Note on the Gliding of a Plate on the Surface of a Stream

Extract

1. The gliding of bodies on the surface of water has received mathematical treatment by Wagner for both two- and three-dimensional cases. In this note, attention is confined to the two-dimensional gliding of a plane plate on a stream of infinite depth. Wagner's method is approximate and only applies when the angle of incidence of the gliding plate to the stream is small. He expresses such quantities as the total lift on the plate, not in terms of the total length of the plate, but in terms of the length of the pressure surface, which is the distance between the trailing edge of the plate and the point of stagnation. Further, his solution requires that the direction of the jet or spray which is formed should be parallel to the length of the plate. If Lis the total normal lift on the plate, β the small angle of incidence of the plate to the stream, V the velocity of the plate, δ the thickness of the spray and c the length of the pressure surface, then Wagner gives