A Numerical Lifting-Line Method Using Horseshoe Vortex Sheets

Document Type

Conference Paper

Journal/Book Title/Conference

Rocky Mountain Space Grant Consortium Meeting Proceedings


Logan, UT

Publication Date



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.

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