Applying Results of Seakeeping Research 

 Heave amplitude 



Wave amplitude 



But when a non-dimensional relationship is appropriate, one may divide by a 

 ship dimension such as length, giving a ratio, Z^/L. This means that we con- 

 sider two ships to have equivalent heaving behavior in comparable conditions if 

 the ratios of heave amplitude to ship length are the same. (This is in contrast 

 to the conventional procedure to comparing heave amplitudes directly.) The pa- 

 rameter ZJL will be the same for geometrically similar ships in similar waves. 

 The response amplitude operator may be obtained by dividing by the wave slope, 

 which is also non-dimensional, thus: 



This operator goes to infinity as wave length becomes very long and z^ ap- 

 proaches infinity. 



Similarly, vertical velocity, Z^ = co^z^, can be non-dimensionalized by mul- 

 tiplying Zg/L hy yjwi, giving TJ^J^ which is a sort of Froude number. The re- 

 sponse amplitude operator is then, 



zyviL 



.2^^a/^j 



ZVN/gL" 



This operator also goes to infinity as wave lengths become very long, but not so 

 rapidly as the above. 



Multiplying the non-dimensional velocity Z^/^J^ again by 

 non-dimensional acceleration previously discussed, z /g. 



iL/g gives the 



Similarly, any other response that is non-dimensional may be related to 

 wave slope. For example, relative bow motion, s^, in relation to length, L, is 

 more significant than the absolute value, S^ , and therefore S^/L is an appropri- 

 ate non-dimensional parameter. Although similar in appearance to the heave 

 parameter, it tends toward zero in very long waves. 



The response amplitude operator for relative vertical velocity between bow 

 and wave, which is of significance in relation to slamming, can be obtained by 

 multiplying s^/L by w ^Tg, giving 



f^ 



/gL 



which is a non-dimensional relative velocity. The response amplitude operator 

 then is. 



221-249 O - 66 - 14 



193 



