduced in the p a s t , and used in t he ex t r apo la t ion

of experimental measurements t o l a rge d i s t ances . Because of t hese s imp l i f i -

ca t ions , the measurements have been performed only in the meridian plane

normal to the p lane of t he a i rp l ane wing. These measurements have been used

to determine by means of the whitham theory, an axially symmetric body

equiva len t to the a i rp lane conf igura t ion which is used to determine the sonic

boom a t l a rge d i s tances . This approach in t roduces two approximations: the

f i r s t is tha t t he r eg ion where the measurements are made i s s u f f i c i e n t l y f a r

from the model, so tha t the d i s turbances a re smal l ; the second is t h a t a l l

dimensions normal to the axis of the a i rplane, including a lso the spanwise

dimensions, are negl igible with respect to such a d is tance so tha t the th ree-

dimensional effects are neglected. Both assumptions are acceptable i f the

regions of the measurements are s u f f i c i e n t l y f a r away from the model; however,

t he d i s t ance r equ i r ed fo r t he va l id i ty o f t he f i rs t approximation is not the

same d i s t ance r equ i r ed fo r t he va l id i ty of the second. For a i rplanes having

good performances, and wings of pract ical span, the f i rs t requirement can be

s a t i s f i e d a t m c h smaller distances than the second.

5

In p rac t i ce , d i s t ances from the model of the station where measurements

are performed cannot be too large because of p r a c t i c a l e x p e r i m e n t a l d i f f i -

c u l t i e s . The prec is ion of the measurements decreases sharply w i t h an in-

crease of d i s tance because o f the f in i te sens i t iv i ty o f the instruments.

Fur thermore , the s ize o f ava i lab le wind tunnels and t h e s i z e o f t h e model

requi red for the tests limits t h e r a t i o between distance of measurements and

length of the model. Another important difficulty is due t o t h e f a c t t h a t

the f low f ie ld produced by a wind tunnel i s not absolutely uniform. In any

wind tunnel, a nonuniformity of a few pe rcen t i n Mach number exists. Such

nonuniformities correspond to waves t h a t i n t e r a c t w i t h t h e wave pa t t e rn

produced by the model. When these d i s turbances in te rac t wi th the f low f ie ld ,

a n e r r o r i s introduced that is cumulative along the waves ca r ry ing d i s tu r -

bances from t h e model to the p lane o f measurement. The s t r eng th o f t he

waves that i s produced by t h e model a t a very l a rge d i s tance from the model is only

s l i g h t l y l a r g e r t h a n t h e waves due t o nonuniformit ies exis t ing even in the

most uniform wind tunnel. Therefore, the error introduced is proport ional ly

l a rge r a t la rger d i s tances . This e r ror t ends to increase wi th Mach number.

Thus, a compromise must be reached between accuracy required and d is tance of

t he measurement where a s i n g l e measurement is acceptable . 12

The problem can be reduced substantially by the in t roduct ion of more

complex techniques for obtaining experimental data, and ex t rapola t ing the

r e s u l t s . Two different approaches have been proposed; one by the f irst

author of this report12 where the measurements are performed i n a plane

located a t some dis tance from the model p a r a l l e l t o t h e p l a n e where the

sonic boom signal must be determined. The deviat ions of the s t ream surface

normal to the p lane are measured i n a region inside the shack generated by

t he f ron t t i p o f t he a i rp l ane . Such devia t ions are detennined along several

s t r a igh t l i nes pa ra l l e l t o t he f l ow d i r ec t ion t o cove r a l l of the f low in-

s i d e t h e shock. A stream surface is defined by the measurements that can be

subs t i tu ted for the a i rp lane . Such a stream surface where the f low dis tur-

bances are small is equivalent to the vehicle placed above. Then, the

Whitham analys is as appl ied by Wa1kden,l3 is used d i rec t ly to de te rmine sonic

boom a t the required dis tance from th i s su r f ace . The Whitham theory a p p l i e s

for th i s ex t rapola t ion provided tha t the d i s turbances are small, s o t h a t

local ly the l inear theory is suf f ic ien t ly accura te . In th i s type of an

approach, the deviation of the stream surface is measured experimentally by

measuring the stream devia t ion in a plane parallel t o t he ground i n t h e

en t i r e r eg ion i n s ide t he f ron t Mach cone. Therefore, the precision of t h i s

method depends on the compromise of two opposite requirements: (1) the

accuracy of the l inearized theory which increases with the dis tance from the

body; and ( 2 ) the precis ion of measurements which decreases when the d i s -

tance increases. However, three-dimensional effects are accounted for

accura te ly . The experiments presented here tend to indicate that a satis-

fac tory compromise can be obtained for these two opposite requirements even

i f t h e measurements are performed a t very small d is tances from the body.

The present experiments have been performed by using the second method

proposed by Landahl, Ryhming, Sorensen, and Drougge.' Here, the s t reamline

devia t ion is measured fo r s eve ra l s t r eaml ines s t a r t i ng on a cy l ind r i ca l t ube

placed around the model having the axis p a r a l l e l t o t h e wind, and a t small

d is tances from the axis. In the experiments performed, the distance is

7

smaller than the l ength o f the model. The deviat ion of each s t reamline of

t h i s t u b e i s measured loca l ly in several meridian planes. Two angles are

measured: one gives the deviation in the meridian plane; and the second

g ives the devia t ion on the cyl inder normal to the meridian plane. These

da t a are used to determine a t t h e axis of the cy l inder the F func t ion tha t

is used i n t h e Whitham theory, by means of higher order approximation that

takes into account second order . terms in t he d i s tu rbance components and

higher order terms in the curvature according to a theory developed by the

proposers of the method.

This method p e r m i t s u s t o u se sma l l e r d i s t ances from the models than

the other; however, i t r e q u i r e s d i f f e r e n t i a t i o n of the measured deviation

which i s d i f f i c u l t t o d o . I n a d d i t i o n , t h e a n a l y s i s assumes t h a t t h e t h r e e -

dimensional and thickness effects are small s o tha t the d i s turbances can be

extrapolated a t t h e a x i s o f t h e body. This last condition can produce F

func t ions t ha t are not s ingly valued. Both approaches are improvements with

respec t to the s tandard method, espec ia l ly a t Mach numbers of 2 or 3 .

111. - Experimental TEchniques

The experiments were conducted in the Trisonic Tunnel of the Aeronau-

t i c a l I n s t i t u t e o f Sweden, FFATLJM 500, a t Mach number 2.718.l The tunnel

has a square t e s t s ec t ion o f 50 x 50 cm2 with perforated walls fo r t he

transonic speed range and a f lex ib le wal l nozz le which a l lows the Mach

number to be var ied cont inuously between 1 and 4 . It is a blowdown tunnel ,

which may be operated with a stagnation pressure up to 12 atmospheres, and

a stagnation temperature range of 300 K - 400°K. A schematic design of the 0

tunnel is shown in F ig . 1.

Pressure measurements were performed on t h e model a t 2.6O and 3.2O

incidence a t two pos i t ions a long the tunnel ax is . The f low f ie ld measure-

ments were conducted a t two r a d i a l d i s t a n c e s from t he model axis correspond-

ing to 0 .271 and 0.558 times the length of the model i n mer id i an p l anes

spaced a t 5' i n t e r v a l s from the plane of symmetry i n t h e r a n g e between 0

and 90'. The meridian planes are defined by the angle 8 with r e s p e c t t o t h e

plane of symmetry. The pressures were recorded almost simultaneously, since

the time between the individual measurements were 1 - 10 sec. Schl ie ren

photographs were taken of the flOV7 f i e ld gene ra t ed by the model and the

pressure probe.

0

-4

The absolu te level of accuracy of t h e r e s u l t s is v e r y d i f f i c u l t t o

es tab l i sh , because of the combined e f f ec t s o f t he many possible sources of

e r r o r . A number of precautions were taken, however, to reduce the magnitude

and p robab i l i t y of s i g n i f i c a n t e r r o r s . The f a c i l i t y i n s t r u m e n t a t i o n con-

sists p r imar i ly o f h ighe r s ens i t i v i ty p re s su re measurement devices for de-

termining both stagnation and reference pressures. These pressures were

ca l ibra ted carefu l ly p receding the inves t iga t ion . The free-stream pro-

perties are considered accurate within the fol loning limits:

M, 4- 0.01 -

P t ,a - + 0.1%

The precis ion with which local f low quant i t ies can be determined i s es-

timated by the Laboratory to be as follo.c7s:

9

M1

E r r o r s a t M, = 3.0

+ - 0.07

- + 1.0 %

= <

= <

+ - o.loo

+ - o.loo

The va lues o f the e r rors in angles quoted here do no t inc lude the in f luence

of the nonuniform flow on the probe. As it w i l l be discussed later, the

i n t e r a c t i o n o f the shock w i t h the subsonic f low in front of the probe,

produces local ly large errors ; therefore , there such a type of measurement is not

accura te . In addi t ion some small inf luence due to Mach number gradients has

been found experimentally. A r e p o r t on such an influence w i l l be made

ava i l ab le later by the FFA group. However such effects are small and do not

a f f ec t t he r e su l t s p re sen ted he re . In o rde r t o ana lyze such e f f ec t s , a

comparison between measured and calculated values was performed fo r t he f ron t

p a r t of t he model t h a t is a x i a l l y symmetric. The ca lcu la t ions performed by

means of a numerical program based on a three-dimensional character is t ic

ana lys i s is as accura te as the numerical approximation. The comparison

t h a t w i l l be presented later, ind ica tes tha t the es t imated va lue o f the

e r r o r f o r and 0 is larger than the maximum di f fe rences found between the

measured and ca lcu la ted va lues .

The def in i t ion o f the angles 0 and 8 , the support of the model, and the

dimensions and point for rotation of the model are shown schemat ica l ly in

Fig. 2. The angles 0 and were measured by means of a probe as shown i n

Fig. 3.

IV. Descript ion of the Model

In references 3 and 4, configurat ions have been invest igated that

10

. - "

according to approximate analyses should produce sonic booms much lower than

present conf igura t ions for equiva len t condi t ions o f f l igh t . In o rder to

determine the val idi ty of such conclusions, and i n p a r a l l e l to experiments

with the more accurate experimental techniques, one of these configurat ions

has been selected for the tests. The conf igura t ion se lec ted is shovm i n

Fig. 4 , where the dimensions correspond to the model t e s t ed . The wing i s

swept back a t 72'. The wing p ro f i l e has 2% thickness and is a symmetrical

c i r c u l a r arc p r o f i l e . The fuselage shape has a c i r cu la r c ros s s ec t ion ;

detai led dimensions of the fuselage area as a func t ion of the d i s tance are

g iven in Table I.

I n t h e a n a l y s i s it has been assumed that the fuselage is sharp a t t h e

f ron t and rear t ips ,and that the w ing p ro f i l e i s a l so sha rp a t the t r a i l i n g

and leading edges. The construction of the model had required some modifi-

ca t ion on the wing leading edge and fuselage front t ip, and on the rear p a r t

of the fuselage. The modif icat ion introduced a t the leading edge i s requi red

in o rder to avoid loca l separa t ion . The modif icat ion a t the rear p a r t of the

fuselage is required because of the presence of the support . The support

increases the equiva len t area i n t h e rear p a r t of the vehicle , and there-

f o r e a f f e c t s t h e s o n i c boom because i t changes the f inal value of the equi-

v a l e n t area d i s t r i b u t i o n .

In order to e l iminate such effects , the equivalence between lift and

cross-sec t iona l area has been ut i l ized, and a co r rec t ion on the planform of

the wing has been introduced. The area of the wing has been reduced i n t h e

region where the fuse lage c ross sec t ion is d i f f e r e n t from the design. The

reduct ion of wing area has been ca lcu la ted to ba lance the increase of c ross -

s ec t iona l area from the reduct ion of l i f t and volume f o r a C of the wing

of 0.060, a t M = 2.70.

L

The des ign of t h e model i s shown i n Fig. 5, where the impor t an t d i f f e r -

ences between the model used i n t h e a n a l y s i s and i n t h e tests are shown.

The configuration does not have a v e r t i c a l t a i l because of the advisabi l i ty

of construct ing a simple model. The volume due t o t h e v e r t i c a l t a i l h a s b e e n

included as an equivalent increase in volume of the fuselage. Actual ly , the

v e r t i c a l t a i l increases the equiva len t l ength and is use fu l i n dec reas ing

t h e i n t e n s i t y of t h e rear shock. This effect is not impor tan t for th i s se t

of tests because the main i n t e r e s t is d i r ec t ed t o t he de t e rmina t ion of the

f ron t shock , i n v iew of the d i f f icu l ty o f ob ta in ing representa t ive rneasure-

ments from the rear shock.

The configurat ion selected does not represent a r e a l i s t i c a i r p l a n e

configurat ion. However, t h e t o t a l e q u i v a l e n t area d i s t r i b u t i o n produced by

t h e model t e s t e d a t t h e s e l e c t e d C has been selected from a more r e a l i s t i c

airplane configuration where the requirements of the volume and l i f t d i s t r i -

L'

bution have been selected from prac t ica l conf igura t ions . This conf igura t ion

i s shown i n Fig. 5b. There a r e two reasons for the se lec t ion of the d i f fe ren t

configurat ions shown i n F i g . 5, cor-responding t o t h e same to ta l equiva len t

area. The f i r s t i s of an ana ly t ica l na ture . The conf igura t ion shown i n

Fig. 5b is more complex; therefore , an approximate analysis that takes into

account three-dimensional and n o d i n e a r e f f e c t s is not poss ib le . Then an

i te ra t ion p rocedure would be required, where the wind tunnel i s used a s an

analog machine to s e l ec t accu ra t e ly t he de t a i l s o f t he con f igu ra t ion t ha t

12

correspond to t he equ iva len t a r ea s e l ec t ed . The second i s of an experimental

nature; a minimum fuselage diameter was imposed by the balance. This required

a reduct ion of t h e wing thickness and in increase o f fuse lage volume.

Once a configurat ion has been obtained that g ives luw sonic boom, c r i t e r i a

are ava i lab le to in t roduce changes tha t permi t se lec t ing an equiva len t p rac t ica l

conf igura t ion similar t o t h e c o n f i g u r a t i o n shown i n Fig. 5b.

V. Possibi l i ty of Obtaining Information on t h e Rear Shock from Wind Tunnel

Tests

The measurements i n a wind tunnel of t h e r e a r shock produced by a model

of t h i s t ype are not ind ica t ive of t he ac tua l phenomena because of the lack

of s imi la r i ty . The p resence o f t he s t i ng , t he d i f f e rence i n t he s i ze of t h e

wake, and the l ack of representa t ion of the engine je ts in t roduce severe

e r ro r s i n t he i n t ens i ty o f t he r ea r shock . The engines p roduce je t s tha t mix

wi th the ou ts idef low producing a displacement thickness equivalent to sub-

s tan t ia l a rea changes . F igure 6 i nd ica t e s t he equ iva len t a r ea va r i a t ion due

t o t h e j e t downstream of one of the engines for an SST configuration which has

four General Electric engines fully expanded. The to t a l equ iva len t c ros s -

s ec t iona l a r ea fo r a complete a i rplane a t cruise i s of the order of 800 f t . The d i f f e rence between f l i gh t cond i t ions and tunne l cond i t ions i n wake d i s -

2

placement thickness produces effects of, the same order . These effects can

be inc luded in the ana lys i s and have been included i n t h e r e s u l t s p r e s e n t e d

i n r e f e r e n c e 4 ; however , t hey a r e d i f f i cu l t t o s imu la t e i n sma l l s ca l e ex-

periments of the type descr ibed here , and require a more complex research

program than i s requi red for the measurements of the front shock.

V I . Resul ts of the Analysis

The configurat ion presented has been analyzed for f l ight condi t ions

a t c ru ise for an a i rp lane having a length of 300 f t i n f u l l s c a l e . An

airplane of this dimension has 10,000 f t of wing area. The volume of t h e

fuselage i s 44,000 f t 3 , w h i l e t h e wing span i s 58.8 f t and t h e wing

volume 10,000 f t .

2

3

The ana lys i s o f the sonic boom has been performed for the conditions

co r re spond ing a t c ru i se a t 60,000 f t , M = 2.70 , and to ta l weight equa l to

460,000 l b s . The analysis has been performed following the method out l ined

by Carlson , which transforms the l i f t i n an equivalent area. The l i f t has

been determined by means of l inear theory wi th some approximate second

4

order cor rec t ions . The ex t r apo la t ion of s i g n a t u r e t o ground level has been

performed by means of the var iab le dens i ty program developed in re fe rence 15 .

Figure 7 i nd ica t e s t he con t r ibu t ion of t he equ iva len t a r ea d i s t r ibu t ion of

t h e d i f f e r e n t components. Table 1 gives the same information. The sonic

boom signature obtained from the ana lys i s i s shown i n F i g . 8 where four

meridian planes are considered. The cut-off angle i s around 60 . For 0

comparison, the constant pressure analysis for average pressure equal to:

- - 'average 7 / 'sea l e v e l '60,000 f t '

has also been performed. The r e s u l t s a r e shown i n F i g . 9 where t h e r e f l e c -

t i o n c o e f f i c i e n t K i s equa l t o 1 .8 . The ana lys i s i nd ica t ed t ha t t he f ron t

14

shock for the weight assumed i s of the order of 0.94. The ground r e f l e c t i o n

c o e f f i c i e n t u s e d i n t h e a n a l y s i s is 1.8. The area curve corresponding to

the sonic boom in F ig . 8 , i s a smooth curve corresponding to sharp leading

edges f o r t h e wing. The wing of the actual model produces a detached shock

because the leading edge has been rounded. Therefore, some pe r tu rba t ions i n

the equivalent area d i s t r i b u t i o n w i l l be produced by t h i s change. It is

d i f f i c u l t t o p r e d i c t t h e a c t u a l i n t e n s i t y o f t h e s e p e r t u r b a t i o n s ; however,

t he qua l i t a t ive t r end o f t he e f f ec t s o f such d i s tu rbances can be p red ic t ed .

The round leading edge w i l l produce i n i t i a l l y s t r o n g e r p r e s s u r e rises than

the sharp leading edge followed by an overexpansion. This i s equiva len t to

a more rap id increase of the var ia t ion o f the c ross -sec t iona l a rea in the

region where the wing s tar ts followed by a more gradual var ia t ion . The wing

starts roughly a t 50% of the length. The var ia t ions of the type of curves

ind ica t ed i n a and b of Fig. 10 can be expected. The sonic boom s igna tu re

for these two dis t r ibu t ions has been ca lcu la ted . The r e s u l t s i n d i c a t e t h a t

t hese l oca l small per turbat ions tend to produce s ignatures that have two

shocks of about the same in t ens i ty , F ig . 11.

The calculat ions have been performed ini t ia l ly for a weight of 460,000

l b s , a t M = 2.70 . The experiments have been performed a t M = 2 . 7 2 , and a

C = 0.055, and CL = 0.066 corresponding to the angle 2.6' and 3.2'. These

condi t ions would correspond to a to ta l a i rp lane weight o f 430,000 lbs and

520,000 lbs . Then the condi t ion of C = 0.055 i s close to the design con- L

d i t i o n s . The sonic boom for these two condi t ions has been calculated and

is shown in F ig . 12. The e f f e c t s of small loca l per turba t ions as shown

L

i n F i g . 13 are also indicated.

VII. Review of the Experimental Data

The experimental data made a v a i l a b l e f o r t h e a n a l y s i s are presented i n

Figs . 14 to 19. Figure 14 presents the measured values OE E: a t r / L = 0.271

f o r d i f f e r e n t v a l u e s of 0 , while Fig. 15 presents the va lues o f 0 f o r t h e

condi t ions. Figures 16 and 17 present the same q u a n t i t i e s f o r t h e d i s t a n c e

r / L = 0.558. For several values of 0 , measurements are a v a i l a b l e f o r more

than one pos i t i on o f t he model a long the ax is o f the tunnel . F igures 18 and

19 present the resu l t s for 0 = 0 and r / L = 0,272 and 0.558 f o r t h e d i f f e r e n t

pos i t i ons . The f igu re i nd ica t e s t ha t t he change o f pos i t i on does no t a f f ec t

the exper imenta l resu l t s , g iv ing an ind ica t ion of the un i formi ty o f the f low.

S i m i l a r configurat ions on 0 and a t the two d i s t ances bu t fo r a = 3.2 are

given in Figs . 20, 21, 22, 23. A s shown in t he f i gu res , t he d i s tu rbances a t

" r - L

0.558 and a = 2.6O are extremely small; therefore , here l inear theory

a p p l i e s f o r t h i s case.

In add i t ion , Sch l i e ren p i c tu re s are a v a i l a b l e f o r a l l of these con-

d i t i ons . F igu res 24a and 24b give the Schlieren photographs a t ? = 0 and

= 90, for a = 2.6 , and Figs. 25a and 25b f o r a = 3.2O. The photographs 0

permit us t o l oca t e accu ra t e ly t he pos i t i on o f t he shocks , and t he re fo re

h e l p i n t h e i n t e r p r e t a t i o n o f t h e e x p e r i m e n t a l r e s u l t s .

VIII. Corrections Introduced on t h e E and J u s t i f i c a t k o n f o r t h e o r r e c t i o n s

The probe that measures the angles and 0 has a diameter of 3 mm and

has a spher ica l nose . The probe produces a shock and the f low region down-

s t ream of the shock near the or i f ices is subsonic. The ca l ib ra t ion o f t he

probe i s based on the assumption that the f low in f ront of the shock i s

16

fa i r ly un i form and the ang le is determined on the b a s i s o f the assumption that

a small i n c l i n a t i o n o f the flow d i r e c t i o n w i t h the axis of the probe corres-

ponds t o the e q u a l r o t a t i o n of the pressure d i s t r ibu t ion a round the axis of

the probe. This assumption is correct everywhere i f the f l o w is continuous

because the probe is small . However, the s i t u a t i o n changes when an ex te rna l

shock interferes w i t h shock of the probe i n the subsonic region. Consider

Fig. 26 uhere the probe and the shock i n t he ex t e rna l f l ow are represented

schematkally. In t e r f e rence w i th t he ca l ib ra t ion starts when the probe i s

behind the external shock, i n p o s i t i o n a, and cont inues un t i l the Drobe has

crossed the shock and is a t pos i t i on b..

Experiments have been performed where t h i s phenomenon has been in- 16

vesfkgated a t h igher Mach number. In Fig. 27 taken from reference 16, the

e€fects on the pres su re d i s t r ibu t ion d,ue t o t h e i n t e r a c t i o n are shown. The

wartation of pres , sure d i s t r ib ,u t ion , due to the i n t e r a c t i o n when the sphere

is in frmt o f the ex te rna l shock is very l a rge (case c of F ig . 27). In

this case i f the p r e s s u r e d i s t r i b u t i o n is used to determine angles on t h e

basis of a uniform fLar calibration, then the measurement would i n d i c a t e

i n c o r r e c t l y that a Large flow devia t iou exists i n f r o n t of the probe. *en

the sphere is behind the external shock, then the interference produces an

opposi te effect, decreasing the va lue o f the actual devia t ion . Because of

t hese effects, the po in t s measured i n the v i c i n i t y o f the shocks have been

discounted and the diagram shown in F ig . 28 has been used for the analysis.

In th i s d iagram the pos i t ion of the shocks have been determined very accu-

r a t e l y from the Schl ie ren p ic tures . The peak deviation behind the shock

has been obtained from the measurements of the shock incl inat ion, and the i

",. . ,. , , . . , ,. , . , , , , . ,. . . . ._ , .. ... .... .._ .. .. , . . .. - ._ "_

f low p rope r t i e s i n f ron t o f the shock.

In Figs. 29 and 30, t he va lue o f e calculated by means of three-

d imens iona l cha rac t e r i s t i c s are shown, and compared with the experimental

da t a . The d i f f e r e n c e s are extremely small and can be due e i ther to small

differences in geometry between the model and the shape used for the cal-

culat ion or to measurements or calculat ion accuracy. Because the da ta o f

the sets of tests agree wel l , t he f i r s t a s sumpt ion seems t o be more probable

In order to determine the importance of some o f t he de t a i l s o f t he

p re s su re d i s t r ibu t ion , two a l t e rna te cu rves , 1 and 2 of Fig. 28 have been

used i n t h e a n a l y s i s . Curve 1 considers only one shock, while curve 2 con-

s iders the ex is tence o f two shocks. The second shock is produced by the

discont inui ty in s lope between fuselage and support .

I X . Descr ip t ion of the Method of Analysis Used - The method used €or the ana lys i s has been descr ibed in re fe rence 1 and

has been developed by M. Landahl, I. Ryhming, H. Sorensen, and G . Drougge of

the Aeronaut ica l Research Ins t i tu te o f Sweden. In o rde r t o s imp l i fy t he

reading of th i s paper , the impor tan t fea tures o f the method are summarized

here by reproducing a sec t ion of the repor t o f re fe rence 1.

According to reference 2 , the per turbat ion veloci ty components a t l a r g e

d is tances from a three-dimensional body in supersonic f low are g iven to

second order by n

where u2, v2¶ w2 are the second-order components r e f e r r e d t o a c y l i n d r i c a l

coordinate system, 8 is the meridian plane angle and r is t h e r a d i a l

d i s t ance from the wind axis I

0 0

x = x - Krov - M ep + K r 2 0 0 ae (4 1

and u, v , w are the corresponding values according to l inear ized theory and

the i r p , s , t en t i a l is q . For large distances the following expansions were

shown to hold :

y = x - B r + k r % F + ( " r ) p - I F p 2 K

00 QO

where k = k 28

The q u a n t i t i e s measured a re the f low def lec t ion angles .e and 0, along l inqs

of cons tan t r bu t i n d i f f e ren t az imutha l p l anes 8 = const . The angle e is

r e l a t e d t o v2 as follows:

-1 v2 = t a n -- l+u2

or s ince u = - v2/p to lowest order 2

v2 = (1 - !L + ... 0

From the ax imutha l def lec t ion angle 0 w e obta in

o r cpe =-cp = = r u

Thus, cp can be determined direct ly from the measurements, and by aid of

numer ica l d i f f e ren t i a t ion o f ate) one can a l so ca l cu la t e cp . From the

measurements of E (x) , cp2 can be determined by numerical integration, since

to the order considered

80

eoeo

r=cons t shock

One can next obtain .v from (2) :

v 3 ( 1 - M u) (1- Ku) v2 1 ( 1 + M2 E) (1 + K E) v2 (16) 2

B B

Furthermore, (5) g ives t ha t

ro - r ( l - - K B e )

We have now the quant i ties needed to ca1.culate F from (7 ) . The Mach l i n e

parameter y and the angle parameter eo, f inal ly , can then be determined from

(11) and (12).

For a n a x i s p e t r i c a l flow f i e l d w is zero as well as 0-der ivat ives .

The measurements and the evaluat ion of the F-funct ion is then s implif ied,

s i n c e i t is only necessary to consider a s ingle azimuthal plane.

X . Application of the Method to the Present Experiments-

The method presented i s an improvement wi th r e spec t t o t he methods

used previously, because i t takes in to account nonl inear e f fec ts which are

impor t an t i n t he nea r f i e ld and because i t in t roduces cor rec t ions for the

near f ie ld e f fec ts due to th ree-d imens iona l phenomena. In applying such a

method to the present experiments, two d i f f e ren t d i f f i cu l t i e s have been

encountered.

The f i r s t d i f f i c u l t y is r e l a t ed t o t he eva lua t ion o f i n equa t ion 7 88

of the analysis , which r equ i r ed d i f f e ren t i a t ion w i th r e spec t t o 0 of the

measured quant i ty 0. Such an operat ion is d i f f i c u l t t o perform accurately,

because small e r r o r s on the measured values of 0 in t roduce var ia t ion o f the

va lue of ep An attempt has been made f i r s t t o p e r f o r m a Four ie r ana lys i s

of a l l the measured values, between 8 = 0 and 90°. However, fo r t he f ron t

part the experimental accuracy is insuf f ic ien t . whi le for the reg ion of the

wing where t h e c o l t r i b u t i o n o f t o t h e f i n a l r e s u l t s h a s s i g n i f i c a n c e ,

t he series does not converge. Therefore, a different approach has been used

88'

88

21

i n t he ana lys i s . I n t he r eg ion o f t he wing the values of 0 between 0 a n d '

30° have been plotted as a funct ion of 8, and a curve has been drawn connect-

ing the experimental points . Then the value of &/ae a t y = 0 has been

obtained from the curve. For the region where the model has ax i a l symmetry,

the values of aJ/ae given by the analysis have been used. The cont r ibu t ion

Of q e e t o t h e F func t ion i n t h i s r eg ion is negligible. Therefore such an

approach is j u s t i f i e d . However the contr ibut ion of the term is important

i n t he r eg ion o f t he wing indicating the importance of the three-dimensional

e f f e c t s .

The second problem encountered in the determinat ion of the F funct ion

i s r e l a t e d t o t h e e x i s t e n c e of double values of the P funct ion due e i t h e r

to the three-dimensional effects or to rapid expansions (corners) a t the

surface of the body.7 This effect i s due t o t h e f a c t t h a t t h e F funct ion

is ca lcu la ted a t t h e a x i s and can be unders tood c lear ly i f a s i m p l e configura-

t i o n i s analyzed. Consider, as an example, a cone cylinder a t zero angle of

a t t ack . A t the expansion corner, a family of expansion waves i s produced.

Fig. 31. I f these expansion waves a re ex t rapola ted to the ax is , then two

s e t s of values corresponding to the same y for the F func t ion in the reg ion

AB of the f igure . S i m i l a r e f f e c t s e x i s t when the model is three-dimensional.

Then waves generated from di f fe ren t po in ts o f the model a t d i f f e r e n t r reach

the same point in the meridian plane analyzed. In order to obtain some

c r i t e r i o n f o r t h e s o l u t i o n o f t h i s d i f f i c u l t y , a de ta i led ana lys i s has been

performed for the case of the cone cyl inder of Fig. 31 for the case, the

a c t u a l stream dev ia t ion E: a t severa l va lues o f r can be numerically obtained

by means of the method o f cha rac t e r i s t i c s . Then i t is poss ib l e t o de t e r -

22

mine the F function that corresponds to the e d i s t r ibu t ion ob ta ined a t some

dis tance from t h e a x i s , and compare wi th the F d i s t r ibu t ion ob ta ined by in-

t roducing the discont inui ty . Such ana lys i s ind ica tes tha t the double va lue

should be eliminated by adding and subtract ing equal areas i n F on the

Mach wave from the corner as discussed in reference 7 , (see Fig . 31) , in

the region where mul t ip le va lues exist. The F function obtained from the

da ta is shown in F ig . 32. Figure 33 shows the F funct ion used in the analy-

sis. The same method of analysis has been used for the data a t r / L = 0.271,

and fo r a = 3.2 . The F funct ion obtained from the data a t 0.558 has been

used t o obtain the sonic boom corresponding to an a i rp lane 300 f t long f ly ing

a t 60,000 f t , f o r t h e C of 0.055 which corresponds to a total weight of

430,000 lbs . Figure 34 gives the sonic boom shape obtained from the F

funct ion by u s h g t h e v a r i a b l e p r e s s u r e program, and Fig. 35 the same re-

su l t s ob ta ined by using constant pressure program corresponding to the

square root of the two values a t t h e f l i g h t and ground l eve l . The ampl i f i -

cat ion due to the ref lect ion of the ground i s assumed to be equal to 1.8

the incoming s i g n a l , and is included in the values presented. In order to

determine the importance of the three-dimensional and nonl inear e f fec ts ,

the calculations have been repeated, by apply ing d i rec t ly the Whitham theory

to determine the F funct ion, and neglect ing a l l the higher order terms,

curve a and only the three-dimensional effects (q ) curve b. Figure 36

shows the sonic boom obtained, w!len these quan t i t i e s are neglected. The

0

L

80

f igure ind ica tes tha t the th ree-d imens iona l e f fec ts are important a t least

when r / L is small. A similar calculation has been performed for the data a t

a = 2.6 and r / L = 0.271. me two d i s t r i b u t i o n s f o r t h e a n a l y s i s are as 0

I1 I I 111 I

shown i n F i g . 37. The r e su l t s ob ta ined are shown i n Fig. 38. They are very

similar t o t h e r e s u l t s of Fig. 35. The pos i t i on of the second shock is

d i f f e r e n t . The same analysis has been performed for the data corresponding to

a = 3.2'. This condi t ion corresponds to a v e h i c l e that has a length of

300 ft, weight of 530,000 lbs, f lying at an altitude of f l i ght of 60,000 ft.

The r e s u l t s are shown i n F i g s . 39, 4 0 , and 41. Figure 39 gives the d i s t r ibu-

t i o n of E a t r / L = 0.558 used in t he ana lys i s . F igu re 40 g ives t he F func t ion

ca lcu la ted and the curve used af ter being corrected by el iminat ing the double

value, and Fig. 41 gives the shape of t he son ic boom derived from the F funct ion.

X I . Conclusions

The experimental invest igat ion performed pe rmi t s us t o reach the fol lowing

conclusions :

1. Sonic booms having peak values of the order of 1 l b / f t 2 as

p red ic t ed ana ly t i ca l ly i n r e f e rence 3 have been measured. The son ic

booms obta ined have near f ie ld s igna tures as p red ic t ed i n r e f e rence 3

f o r c r u i s e c o n d i t i o n s and in r e f e rence17 fo r t he acce le ra t ion phase .

The d i s t r i b u t i o n of equivalent cross-sect ional area tes ted corresponds

t o an a i rp lane shape tha t has the volume, l eng th , and l i f t r equ i r emen t s

of a p rac t i ca l a i rp l ane conf igu ra t ion ; however, s u b s t a n t i a l a d d i t i o n a l

work is r e q u i r e d t o i n v e s t i g a t e i f a l l other aerodynamic requirements

r e l a t e d t o a p r a c t i c a l c o n f i g u r a t i o n can be m e t .

2. The nonlinear and three-dimensional effects are of primary importance

for the de te rmina t ion of the cor rec t va lues o f the sonic boom from

measurements a t small d is tances from t h e model.

3. More complex experimental techniques where such effects are determined

24

are required when near field measurements are made as recummended in

references 1 and 12.

4 . The experimental method proposed in reference 1 gives satisfactory

results.

5. Improvements are still required in the experimental techniquzs

and in the analysis in order to measure and determine with better

accuracy all of the required quantities.

1. Landahl, M., Ryhming, I . , Sorensen, H., and Drougge, G. : It A New Method for Determining Sonic Boom Strength from Near-Field Measurements." NASA Third Conference on Sonic Boom'Research, NASA SP-255, October 1970, pp. 285- 295

2a. Landahl, M., Ryhming, I . , and Hilding, L. : "Nonlinear Effects on Sonic Boom In tens i ty ." NASA Second Conference on Sonic Boom Research, NASA SP-180, May 1968, pp. 117-124.

3, F e r r i , A. and Ismail, A. : "Report on Sonic Boom Studies - P a r t I - Analysis of Configurations." NASA Second Conference on Sonic Boom Research, NASA SP-180, May 1968, pp. 73-88.

4. Ferri, A. : "Pract ical Aspects of Sonic Boom Problems." NYU Report AA-70-22, September, 1970, and presented a t 7 t h I C A S Congress, Rome, I t a l y , September, 1970. Also presented a t NASA Third Conference on Sonic Boom Research, NASA SP-255, October 1970, under t i t l e "Airplane Configurations for LOW Sonic Boom," pp. 255-275.

5 . Whi tha , G.B. : "The Flow P a t t e r n of a Supersonic Project i le ." Corn. Pure Appl. Math., 5:301-48, 1952.

6 . Whitham, G.R.: "on the Propagation of Weak Shock Waves." J. Fluid Me&. 1:290-318 .

7 . L i g h t h i l l , M. J. : "Higher Approximations i n Aerodynamic Theory." Princeton Universi ty Press , 1960.

8. Hayes, W.D.: "Linearized Supersonic F l o w . " Ph.D. t h e s i s , C a l i f o r n i a I n s t i t u t e of Technology, microfiche available, North American Aviat ion, Inc. , Aerophysics Lab., Rep. AL-222. Reprinted, Princeton University Aerospace Mech. Sc i . Rep. 852.

9. Carlson, Harry W. : "An Inves t iga t ion of Some Aspects of the Sonic Boom by Means of Wind Tunnel Measurements of Pressureabout Several Bodies at a Mach Number of 2.01." NASA TN D-161, 1959.

10. Carlson, Harry W . : "An Inves t iga t ion of the Inf luence o f L i f t on Sonic Boom In tens i ty by Means of Wind Tunnel Measurements of the Pressure Fields of Several Wing-Body Combinations a t Mach Number of 2.01." NASA TN D-881, 1961.

11. Hicks, R . , Medoza, J. : "Predict ion of Aircraf t Sonic Boom Charac te r i s t i c s from Experimental Near Field Resul ts ." NASA TM X-1477, 1967.

12. Ferri,A. and Wang, Huai-Chu: "Observations on Problems Related t o Experimental Determination of Sonic Boom." NASA Third Conference on Sonic Boom Research, NASA SP - 255, October 1970, pp. 277-284.

27

13. Walkden, F.: "The Shock P a t t e r n -of a Wing-3ody Combination Far From t h e Flight path." Aeronaut. Quart. 9:164-94, 1958.

14. Carlson, H.W.: "The Lower Bound of At ta inable Sonic Boom Over-pressure and Design Methods of Approaching This Limit ." NASA TN D-1494,October 1962.

15. Hayes, W.D., Haefe l i , R.C., and Kulsrud, H.E.: "Sonic Boom Propagation i n a S t r a t i f i e d Atmosphere wi th Computer Program." NASA CR-1299, 1969.

5

16, Edney, B. : "Anomalous Heat Transfer and Pressure Dis t r ibu t ions on Blunt Bodies a t Hypersonic Speeds in the Presence of an Impinging Shock." The Aeronaut ical Research Inst i tute of Sweden, FFA Report 115, February 1968.

Large Airplanes." NASA TN D-2877, June 1965. 17. McLean, Edward F.: "Some Nonasymptotic Effects on the Sonic Boom of

28

L

Table 1

STATION

XIFTI

. 0 0 O O O 5.00000 10.00000

20.00u00 15.00000

~.."

25mOUOOO 30.0U000

40.00000 35.00000

95.00000 5U.UOOOO

65.00000 60.00U00

7S.OU000 70.00000

no.ooooo

90.00000 85.00UOO

100.00000 95.00000

105.00000 Ilo.ouooo 115.00000

125.0000C 120.00000

130.00000 135.00000 140.00000

s5.onooo

145.0Cl000 150.00000 155.00000 160~00000 165.00000 170.00000 175.00000 180.0U000

190.00000 18s.00000

195.00000 200.00000 205.00000 210.00000 215.00000 220.00000

225.00UOO

235.00000 230.00000

240.00000 24s.00000 250.00000 255.0UOOO 2b0.00000 265.00000

275.00000 270.00000

280.00000 285.00U00

295.00000 290.OU000

300.00

FUSELAM RADlUS RIFT1

.00000 1.03617 1 -6W82 2.15532 2.61099 3.02978

3.7?16b 3.42136

4.16468 4.98325 9.80998 5.12499 5.43107 5.72875 6.01889 6.30099 be57290 6.83722 7.09435 7.39506 7.58997 7.82964 8.06452 8.29503

8.74431 8.95296 9.13796 9.30072

9.56392 9.44239

9.66600 9.72976 9.74122 9.70294 9.61763 9.48824 9.31796 8.11026 8.86890

8.30156 7.98447 7.65147 7.30760

n.52152

8.59789

EQUIV.AREA AREA TOTAL FySCLAOE WIN8 AREA FUSELAK LIFT DUE TO LIFT WE TO LIFT DUE TO YOOEL SCALE

*WIN6 FUSELAGE 11W AE ~FlS0.Fl.l AW(5o.CT.l AFYISO.CT.I XLEF XLLl

3.55690 .ooooo

8.96156

22.58173 15.58765

50.90679 38.776W 97*622a3 56.90259 66.57898

87.00208 76.62030

108.70971 97.70596

120.00000 131.991n9 143.10721

166.71955 159.84836

178.70578 190.82203 203.06332 215.42965

240.53740 253.278R2 266.19518 279.13678

227.921n1

292.25330 305.49407 318.86146 332.353n8 345.96975 359.71144 373.57817 317.569.4

415.92857 401.68673

430.29543 444.78733 459.40426 479 - 14622 504.00526 519.12233

489.013a3

6.95810 534.36493

6.26364 565.22373 5.92921 580.84093 5.60980 596.58317 5.30930 612.45099 S.03033 628.44279 4.77345 644.56007 4.53641 660.80244

4.09148 693.66228 9.31300 677.16985

3.55963 727.02227 3.851e1 710.27976

2.96332 760.88238 3.1eqen 793.8e9n1

0.0 110.00

b.6on33 5~9.73156

.00000 3.37297 8.49935

21.61702 16.59199

28.8389I 36.77455 95.16510 53.96750 63,14952 72.66891

02.66605 02.51557

103.10272 113.81069 129.70909 135.72608 146.86166

169.48857

___"~ .~

15e.11582

180.97989 192.58981 204.31830 216.16539 228.13106 240.21531 251.81580 262.35020 271.75848 280.10065

293.52362

298.11031 297.40892

295.77173 290.59351

272.76670 2h0.74239 247.10927 232.23829 216.50557 200.28223 183.92436 167.76402

28r.35672

28z.nz697

.DO000

.ooooo

.ooooo

.00000

.ooooo

.ooooo

.ooooo .00000

.ooooo

.ooooo

.00000

.ooooo

.ooooo

.00000

.ooooo

.00000

.ooooo

.ooooo

.ooooo

.ooooo

.00000

.ooooo

.00000

.ooooo

.ooooo

.00000

.ooooo

.ooooo

.ooooo

.ooooo

.00000

1.26696 .00322

4.74267 10.27847

26.63158 17.66309

36.87343 48.04102 59.75972 71.63831

94.29967 83.28049

112.96305 104.30555

152.10056 119.95144

123.25469 127.87677 137.19335 122.99733

110.44454 128.42117 90.86529 126..52257 88.55741 122.13829 79.99594 115.29517 71.58379 106.09901 64.65091 99.71567

52.59094 66.61950 58.93982 81.93113

96.61008 50.80186 39.80701 39.70598 31.17009 19.39856 19.06296 6.60478

0.0 0.0

1.37297 .00000

8.69955 14.593W 21.41702 28.85868

*5.16%0 366.77655

53.%750 63.16652 72-6-61 82.51157 92.66605 103.10272

121.70909 113.81069

135.72608

158.11582 146.86166

169.48857 180.91989 192.58981 204.31830 216.16539 228.13106 240.21531 251.81580 262.33020 271.75848 280.10065 287.35672 293.52685 298.67588 302.85298 3U6.05019 308.25655 309.45855 309.64013 308.78337 306.86899

299.78601 303.87659

294.57690 288.22991 280.72706

272.05199 262 m 19067 251.13196 238.86571

210.69570 225.38786

199.79061 177.67780 159.36658 139.87099 119.21049 97.61195 74.51299

25.66774 50.56860

0.0

.00000

.e6222

.I8393

,79366 1 16971 1.56831 1.99989 2.95623 2.93989 3.433% 3.95189 6.68790 5.03991 5.60698

6.78199 6.18931

7.38112 7.98670 8.59873 9.21721

10.97351 9.84219

11.75561 12.90633 13.06351 13.69437 14.26617 14. 77890 1.5.23257 15.62717 15.96255

16.21198 16.08980 15.80320 15.38083

19.17982 14.83373

12.62970 13.43842

11.77411 10.89185 10.00226 9.12342

11.11134

16.1730~

8.27161

6.70290 7.96092

6.00625 5.37659 9.81597 4.32316 3.89290 3.51588

2.06003 3.17810

2.16480 2.53477

1.69510 1.03669 0.0

.00000

.00000 .00000 .00000 .00000 .OOOOO .00000 .00000 .00000 .00000 .00000 .00000 .ooooo .00000 .00000 .ooooo .00000

.ooooo

.00000

.00000

.000OO

.00000

.ooooo

.00000

.00000

.00000 -63510

2.54041 5.71592 10.16163

22.86367 15.87755

31.12000 40.64653

b3.51020 51.49326

76.84735 91.45469 107.33224 129.48000 142.89796 162.58612 185.59449 205.77306 229.27183

254.09081 280.07999 307.38939 335.96898 365.81877

929.32898 462.98938 497.91999

571.59183 534.12081

650.39998 610.33305

691 m626ll 736.17795

396.93877

na .00

.00000

.9622?

.I8393

-79566 1.16471 1.56831

2.*5623 I .9W89

2.93U89 3.45396 3.95189

5.60698 5.03941

6.78199 6.18931

7.38112

8.59873 7.98670

9.21721

10.97351 9.84214

11.11134 1 I .'75561 12.40633 13.06351 14.32947 16.80658 20.49482 25.39420 31.50472 38.82622 97.29364 56.85851 67.52807 79.31340 92.22818 106.28842 121.51206 137.91842 155.52765 179.36023 199.U3633 215,77532 238.39526

6.9874n

.000

-361 .I81

-562 -723 -903

1.089 1.265 I .e45 1.626 I a807 1.987

2.349 2.168

2.529 2.710 2.891

3 252 3.071

3.433 3.613 3.794

4.155 3.975

4.336 4.517 4 .697

5.059 4.878

5.239 5.420 5.601

5.962 6.143 6.323 6.509

6.065 6.685

7.046 7.227 7.407 7.588 7.769 7.949

5.7~1

.noo

,059

,1394

-037

-078

.109 I24

,137 .150'

.174

. I62

.185 a196 -207 ~217 .22n .23n .297 -256 -265 -274 .P83

.300

.201

-316 .324

-336 ,330

,341 a346 .349

-352 .352

..?Is1 .348 .343

-329 .337

.320

.311

.300

-2.76 . 2hU

. m e

.2n9

25

262.31292 8.130 -251 287.54091 8.311 -239 319.09228 8.491 a226 341.97522 8.672 a219 371.19531 8.853 m203 401.75479 9.033 -192

966.88229 9.395 e172

537.29891 9.756 -156 501.93587 9.575 ,164

574.45185 9.937 - 1 4 8 612.86782 10.117 -139

693.32121 10.979 -114

778.00 735.21964 10.659 -089

10.840 0.0

433.65213 9.219 .in2

652.50928 10.290 .129

W 0

t ransducer 50 psia 7- / transducer 15 p s , I-

w. Schematical view of test set-up.

. "

\ I Probe center l ine

V VI

d = 3 rnrn 4=6 mm I 7 " t " I

t

c "

B-8 C-C

Fig. 3 Design of yaw probe

W w

Fig. 4 Design of airplane configcration

W c

10.840' ( 2 7 5 . 4 m m )

I -" I

-r I I I \MODEL LEADING

E W E

Fig . 5a Moael design

MEAN WING CHORD (1=2.4"

- \, APPARENT I 2 . 5 O

- .-.

." SOURCE LINE

-\ 1

0 40 80 I20 I60 200 240 280 320 360

W Ln

Fig. 5b Airplane configuration corresponding to the area

distribution of the model of Fig. 4

Fig. 6 Variation of Total Equivalent Area Due to the Jet Exhaust of an engine a s a Function of Distance from the Exit of the Jet.

X (FT)

Fig. 7 Equivalent area distribution

Fig. 8 Sonic boom signature L = 300 ft, h = 60,000 ft, w = 460,000 lb, M = 2.70 var iab le p ressure program

Lor" L B.IF T'

I \

-200 -loo O L

IO0 -9

500 600 700

, . . . - . . . 1

0 I(

I " MODIFIED CURVE b

3 200 FT

Fig. 10 Perturbation of the area distribution curve M = 2.70, w 460,000, h = 60,000 L = 300

F t

Fig. 11 Sonic Boom Signature Corresponding to Area Curve B of Fig. 10

A P ( L B / F T ~ ) 1.2,

FT '\\

-Ob4 t Fig. 12 Sonic boom s i g n a t u r e a t M = 2.718 L = 300 ft, h = 60,000 ft, W 1 = 430,000 l b & = 0.055)

w2 = 516.000 l b , ( 6 = 0 .066)

7cx)

600

500

400

FT'

300

20c

IO0

0

- C U R E a

CURVE b -" -

0 5 0 1 0 0 I5 0 200 250 300 350

FT

Fig . 13 Varia t ion of equivalent area dis t r ibut ion corresponding to curve c of Fig. 1 2

43

175 225 275 325 375 425 475 525 X(mm)

Fig. 14a Experimental values of as function of distance 44 at s evera l meridian planes r/Lo = 0.271 a = 2.6'

175 225 275 325 37 5 425 475 525

x (mm)

45 Fig . 14b Continued

46

a

+E

P

!E

I

r / L o = 0 . 2 7 1

= = 2.60 I

,

0

0

0

0

A

A I

A

A I

* aa

Q

175 225 275 3 25 37 5 425 415 525 X ( m m )

Fig. 14c Continued

I .-

A h A A A

I75 225 275 325 3 75 42s 475 52 5

x ( m m )

47 Fig. 14d Continued

t' - E

r/Lo = 0.2 I 0 = 2.60

3 ~ Q Q G

I

0

e

1 0

1

0 Q

R

Q

0

0

I Q T Q"

"

I7 5 225 2 75 325 315 4 25 47s 5 25

X (mm)

48 Fig. 14e Continued

175 225 '\ 275 ses 375 425 415 525

X (mm) Fig. 14f C O U t i l l U e d

49

. ..

Q

Q

0

4

Q

"- A€ =0.5*

G

Q

0

O Q

t

175 2 25 2 75 325 375 425 47 5 525

X ( m m l Fig. 14g Continued

A 6= O S o

175 225 275 325 375 4 25 475 525

X (mm) Fig. 15a Experimental values of ,, as function of distance at several meridian planes

51

El E l f 3

0 0 1

0

0 I

t 0

17 5 2 25 27 5 325 37 5 425 475 525

x (mm)

52 Fig. 15b Continued

I

I "b

I75 2 25 275 325 3fS 425 415 525

X (mm)

Fig. 15c Continued

53

i T

I

r/Lo=0.558 I =2.6O

7" 4"""

0

0

0

0 0

9

+ 4-

v c

7 v

vv " 9 A m v

V v

v

350 400 450 500 550 600 650 700

X (mm) Fig. 16a Experimental values 05 e as function of distance at several meridian planes

r / L o = 0.558, a = 2.6

54

Q "

m

A

f.. -2

.

" O Q O C

" & . c l 1

400 4 0 600 650

Fig. 16b Continued 55

*A

vV

I

V

350 400 450 so0 550 600 650 700

Xtrnrn)

Fig. 16c Continued

56

0

B

A ". -

A r

Lo ~ 0 . 5 5 8

=2.60 I

-A AA

f

0

Q

0

A

A A

A

350 400 450 SO0 550 600 650 100

X (mm)

I . "

F i g . 16d Continued

57

r/Lo =0.558 a =2.6

350 400 450 500 550 600 650 700

X ( m d

Fig. 16e Continued

58

350 400 450 500 550 600 6 50

N m m )

F i g . 16f Continued

r/Lo=0.558 a= 2.6.

350 400 450 500 550 600 650 700

x m m 1

60 Fig. 17a Experimental values of Gas function of distance at several meridian planes

r /Lo =0.558 I f 1 a = 2.6. I A Q= 0.So

1 350 400 450 600 5 5 0 600 650 700

X (mm) 61

Fig. 17b Continued

35 0 400 450 500 5 5 0 600 650 700 X(mm 1

Fig. 17c Continued

62

1.6,

1.2,

E" .8

.4

0

- .4

- .0

% ? X

t x %

0 x

0 . Jt

0 b

x b

e*

? X 0

c 0 e X

PA X

I I I . O - X(mm) I

I I

125 225 03 25 425 525 0

K

0 s 1

0

Fig. 18 Distribution of deviation angle 6 at = 0.271, c = 0 . 0 5 5 ( ~ = 2 . 6 >, for different 0

Lo n

longitudinal locations of the model

- .0 1 Fig. 19 Distribution of E for different longitudinal location of the model - = 0.558 a = 2.6' r

Lo

r/Lo 0.271

I

0

W

C h 0

A A

A A m

br A

- m *

a

t A ae 80.5. I

I75 225 275 325 375 425 475 525

N m m ) Fig . 20a Experimental values of t as function of distance at several meridian planes

a - 3.2O, r/Lo = 0.271 65

e

, , . . . . .. ".

I75 225 275 325 375 425 475 525 X(mrn1

Fig . 20b Continued

66

175 225 275 325 375 425 475 525

x (mm)

67 Fig. 20c Continued

I I A l A l ?/LO =0.271 z = 3.2O Ar=0.5°

175 225 215 325 375 425 475 525

H m m ) Fig. 20d Continued

175 225 275 325 A375 425 415 525

Nmm 1 F i g . 20e Continued

r/Lo =O. 2i a = 3.Z0(FOR 8 ~ 7 5 ~ ) 083.1 (FOR 8. 80°)

I

I75 225 275 325 375 425 475 525

X (mm) m 8

Fig. 20f Continued

70

175 225

F i g . 20g Continued

Q

175 e25 275 325 375 425 47 6 52s X (mm)

Fig.2la Experimental values of (3 as function of distance at several meridian planes

I

I75 2 25 21 5 325 375 425 475 525 X(mn)

Fig. 21b Continued 73

175 225 276 325 375 425 476 525 X(mm)

Fig. 21c Continued

74

I

350 400 450 500 550 600 65 0 too x (mn)

Fig. 22a Experimental values of e as function of distance 75 at several merMian planes

I

t "r"

35 0 400 450 500 550 600 6 5 0 700 x (m)

Fig. 22b Continued

I

350 400 450 SO0 550 600 650 100 x (m)

Fig. 22c Continued

77

0

E)

Ad +€ t -€

V

I " 4

350 400 450 500 550 600 650 700 X h m 1

Fig. 22d Continued

e o e e o 0

0 0 '1

0

@

B

A

A

3 SO 400 450 600 550 600 660 100 X(mn 1

Fig. 22e Continued

73

I I II I I II

350 400 450 500 550 600 650 700

X (mm 1 Fig. 22f Cont’inued

i' aJg

I -- - €

r/Lo = O S 5 8 U83.20

E

"-- A-€ = OS*

350 400 450 500 550 600 650 100

X (mm) Fig. 22g Continued

350 400 4 50 500 550 600 650 700

X(mm1 Fig. 23a Experimental values of (5 as function of distance at several meridian

planes , a = 3.2', r/Lo = 0.558

82

45o.c

5oo.c

55O.C

600.a

65O.C

7 0 O . C

7 50.0

_ .

0

I

I r/Lo 10.558

350 400 450 500 550 600 650 700 X( mm)

F i g . 23b Continued 83

&80°,0

85O.O

9oo,o

+u t I "d + I

350 400 450 500 550 600 650 700

N m m )

Fig. 23c Continued

84

Fig. 24a Schlieren Photographs at a = 2.6, 8 = 0 0 u

I

Fig . 24b Sch l i e ren pho tographs a t a = 2.6' , 8 = 90'

Fig. 25a Schlieren Photographs at a. = 3.2, 8 = 0 0 0

03 03

F i g . 25b Sch l i e ren pho tographs a = 3.2', 0 = 90'

DISTURBED POSITION b

/

FREESTREAM

,POSITION a x It, /Y ' I'

?

LSUBSONIC /' m

REGION

ZONE WHERE INTERACTION IS PRESENT

Fig. 26 Determination o f region o f i n t e r f e rence between probe and shock \

N - XIL 0

N N

N - XIL O N N - XIL O N

F i g . 27 Pressure distribution on a hemisphere, Mo= 4.6 interacting with a shock that deflects the flow of 5 . Arrow indicates point a t which disturbance meets model surface.

90

-1.2 "1 W F

! Fig. 28 D i s t r i b u t i o n of a t r / L = 0.558, a = 2.6 , 0 = (, 0

\ J

1.0

.8

.6

Eo .4

.2

0 1

I I I 1

THEORETICAL DATA , M,, 2.7 15 EXPERIMENTAL DATA, WJ 2.7 10

8= 0" PLANE a= 2.6O

1.5 1.6 1.7 1.8 I .a

x /L Fig. 29 Comparison between experimental and calculated values

I

. a

.?

.6

.5

E' .4

.3

. 2

.I

0 I

- THEORETICAL DATA, Yo= 0.718

0 EXPERIMENTAL D A T A , M&= 2.717 I

X/L

93 Fig. 30 Comparison between experimental and calculated

values

.O 3

.o I

0

0.02 1

Fig. 31 Double values of F (y) for cone cyl inder

.2

. I

0

-.I

- .2 \L, wl

F(y 1 - DATA FROM EXPERIMENTS

CHARACTERISTICS THEORY n - -"

Fig. 32 Distribution of F function as function of y corresponding to curve 1 of Fig. 28

Fig . 33 J? (y) used i n the analys is cor responding t o curve 1 of Fig. 28, a = 2.6 , r/L = 0.558 0

X / L e

F i g , 34 Sonic b o a signature a t r/L0= 200, for Lo= 300 ft and Lo= 0.555, variable density program (Curve 2 of Fig . 28)

.. I, *CURVE: I o F " l "

I * FIG. 28 .m

0 . I 1 8 I * 1 8 b I I I \, 1 I I I 8 t H -200 - 100 100 200 \ 300

Fig. 35 Sonic Boom Signature (constant pressure) at r/L = 200 Kp = 1017 lb/ft2

I

1.6

1.2

.8

.4

0

0.4

-SECOND ORDER THEORY

----to NEGLECTED

-.- LINEARIZED THEORY

1

G 2.0 0

I .6

1.2

a

.4

0

- .$

0.8

FIRST RUN @SECOND RUN XfHIRD RUN

"- CURVE o

AT DIFFERENT ""- CURVE b POSITIONS

I b.

0 3151 4 .#m: I

8 S 236 SHOCK POSITIONS MEASURED FROM

SCHLIEREN PHOTO.

Fig. 37 Measurements of deviation angle of SST model a t r h o = 0.271, %= 0.055, a = 2.6' a t several position8

""- BY CURVE I

BY CURVE 2

. -.-r-

Fig. 38 Sonic boom signature for a = 2.6', = 0,055 a t r/Lo= 200 from data a t r/Lo= 0.271, Kp = 1017 l b / f t 2

1.6- I"

x

@"

DISTRIBUTION .8 .. . .

X . ,-. I ,

. .

. .

.9 ..

X (mm)

-4 ' SHOCKS LOCATED FROM

SCHLIEREN PHOTOBRAPHS

0.8

- 1.2 I

I

Fig. 40 F(y) curve for a = 3.2' from data at r h o = 0.558

W 0'

. I I m

-IO0 0 100

-. 4 X- B r ( m m )

I nnA

Fig . 41 Sonic boom s i g n a t u r e fo r a = 3 . 2 , = .066 r / L = 200 Kp = 1017 l b / f t 0 2

N