Distribution of Hydrodynamic Forces on a Shipmodel 



The calculated values are in line with the experimental results. The natu- 

 ral frequencies for pitch and heave are respectively w = 7.0/6.9 rad/sec and in 

 this important region the calculation of the damping cross-coupling coefficients 

 is quite satisfactory. The zero speed case will be studied in the near future by 

 oscillating experiments in a wide basin to avoid wall influence. 



Another comparison of theory and experiment concerns the distribution 

 along the length of the shipmodel of the damping coefficient and of the damping 

 cross-coupling coefficient e . From Eq. (14): 



b' = N'-V^ , 

 dx 



N'x - 2Vm' - xV 



dm' 

 dx 



Again using Grim's two-dimensional values for N' and m', these distributions 

 could be calculated. An example is given in Fig. 14. Also in this case the 

 agreement between the calculation and the experiment is good. For high speeds 

 negative values of the cross-sectional damping in the afterbody can be explained 

 on the basis of the expression for b' , because in that region dm'/dx is a posi- 

 tive quantity. 



Finally the values for the coefficients A, B, a and b for the whole model, 

 as given by the Eqs. (13) were calculated and compared with the experimental 

 results. Figure 15 shows that the damping in pitch is over-estimated for low 

 frequencies. The other coefficients agree quite well with the experimental re- 

 sults. 



'E 



^ 



^ 



Fig. 14 - Comparison of the calculated distribution of e 

 and b with experimental values for Froude number 0.20 



243 



