A Numerical Lifting-Line Method Using Horseshoe Vortex Sheets
Rocky Mountain Space Grant Consortium Meeting Proceedings
A numerical method based on the original lifting- line theory of Prandtl is developed which includes the influence of horseshoe vortex sheets. The method is an attempt at developing a higher-order method than previous delta-function methods of the same type. The definition of a horseshoe vortex sheet singularity is introduced and the velocity induced at an arbitrary point in space by the singularity is developed. No closed-form solution for this induced velocity was found for points not collinear with the bound portion of the singularity. Additionally, the velocity induced along the bound portion of a horseshoe vortex sheet with sweep is indeterminate. The singularity was used to develop a numerical method capable of predicting the aerodynamic forces and moments on a system of lifting surfaces. The method gives results within the accuracy of other similar methods, but requires higher grid refinement and more computation than previous methods.
Hunsaker, D. F., “A Numerical Lifting-Line Method Using Horseshoe Vortex Sheets,” Rocky Mountain Space Grant Consortium Meeting Proceedings, Logan, Utah, May 2011.