Ochi 



Thus, the probability density function of the relative velocity associated 

 with slamming is a truncated Rayleigh distribution. The truncation should be 

 made at the threshold velocity, f*, which is a function of a ship length as was 

 mentioned earlier. 



From the probability density function given in Eq. (11), the average of one- 

 third highest (significant), fj/3, and one-tenth highest, r^^^^, values of the 

 relative velocity can be obtained as follows: 



r: 



3 e 



where 



(^1/3)^ 



1/3 



(12) 



1/3 = Y'^i - K- ^°gi 



«)(u) 



e ^ dt 



R. 



1/10 - 10 e ^ 



where 



('■1/10) 



+ \A^ J 1 - 



(13) 



/ 



"2 n ' 1 1 



r;: - R. log -7- 

 r 10 



The derivation of these formulae is given in Appendix 2. 



A comparison between theoretical probability density function and the his- 

 togram of the relative velocity obtained from tests conducted on a MARINER 

 model is shown in Fig. 6 (values are converted to those for full scale). The ex- 

 ample shown in the figure is for tests conducted in a severe Sea State 7 at a 

 10-knot ship speed, the same condition as was shown in Fig. 1. As can be seen 

 in Fig. 6, the prediction curve agrees well with the observed histogram. Also, 

 the average of the one-third and one-tenth highest values calculated by Eqs. (12) 

 and (13), respectively, agree well with the measured values. 



Prediction of the Magnitude of Impact Pressure Associated 

 with Slamming 



It was shown earlier that the impact pressure associated with slamming is 

 approximately proportional to the square of the relative velocity and that the 



558 



