A calculation method for the pitch magnification factor, using an approximation for the 

 pitch damping, cannot be obtained as simply as in the case of heave. For pitch, the damping 

 moment is more strongly related to the distribution of the various sections along the ship's 

 length than it is to the average dimensions. Any parameter that relates pitch damping to basic 

 hull coefficients, therefore, must include a "weighted" factor which takes into account the 

 relatively larger effects on pitching of fore and aft sections compared with midship sections. 



Two possible "weighted" factors are the mean beam per unit length C B/L and the 

 mean draft per unit length C^H/L. A combination of the two is contained in the parameter 



,1/3 



L 

 C..B 



L 



1/3 



which was used in Figures 14 through 16 to show the variations in dimensionless pitch ampli- 

 tudes among the five models. The use of this parameter can be justified only by the apparent 

 consistency of the experimental data. Other parameters can perhaps be found which fit the data 

 equally well, but the ultimate choice of a "best" parameter must depend on the amount of 

 empirical data available. As in the case of heave, the pitch results can be regarded as a first 

 approximation that needs further verification through additional model tests. 



APPLICATIONS 



The results presented in this report are intended for use primarily as an empirical method 

 for obtaining pitch and heave parameters of ship forms which have characteristics similar to 

 the five forms of this investigation. The results can also be used as a basis of comparison to 

 determine the relative performance of various ships in waves. Care should be used in inter- 

 preting such comparisons, however, since the nondimensional parameters which were used 

 (Froude number and tuning factor) represent different speed and wave conditions for different 

 ships. An example of the variations in actual operating conditions is given in Table 2. The 

 table lists full-scale values of ship speeas and wave lengths, for the five ships represented by 



TABLE 2 



Wave Lengths and Ship Speeds Corresponding to 

 A = 1.0 and F =0.20 





Model 



1 



2 



3 



4 



5 



Wave-Length/Ship-Length Ratio 

 V/ave Length, ft 

 Ship Speed, knots 



1.195 

 478 

 13.5 



1.165 

 615 

 15.5 



0.965 

 764 

 18.9 



0.910 

 604 

 17.3 



0.910 

 446 

 14.9 



16 



