TABLE OF CONTENTS This and subsequent sections present four related aerodynamic theories that were originally formulated either for fixed-wing applications and subsequently made applicable to the rotary-wing case or derived for the rotary-wing case directly using established fixed-wing theoretical methods. The four theories all make the small-perturbation assumption (including the assumption of a "thin" airfoil). In addition, the following specific assumptions are made consistent with linearized theory:
The airfoil section consists of a flat plate with "small" initial angle of attack, with a wake shed from the trailing edge of the airfoil rearward to infinity without any downward velocity or vertical distortion.
The flow is inviscid and incompressible ( M = 0).
The flow is governed by linear potential flow; the nonlinearities arising from stall are omitted.
The disturbances, whether in the motion of the airfoil or in the flow, are simple harmonic.
The four theories deal, respectively, with motion of the airfoil in pitch and plunge (the Theodorsen problem), vertical sinusoidal gustiness imbedded in the flow into which the airfoil is moving with constant speed (the Sears problem), an expansion of the Theodorsen problem with an accounting of the returning wakes from the same and other rotor blades (the Loewy problem), and sinusoidal variations of the flow in the longitudinal (streamwise) direction (the Isaacs problem).
The two-dimensional theory formulated by Theodorsen is one of the most enduring (and probably overused) theories transcribed from fixed-wing aerodynamics. This theory relates to the perturbational plunging (
