Optimum Downwash Behind Wings in Formation Flight

摘要

The calculus-of-variations approach previously used by Jones for determining minimum induced drag of single wings has been extended to handle multiple wings in formation flight with constraints on the lift and rolling moment for each wing. The approach shows that the lift distributions for wings in formation flight with constraints on the lift and rolling moment on each wing must result in a linear variation in the Trefftz-plane downwash for the total induced drag of the formation to be a minimum. This simple and elegant result illustrates the power of the optimum-downwash approach pioneered by Munk and Jones. The optimum lift distribution was obtained from the optimum downwash using a discrete vortex lattice method similar to that described by Blackwell.8 The results from the current approach agree identically with those obtained using a constrained-minimization approach. The current approach considers only wings in formation flight and needs to be extended to handle aircraft in formation, with each aircraft being in longitudinal trim, as was done in Ref. 4. Additionally, like the constrained-minimization approach, the current formulation is also valid only for formation geometries in which the wake traces of the wings in the Trefftz plane do not intersect or overlap with each other. Although there does not appear to be any significant computational advantage to the present method when compared to that of a constrained-minimization technique, the present method provides a simple closed-form expression for the optimum downwash and, thus, provides additional insight into the aerodynamics of ideal formation flight.