Velocity Prediction of Wing-Sailed Hydrofoiling Catamarans

Abstract

The paper presents a Velocity Prediction Program for hydrofoiling catamarans with solid wing sails. Starting from a description of the mechanical model, suitable models are identified for the forces that act on the boat components. The study is deliberately limited to means for restricted methods where computational resources and budgets are limited. Enhanced lifting line approaches are described for the wingsail and appendages. Windage is calculated from force coefficients and dynamic pressure while hull resistance is determined by means of a potential flow solver. The description of the implementation is followed by the presentation of the results. An approach for processing of measurement data is shown in preparation to compare measured and predicted performance. Good agreement was found for upwind conditions whereas varying differences are found for most of the remaining wind angles. Finally, some of the challenges encountered during the study are discussed. A Reference area [m²] AoA Angle of attack [°] AWS Apparent wind speed [m s-1 ] BS Boatspeed [m s-1 ] cF Coefficient of force [-] cL Coefficient of lift [-] ci, í µí± + ,,⃑ Local chord/chord vector [m] d Perpendicular distance between vortex filament and collocation point [m] dcore Diameter of viscous vortex core [m] F Force [N] k Vortex strength reduction factor [-] M Moment [N m] í µí±Ÿ ⃑ Vector between start of free vortex filament and collocation point [m] Re Reynolds number [-] si, í µí± + ,,⃑ Local span/span vector [m] TWA True wind angle [°] TWS True wind speed [m s-1 ] u Incident flow velocity [m s-1 ] vindC Velocity induced at point PC [m s-1 ] í µí±£ + ,, ,⃑ Total induced velocity vector [m s-1 ] í µí±£ +,> ,,,,⃑ Induced velocity vector [m s-1 ] í µí±£ ?+,> ,,,,,,,,⃑ Mirror image induced velocity vector [m s-1 ] í µí±¤ + ,,,⃑ Total velocity vector [m s-1 ] z Vertical distance [m] zC Vertical collocation point position [m] 67 Γ Vortex strength [m 3 s-1 ] r Density of water/air [kg m-³]