The Calculation of Aerodynamic Loading on Surfaces of Any Shape
AERONAUTICAL RESEARCH COUNCIL LONDON (UNITED KINGDOM)
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This report seeks to establish a routine method for calculating aerodynamic loads on wings of arbitrary shape. The method is based on potential theory and uses a general mathematical formula for continuous loading on a wing which is equivalent to a double Fourier series with unknown coefficients. To evaluate the unknown coefficients, the continuous loading is split up into a regular pattern of horseshoe vortices, the strengths of which are proportional to the unknown coefficients and to standard factors which are given in a table. Total downwash at chosen pivotal points is obtained by summing the downwashes due to the individual vortices, a process which is simplified by use of specially prepared tables of the properties of the horseshoe vortex. By equating the downwash to the slope of the wing at each pivotal point, simultaneous equations are obtained, the solution of which defines the unknown coefficients. The first layout involves a total of 76 vortices over the wing, and a second layout, involving a total of 84, is shown to be of superior accuracy. The effect on the solution of the number of pivotal points is investigated and it is concluded that by a suitable choice, it is unnecessary to use a large number. Results for a rectangular wing at 0 deg, and an elliptic wing at 0 deg and 30 deg yaw are compared with those obtained by other workers and it appears that there may be errors of the characteristics of actual sweptback wings, including rotary derivatives, and future development includes also applications in wind tunnel design and technique.
- Fluid Mechanics