TABLE OF CONTENTS The development of unsteady aerodynamic theories, suitable for predicting time histories of arbitrary motions of the aeroelastic responses, has in one sense paralleled the early work on aerodynamic theory for sinusoidal motion, as described earlier. The Theodorsen and Sears problems, which relate respectively, to sinusoidal airfoil motion in an otherwise motionless air mass and to a motionless airfoil entering an air mass in sinusoidal motion, have counterparts in the time-history domain in the Wagner and K ssner problems. In these latter (arbitrary motion) theories the problem statements are the same (as for the Theodorsen and Sears problems), except that the motions are defined in terms of unit step functions.
Development of more general rotary-wing formulations in the time-history domain is a current direction being actively pursued. Much work is in progress, and much yet remains to be accomplished. As developed in the ensuing sections, the relationship between the Theodorsen and Wagner functions is that of a Fourier transform pair. The characteristics of the Wagner problem have pointed the way to a more general formulation of the rotor unsteady aerodynamic problem. The Wagner problem and a more general implementation of it are presented in the following material.
Recall from earlier sections that the lift and moment on a two-dimensional airfoil can be characterized by the presence of noncirculatory (virtual mass) and circulatory terms that have the following features:
The noncirculatory terms are already defined in the time-history...
