Prediction of Ship Slamming at Sea 



operator of relative motion at this location. Then, by applying the superposition 

 principle, the energy spectra of the relative motion and the velocity and thereby 

 the variances for a given sea state can be obtained. That is 



(A.l) 



H 



2 



where 



cr^ - variance of relative motion, 

 a-? = variance of relative velocity, 



r 



Ej. = cumulative energy density of relative motion, i.e., the area under 

 the relative motion spectrum, 



^r('^e) - energy density of relative motion, 



co^ = frequency. 



For a constant speed test it is possible to obtain the response amplitude 

 operator of the relative motion by installation of an accelerometer in the model 

 at the location of interest, and a wave-height probe on the carriage so that it is 

 in line with the accelerometer. The above two methods are the direct methods 

 for obtaining the relative motion and velocity at a specific location. 



It is necessary in practice, however, to evaluate the variances of relative 

 motion and velocity at arbitrary points along the ship length for a given sea. 

 For this, the response amplitude operators of relative motion at the points of 

 interest may be evaluated from the pitch, heave, and wave motions including 

 their respective phases. Another approximate method to estimate the variances 

 of relative motion and velocity at arbitrary points is to use the correlation co- 

 efficients if the variances of vertical motion and/or acceleration are known at 

 two points along the ship length. The method is as follows: 



The variance of the relative motion at an arbitrary point along the ship 

 length is given by 



a^-a^ + cr^-2p o- a (A.2) 



where 



o-^ = variance of relative motion between wave and ship bow at point x, 



crj = variance of wave motion, 



o-^ = variance of vertical motion at point x, 



p^x = correlation coefficient between wave and vertical motion at point x. 



581 



