Grim method yields a better approximation. It should be noted that a three-dimensional cor- 

 rection, especially at the lower frequencies, would tend to reduce the damping and so improve 

 the prediction. 



Both theoretical procedures, although differing on the existence of zeros, predict very 

 small damping at higher frequencies. As mentioned in an earlier section the accuracy of the 

 measured damping coefficient at higher frequencies is severely limited by inaccuracies in the 

 phase-angle determination. Therefore, it is not possible for the experiment to resolve the 

 question concerning multiple zeroes. 



At the higher frequencies the experiments show the damping falling toward zero and 

 then increasing with the increasing frequency. In spite of the experimental error, there is 

 clear evidence that at higher frequencies this increase with increasing frequency does in fact 

 exist. This rise in damping cannot be explained by means of the suggested theories, for at 

 frequencies above co yB/g = 2.5 they would predict essentially zero damping. One might 

 speculate that another damping law is indicated at high frequencies. 



PREDICTION OF ADDED MASS 



The common method used for prediction of the added mass of surface ships for vertical 

 motion is based on the familiar work of Lewis^. By suitable conformal mapping, the circle is 

 transformed into a ship-like section which has been reflected about the waterplane. The ad- 

 ded mass of the ship section is assumed to be one-half that of the ship and image together in 

 an infinite medium. This procedure is theoretically correct only at high frequencies since the 

 influence of gravity on the free surface is neglected. The section characteristics are inte- 

 grated over the length of the body and are then corrected by a factor to account for the three- 

 dimensional effects. This factor is chosen to be the ratio of the exact solution and the inte- 

 grated two-dimensional results for an ellipsoid whose three axes are equal to the principal 

 dimensions of the ship plus image. Thus the procedure yields an added mass which is inde- 

 pendent of frequency, amplitude of oscillation, and speed of advance. 



Prohaska^ extended this procedure by assuming that the added mass of a ship section 

 was dependent on the fullness and beam-to-draft ratio of the section alone. The Lewis trans- 

 formation was used to set up this dependency and all other forms were assumed to follow the 

 same law. Some experimental evidence was used to substantiate this assumption. 



The Lewis-Prohaska procedure was used for the model being tested and the results 

 compared with the experiments. Since the calculations involved two distinct processes (that 

 is, the integration of section characteristics and the correction for three-dimensional effects), 

 it is not possible to ascribe differences between calculation and theory to a shortcoming in 

 either step. In Figure 8, it is clear that the constant value obtained in the calculation can- 

 not represent the strong frequency dependence of the added mass. In fact the added mass 



20 



