A body of revolution, representing the equivalent area distribution of a low boom aircraft design cruising at 24,384 meters at a Mach number of 4, was tested to determine whether its theoretical sonic boom characteristics could be experimentally verified. Results indicate that the essential features of the ground signature are well predicted

Howard, F. G.

Morris, O. A.

English

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NASA TECHNICAL NASA TM X-72013
MEMORANDUM COPY NO.
AT MACH 4
by
Floyd G. Howard and Odell A. Morris
O -
WIND TUNNEL TEST OF
LO BOO EQUVALOW BOOM EQUIVALENT B CSCL 01A nclaODY
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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
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1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.
TM X-72013
4. Title and Subtitle 5. Report Date
WIND TUNNEL TEST OF LOW BOOM EQUIVALENT BODY September 19746. Performing Organization Code
AT MACH 4 37.710
7. Author(s) 8. Performing Organization Report No.
Floyd G. Howard and Odell A. Morris
10. Work Unit No.
9. Performing Organization Name and Address
NASA Langley Research Center 11. Contract or Grant No.
Hampton, VA 23665
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Washington, D. C. 20546
15. Supplementary Notes
Special technical information release, not planned for formal NASA
publication.
16. Abstract
A body of revolution, representing the equivalent area distribution
of a low boom aircraft design cruising at 24,384 meters at a Mach number of
4, has been tested to determine whether its theoretical sonic boom charac-
teristics could be experimentally verified. Results indicate that the
essential features of the ground signature are well predicted.
17. Key Words (Suggested by Author(s)) (STAR category underlined) 18. Distribution Statement
Aircraft
Sonic Boom
Measured Wind-Tunnel Pressure Signature
Equivalent Body of Revolution
Ground Signatures
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Unclassified Unclassified 14 $3.00
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WIND TUNNEL TEST OF
LOW BOOM EQUIVALENT BODY
AT MACH 4
by
Floyd G. Howard and Odell A. Morris
SUMMARY
A wind tunnel investigation of a body of revolution has been conducted
to determine whether the midfield low sonic boom characteristics at ground
level, designed into the body through its equivalent area distribution by
sonic boom theory (Whitham, Hayes, refs. 1 and 2), could be experimentally
verified at Mach number 4. The results indicate that the essential features
(signature shape, shock strength, and impulse) of the measured signature
extrapolated to ground level are well predicted. Although not conclusive, a
secondary finding suggests that the use of normal cross-sectional areas,
rather than the more complex projection of Mach plane-body area intercepts,
for inversely designing a fuselage to meet equivalent area due to volume
requirements may be sufficiently accurate for preliminary design of low boom
aircraft.
INTRODUCTION
The sonic boom theory developed by Whitham (ref. 1) and modified by
the supersonic area rule concepts of Hayes (ref. 2) and Lomax (ref. 3)
relates the aircraft to its sonic boom signature through the aircraft's
equivalent area distribution. In this context the aircraft is replaced
by an equivalent body of revolution that represents the aircraft's dis-
tribution of volume and lift along its length. During the design of
aircraft to produce low sonic boom characteristics, then, the equivalent
area distribution that produces these characteristics becomes a fundamental
design requirement that the aircraft must satisfy.
Studies of these low boom aircraft have resulted in the definition of
a number of equivalent area distributions that theoretically produce, at
ground level, midfield signature shapes and shock strengths less than 48
N/m2 (approximately 1 psf) for Mach numbers up to 4. At lower Mach numbers
the theory gives reasonably good predictions of the experimental sonic boom
signatures from equivalent bodies of revolution (ref. 4). At higher Mach
numbers, however, the validity of the theory is questionable, especially for
low boom area distributions, because higher order terms than those considered
in the theory may become important. Wind tunnel tests, reported herein, were
therefore made on a low boom equivalent body of revolution to allow a com-
parison of its theoretical and measured sonic boom characteristics at a
Mach number of 4.
SYMBOLS
ALT altitude
h distance from body centerline
L equivalent body length
M free stream Mach number
p. free stream static pressure
AP pressure differential due to flow field 
of model
R body radius
R maximum body radius
MAX
RF reflection factor
S equivalent area
S maximum equivalent area
MAX
X longitudinal distance
p arcsin
BACKGROUND
The area distribution that provided the basis for this study 
is shown
by the dashed line in figure 1. This low sonic boom 
equivalent area distri-
bution determined by Dr. A. Ferri under NASA Grant NGL 33-016-191 is
representative of a Mach 4 transport weighing 211,812.5 
kilograms (466,967
pounds) at a cruise altitude of 24,384 meters (80,000 feet). For sonic 
boom
calculations, according to theory, this area distribution can 
be represented
by a body of revolution having a corresponding distribution 
of equivalent
areas composed of frontal projections of the body areas intercepted by
Mach cutting planes. As a first approximation to this body, the 
contour
shown in figure 2 was defined by simply using the normal cross sectional
area distribution, R(X) = tS(X)/r, as the equivalent area. The correct
equivalent area distribution (from Mach plane cuts) for 
this shape was then
determined by the method described in reference 5. The resulting area
distribution (solid line, figure 1) agreed very well with the desired 
distri-
bution except near the maximum area where the area slope discontinuity was
eliminated.
2
The sonic boom signatures for both of these area distributions were
determined by applying the numerical method of Carlson (ref. 6) to obtain,
at two body lengths from the body axis, pressure signatures which were then
extrapolated through a standard atmosphere to ground level by the method of
Thomas (ref. 7). A ground reflection factor of 1.9 was used. The resulting
signatures (fig. 3) differed somewhat in detail, but gave about the same
value of AP = 43 N/m2 for the maximum positive overpressure with the Mach
cut area distribution giving the lower AP for the rear shock because of the
area smoothing already noted. Since the body shape of figure 2 gave a
sufficiently accurate approximation to the desired pressure signature, no
further iterations on body shape were made and this contour formed the basis
for the test model.
MODEL, APPARATUS, TESTS
The test model (figure 4) consists of a forebody, which corresponds to
1/645-scale reduction of the contour of figure 2 and a cylindrical afterbody
having a diameter equal to the maximum forebody diameter. Model dimensions
were within 0.0076 cm of those specified.
A sketch of the wind tunnel apparatus is shown in figure 5. Both the model
and the pressure measuring probes were mounted on support systems which pro-
vided for remote control adjustments of their longitudinal positions. The
pressure measuring probes were slender cones (40 total angle) with two 0.0889
cm diameter static-pressure orifices leading to a common chamber. Orifices
were circumferentially located 1800 apart in a horizontal plane. Two gages
having load limits of 7.182 N/m2 (D.15 psi) and 2.394 N/m2 (0.05 psi) were used
to measure the pressures simultaneously. The agreement between the data from
both gages was excellent throughout the tests.
Tests were made in the Langley Unitary Plan wind tunnel at a Mach number
of 4 with a stagnation temperature of 3530K, and a stagnation pressure of
281.5 x 103 N/mz . Pressure signatures were measured at 15.24 and 30.48 cm
(h/L values of .645 and 1.29) from the body axis in the vertical plane con-
taining the probe and model axis.
RESULTS AND DISCUSSION
The experimental pressure signatures obtained at both h/L values are
compared with theoretical signatures in figure 6. The signatures are located
with respect to each other by equating X values for AP = 0 on the expansion
portion of the signature. The experimental signatures do not show a step rise
in pressure across shocks. Instead, a gradual pressure rise occurs followed
by a rounding at the peaks. This behavior is primarily due to vibration of
the model and measuring probe and is discussed in more detail in reference 6.
The theoretical signature (based on Mach cutting plane equivalent areas
using method of reference 6) shows many low magnitude internal shocks. Many
of these are not real but result from unavoidable inaccuracies in equivalent
3
area developments. (For example, in figure 7 the pressure signature calculated
from an analytically defined area distribution S(X) = Sa X (x/L)5/6 does not
contain the many internal shocks displayed by the signature calculated from a
corresponding area distribution read from the hand-faired area curve.) Taking
this into account, the agreement between experiment and theory is reasonably
good. By converting to full-scale dimensions and applying the method of
reference 7, the ground signatures represented by these experimental data were
obtained. These signatures are shown in figure 8 along with the theoretical
predictions. The data points extrapolated from h/L values of 0.645 and 1.29 are
in excellent agreement and the theory gives a very good prediction of the posi-
tive portion of the signature (indicating a good impulse prediction) and both
front and rear shock strengths.
It seems reasonable to conclude then, that an equivalent area distribution
composed only of volume terms and designed by the theory of references 1 and
2, to give midfield low sonic boom characteristics at ground level, will in
fact produce an excellent approximation to these characteristics for Mach
numbers as high as 4. Until additional investigations of lifting configurations
are made, this conclusion should not be extended to an equivalent area distri-
bution that is composed of both volume and lift terms.
As an additional point of interest, the ground signature given by theory
using normal plane equivalent area is also included in figure 8; and although
agreement with the experimental signatures is not as close as that using
Mach cutting planes, a reasonable prediction is still provided especially
with regard to the front shock strength. Because of its simplicity of
application, therefore, the use of normal plane equivalent areas, rather than
Mach plane areas, may be sufficiently accurate for preliminary design of the
fuselage for low boom aircraft. This approximation should improve at lower
design Mach numbers.
CONCLUDING REMARKS
A wind tunnel investigation of a body of revolution has been conducted
to determine whether the midfield low sonic boom characteristics at ground
level, designed into the body through its equivalent area distribution by
sonic boom theory (Whitham, Hayes), could be experimentally verified at Mach
number 4. The results indicate that the essential features (signature shape,
shock strength, and impulse) of the measured signature extrapolated to ground
level are well predicted. Although not conclusive, a secondary finding
suggests that the use of normal cross-sectional areas, rather than the more
complex projection of Mach plane-body area intercepts, for inversely designing
a fuselage to meet equivalent area due to volume requirements may be
sufficiently accurate for preliminary design of low boom aircraft.
4
REFERENCES
1. Whitham, G. B.: The Flow Pattern of a Supersonic Projectile.
Commun. Pure and Appl. Math., Vol. V, No. 3, Aug. 1952, pp. 301-348.
2. Hayes, Wallace D.: Linearized Supersonic Flow. 
Rept. No. AL-222,
North Am. Aviation, Inc., June 18, 1947.
3. Lomax, Harvard: The Wave Drag of Arbitrary Configurations in
Linearized Flow as Determined by Areas and Forces 
in Oblique Planes.
NACA RM A55A18, 1955.
4. Carlson, Harry W.; McLean, F. Edward; and Shrot, Barrett L.: A Wind
Tunnel Study of Sonic-Boom Characteristics for Basic and Modified
Models of a Supersonic Transport Configuration. NASA TM X-1236, 1966.
5. Harris, Roy V.: An Analysis and Correlation of Aircraft 
Wave Drag.
NASA TM X-947. 1964.
6. Carlson, Harry W.: Correlation of Sonic-Boom 
Theory with Wind Tunnel
and Flight Measurements. NASA TR-R-213, 1964.
7. Thomas, Charles L.: Extrapolation of 
Sonic-Boom Pressure Signatures
by the Waveform Parameter Method. NASA TN D-6832, 
1972.
1.0
.8
NORMAL AREAS
.6
MAXl
.2 
.
PROJECTED MACH
PLANE AREAS
S.2 
.4 .6 .8 1.0 1.2 1.4
L
FIGURE 1.- COMPARISON OF EQUIVALENT AREAS.
M = 4; SMAX = 128.58 m2; L = 152.4 m.
1.0
.8
.6
R
.4
.2
0 .2 .4 .6 .8 1.0
x
FIGURE 2.- EQUIVALENT BODY CONTOUR.
L = 152.4 m; R MAX = 6.388 m.
1.2 60
PROJECTED MACH
r, PLANE AREAS
.8 .
.4 20 - N
NORMAL AREAS
lbs N
P FT 2  M2
O- o
-.4 
-20 
-
-.8 - .-40 
0
-1.2 - 6
-60
0 100 200 300 400
X,m
FIGURE 3.- GROUND SIGNATURE.
AlT - 9AP A m -D 1 Q
L = 23.623 cm
1.9807 cm
X/L RL X/L R/L X/L R/L
0.0 .000 
.40 .02245 
.80 .03635
.02 .001596 
.42 .02323 
.82 .03694
.04 .002764 
.44 .02404 
.84 .03756
.06 .003909 
.46 .02493 
.86 .03818
.08 .005046 
.48 .02578 
.88 .03883
.10 .006180 
.50 .02665 
.90 .03944
.12 .007399 
.52 .02743 
.92 .04005
.14 .008740 
.54 .02814 
.94 .04065
.16 .009707 
.56 .02883 
.96 .04118
.18 .01117 
.58 .02949 
.98 .04163
.20 .01226 
.60 .03015 1.00 .04192
.22 .01340 
.62 .03086 1.2
.24 .01449 
.64 
.03151 1.4
.26 .01568 
.66 .03215 1.60
.28 .01693 
.68 .03276 1.80
.30 .01809 
.70 .03334 1.93
.32 .01915 
.72 .03368
.34 .02012 
.74 .03458
.36 .02099 
.76 .03514
.38 .02176 
.78 .03574
FIGURE 4.- TEST MODEL.
Tunnel sidewall
Model
Model Actuator (longitudinal motion)
Bow shock Pressure orifices
Reference orifices Permanent sting
(lateral motion)
Permanent strut
(longitudinal motion)
Tunnel sidewall
CO
FIGURE 5,- PLAN VIEW SKETCH OF WIND TUNNEL APPARATUS.
.©
.04
000
TUNNEL DATA0 , 
.03THEORY
0
.01 0 0
0
O
-.01 - 0
-.02
-.030
o .2 .4 .6 .8 1.0 1.2 1.4 1.
r
(a) h/L = 0.645.
FIGURE 6.- MEASURED AND THEORETICAL SIGNATURE.
L = 23.623 cm.
.04
3 .03
oc o TUNNEL DATA
.02 0
0 0
0 0
.01 THEORY
AP 0
P.
0*
O O
0 0
-.01 0 00 0  00
-.02
-.o03 I I I I I
0 .2 .4 .6 .8 1.0 1.2 1.4 1.6
X
L
(b) h/L = 1.29.
FIGURE 6.- CONCLUDED.
.03
AREA POINTS ANALYTICALLY DEFINED
.02
AREA POINTS INPUT FROM FAIRED AREA CURVE
.01
AP
-.01 -
-.02
-.03
0 .2 .4 .6 .8 1.0 1.2 1.4 1.6
X/L
FIGURE 7.- EFFECT OF EQUIVALENT AREA ACCURACY OF PRESSURE SIGNATURE.
M = 4; h/L = 1.29.
1.2
THEORY (PROJECTED MACH PLANE AREAS)
tr. P, THEORY (NORAL AREAS)
.8 40
C',
I 0
o- o
ol
-. 4- -20 o DATA EXTRAPOLATED
FROM h/L = .645 I
[3 DATA EXTRAPOLATED
FROM h/L = 1.29
.8 
-40
-1.2 -
-60 I I
0 100 200 300 400
X,m
FIGURE 8.- COMPARISON OF GROUND SIGNATURES.
ALT. = 24383 m; RF = 1.9.


Wind Tunnel Test of Low Boom Equivalent Body at Mach 4

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