Aerodynamics of slender lifting surface in accelerated flight

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HERE are many researches into the aerodynamics of lifting surfaces in unsteady motion. Most of these, however, concern out-of-plane motions at a uniform flight speed, with few studies for nonuniform flight speeds.1'2'3 These problems have become increasingly more important, because recent airplanes, such as STOL or supersonic, can experience considerable acceleration during the take-off climb or landing approach. More precise estimation of take-off or landing distance would require some aerodynamic theories for accelerated flight. In Ref. 4, a fundamental formulation was made for wings in nonuniform motion in an inviscid incompressible flow. A Fourier transform for the in-plane coordinate variables was used. In Ref. 5, application was made to two-dimension al airfoils with a sinusoidally pulsating speed. A significant result was the fact that the difference between unsteady and quasi-steady lifts is significant, as was also shown by the previous writers.2'3 In general, the lift of a wing depends on the complete history of its motion, and not just on the instantaneous acceleration. In this paper, we treat the problem of slender wings in accelerated motion. This problem also is solvable and represents the low aspect ratio limit of wing theory opposite that of the two-dimensional problem. An interesting result has been obtained in that the lift force for slender wings is shown to depend only on the instantaneous acceleration and not on the history of its motion. An acceleration (deceleration) increases (decreases) the lift from that for the uniform flight speed. II. General Formulation In this section, a general formulation is given for the case of a wing in nonuniform motion (flight speed) in an inviscid fluid. The analysis employs a moving axes system fixed to the wing. According to Reissner, 6 the unsteady linear equations of aerodynamics expressed in a moving axes system can be written as follows: