Improving the Convergence of the Doublet-Lattice Method Through Tip Corrections (2003)


In 1973 Hough studied the slow convergence of the Vortex-Lattice Method (VLM) as the number of spanwise divisions (strips) is increased. Specifically, the lift curve slope of a lifting surface was shown to decrease significantly as the resolution of the lattice was increased, converging to the “true” value only with relatively fine spanwise divisions. Impressive improvements in the converged results were achieved when equally spaced divisions of the lifting surface were inset from the tip by a fraction of the strip width. Hough demonstrated the improvement via the tip inset on a number of wing planforms at a constant angle of attack.

Hough’s argument was based on an elliptical lift distribution which is a reasonable assumption in the steady, symmetric case. The present paper investigates also cases where elliptical lift distributions are not expected, specifically, the antisymmetric motion of rolling, elastic motions, and oscillatory motions with high reduced frequencies. The beneficial effect of the tip inset is observed in all cases investigated