Transition dynamics of VTOL aircraft

Asymptotic approximations using multiple time scales are developed for the longitudinal dynamics of VTOL vehicles during the hover, forward-flight transition. After reviewing the method briefly, the transitional equations of motion whose coefficients vary with flight velocity are studied. Rapid and slow motions of the vehicle are extracted individually and combined to yield a composite solution. The time scales are necessarily nonlinear functions and complex quantities to describe nonautonomous phenomena. Aircraft in steady flight arise as a natural limit. The present method thus generalizes earlier time scale analyses. The technique is applied to VTOL vehicles exhibiting typical stability derivative variations, first to the two degree-of-freedom case and then the three degree-of-freedom case. The asymptotic approximations are compared with exact numerical integrals. An analytical description of the aircraft motion is thus obtained. The problem of transition points is outlined.

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