Wave Excitationless Ships Forms 



DISCUSSION 



W. Frank 



David Taylor Model Basin 



Washington, D.C. 



After hearing of the authors' remarkable and extensive investigations on the 

 heaving force of bulbous bodies in regular waves, we at the David Taylor Model 

 Basin were in a position to compare some of their results with results obtained 

 by a computer program which calculates the added mass and damping of two- 

 dimensional bodies. 



The added mass and damping coefficient are evaluated by distributing wave 

 sources over the cross section of the submerged body, the source strengths 

 being determined from an integral equation obtained from the kinematic bound- 

 ary condition on the body. The amplitude of the heaving force — in the authors' 

 normalized form — was evaluated by the Newman- Haskind relation between the 

 damping coefficient of a sinusoidally oscillating two-dimensional body and the 

 exciting force on the Sa^ie body restrained in regular waves, as expressed by 

 Eq. (3) in the paper. 



We have considered some of the geometries investigated by the authors. 

 Figure D4 shows our results for three circular cylinders with strut as com- 

 pared with the authors' experimental data in their Fig. 7(b). The circles repre- 

 sent the experimental data for B= 1.5a, the squares give the measured results 

 for the case B= a, and the triangles designate the authors' measurements for 

 B= 0. 5a . We see that our theory predicts the occurrence of minimum force am- 

 plitudes fairly well, and we notice good agreement between our theory and the 

 experimental data in the lower end of the frequency range. 



Figure D5 compares our calculations for an elliptic cylinder with strut 

 with Motora and Koyama's measurements taken from their Fig. 9(a). Again we 

 notice good agreement between the curve and the measurements for the lower 

 frequencies, and we see that the zero of the curve occurs at the frequency of 

 lowest measurement. 



We have calculated the damping of circular cylinders with various strut 

 lengths and we have found, just as Motora and Koyama have, that, for fixed 

 beam-to-diameter ratio, zero damping occurs at nearly the same frequency for 

 all draft-to-diameter ratios considered. This result holds also for the limiting 

 case of ogival cylinders — that is, circular cylinders without strut but more 

 than half submerged. 



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