THE LIFTING LINE EQUATION FOR A CURVED WING IN OSCILLATORY MOTION

An unsteady linear lifting line method for the determination of the ci rculation and lift distribution along the span of a curved wing subjec t to harmonic small amplitude oscillations is presented. The method re lies on the Pistolesi-Weissinger 3/4-chord steady lifting line theory and couples it to the unsteady theory developed by Possio Sor the moti on of lifting surfaces. It leads to an integro-differential equation o f a modified Prandtl's type, where the unknown is the circulation. Thi s equation has been carefully analysed in order to evidence ail the si ngularities and to treat them in the most convenient way. The numerica l procedure consists of a gaussian quadrature technique based an Cheby shev's polynomial approximation of the unknown function. The method ha s been appraised through the comparison of a number of solutions, pert aining to different wing configurations; with existing solutions based on lifting surface theory.