Ideal aerodynamics of ground effect and formation flight

The theoretical induced-drag benefits are presented for ideally loaded wings flying in formation and ground effect. An optimum-downwash approach using a vortex-lattice implementation was used to study formations of wings loaded optimally for minimum induced drag with roll trim. An exact approach was also developed to examine the drag of elliptically loaded wings in formation. The exact approach allows for decomposition of the benefits by considering the mutual-interference contributions from different pairs of wings in a formation. The results show that elliptically loaded wing formations have nearly the same drag as optimally loaded wing formations. For a formation of planar wings, in or out of ground effect, the optimum lateral separation corresponds to a 10% span overlap of wing tips. At this optimum lateral separation, a formation of 25 elliptically loaded wings flying out of ground effect experiences an 81% drag reduction compared to 25 wings flying in isolation. For large formations, in or out of ground effect, multiple local optima are seen for the lateral separation. Large formations experience small additional benefits caused by ground effect even at relatively large ground clearances of four wing spans. The shape of vee formations, for equipartition of drag benefits, is found to be nearly independent of flight in or out of ground effect.