Understanding and Prediction of Ship Motions 



*E. T. Whittaker and G. N. Watson, 1963. Researches on Seakeeping Qualities of 

 Ships in Japan. Vol. 8, 60th Anniversary Series, The Society of Naval 

 Architects of Japan, Tokyo 



APPENDIX A 



Calculation of Force and Moment 



It has been remarked several times that, in order to calculate force and 

 moment on the ship, the pressure must be evaluated on the actiial instantaneous 

 position of the ship hull. However, it is quite inconvenient to have a changing 

 domain of integration, especially since finding the domain is part of the prob- 

 lem. (A priori, the location and orientation of the ship at any instant are un- 

 known, and so one does not know where to evaluate the pressure.) Therefore we 

 choose to express the pressure at a point of the hull surface, s, in terms of the 

 pressure at the corresponding point of s^, the undisturbed position of the hull. 

 The resulting expressions will involve the unkno-'vn motion variables, but they 

 will appear in an explicit manner and not as arguments of functions. 



The pressure at any point in the fluid can be expressed as follows: 



P - -PgX3 + P3 + P„,, 



where 



0^51 Cq^l 1 , 



We assume that the steady motion and the unsteady motion problems have both 

 been linearized in some way, and so we neglect certain quadratic terms,* re- 

 taining only the following simplified expressions: 



It would not generally be proper to assume also that we could neglect the term 

 -pVcp^ • VcPi in p^, although in practice this quantity may be quite small. The 

 reason for this is discussed in detail in Chapter V: The steady motion problem 



*This step may not be proper in certain cases, e.g., a deeply submerged body 

 or a slender body. 



69 



