Some Considerations Regarding the Application of the Supersonic Area Rule to the Design of Airplane Fuselages Page: 4 of 24
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NACA RM L56E23a * " * " 3
Effect of Reflections Produced by the Wing or Tail Surfaces
The problem of reflections of disturbances by the wing or horizontal
tail for asymmetrical configurations is illustrated by the sketch in fig-
ure 3. Shown is the side view of a symmetric wing in combination with a
fuselage indented only above the wing. Most of the disturbances from the
indentation above the wing which are directed downward are reflected
upward by the wing as shown; thus, the body shaping above the wing should
have little effect on the flow below the wing and an exaggerated effect
above the wing. (For symmetrical configurations, the reflection of dis-
turbances produced by changes in the fuselage shape below the wing replaces
the disturbances produced by the upper part which could not pass through
the wing. For such configurations, the reflection effects are accounted
for by the basic area rule.)
The adverse effects that may be associated with such reflections of
disturbances by the wing for asymmetrical configurations are illustrated
by the zero-lift drag results presented in figure 4, which were obtained
from reference 6. A delta wing having symmetrical airfoil section was
investigated in combination with an unindented fuselage and two indented
fuselages. In one case the normal cross-sectional areas of the wing were
removed axially symmetrically from the fuselage. In the other case the
total wing cross-sectional areas were removed only above the wing. With
the asymmetrical indentation, the incremental drag coefficient LCDo, which
is based on fuselage frontal area, was considerably higher than that for
the symmetrical indentation throughout the Mach number range of the test.
Further, the asymmetric indentation produced adverse effects on the drag
compared with those obtained with no indentation at Mach numbers above 1.1.
Similar adverse effects would be expected for an airplane configuration
with symmetrical wing sections with fuselage shaping concentrated above or
below the wing. For lifting conditions, an asymmetric fuselage of the type
shown in figure 4 may result in reductions in wave drag.
For the usual design conditions, the problem of determining these
reflected effects exactly is extremely complex since the reflection is
only partial. However, a reasonable approximation of the effect is
obtained by assuming that the reflection is complete for disturbances
originating in the region of the wing and is not present for disturbances
produced by the fuselage ahead of and behind the wing root. With such
an assumption, the areas of the fuselage above and below the plane of
the wing are considered separately; while ahead of and behind the wing,
the complete fuselage areas are utilized. Such a procedure is strictly
applicable only when the wing leading edge is supersonic. However,
experimental results for several asymmetrical configurations, including
those presented in figure 4, have indicated that fuselage contours based
on these separate area developments provide increased reductions in drag
even at lower Mach numbers. The areas above and below the horizontal
tail are separated in a similar manner.
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Whitcomb, Richard T. Some Considerations Regarding the Application of the Supersonic Area Rule to the Design of Airplane Fuselages, report, July 3, 1956; (https://digital.library.unt.edu/ark:/67531/metadc53074/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.