Reduction of wave drag of wing-body combinations at supersonic speeds through body distortions Page: 3 of 10
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NACA RM A56Bo10
undistorted body, so that negative values represent drag reductions. The
theoretical drag reduction at the design Mach number is shown. A signif-
icant portion of this reduction is also realized experimentally over the
Mach number range of 1.1 to 1.4.
In reference 2 a different approach to the problem of determining
the body distortions is used. The basic difference is that in reference 1
multipoles are distributed along the body axis, whereas in reference 2 the
boundary conditions on the wing and body surfaces are satisfied by using
the quasi-cylindrical theory of reference 3. The body shape is obtained
by minimizing the expression for the drag of the entire combination by
the standard method of the calculus of variation. The shape of the body
distortions is the minimizing variable. Both axisymmetric and nonaxisym-
metric distortions are obtained. The quasi-cylindrical restriction in
this theory adds flexibility in that it makes possible direct computation
of the drag reduction to be expected from the optimized configuration if
it is operated at off design conditions.
In figure 3, the model to which this theory was applied is shown.
The design Mach number is f. The wing leading edge is sonic. This model
and models with wings of two other aspect ratios were tested to determine
the sensitivity of the theory to aspect ratio. Several bodies were tested
to determine the effect of the two types of distortion. Body B1 is an
undistorted cylindrical body with a conical nose, and B2 contains the
axisymmetric distortion. It is this distortion that removes volume from
the body. The other distortions rearrange the volume without removing
any. Bodies B3 and B4 contain both the distortion of B2 and non-
axisymmetric distortions. Body B4 is a modification of the optimized
body B3. The dashed curves in the upper sketch show the plan-form sec-
tion of B4.
The ability of each of these body distortions to produce a drag
reduction at the design Mach number is shown in figure 4. Transition
was fixed on all models to minimize change in viscous effects. The drag
reduction due to the axisymmetric distortion is shown in the upper left
of the figure. This is obtained by subtracting the drag of the model
with the undistorted body BI from the drag with the body B2. Simi-
larly, the drag reductions due to the nonaxisymmetric distortions are
obtained by subtracting the drag with the distorted body B2 from the
drags with bodies B3 and B4. These results are shown in the upper
right and lower left parts of .figure 4. The fourth part of the figure
shows the total effect of both types of distortion by comparing bodies
B4 and B1. As before, negative values of D indicate drag reduc-
tion. The axisymmetric distortion provides a significant drag reduction
for all aspect ratios although not to the extent predicted by theory.
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Pitts, William C. Reduction of wave drag of wing-body combinations at supersonic speeds through body distortions, report, April 13, 1956; (digital.library.unt.edu/ark:/67531/metadc62821/m1/3/: accessed September 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.