298 



THEORY OF SEAKEEPING 



40i_ 



6.0 ft /sec 85% o-f calculated valt 



Fig. 45 Calculated and measured elastic responses of a destroyer model (from Dalzell, 1959) 



not exist at slightly lower and higher speeds of 5.8 and 

 6.8 fps. The comparison of calculated and experimental 

 data in Fig. 45 is based, therefore, on these latter speeds. 

 The exaggeration of the exciting bending moment, shown 

 in Fig. 44 would lead to the exaggeration of computed 

 responses. The "calculated 6.0 fps" curve in Fig. 44 w-as 

 draw-n, therefore, taking 83 per cent of the original Dal- 

 zell's data in order to liring out more clearly the com- 

 parison of the time behavior of bending moments. The 

 calculations brought out the, experimentally observed 

 large magnitude of the sagging moment as compared to 

 the hogging one. Calculations also brought out the 

 existence of experimentally observed vibrations, although 

 details of the calculated and observed vibrations did not 

 agree. Indeed, it appears to be almost hopeless to re- 

 produce a detailed pattern of vibrations by calculation 

 considering the rapidity with which this pattern changes 

 with small changes of model speed in experiments. All 

 one can expect is to evaluate the amplitude of the vi- 

 bratory response which must be added to the quasi-static 

 wave-caused bending moment. 



5.6 Statistical Theory of Slamming. It is apparently 

 impossible to predict the e.xact shape of a wave in an 

 irregular sea at a given instant and to predict a ship's 

 attitude with respect to it. The detailed description of 

 the condition.s leading to a slam in irregular sea, there- 

 fore, cannot be formed. Valuable information, how- 

 e\^er, can be obtained by the modern methods of mathe- 

 matical statistics. Any characteristic of a ship's re- 

 sponse to regular waves can be established either by cal- 

 culation or by towing-tank tests. Such characteristics 

 can include, for instance, the vertical motions of a ship's 

 forefoot and the vertical velocity of the bow. From 

 experience, a set of characteristics significant to slamming 

 can be specified and the joint probability of their oc- 

 currence can be statistically evaluated. Thus, L. J. 

 Tick (3-1954) has establi-shed the joint probability of the 

 bow emergence and a vertical velocity of the bow exceed- 



ing a specified value. However, a slam will occur only 

 if a ship's keel is nearly parallel to the water surface over 

 an apprecialile part of the ship's length near the bow. 

 In computing the joint probability, L. J. Tick (3-1958) 

 extended his work to include a specification of a certain 

 small keel-to-water angle. Tjpical slamming condi- 

 tions are well defined by the joint probability of the bow 

 emergence, a certain small angle of the keel to water and 

 a certain vertical velocity of the bow. The significant 

 values of two necessary parameters, the keel-to-water 

 angle and the bow velocity, can next be defined by the 

 analysis of slamming records at sea. They evidently will 

 depend on the ship-form parameter, such, for instance, 

 as Ochi's section coefficient at 10 per cent of the ship's 

 length at 50 per cent of design draft. 



The statistical methods developed by Tick do not 

 du'ectly indicate the severitj' of a slam. This, however, 

 can be evaluated indirectly. The probability of oc- 

 currence of various vertical bow velocities can be com- 

 puted. For any specified vertical velocity the hydro- 

 dynamic impact force can be computed by the Wagner- 

 Szebehely-Todd method. 



6 Statistical Data on Ship Bending Stresses- 

 Related to Sea Conditions 



In this section, attention will be called to statistical 

 data on ship bending stresses which are related to sea 

 conditions. These latter are not measured but are 

 given on the basis of visual observations, ship's log 

 data, or sometimes even wave forecasts. Only the 

 general conditions prevailing at the time of stress meas- 

 urement are given. Detailed relationships between 

 wave profile and stre.s.ses, which were discussed in earlier 

 sections, are not available in the records which are dis- 

 cussed here. 



The data of the type just described are available from 

 the following sources: 



