Hydrodynamic derivatives

Hydrodynamic derivatives are the coefficients in a Taylor-series expansion of the sway force Y and yaw moment N about straight-line motion, such as Y_v, Y_r, N_v, and N_r, plus the acceleration terms Y_vdot and N_rdot. They appear in the linear maneuvering equations of motion and fully define a hull’s course stability and turning response. The course-stability criterion is C = N_v (Y_r - m) - Y_v (N_r - m x_G) > 0; a directionally stable hull has positive C. Derivatives are obtained from planar motion mechanism (PMM) tests, captive rotating-arm tests, system identification of trials, or CFD. Their signs and magnitudes feed any simulator.