Tacking Simulation of Sailing Yachts - Numerical Integration of Equations of Motion and Application of Neural Network Technique

The question, "What is the best tacking procedure?", has challenged sailors for a long time. In order to answer this question, it might be best to clarify the mechanism of tacking motions of sailing boats theoretically. However, tacking is a complicated maneuvering motion. Many factors affect tacking, including maneuverability, rolling characteristics, sail performance, etc. The first step to tackle this problem, therefore, is to make a proper model which represents tacking motions. In the present paper, two models are proposed to represent the tacking motions of sail boats. One is a mathematical model and another is a neural network model. In the mathematical model, the tacking motion of the boat is described by partial differential equations with the coordinate system using the horizontal body axes. The hydrodynamic derivatives of the equations are mainly given by model test results and/or full scale measurements. Such coefficients as added mass and added moment of inertia are calculated using the strip method. These equations are integrated using an integration method. In the neural network model, on the other hand, the tacking motion of the boat is regarded as a neural network system consisting of several layers. In the present paper, two hidden layers are used besides the input and output layers. The network constants are tuned using back-propagation procedure. If the rudder angle is inputted, the boat motion can be obtained step by step using the network. Comparing the results obtained by these two methods with the full-scale experiments of a sailing boat, the merit and the demerit of these models are discussed.