The Rolling Up of the Trailing Vortex Sheet and Its Effect on the Downwash Behind Wings

The motion of the trailing vortices associated with a lifting wing is investigated by theoretical and visual-flow methods for the purpose of determining the proper vortex distribution to be used for downwash calculations. Both subsonic and supersonic speeds are considered in the analysis. I t is found that the degree to which the vortices are rolled up depends upon the distance behind the wing and upon the lift coefficient, span loading, and aspect ratio of the wing. While the rolling up of the trailing vortices associated with high-aspectratio wings is of little practical importance, it is shown that, with low-aspect-ratio wings, the trailing vortex sheet may become essentially rolled up into two trailing vortex cores within a chord length of the trailing edge. The downwash fields associated with the two limiting cases of the flat vortex sheet and the fully rolled-up vortices are investigated in detail for both subsonic and supersonic speeds. The intermediate case in which the rolling-up process is only partially completed at the tail position is also discussed.