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National Advisory Committee for Aeronautics, Report - A Theoretical Study of the Aerodynamics of Slender Cruciform Wing Arrangements and Their Wakes

A theoretical study is made of some cruciform-wing arrange-

ments and their wakes by means of slender—body theory. The.

basic ideas of this theory are reviewed and equations are de—
veloped for the pressures, loadings, and forces on slender cruci-
form wings and wing-body combinations. The rodingmp of
the vortex sheet behind a slender cruciform wing is considered
at length and a numerical analysis is carried out using 40
cortices to calculate the walee shape at various distances behind
an equal-span cruciform wing at 45° banle. Analytical ea-
pressions are developed for the corresponding positions of
the rolledntp cortex sheets using a 4-22on approximatién to
the wake, and these positions are compared with the positions
of the centroids of vorticity resulting from the numerical analysis.
The agreement is found to be remarkably good at all distances
behind the wing.

Photographs of the walce as observed in a water tanlc are
presented for various distances behind a cruciform wing at 0°
and 45° bank. For 46° bank, the distance behind the wing
at which the upper two cortices pass between the lower two is
measured cvperimentally and is found to agree well with the
4-vorter analysis.

The calculation of loads on cruciform tails is considered in
some detail by the method of reverse flow, and equations are-

developed for the tail loads in terms of the vortex positions
calculated in the earlier analyses.

The importance of the rolling—up of the vortex sheet in
determining the downwash behind slender wings is now
generally recognized and has been discussed at some length
in reference 1. The current use of cruciform wings has
caused the missile designer further concern regarding the
downwash field in the vicinity of the tail. Such calculations
are generally considerably more complicated than those for
planar wings. However, since the wings on missiles of this
type are generally of low aspect ratio and the tail lengths
are long, it is often assumed that the vortex sheet shed from
each panel of a cruciform Wing is completely rolled up into a
single vortex line at the tail position. One of the purposes
of this paper is to investigate the usefulness of such an ap—
proximation at various distances behind the wing.