Calculation of the flow past slender delta wings with leading edge separation

The flow past a slender delta wing with a sharp leading edge, at incidence, usually separates along this edge, i.e. a vortex layer extends from the edge and rolls up to form a "core" (a region of high vorticity). A potential flow model of this is constructed in which the layer is replaced by a vortex sheet which is rolled up into a spiral in the region of' the "core". This problem is reduced to a two-dimensional one by assuming a conical field and using slender wing theory. The shape and strength of the sheet are determined by the two conditions that it is a stream surface and sustains no pressure difference. Use is made of results previously obtained for the core region and the remaining finite part of the sheet is dealt with by choosing certain functions for its shape and strength. The parameters in these functions are found by satisfying the two conditions stated above at isolated points. Results are Obtained for the pressure distribution, chord loading and normal force coefficient as functions of the ratio of the incidence to the apex angle. The lift for a given incidence is about 15% below that found by Brown and Michael. Flow patterns are indicated in two typical cases. The effect of separation on the drag due to lift of a wing with small thickness is discussed.