where M* is the added mass, ii is the volume-averaged water particle 

 acceleration, and x is the acceleration of the ship. This brings no 

 complication to linearized equations except that it seems inconsistent 

 with the definition of added mass, but it is probably not incorrect. We 

 decided to ignore this possible correction term. 



Viscous terms are normally expressed with the help of a viscous 

 resistance coefficient and wetted surface area. In the application, one 

 can find the usage of net velocity as: 



F . = -£- c^ s(u - x)(u - x) 

 viscous 2 f 



or in linearized form 



S, 

 F . = -ttcJ^ s(u - x) 

 viscous 2 f 



These definitions exclude separation and form drag. Dynamic viscous 

 effects are neglected in the present calculations in comparison to wave 

 pressure loads. 



Added mass and damping coefficient values for shiplike shapes are 

 available for periodic motions for high frequencies (Lewis form) and for 

 variable frequencies to the first or higher orders. These values are 

 then assembled according to the relevant theory, such as strip theory. 

 End effects are, therefore, usually neglected, and L is assumed to be 

 very high compared to B and D. The real limitation from these calcula- 

 tions is that the values obtained make sense only for periodic motion. 



Calculation of hydrostatic restoring forces is done using the 

 well-known ship parameters TPI, GM, GM' , etc. Again, pitch and roll 

 interaction effects have to be neglected due to linearization. The 

 assumption that the mean position of the ship is the upright one is not 

 always valid as external effects, operation conditions, and damaged 

 ships might have a large trim or heel, and a correction term is therefore 

 necessary for these calculations. A complete, tested program is being 

 coupled to the main program for the computation of hydrodynamic forces. 



ASSUMPTIONS ON EXTERNAL CONDITIONS 



It is assumed that the wind speed and its direction are constant 

 and the boundary layer effect is neglected. Similarly, current speed 

 and direction are taken as constant. Incoming waves are assiuned to be 

 periodic, small in amplitude, and consistent with linearizations so far 

 introduced. Superposition is accepted in the form of known spectral 

 densities ($) , such as Pierson-Moskowitz or Bretschneider , of the form: 



A 



(■*) 



150 



