302 



10,000.00 



1,000.00 



100.00 





THEORY OF SEAKEEPING 



o 

 c 



10.00 



<^ LOO 



0.10 



0.01 



2 3 4 5 6 7 8 9 10 11 12 

 Average Wind Force, Beaufort 5cale 



Fig. 46 From E. V. Lewis, 1957 



'.O.OOO.OO 



1,000.00 



o 



100.00 



10.00 



1.00 



O.IO 



0.01 



8,000- 12,000 psi 

 3 rd. Range of Stress Counts 



A Beam Sea 



D auar+ering 8c Following Seas 



1 23456789 10 II 12 

 Average Wind Force, Beaufort Scale 



Fig. 47 From E. V. Lewis, 1957 



ship liendiiig moments and stresses can be computed. 

 The conventional static method has served well as a 

 j-ardstick for the evaluation of bending moments. How- 

 ever, it does not represent the physical conditions of a 

 ship moving among wa\'es. During several decades in 

 the past, isolated attempts were made to include in the 

 analysis various aspects based on the wave and ship 

 dynamics. In the past few years it liecame possible to 

 combine these separate attempts into a single logical 

 system of bending-moment calculation. This system 

 was outlined in Section 2 and it can now serve as the 

 basis for further research. 



8.1 Ship Motions and Damping Forces. It has been 

 demonstrated that the load distribution is composed of a 

 number of components defined by displacements, veloci- 

 ties, and accelerations of ship masses as well as of water 

 in waves. The evaluation of ship motions is therefore a 

 necessary prerequisite to the evaluation of the structural 

 loading curve and of bending moments. Therefore all 

 suggestions for research, made in connection with Chap- 

 ters 2 and 3 are directly relevant to calculations of bend- 

 ing moments. In particular, the poor state of knowledge 

 in regard to damping forces must be emphasized. 

 Neither of the two available methods of damping-force 

 calculations'" is found to agree with experimental data.''* 

 There is an acute need for both theoretical and e.xperi- 

 mental data on damping forces of prismatic bodies as 



'^ Holstein-Havelock's and Grim's methods. 

 33 Golovato (3-195B, 1957); Gerritsma (1957). 



well as on the distribution of these forces along a ship. 

 The inadecjuacy of the available data adversely affects 

 but does not invalidate ship-motion data. However, 

 the bending-moment calculations recjuire greater ac- 

 curacy and are more strongly affected. 



8.2 Need for Ocean-Wave Data. Bending moments 

 as well as ship motions at .sea can be estimated in two 

 steps: (a) The response of a ship to regular waves must 

 be evaluated; and (2) a ship's behavior in irregular sea 

 waves can be determined by the methods of mathemati- 

 cal statistics. The second step is based on the knowledge 

 of ship responses to regular waves and of the irregular 

 sea spectrum. Re^"iew of the ocean-wave knowledge 

 was made in Chapter 1 and it was shown that the avail- 

 able knowledge is inadequate. Even if only the wave 

 spectrum at a point is considered, there is no unanimity 

 of opinion among different research groups as to the spec- 

 trum form and as to the wa\'e height corresponding to 

 given atmospheric conditions. There appears to lie 

 practically no data on the directional spectrum in an open 

 ocean. Yet, the directional spectrum, which causes the 

 wave short-crestedness, is ver_v important in defining 

 sliip motions and ship stresses. In Section 6 and in 

 Figs. 46 and 47, it is shown that high stresses occm' fre- 

 ([uently in a beam sea and this fact is evidently caused 

 by the wave short-crestechiess. As far as the rational 

 evaluation of a ship's bending moment at sea is concerned, 

 the lack of reliable data on the sea wave spectrum ap- 

 pears to be by far the most important factor. 



In view of the foregoing, the evaluation of the sea 



