A mathematical model for acceleration phase of aerodynamically alleviated catamarans and minimizing the time needed to reach final speed

摘要

Racing catamarans use aerodynamic alleviation concept which in existing extreme ground effect significantly enhances the performance. Beside design measures, controlling strategies may be employed as convenient solutions to improve the performance and address concerns regarding poor stability in these crafts. Being of substantial importance for a racing catamaran to reach the final speed as soon as possible, this study attempts to find the optimal form of changing the drive angle (as control variable) to minimize its acceleration time. In this regard, a mathematical model is developed for forward acceleration phase of these catamarans based on empirical and theoretical methods. Then the formulation and solution algorithm for the time-optimal problem are described according to an indirect method. Results for a representative racing craft have been presented in uncontrolled and controlled conditions. Problem in controlled condition has been solved without and with a predefined constraint regarding stability margin. Optimal controlling of the drive angle without stability constraint during the acceleration results in 40 % reduction in time required to reach the speed of 110 kn and 14 % reduction in resistance at this speed in comparison to the uncontrolled case. Addition of the stability constraint changes optimal solution for drive angle and causes craft trim angle follow a decreasing trend at higher speeds.