Experimental pressure distributions over two wing-body combinations at Mach number 1.9

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' SEARCH MEMORANDUM




itCP:ERlIRU ENT)AL PRESSURE DISTRIBUTIONS OVER TWO WING-BODY
COMBINATIONS AT MACH NUMBER 1.9
By Barry Moskowitz and Stephen H. Maslen
'" Lewis Flight Propulsion Laboratory
'' Cleveland, Ohio


S UNNV snY OF FLORIDA
DOCUMeIbnTS DEPARTMENT
120 m mRN SCIENCE LUARY
PO. BWX 117011
P GN EaILE, FL 32611-7011 USA




NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
WASHINGTON
February 5, 1951
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NACA RM E50J09


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


RESEARCH MEMORANDUM


EXPERIMENTAL PRESSURE DISTRIBUTIONS OVER TWO WING-

BODY COMBINATIONS AT MACH NUMBER 1.9

By Barry Moskowitz and Stephen H. Maslen


SUMMARY

Pressure distributions on two wing-body combinations have been
obtained at a Mach number of 1.9 to investigate the wing-body inter-
ference. A rectangular wing, a triangular wing, and a cylindrical
body with an ogive nose were studied alone and in combination. Both
wings had a span of 14 inches, an aspect ratio of 2 and a 5-percent-
thick double-wedge cross section. The wings were mounted on the cylin-
drical portion of the body. The investigation was conducted over a
range of angles of attack varying in 20 increments from -40 to 40

The pressure distributions over the wing-body combination com-
pared favorably with theoretical calculations based primarily on a
generalization of the method of Nielsen and Matteson, except at the
root section of the wings where the boundary layer of the body modi-
fied the flow.


INTRODUCTION

Although the characteristics of the flow about thin wings and
about slender bodies of revolution in a supersonic stream have been
extensively studied in the past few years, information concerning
the effects of interference between wing and body is still needed.
Theoretical studies of the problem using linearized theory are pre-
sented in references 1 to 5. In reference 6, the method of charac-
teristics was used. Little experimental data are available, however,
particularly on pressure distributions. Van Dyke (reference 7) has
reported force measurements and Cramer (reference 8) has given some
results that are compared with Ferrari's studies (reference 2).








NACA RM E50J09


In the investigation reported herein, which was conducted at the
NACA Lewis laboratory, static-pressure surveys were made at a Mach
number of 1.9 on two wing-body combinations; one wing was rectangular
and the other triangular. The wings and the body were investigated
separately for comparison. The results are compared with theoretical
calculations based primarily on the method of reference 4, which was
generalized to include some angle-of-attack effects.

APPARATUS AND PROCEDURE

The wing-body combinations were investigated in the NACA Lewis
18- by 18-inch supersonic wind tunnel. The Mach number, obtained
from a tunnel calibration survey, was 1.90 +.01 in the vicinity of
the models. The total-pressure variation along the models was
+0.5 percent and was therefore neglected. The test Reynolds number,
based on the mean wing chord, was 1.64 x 106.

A photograph of the models investigated is shown in figure 1
and a sketch of the models showing principle dimensions and the loca-
tion of static-pressure orifices is presented in figure 2. Pressure
surveys were taken at 20 increments in angle of attack from -4 to 40.
The pressures were photographically recorded from multiple-tube mano-
meter boards using tetrabromoethane as the working fluid.

The angle of attack of the model was measured with a catheto-
meter during each test. Angles were accurate to +.010. Because of
the low aspect ratio of the wings, aeroelastic deformation of the
wing sections was considered negligible.


THEORY

The differential equation for linearized potential flow is
assumed to apply. Solutions may be linearly superposed to obtain
the flow over a particular configuration. The boundary condition
for the flow is that the normal velocity is zero at the surface.

The wing-body problem may be solved by starting with the solu-
tion for the wing alone (reference 9 or 10) and the body alone (refer-
ence 11 or 12). When these solutions are combined, the boundary con-
ditions are no longer satisfied because the body (at angle of attack)
generates an upwash in the plane of the wing and the wing causes a
flow through the body. A wing-interference potential and a body-
interference potential are introduced, whose respective functions are
to cancel the upwash in the plane of the wing and to cancel the flow
through the body.








NACA RM E50J09


Consider the ,ing in the presence of the known body upwash field
(reference 12 or 13). The required wing interference potential is
readily found by the method given in reference 14, which amounts to
considering a wing with a local angle of attack equal to the local
upwash induced by the body divided by the free-stream velocity. In
order to avoid infinite sidewash at the wing-body juncture, the
upwash is taken to be continuous through the blanketed portion of the
wing (region of the wing covered by the body).

The wing-interference potential plus the two basic solutions
satisfy the boundary conditions on the whole wing and on the body in
the region of no interaction. The remaining problem consists in can-
celing the flow generated through the body by the two wing potentials,
without disturbing the boundary conditions on the wing. The latter
condition will automatically be satisfied if the problem can be
treated as symmetric with respect to the plane of the wing.

In reference 4, Nielsen and Matteson describe an approximate
method to determine the body interference solution for symmetric-
flow problems. The body is symmetrically divided into plane control
areas with finite line pressure sources placed on each control surface
normal to the free stream. The normal velocity is averaged over each
area and the strengths of successive sources are determined taking
into account the effect of one line source on another. Because the
procedure of reference 4 gives a symmetric solution, no flow is
induced across the plane of the wing.

For a symmetrical wing mounted on the body at the center line
with both wing and body at zero angle of attack, the flow is symmetric.
Also,those portions of an unsymmetric flow may be treated as symmetric
that are not influenced by any portion of the body (in the region of
interaction) lying on the opposite side of the plane of the wing.
For example, in the configurations shown in the following sketch, no
body-interference potential is required in region I; in region II,
the body interference potential may be found by considering a symmetri-
cal problem; and in region III the problem must be considered as
unsymmetric.








NACA RM E50J09


(a) (b) (c)


With the procedures previously discussed, the pressure distri-
bution for a rectangular wing-body combination can be calculated in
regions uninfluenced by the wing trailing edge (similar to the con-
figuration in sketch (a)). The triangular wing investigated actually
had a slightly subsonic leading edge but was assumed, for ease in com-
putations, to have a sonic edge and is consequently similar to
sketch (b). The triangular-wing solution yields infinite sidewash
at the intersection of the leading edge with the body. This infinite
sidewash was reduced to finite values, before calculating the body
interference potential, by distribution line sources and sinks in the
manner discussed in reference 4.

Superposition of the rectangular-wing solution, the wing-
interference solution, and the body solution results in discontin-
uities in the pressure distribution on the body. The body-interference
solution should therefore have corresponding discontinuities of the
same magnitude but of opposite sign, inasmuch as the pressure distri-
bution on the body should be continuous. This continuity of the pres-
sures on the body is known from the fact that all disturbances on the
body due to the wing are propagated along Mach cones, which generate
no pressure discontinuities in linearized theory. The normal velo-
cities, however, are averaged over given regions of the body; con-
sequently, the body-interference solution fails to give these dis-
continuities. For this reason, the body-interference pressures were
so adjusted on the body that the pressure distributions were contin-
uous on the body.








NACA EM E50J09


Another effect of averaging the normal velocities is that the
pressures due to the presence of the wing acting in the region on
the body between the Mach wedge from the leading edge of the rectan-
gular wing and the intersection of the body with the Mach cones from
the foremost part of the wing-body juncture are not zero. An adjust-
ment was therefore made so that the body-interference pressures
exactly canceled the pressure on the body due to the wing solution
in this region. Nielsen of the NACA Ames laboratory pointed out that
this region should actually extend slightly farther downstream because
the disturbances generated by the junction of the body and the wing
leading edge will be propagated along the body surface at the Mach
angle rather than along Mach cones. Thus, for example, the disturb-
ance will first reach the top of the body a distance ORn/2, where
0 is the cotangent of the Mach angle downstream of the wing leading
edge and R is the body radius, rather than 3Rt// as assumed in
the computation. The last value was used because it is the result
indicated by ordinary linear theory.


RESULTS

Experimental data are presented and compared with theoretical
results in figures 3 to 13. The pressure coefficient Cp and the
change in pressure with angle of attack dCp/da, both evaluated at
a = 0, are plotted for each orifice location. Within the limited
range of angles of attack of the investigation, the faired variation
of Cp with angle of attack was approximately linear. The experi-
mental results for the body alone, rectangular wing alone, and tri-
angular wing alone are given in figures 3, 4, and 5, respectively. In

figure 3 the experimental value of dC~/ where e is the angle
sin e
measured around the body from the plane of the wing, is obtained by
dC /da
averaging the various values of -P The agreement between theory
sin 0
and experiment in figures 3, 4, and 5 is the basis for determining
the accuracy of the interference calculation. For example, if the
difference between experiment and theory for a component in combi-
nation is within the order of agreement existing between theory and
experiment for the component alone, the agreement is considered good.


Rectangular Wing and Body

Results for the rectangular wing in the presence of the body are
presented in figure 6. Because of the large nose angle of the body








NACA RM E50JOE


(300 half angle), a fairly strong shock was generated (fig. 14). In
the neighborhood of the wing tip, the shock wave occurred approxi-
mately 2 inches upstream of the Mach wave assumed by linear theory.
As a result the pressures predicted by linear theory, in the forward
part of the tip region, are higher than the experimental values. As
shown in the schlieren photograph, the nose shock reflects off the
tunnel walls and intersects the wing tip. Because of the increase
in pressure across the reflected shock, the experimental values are
higher than those obtained by linear theory in the rearward portion
of the tip region. In the plane of wing, however, the body does not
directly cause any change in pressure due to angle of attack. More-
over, the shock position does not vary appreciably over the range of
angles of attack of the investigation. The effects of the shock and
its reflection therefore cause no discrepancy between the theoretical
and experimental values of dCp/da on the wing.

At the root section, the boundary layer of the body modified the
flow over the wing. In particular,the discontinuity in the slope
of the wing was softened, thereby decreasing the pressure change pre-
dicted by linear theory. At the wing midspan position, none of these
difficulties occurred and close agreement between linear theory and
experiment was obtained.

In order to illustrate the effect of the presence of the body on
the pressures acting on the rectangular wing, the increments ACp and

AdCP due to the presence of the body are presented in figure 7. The
da
theoretical curves and the experimental points were obtained by taking
the difference between corresponding values in figures 6 and 4. For
zero angle of attack, the section wave drag of the wing in combination
is less than the corresponding section wave drag of the wing alone,
if the increment in pressure is negative over the positively sloped
portion of the wing and positive over the negatively sloped portion.
In the root section the experimental points, but not the theoretical
curve, indicate less section drag. In the midspan region the experi-
mental points indicate slightly less section drag, whereas the section
drag indicated by the theoretical curve remains about the same. In
the tip region, both theoretical and experimental values indicate an
increase in the section drag, which is to be expected inasmuch as the
tip region of the rectangular wing is influenced by the pressure gra-
dient associated with the nose of the body. Because of a large reduc-
tion in the drag of the wing due to the blanketing of the center sec-
tion, the over-all wave drag of the combination is probably less than
the sum of the wave drags of the components.








NACA RM E50J09


Inasmuch as the increment in dCp/da is negative on the top sur-
face of the wing, the sectional lift is greater than the corresponding
sectional lift of the wing alone. This result is to be expected
because the presence of the body at angle of attack causes an upwash
field, which increases the effective wing angle of attack. (See the
section THEORY.)

The experimental variation of Cp and dCp/da on the body in
the presence of the rectangular wing is presented in figures 8(a)
and 8(b), respectively. Close agreement was obtained for the slope
of the pressure coefficient curve. For zero angle of attack, the
trend of the experimental points and the theoretical curves appear
to be similar. The quantitative agreement is of the order obtained
for the wings and the body alone.

The increments in Cp and dCp/dc on the body due to the
presence of the wing are presented in figures 9(a) and 9(b),
respectively. In figure 9(a) the direct influence of the wing is
noted in the increases and decreases in body pressure coefficient
in the regions influenced by the positive and negative wing slopes,
dCp
respectively. Because the A-h- curve in figure 9(b) is negative,
an increase in lift results on the body due to the presence of the
wing.


Triangular Wing and Body

The experimental results for the triangular wing in the presence
of the body are shown in figure 10. Reasonably good agreement with
linear theory was obtained at all stations except for the root sec-
tion at a = 0, where, as was noted in the case of the rectangular
wing, the theoretical discontinuity in pressure is modified by the
boundary layer of the body. Inasmuch as the body nose shock was
not near the triangular wing at any point, the poor correlation
between theory and experiment noted in the outboard region of the
rectangular wing does not occur for this case.

dCp
The increments AC and A- d on the triangular wing due to
p dm
the presence of the body are presented in figure 11. At the outboard
section A, the experimental points and the theoretical curve for
a = 0 indicate a slight decrease in section drag relative to the drag
of the wing alone. At the midspan section B, the experimental points
indicate a slight decrease in section drag, whereas the theoretical








NACA RM E50J09


curve indicates that the section drag remains about the same for a = 0.
Both the experimental points and the theory at the inboard section C
show a sizeable decrease in section drag over that for the triangular
wing alone at a = 0. Thus at zero angle of attack, the over-all
wave drag of the triangular wing-body combination is less than the
sum of the wave drags of the components. At sections A and B, the
fact that the experimental points of AdCp/da are negative indicates
a slight increase in section lift, although the theoretical curves at
these stations indicate that the section lift remains unchanged. At
the root section C, both linear theory and experiment show a decrease
in section lift.

Experimental results for Cp and dCp/da on the body in the
presence of the triangular wing are presented in figures 12(a) and
12(b), respectively. The difference between experiment and linear
theory in figure 12(a) is very nearly that displayed by the curves
for the body alone (fig. 3), which indicated that the interference
was accurately predicted by the theory. This agreement is also shown
in figures 13(a) and 13(b), where the differences in Cp and dCp/da
for the body in combination with the triangular wing and the body
alone are presented.


CONCLUDING REMARES

Experimental pressure distributions at a Mach number of 1.9 were
obtained for a rectangular wing and a triangular wing in combination
with an ogive-nose body.

The procedure of Nielsen and Mtteson was applied at zero angle
of attack and a generalization of this method was used to calculate
interference effects at angle of attack. The experimental results
compared favorably with these theoretical calculations, except at the
root section of the wings, where the boundary layer of the body modi-
fied the flow over the slope discontinuity of the wing and thereby
decreased the pressure change predicted by linear theory.


Lewis Flight Propulsion Laboratory,
National Advisory Committee for Aeronautics,
Cleveland, Ohio.









NACA RM E50J09


1. lagerstrom, P. A., and Van Dyke, M. D.: General Considerations
about Planar and Non-Planar Lifting Systems. Rep. No. SM-15432,
Douglas Aircraft Co., Inc., June 1949.

2. Ferrari, Carlo: Interference between Wing and Body at Supersonic
Speeds Theory and Numerical Application. Jour. Aero. Sci.,
vol. 15, no. 6, June 1948, pp. 317-336.

3. Spreiter, John R.: The Aerodynamic Forces on Slender Plane- and
Cruciform-Wing and Body Combinations. NACA Rep. 962, 1950.
(Formerly NACA TNs 1897 and 1662.)

4. Nielsen, Jack N., and Matteson, Frederick H.: Calculative Method
for Estimating the Interference Pressure Field at Zero Lift on
a Symmetrical Swept-Back Wing Mounted on a Circular Cylindrical
Body. NACA RM A9E19, 1949.

5. Browne, S. H., Friedman, L., and Hodes, I.: A Wing-Body Problem
in a Supersonic Conical Flow. Jour. Aero. Sci., vol. 15, no. 8,
Aug. 1948, pp. 443-452.

6. Ferrari, Carlo: Interference between Wing and Body at Supersonic
Speeds Analysis by the Method of Characteristics. Jour. Aero.
Sci., vol. 16, no. 7, July 1949, pp. 411-437.

7. Van Dyke, Milton D.: Aerodynamic Charcteristics Including Scale
Effect of Several Wings and Bodies Alone and in Combination at
a Mach Number of 1.53. NACA RM A6K22, 1946.

8. Cramer, R. H.: Some Theoretical and Experimental Results for
Wing-Body Interference at Supersonic Velocities. Bull.
Bumblebee Aero. Symposum (Johns Hopkins Univ.), Nov. 4-5, 1948,
pp. 267-276.

9. Evvard, John C.: Use of Source Distributions for Evaluating
Theoretical Aerodynamics of Thin Finite Wings at Supersonic
Speeds. NACA Rep. 951, 1950.

10. Iagerstrom, P. A.: Linearized Supersonic Theory of Conical Wings -
(Corrected Copy). NACA TN 1685, 1950.
1
11. von Earman, Theodor, and Moore, Norton B.: Resistance of Slender
Bodies Moving with Supersonic Velocities, with Special Reference
to Projectiles. Trans. A.S.M.E., vol. 54, no. 23, Dec. 15, 1932,
pp. 303-310.







10 NACA RM E50J09


12. Tsien, Hsue-Shen: Supersonic Flow over an Inclined Body of
Revolution. Jour. Aero. Sci., vol. 5, no. 12, Oct. 1938,
pp. 480-483.

13. Beskin, Leon: Determination of Upwash around a Body of Revo-
lution at Supersonic Velocities. DEYF Memo. BB-6, Consoli-
dated Vultee Aircraft Corp., May 27, 1946.

14. Mirels, Harold: Theoretical Method for Solution of Aerodynamic
Forces on Thin Wings in Nonuniform Supersonic Stream with an
Application to Tail Surfaces. NACA TN 1736, 1948.







NACA RM E50J09


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NACA RM E50J09


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14 NACA RM E50J09




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Figure 3. Values and slopes of pressure coefficient for body alone at zero
angle of attack.









NACA RM E50J09


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NACA RM E50J09


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NACA RM E50J09


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Figure 5. Concluded. Values and slopes of pressure coefficient for triangular
wing alone at zero angle of attack.












NACA RM E50J09


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Figure 8. Values and slopes of pressure coefficient on body in presence of
rectangular wing at zero angle of attack.










NACA RM E50J09


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Figure 8. Concluded. Values and slopes of pressure coefficient on body in
presence of rectangular wing at zero angle of attack.


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NACA RM E50J09






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Figure 9. Incremental values and slopes of pressure coefficient on body due
to presence of rectangular wing at zero angle of attack.









NACA PM E50J09 23







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Figure 9. Concluded. Incremental values and slopes of pressure coefficient
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NACA RM E50J09


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Figure 12. Values and slopes of pressure coefficient on body in
presence of triangular wing at zero angle of attack.









NACA RM E50J09












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Figure 12. Concluded. Values and slopes of pressure coefficient on body
in presence of triangular wing at zero angle of attack.









28 NACA RM E50J09






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Figure 13. Incremental values and slopes of pressure coefficient on body due
to presence of triangular wing at zero angle of attack.


















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Figure 13. Concluded. Incremental values and slopes of pressure coefficient
on body due to presence of triangular wing at zero angle of attack.


NACA RM E50J09


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