Vien and Lee 



sectional heave -damping force in the form of 



F „ = b oo w (t) + c. U W + r Iwl W (56) 



where W(t) = s 3 -x £ , and c, and c_ are constants. An expres- 

 sion similar to Equation (56) is given in Thwaites (I960) for a slen- 

 der body for a moderate angle of incidence in an unbounded fluid. The 

 second term of the right side of Equation (56) is called viscous lift 

 and the third term is called cross-flow drag. From the model test 

 results, it was found that the damping obtained from theory for the 

 case of zero speed seemed adequate. Thus, addition of the cross- 

 flow drag which is independent of speed was considered unnecessary. 

 However, the viscous -lift term, which depends on forward speed, 

 seemed proper to be retained. Use of the test results for c. , given 

 in Thwaites (i960, pp. 415-416), and a modification of the sectional 

 heave damping obtained by adding c« U to b _ , has not been 

 successful. From this trial-and-error approach, it was learned that 

 additional damping seemed to depend on a parameter uU/g. This 

 parameter is the ratio of ship speed to the celerity of motion-gene- 

 rated waves. When the ratio is less than one-fourth, there can be 

 generated a chain of ring waves propagating ahead of the ship; see 

 Wehausen and Laitone (I960, p 494). Dependence of the supplemental 

 damping on this parameter implies that the hitherto neglected inter- 

 action effect between two wave systems, one produced by oscillation 

 and the other by translation of ship, is important. 



The strip approximation may exaggerate the effect of the 

 hydrodynamic interaction between the two hulls. When a catamaran 

 sails with a forward speed so that coU/g> l/4, the motion-generated 

 waves will be swept back by the forward speed. Especially between 

 the two hulls, the steady horizontal flow can be accelerated by a chan- 

 nel effect which leaves less chance for the oscillation-generated 

 waves by the two hulls to interact in this region. To examine whether 

 the foregoing postulation is true, the heave damping and heave and 

 pitch amplitudes of Model 5061 and the demihull of this model are 

 compared in figure 9 together with experimental results for twin 

 hulls. There seems little change in the motion results between the 

 twin and the demi-hulls except at the resonant wavelengths. At the 

 shorter wavelengths, the heave damping of the demihull shows a bet- 

 ter agreement with the experimental values. However, a similar 

 comparison to that previously described for the heave and pitch 

 amplitudes of 5266 at 30 knots revealed that the demihull has higher 

 motion amplitudes at the resonant wavelengths than the twin hulls do. 

 This seems to imply that for LWP catamarans, the underestimation 



492 



