Joosen 



Of the order of the ship length. For short waves, however, a rather serious 

 discrepancy occurs. This can be explained by a simple theoretical considera- 

 tion. 



The expression for the longitudinal drift force depends on the radiation 

 potential only. It is proportional to the square of the motion amplitude. The 

 diffraction effect of the waves is of negligible order of magnitude. This is cor- 

 rect provided that the motion amplitude is of the same order of magnitude for 

 the whole frequency range. For short waves, however, the motion amplitudes 

 appear to be much smaller than in the case of larger wavelengths. Therefore it 

 is to be expected that for higher frequencies the diffraction effect becomes more 

 and more important in relation to the radiation effect. In the limiting case for 

 infinite small wavelength the added resistance is caused by the diffraction effect 

 only. To get an impression about the diffraction effect a correction term is 

 added to the theoretical curve in Fig. 1. For this correction term an expression 

 is taken for the drift force in very short waves, obtained by Havelock (8) de- 

 pending on the wave diffraction only: 



2e- 



sin a dy , 



where a is the angle between the tangent of the water plane curve and the x axis. 

 The agreement between theoretical values and experimental data then becomes 

 much better. 



As a second example the added resistance is calculated for a fast cargo 

 ship with a block coefficient Cg = 0.62, The values for Froude number F^ = 

 0.225 are represented in Fig. 2 together with the experimental results (9). Es- 

 pecially the peaks show an excellent agreement. It is plausible that the discrep- 

 ancy in the high frequency range is again due to the diffraction effect, while the 

 discrepancy in the low-frequency range can be explained by a failure of the 

 theory, since it is derived for rather high frequencies. 



Finally, experimental data of Sibul (10) are compared with theoretical cal- 

 culations. For three "Series 60" models (Cg = 0.6, 0.7, 0.8) the results are 

 plotted in Fig. 3. The model with block coefficient 0.8 shows a remarkable 

 discrepancy. In Fig. 4 the peak values are represented as a function of the 

 Froude number. 



CONCLUSIONS 



The first-order term of the longitudinal component of the drift force is 

 proportional to the square of the motion amplitude. The diffraction effect is 

 found to be of negligible order. Except for a coupling term the expression ob- 

 tained is equivalent to the result of Havelock. From a calculatory point of view 

 the formula is more useful, since it is easier to calculate the damping coeffi- 

 cient than the phase difference between exciting force and ship motion. 



644 



