Some series-expansion solutions for slender wings with leading-edge separation

Abstract

The vortex formed above each leading edge of the wing is represented by a line vortex, as in the treatment of the flat delta wing by Brown and Michael, and the slender-body approximation is made. Four problems are treated: the thick, conical delta wing with rhombic cross-sections; the thick, conically-cambered delta wing formed by one-half of a circular cone; the flat-plate wing with curved leading edges; and a wing with a partially unswept leading edge and lengthwise camber. The quantities of interest are the position of the vortex and its circulation, and the non-linear lift and pitching moment of the wing. In each problem the solution is presented as an asymptotic series in a small parameter representing the scale of the separation. The solutions are used to shed,light on a number of problems arising in the aerodynamics of slender wings.