The Severity of Supposed Wave Conditions in Estimating Extreme Values of Wave Induced Response Variables of a Ship

Abstract

In the case when the long-term distribution of wave induced variable of a ship is estimated theoretically, it becomes usual to suppose wave condition on the North Atlantic Ocean. It is the reason why the condition is chosen, that accurate wave statistics on the sea zone are prepared and the sea zone is regarded as one of the severest main trade routes, so supposing the condition means estimating the distribution at a safety side. Though it is known that the long-term distribution changes according to supposed wave condition, analytical study on the problem that by what factor of supposed wave statistics the severity of supposition is evaluated has never been made.From investigation of character of the extreme value of the response variable, author finds that severity of supposed wave statistics is evaluated by such factors as the maximum wave height in each wave period interval. Thus the severity of a given wave condition is shown by drawing a curve which shows change of the maximum wave height along the abscissa of wave period. Comparing a given condition with another one, the condition is regarded severer than another one for smaller ships but moderate for larger ships when the maximum wave height is higher than that of another condition in shorter wave period range and it become lower than that of another condition in longer range. By drawing the curve from the wave statistics by Walden, the curve from those by Roll, and the curve from those by Hogben and Lumb, it is clarified that the estimated extreme value changes largely by supposed wave statistics in some case. Being so high the maximum wave height in the wave period interval from 5 sec. to 7 sec. of the wave statistics by Walden, the effective wave height curve corresponding the extreme value of wave bending moments of similar ships of various length has a hump and hollow when the wave statistics are supposed in estimation.The height of the maximum wave height is determined by result of only several observations. So the height of each wave statistics is not accurate. By assuming the frequency distribution of wave heights in each wave period interval is described by the Weibull distribution, author corrects the maximum wave height in each wave period interval of wave statistics including those by Walden, those by Hogben and Lumb, those on the sea zone 3, and those observed on board of a Japanese patrol ship is corrected. And the severity of the corrected wave condition on the North Atlantic Ocean are compared with that of the one on the North Pacific Ocean. From the comparison, it is found that the wave condition on the North Pacific Ocean has at least the same severity as that on the North Atlantic Ocean, when wave period is less than 10 sec. And when the period is over 10 sec, it becomes slightly moderate in comparison with that on the North Atlantic Ocean.