Improvement of Sailing Yacht Performance Prediction by Including Force-Moment Equilibrium for the Calculation of Helm Angle in a Velocity Prediction Program

Abstract

Contemporary Velocity Prediction Programs (VPP's) consider the equilibrium of forces acting on a sailing yacht in the thrust direction and in the direction of the developed side force on canoe body and appendages. In addition, force-moment equilibrium is considered in the transverse plane of the yacht. In this way a solution is found for the three main unknowns in performance prediction, viz: boat speed, leeway angle and heel angle. The impact of helm angle on performance is herein ignored. In the velocity prediction program developed by Van Oossanen & Associates, a fourth equilibrium condition is included, viz: force-moment equilibrium in the horizontal plane for the calculation of the helm angle required for the equilibrium sailing condition. In this paper a description is given of some of the main problems that need to be solved when introducing this fourth equilibrium requirement. One of these is associated with the development of accurate mathematical expressions for the calculation of rudder side force and resistance, as influenced by heel angle and the proximity of the free surface. Model tests can be utilized for obtaining insight into the physical phenomena involved in such cases. Model tests were carried out in the context of an optimization study for the design of a yacht according to the International Level Class 40 (ILC40) Rule, under the International Measurement System (IMS). The analysis of some of the results of these tests with respect to improving the mathematical model for rudder side force and resistance, is described in the paper. The effect of including this mathematical model in a VPP is demonstrated in the paper by providing the results of calculations which reveal that a variation in rudder angle causes significant speed differences. It is shown that the IMS VPP that is used to calculate the rating and speed potential of ILC40 and other IMS Class yachts, in not taking into account the significant variations in performance associated with different values of the equilibrium rudder angle (and the associated rudder side force and resistance), is not sufficiently accurate.