Aircraft Spacings that Produce a Vortex-Free Region Below Flight Formation

Theoretical estimates are presented for the motion of vortex wakes shed by multiple aircraft flying in close formation. The purpose of the theoretical study was to determine whether the spacings between adjacent aircraft in close formations could be designed so that the lift-generated vortices being trailed would move upward rather than downward. In this way, a region below the formation is produced that is free of vortices. It was found that aircraft can be arranged in formations so that the inboard wake vortices all move upward rather than downward. The two outboard vortices travel downward at a greatly reduced velocity that depends on the number of aircraft in the formation. If the desired motions are to be produced, the lateral spacings between adjacent aircraft centerlines must be between 1.1 and 1.5 wingspans, and the vertical spacings between -0.025 and -0.15 wingspans. Since the range of acceptable spacings is small, it is recommended that the position accuracy between aircraft in the formation be kept within about + or - 0.01 wingspan of the center of acceptable spacings so that aircraft meandering do not cause unwanted vortex excursions. It was also found that, if the in-trail spacings between adjacent aircraft are more than 4 wingspans, the foregoing vertical spacings must be adjusted to allow for the additional downward travel of the vortices shed by leading aircraft.