Multi-condition hydrofoil optimisation using an adjoint velocity prediction program

Hydrofoils are usually operated across a wide range of conditions. This results in different states and trims of the vessel and must be considered in hydrofoil optimisation. Therefore, an adjoint velocity prediction program (VPP) is developed and integrated it into a gradient-based optimisation routine. The method allows accurate optimisation with the full yacht model and hundreds of design variables at a small computational cost. The framework has previously been used for single condition optimisation but is now extended for multiple conditions. This is achieved by solving the VPP for different conditions and averaging the resulting velocities made good ($V_{\text{MG}}$) and gradients. The method is applied to an AC75 America's Cup yacht. Its hydrofoils are optimised for six conditions derived from historical weather data. The optimal foil is 7.2 % faster than the initial foil in terms of average $V_{\text{MG}}$ which results in an 81.9 s timesaving over a race. The multi-condition foil is compared to foils optimised for the individual conditions. The individual foils perform best in their respective niches, whereas the multi-condition foil performs best across the range of conditions. The multi-condition optimisation can be performed at no additional cost and demonstrates the immense capabilities of adjoint VPP-based hydrofoil optimisation.