A numerical vortex box technique for calculations in lifting surface theory

At present, a number of lifting surface theories exist. By and large most of these theories assume superimposed chordwise and spanwise lift distributions which can be represented in series form, thereby resulting in some very unwieldy relations that must be solved by numerical means. Many theories which utilize discrete vortices to represent the wing have also come into vogue. However, regardless of how pliable and accurate the theories have been to date in predicting air loads, it is difficult to justify on physical grounds certain of the basic assumptions made, namely that the vortex element should be at the 1/4 chord point and the downwash should be calculated at the 3/4 chord point of each box. The present method derives its working form directly from the physical interpretation of the basic equation from which all solutions in subsonic wing theory are developed. In this paper, the method is formulated for both the two and three-dimensional cases, with the working form generated from comparisons with the known exact value for a flat plate at incidence. Results are generated in the three-dimensional case for rectangular wings and swept wings of various aspect ratios. The results are compared to several methods in existence. The general conclusion is reached that the method compares very well with the known exact solution in the two-dimensional case and with the various solutions in the three-dimensional case. Furthermore, the present method is physically justifiable due to the fact that it is obtained directly from the general equation of wing theory