An alternative formulation of the lifting line wing equation and its solution

Abstract

In the report, the standard wing equation, as normally derived from lifting line theory, is further refined and a solution procedure more basic than the usual collocation technique is developed. The calculation method adopted avoids the necessity of performing an explicit matrix inversion; all equations can be solved sequentially, one at a time. On the other hand this technique involves the evaluation of numerous integrals over the span. The calculations are cumulative, and can be carried as far as necessary to achieve any required degree of accuracy. The analysis is interesting not only for purposes of practical calculation but also for the light it sheds on the essential mathematical structure of the basic aerodynamic phenomena involved. This same general method of calculation can also be readily adapted to the solution of other common types of engineering problems. (Author)