An analytical investigation of two-dimensional and three-dimensional biplanes operating in the vicinity of a free surface

In the present article, the classical two- and three-dimensional lifting theories are generalized to the biplane operating in proximity to a free surface. The singularity distribution method is employed to calculate the lifting force for a two-dimensional biplane subjected to wing-in-ground effect in the vicinity of a free surface, and the three-dimensional correction is carried out by the aid of the Prandtl lifting line theory. The essential techniques lie in finding the three-dimensional Green's function for the system of horseshoe vortices operating above a free surface and ensuring numerical implementation. Extensive numerical examples are carried out to show the lift coefficient for the two-and three-dimensional biplanes in the vicinity of a free surface with the variation of the clearance-to-chord ratio and the height-to-chord ratio. Incidentally, the induced (inviscid) drag coefficients as well as the lift-to-drag ratio for a three-dimensional biplane are also computed. Good agreement can be found among results obtained from this study and the experiment.