Unsteady Force on Slender Aircraft with Free Vortices in Inviscid Flow

Abstract

Expressions are derived for the force on circular and wing-body contours induced by a vortex pair in a twodimensional uniform unsteady inviscid e ow, such as arise in the slender-body approximation of an aircraft. Zeroforce curves fortheclassical vortex pairbehind a circularcylinder in oncoming e ow arefound, and it isshown that the direction of the force can be upwind as well as downwind. A convenient expression for the force on a contour in a symmetric e owe eld is obtained by conformal mapping, involving only the e rst- and second-order derivatives of the required transformation-function. A result of practical interest for free vortices intended to enhance the lift force of an aircraft is that the force on the crosse ow contour induced by vortices with a certain strength generally decreases when enlarging the width of the contour perpendicular to the direction of that force. So span reduction increases the lift generated by vortices above the wings. The position of the vortices in relation to the contour is critical, however, as there are areas that are shown, where the lift caused by the vortices is negative. The force caused by the symmetric vortex pair on the symmetric contour is independent of the speed of the oncoming e ow; the pressure distribution on the contour, however, does vary with changing speed of the oncoming e ow.