Planing craft modeling in forward acceleration mode and minimisation of time to reach final speed

Abstract

Properly adjusting the trim angle during the craft speed up will be extremely important in special cases as in sports competitions or military missions. In such applications, the goal of trim adjustment is to reach final speed in a minimum possible time which is an advantage to just passing the resistance hump. Present study tries to provide insight into how the angles of the drive system and trim tab of a planing craft should be changed during speed up so as to minimise the time to reach the final speed. This is a time-optimal control problem with the drive and trim tab angles as the control variables. Optimal control theory has been used previously for the motion control of marine vessels in the applications such as seakeeping, manoeuvring and navigation. This study introduces a new application of this theory for increasing the craft speed performance. Conventional empirical relations are used in the equations of motion for calculating hydrodynamic forces to develop the dynamic model. To calculate the forces due to the propulsion system, attempts are made to take into account the propeller, the drive system and the engine concurrently in a simplified manner. The solution algorithm is explained and the results for a planing vessel with two different longitudinal centers of gravity are presented. Optimal solution for control variables shows a simultaneity and similarity in trend with the hull instantaneous trim angle. However, the optimal signals are restricted by upper physical margins.

Formulation of a nonlinear mathematical model to simulate accelerations of an AAMV in take-off and landing phases

“…However, the above equations can be solved by using a quasi-steady approach in time domain. Quasi-steady means that in each time step the hull condition is considered stationary and the velocity is assumed constant (Yangeneh et al 2014). The solution to the problem starts with the specified initial values for x 3 , x 5 and V. After substituting the derivative term in Equation (13) with the forward finite difference approximation, the mentioned equation is turned into the following equation:…”