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National Advisory Committee for Aeronautics, Technical Notes - Behavior of Vortex System Behind Cruciform Wings - Motions of Fully Rolled Up Vortices

The motions of four fully rolled-up vortices representing the vortex
system trailing behind cruciform wings are studied by theoretical and
visual-flow methods. The analysis applies throughout the Mach number
range.

Equations are developed for the three—dimensional paths traced by
the vortices behind a cruciform wing banked #50 , and calculations are
made of the distance behind the wing at which the upper two vortices
pass through the lower two. It is found that this "leapfrog" distance
depends upon the lift coefficient, aspect ratio, and span loading of the
cruciform wing, and that for low—aspect-ratio cruciform wings leapfrog-
ging may occur within two chord lengths of the trailing edges.

The various types of vortex motion to be expected throughout the
angle—of-attack range are considered in some detail, and the interaction
of the two vortex sheets shed from the cruciform wing is taken into
account. Results of some water—tank studies are also presented and
compared with the theory.

The downwash behind plane wings has been studied theoretically by a
number of authors and considerable attention has been given to the
rolling up of the trailing vortex sheet. The analysis of Kaden
(reference 1) predicted the distance behind the wing at which the sheet
msy'be considered to be fully rolled up into two trailing vortices, and
this work was later used (in reference 2) to demonstrate the usefulness
of the single horseshoe-vortex approximation for the calculation of the
downwash behind wings of low aspect ratio. Since at the present time
cruciform configurations are largely confined to wings of low aspect
ratio, the rolling up of the trailing vortex sheets is again of major
concern, and the behavior of the fully rolled~up vortices is again of
considerable interest.

While in the case of the plane wing the vortex sheet became rolled
1m into a vortex pair which simply moved downward at a uniform speed at
great distances behind thewing, the analogous problem for cruciform
wings is necessarily mOre complicated. Instead of the two rolled-up
vortices, there are now presumably four (one from each wing panel) and
their induced effects @on one another are such as to produce quite
intricate paths of motion. The downwash field, of course, may therefore
become extremely involVed., This report is concerned with a study of the
motions of the four rolled-up vortices and their effect on the downwash
behind cruciform wings.