where Xu, Yv, Z„ , Kp, Mq, and Nr are the linear damping coefficients. Y„w, Z„k|, KpM, Mq\q\, Xu\u\, and Nr\r\ are the quadratic damping coefficients. M0 and Z0 are the effect caused by the dissymmetry on xoy plane.
The external force and moment vector produced by trusters trop is defined as
T prop LTprop
where L is a mapping matrix, and T is the thrust vector produced by thrusters given by
The number n in Tprop depends on the number of thrusters. The mapping matrix L is a 6*n matrix that uses Tprop to find the overall force and moment acting on the vehicle. Hydrodynamics of a single thruster is usually obtained through the in water test. A series of advance coefficient J corresponding to the thrust coefficient KT data can be obtained from the in water test. Data from an in water test are shown in Fig.2. We fit the curve by the method of least squares and then obtain the fitted J - KT curve. In practical appilcations, we get advance coefficient J and substitute it into fitted J - KT curve to obtain KT . Finally, the thrust can be obtained. Detailed process is as follows:
1. We get the advance coefficient J from fluid velocity cross the propeller Vprop, the propeller diameter D, and the screw propeller rotate speed n (n is determined by controller): J
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