M.Sc Student M.Sc Thesis Gabay Keren Roz Optimization of Forces on Airplanes in Formation Flight Department of Aerospace Engineering RESEARCH PROFESSOR E Daniel Weihs PROF. Gil Iosilevskii

Abstract

Reduction of induced drag in formation flight has been known from the early days of aeronautics. In this work, two models based on lifting line theory are developed to calculate secondary effects of formation flight. The models are used with formations of identical elliptic wings having aspect ratio of 6.4, NACA 2412 cross section, and flying at lift coefficient of 0.37.

The first model is derived for two-wing planar formations only. The effect of formation is calculated for both wings. Lift distributions of the wings are found by applying lifting line theory and solving it for both wings simultaneously. This model is applied for three cases. In all the three cases the lift of each wing in the formation equals the lift in the nominal case. In the first case there was no attempt to counteract the rolling moment induced the wings by the formation. In the second case and in the third case, the rolling moment was neutralized respectively by twisting the wings and by deflection of the wings ailerons. The induced drag reduction obtained for the rear wing in the third case, reaches a maximum value of 49%. Ailerons deflection responsible for neutralizing the rolling moment carries a penalty of 3% in drag reduction (derived by comparison to the first case results).

The second model is derived for multi-wing, not necessarily planar, formations. The effect of formation is calculated only for one (influenced) wing, avoiding the question of its influence on the other wings. Each of these other wings is represented by a horse shoe vortex and the lift distribution of the influenced wing is found by applying a standard lifting line theory. When applying this model to a two wing formation the maximum induced drag reduction obtained for the rear wing equals 44%; it corresponds to the case when both wings are in the same plane. Increasing the number of wings in the formation increases the total induced drag saving of the formation, from 22% for the 2 wing formation to 57% for a formation of 50 wings.