Applying Results of Seakeeping Research 



For use with a slope spectrum it is convenient to adopt the modified coeffi- 

 cient, 



AP (VL) ^ 

 ' PgC^VB 



Study of Gerritsma's model results [7] shows that the trend with k/L indicated 

 by this coefficient is roughly correct for values of VL greater than about 1.0, 

 but it reverses for VL < 1.0. Nevertheless, the coefficient appears to be en- 

 tirely suitable for use with a wave slope spectrum. 



So far mention has been made only of the simple case of ship response to 

 long-crested irregular head seas. The method of presenting data can easily be 

 extended to the case of short- crested seas and any ship heading — provided, of 

 course, that model test results in oblique seas are available. The short-crested 

 sea is represented by a family of curves showing the magnitude of wave compo- 

 nents coming from different directions. Response amplitude operator curves 

 are also prepared for different wave directions, and each of the directional 

 spectrum curves must be multiplied by the appropriate response amplitude op- 

 erator curve. The resulting family of response spectral components can be in- 

 tegrated to obtain a single response spectrum on a base of log^aj. This proce- 

 dure will be illustrated in the section on results. 



The computations required to obtain the curves that have been discussed 

 can be conveniently carried out by slide rule or desk computer with the use of a 

 suitable computation form. The form and procedure developed at Webb Institute 

 of Naval Architecture, mainly in connection with work for the American Bureau 

 of Shipping, is described in [10]. It has also been programed for solution on an 

 IBM 1620 computer. 



RESULTS -WAVE BENDING MOMENTS 



The application of the procedures discussed above can be illustrated first 

 by considering trends of wave-induced bending moments for a series of ships 

 for which model results in regular waves were available [3]. This work was 

 carried out under the sponsorship of the American Bureau of Shipping. 



Figure 3 has been prepared to show graphically the calculation for the case 

 of the 0.80 block ship heading into short-crested irregular seas. The upper 

 portion of the figure shows a spectrum based on the average of the 13 worst 

 records reported by Pierson [5], with directional components obtained by apply- 

 ing a "spreading function" of 2/77 cos^ ^^ to approximate the effect of short- 

 crestedness. The second part of the figure shows the family of curves repre- 

 senting the response amplitude operators derived from the model test results, 

 each curve for the 600-foot ship length defining the response of the model to the 

 waves coming from a particular angle. The curves are labeled with the angles 

 M indicating the responses to the same angular wave components as those shown 

 in the sea spectrum. Each of these component response curves was derived 

 from the model tests at a particular angle to the waves by picking off the results 

 at the appropriate angles. 



195 



