The spreading phase in Lighthill's model of the Weis-Fogh lift mechanism

Abstract

Lighthill's analysis (J. Fluid Mech., vol. 60, 1973, p. 1) of the Weis-Fogh lift mechanism is extended to include the spreading phase of the cycle. Lighthill proposed a two-dimensional inviscid irrotational analytical model to compute the circulation around two flat plates (the wings) as they open out, in opposite directions, about a common centre of rotation taken to be at the point of contact of an edge of each plate (the ‘opening phase’). At a critical opening angle, the plates separate and move apart horizontally (the ‘spreading phase’). During this second phase, the fluid region becomes doubly connected and is not analysed by Lighthill. It can, however, also be studied analytically and the results are presented here. We also extend a similar analysis, in an application to turbomachinery, due to Furber & Ffowcs Williams (J. Fluid Mech., vol. 94, 1979, p. 519).