-c?C(j + / = — ^ cos a 



= y SI I 



[3b] 



In [la] the coefficient A is recognizable as the virtual mass, the sum of the mass 

 suspended beneath the balance m and the hydrodynamic added mass m^. The damping force 

 Si represents, primarily, the energy dissipated by the system in progressive gravity waves. 

 The coefficient C is the effective "spring" constant or buoyant force coefficient. For the 

 range of amplitudes used in these tests, the ship is essentially wall-sided so that C can be 

 assumed constant. 



Solving for the unknown hydrodynamic coefficients in terms of known or measurable 

 quantities, we obtain, 



F 

 C -_o cos S 



-^ sin 8 



[4a] 



B = 



The hydrodynamic moments imposed on the ship by the heaving motion are given in 

 Equation [lb] and results in the coupling of the heaving and pitching motions. Since the mo- 

 del in these tests has fore-and-aft symmetry and nearly wall sides, it can be assumed that 

 there is negligible buoyancy moment due to heave so that / = 0. 



Solving for the cross-coupling coefficients in Equation [3b] 



—}L cos a ^ , , 







e = 



