G. Chiocchia et al., THE LIFTING LINE EQUATION FOR A CURVED WING IN OSCILLATORY MOTION, Zeitschrift fur angewandte Mathematik und Mechanik, 77(4), 1997, pp. 295-315
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.