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National Advisory Committee for Aeronautics, Report - Theoretical and Experimental Investigation of the Subsonic Flow Fields Beneath Swept and Unswept Wings with Tables of Vortex Induced Velocities

The almost universal present-day employment of external
stores, such as missiles, bombs, or fuel tanks on fighter
airplanes, and nacelles on bomber airplanes, has indicated
the need for more detailed information regarding the flow
characteristics in the vicinity of the wing in order to estimate
the aerodynamic loads on these objects when fixed in the
Wing flow field and to evaluate the launching and jettison
characteristics of missiles, bombs, or fuel tanks. In addition,
numerous present-day airplanes are incorporating wing
sweep, lower aspect ratios, and shorter tail length, all of
which may tend to bring the various airplane components in
closer proximity to the wing.

For airplane designs of the past, in which the component
parts (for example, the wing and the tail) were separated by
reasonable distances, the wing-interference effects could be
calculated with sufficient accuracy by a number of horseshoe
vortices distributed along a single lifting line (refs. 1 to 4).
However, because of the mathematically singular nature of
the single vortex, this theory is valid only for regions that
are at a distance of at least one wing chord from the vortex
location.

The purpose of the present report is to show that the flow
characteristics beneath the wing can be calculated if the
lifting wing is assumed to be represented by a multiple ar-
rangement (both chordwise and spanwise) of horseshoe
vortices and if the effects of thickness are accounted for.
The velocities induced by the airfoil-section thickness
distribution, which are often neglected, are considered by
using the appropriate singularity (source sink) distribution
(ref. 5) in conjunction with simple sweep theory (ref. 6).
Detailed experimental flow fields were obtained around swept
and unswept wing-fuselage combinations and are compared
with the wing-alone theoretical flow fields.