The spanwise lift distribution on a wing from flow-field velocity surveys

The application of the incompressible three-dimensional momentum integral equation to a finite wing is reviewed. The objective is to interpret the resulting equations in a way that suggests an alternate experimental method for determining the span-wise distribution of lift. Consideration is given to constraints that must be placed on the character of the vortex wake of the wing to provide the familiar relationship between lift and bound vorticity. A novel technique is then presented for obtaining, from behind the wing, the spanwise lift distribution from velocity surveys that are made over only a short distance above and below the wing trailing edge. The necessary formalism is developed to use these measured values to obtain the actual span loading by using an equivalent single horseshoe vortex model to account for the unmeasured portion of the downward (or upward) momentum. The results of a numerical simulation are presented for a typical loading distribution. The technique is then verified experimentally using laser velocimeter data for the flow field around a model wing.