Prediction of Ship Slamming at Sea 

 (a) (b) 



J.*. 0.4 



Jr 



amNjt, 



10 15 20 25 30 



2N,T 



Fig. 16 - The probability integral of the incomplete gamma function, Ref. 9 



Prob {t > T} 



't r(m) 



dt 



r N" 

 — ^ t' 



(25) 



dt 



The integral value of the numerator in the above equation for various m, N^, 

 and T, appropriate for full scale ships are given in Fig. 16(b). 



A numerical example of Eq. (23) will be given as follows: Consider the 

 MARINER to be operating at light draft condition (40 percent of cargo loading) 

 at a 10-knot speed in a severe Sea State 7. We will evaluate the probability 

 density of the time interval between two severe slams for which an impact pres- 

 sure of 50 psi or greater will be applied at the location 0.10 L aft of the forward 

 perpendicular. In this case, we have 



2C = 0.086 psi-secVft^, 



P„ = 50 psi, 



P* = 2Cf 2 = 12.4 psi, 



r; =605 ft 2 (see Table 2), 



r: =305 ftVsec^ (see Table 2), 



r 



N^ = 0.0435 1/sec [by Eq. (6)], 

 t* = 7.6 sec, 

 m = 4.19 [by Eq. (21)]. 

 571 



