Fluid Forces on a Hydrofoil for Kitefoil and Windfoil Boards: Experimental Investigation on Their Dependence on the Froude Number Based on Submergence

Abstract

Races using kitefoil and windfoil surfboards have been in the Olympic Games for the first time in Paris 2024, signalling their relevance in sailing sports. However, the dynamics of these devices is yet not well understood, in particular the influence on the hydrodynamic forces and moments of the distance of the foil to the free surface. Considering this, the present paper documents an experimental investigation in which forces and torque produced, under uniform flow, by a full-scale state-of-the-art hydrofoil (suitable both for kitesurf and windsurf) were measured. A range of velocities, angles of attack, and submergences were tested, leading to Froude numbers based on submergence with maximum values around five, a typical range in actual sailing conditions. From these tests, formulae for the hydrodynamic coefficients have been proposed. They can be used for developing Velocity Prediction Programs (VPP) for this kind of craft, a necessary tool to plan racing configurations and to analyze their racing performance. With the aim of making the experimental data useful for benchmarking numerical models and for future research on related topics such as foil ventilation and transition to turbulence, the specimen’s 3D file is provided as supplementary material to this paper.

Keywords

Hydrofoil / Kitefoil / Windfoil / Velocity prediction programs / Lift coefficient / Drag coefficient

References

[1] AngelouM, SpyrouKJ. Modeling of transient hydrodynamic lifting forces of sailing yachts and study of their effect on maneuvering in waves. Ocean Engineering, 2019, 173: 531-547

[2] BardenT, BinnsJ. On the road to establishing ventilation probability for moth sailing dinghies. 18th Australasian Fluid Mechanics Conference, Launceston, Australia, 2012 1-4

[3] BeaverB, ZseleczkyJ. Full scale measurements on a hydrofoil international moth. 19th Chesapeake SailingYacht Symposium, Annapolis, USA, 2009

[4] BinnsJ, BrandnerP, PlouhinecJ. The effect of heel angle and free-surface proximity on the performance and strut wake of a moth sailing dinghy rudder t-foil. High Performance Yacht Design Conference, Auckland, New Zealand, 2008 121-129

[5] BonnardH, ChatellierL, DavidL. Investigation of 3D effects and free-surface proximity influence on the flow around a hydrofoil using piv measurements. 20th International Symposium on Applications of Laser and Imaging Techniques to Fluid Mechanics, Lisbon, Portugal, 2022 1-9

[6] CampbellI, OwenM, ProvincialiG. Dagger-board evaluation for an imoca 60 yacht. Ocean Engineering, 2014, 90: 2-10

[7] CarterAW, ButlerRV Experimental investigation of the flow field behind an aspect-ratio-10 hydrofoil near the water surface, 1953 Washington, United States National Advisory Committee for Aeronautics

[8] CuiX, ZhouZ, YuY, YuL, LiY, ZhouT. Numerical analysis and improvement of longitudinal moment pitch-up characteristics for civil aircraft. Journal of Physics: Conference Series, 2021, 2010(1): 012075

[9] DaskovskyM. The hydrofoil in surface proximity, theory and experiment. Ocean Engineering, 2000, 27(10): 1129-1159

[10] DayS, CocardM, TrollM. Experimental measurement and simplified prediction of t-foil performance for monohull dinghies. 23rd Chesapeake Sailing Yacht Symposium, Annapolis, USA, 2019

[11] DucoinA, YoungYL. Hydroelastic response and stability of a hydrofoil in viscous flow. Journal of Fluids and Structures, 2013, 38: 40-57

[12] GiallanzaA, MarannanoG, MoraceF, RuggieroV. Numerical and experimental analysis of a high innovative hydrofoil. International Journal on Interactive Design and Manufacturing, 2020, 14: 43-57

[13] GlauertH The elements of aerofoil and airscrew theory, 1948 Cambridge, UK Cambridge University Press

[14] Gomez TiernoMA, Pérez CortésM, Puentes MárquezC Mecánica del vuelo, 2012 Madrid, Spain Garceta Grupo Editorial (in Spanish)

[15] HarwoodCM, YoungYL, CeccioSL. Ventilated cavities on a surface-piercing hydrofoil at moderate Froude numbers: Cavity formation, elimination and stability. Journal of Fluid Mechanics, 2016, 800: 5-56

[16] HoughG, MoranJ. Froude number effects on two dimensional hydrofoils. Journal of Ship Research, 1969, 13(1): 53-60

[17] ITTC. General guideline for uncertainty analysis in resistance tests. International Towing Tank Conference, Copenhagen, Denmark, 2014 7.5-02-02-02

[18] ITTC. Guide to the expression of uncertainty in experimental hydrodynamics. International Towing Tank Conference, Copenhagen, Denmark, 2014 Revision 02 7.5-02-01-01

[19] ITTC. ITTC quality system manual, recommended procedures and guidelines, guideline to practical implementation of uncertainty analysis. International Towing Tank Conference, Wuxi, China, 2017 7.5-02-01-07

[20] ITTC. ITTC quality system manual, recommended procedures and guidelines, procedure: Seakeeping experiments. International Towing Tank Conference, Wuxi, China, 2017 7.5-02-07-02.1

[21] JentzschM, DahmsJ, WoszidloR, NayeriCN, PaschereitCO. Free surface effects and the utility of a skim plate for experiments in a water towing tank at steady and unsteady model velocity. Experiments in Fluids, 2022, 63: 164

[22] Marimon GiovannettiL, FarousiA, EbbessonF, ThollotA, ShiriA, EslamdoostA. Fluid-structure interaction of a foiling craft. J. Marine Science and Engineering, 2022, 10(3): 372

[23] Miguel MonteroF, MinervaL. Experimental methods for investigation of foiling crafts. 26th International HISWA Symposium on Yacht Design and Yacht Construction, 2020 1-32

[24] MollandAF, TurnockSR Marine rudders and control surfaces: Principles, data, design and applications, 2007 Oxford, UK Butterworth Heinemann

[25] MünkMM Elements of the wing section theory and of the wing theory, 1924 Washington, United States National Advisory Committee for Aeronautics 191

[26] NiZ, DhanakM, SuTC. Performance of a hydrofoil operating close to a free surface over a range of angles of attack. International Journal of Naval Architecture and Ocean Engineering, 2021, 13: 1-11

[27] Ocana BlancoD, Castaneda-SabadellI, Souto-IglesiasA. CFD and potential flow assessment of the hydrodynamics of a kitefoil. Ocean Engineering, 2017, 146: 388-400

[28] SouppezJB, DewavrinJM, GohierF, LabiGB. Hydrofoil configurations for sailing superyachts: Hydrodynamics, stability and performance. Design & Construction of Super & Mega Yachts, Genoa, Italy, 2019

[29] TisserandC Des hydrofoils a la portée de tous, 2005 [Accessed on May 29, 2025] (in French)

[30] VanillaT, BenoitA, BenoitP. Hydro-elastic response of composite hydrofoil with FSI. Ocean Engineering, 2021, 221: 108230

[31] VellingaR Hydrofoils: Design, build, fly, 2009 Tacoma, United States Peacock Hill Publishing

[32] WadlinKL, RamsenJA, McGeheeJR Tank tests at subcavitation speeds of an aspect-ratio-10 hydrofoil with a single strut, 1950 Washington, United States National Advisory Committee for Aeronautics RM L9K14a

[33] WadlinKL, ShufordCL Jr, McGeheeJR A theoretical and experimental investigation of the lift and drag characteristics of hydrofoils at subcritical and supercritical speeds, 1955 Washington, United States National Advisory Committee for Aeronautics NACA-TR-1232

[34] WangJ, SanthoshS, ColomésO, CapaldoM, YangL. Experimental study of dynamic response of passive flapping hydrofoil in regular wave. Physics of Fluids, 2023, 35(7): 077127

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Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature