Three-Dimensional Unsteady Linearized Lifting Flows

For a wing of finite aspect ratio, all derivations can be carried out to the order of 0(h), which is practically enough to provide reliable information for relative ground clearances up to 0.1-0.15. However, here the analysis will be restricted to the least cumbersome (from the viewpoint of the algebra involved) case of the extreme ground effect. Moreover, the concrete case of an oscillating flat plate with a rectangular planform will be considered. Due to linearization, the effects of camber can be superimposed.

Let a finite wing perform heave oscillations with the following description of its instantaneous position with respect to the ground:

different magnitudes of the Strouhal number. For A -> oo, formulas (3.101) and (3.102) yield results of the corresponding unsteady two-dimensional flow problem. For A —> 0, the following expressions are obtained: