The behaviour of a conical vortex sheet on a slender wing near the leading edge

Abstract

The inviscid flow field past a slender delta wing at incidence with leading-edge separation can be considered as conical. The shape of the resulting vortex sheet has been calculated by J. H. B. Smith and others. Here the behaviour of the sheet near the leading edge of the wing is investigated and an expansion of the solution in this neighbourhood is found by the application of certain theorems of the theory of complex functions. It is shown that in a cross-flow plane (normal to the undisturbed flow) the slope of the sheet can be expressed in powers of the square root of the arc length measured along the sheet. A related series expansion is found for the strength of the vortex sheet. The sheet is always tangential to the pressure side of the wing. On the suction side of a wing with thickness the flow is parallel to the leading edge, so that the strength of the vortex sheet at the leading edge is directly related to the overall circulation around the sheet.