Ochi 



^(P-Pj 



f(p) 



(15) 



2cr: ' = . . 



r 



where 



p - impact pressure = 2Cf^, 



p* = threshold pressure = 2Cf^2. 



The probability that an impact pressure exceeds a certain magnitude, p , 

 per cycle of wave encounter can be obtained 



Prob {P>P„} = f(p) dp = e ^ , Po ^ P* • (^^^ 



Po 



It is of importance to note here that Eq. (16) is a conditional probability; 

 namely, it represents the probability that an impact pressure exceeds a certain 

 magnitude given that a slam occurred. Hence, the probability that an impact 

 pressure exceeds a certain magnitude in a given sea state and at a given ship 

 speed is the product of the two probabilities given by Eqs. (5) and (16). Also, 

 the problem concerning how many times an impact pressure exceeds a certain 

 magnitude in a prescribed ship operation time can be obtained by multiplying 

 the operation time by the product of Eqs. (6) and (16). 



The averages of one-third highest, p J/ 3 and one- tenth highest, Pj/jq pres- 

 sures are given by the following formulae: 



2C t' + 2.10 R:] (17) 



2C i^ + 3.30 r: 1 . (18) 



Derivation of Eqs. (17) and (18) are given in Appendix 2. 



Figure 7 shows a comparison between the theoretical probability density 

 function and the histogram of impact pressure obtained at 0.1 L aft of the for- 

 ward perpendicular of the MARINER in a severe Sea State 7 at a 10-knot ship 

 speed. The value 2C = 0,086, determined from Fig. 1, was used in the calcula- 

 tion. Included in the figure are the predicted average of the one-third and one- 

 tenth highest pressures calculated by Eqs. (17) and (18) as well as the observed 

 values. As can be seen in the figure, the theoretical density function is trun- 

 cated at 12.4 psi due to the threshold relative velocity. Although pressures 

 lower than 12.4 psi were actually observed a few times during the tests, reason- 

 able agreement between theoretical and experimental results can be seen in the 

 figure. The discrepancy is of the order of 10 percent for the average of the 

 one-third highest, and 20 percent for the average of the one-tenth highest values. 



560 



