Time Optimization for Laser Sailing Races

Abstract

Sailing against the wind follows a zig-zag trajectory. To find the optimal time and path-trajectory to move from one target to another during a race, this study analyzes how the wind determines the optimal time-path of Lasers, one of the smallest sailboats that compete during the summer Olympic Games.
To answer this question, this study uses four wind models in an algorithm developed in MATLAB to find the optimal time-path. The wind models were forecasts and wind measurements for the area of race R1 from the World Cup Series 2018 at Hyères, France. One of the wind models used were a Weather Research and Forecasting model (WRF) with a grid resolution of 1km, a time step of 10 minutes. On the other hand, the most basic model was a constant and uniform wind field.  The race R1 has three lines, limited by two buoys, and one point(buoy), one line and one point define a leg. R1 has five legs and two of them are against the wind. The results, time and path-trajectories, of each of the wind models, were compared with the results of the top 10 winners of the race. They showed that the legs sailed against the wind are also characterized by the location of the sailboats on the start line. The times of these legs using the WRF wind model and the race-time had an error of less than 5%. For the prediction of the start location, it was the same as the winner of the race. However, the direction of the paths was not predicted accurately for these legs. Using the constant and uniform wind scenario, the percentage error of the race-time respect to the winner is about 7%. However, the direction of leg 2 is not even similar to the winner. To review the effects of the heights of the waves this study proposes to model the sailboat in 3-dimensions including the X-coordinate of the sail-man position. In addition, a 3D model allows the analysis of how the center of effort (CE) on the sail is affected by the current and waves.