Motion and Resistance of a Low-Waterplane Catamaran 



of damping does not necessarily arise from an over-estimation of the 

 mutual hydrodynamic interaction effects of the two hulls by the strip 

 approximation. 



The dotted curves in figure 8 are obtained with modified 

 heave and pitch damping values. These are obtained by modifying the 

 sectional heave damping by b 33 *(x) = b 33 (x) + a puStfx) coU where 

 b_ 3 (x) is the old heave damping at a cross section at x, p is 

 the density of water, S fl (x) is the sectional area and a =3.0 for 

 Model 5266. The constant a is a function of ship geometry and is 

 obtained at present from the comparison of the theoretical and the 

 experimental results of motion. The hydrodynamic coefficients affect- 

 ed by this change are B _ , A 5 , A _ , and Bg 5 (Table l). 

 A further investigation to remove the discrepancy of the motion pre- 

 diction at the resonant wavelengths by better techniques seems to be 

 definitely necessary. 



The absolute and relative vertical motions of Model 5266 at 

 a speed of 30 knots, which are computed with the modified damping, 

 are shown in figure 10 . If we assume the height of the cross-deck 

 of Model 5266 from the designed waterline is 30 feet, the water con- 

 tact could be made when a sinusoidal incoming wave having an ampli- 

 tude of 27 feet is encountered with an interval period of 18 seconds 

 as the ship runs at 30 knots. The irregular- sea computation showed 

 that the chance of water contact of the cross -deck of Model 5266 is 

 zero to a significant wave height of 20 feet at 30 knots. 



The results presented in this section cover only part of the 

 analysis made in part 1. Numerical results for the sway, roll and 

 yaw motions and the hydrodynamic loads were not available at the 

 time of this writing. 



1.5- Concluding Remarks on the Prediction of Motion of Catamarans. 



1. The strip approximation seems to yield a satisfactory 

 motion prediction, except at the resonant wavelengths. The short- 

 coming of the strip approximation is considered to arise from inabi- 

 lity to account for the correct forward speed effect on the hydrody- 

 namic coefficients over the range of resonant frequencies. The area 

 to be improved in the theory seems to be the evaluation of the dam- 

 ping coefficients. Proper incorporation of the interaction effect bet- 

 ween the waves generated by the forward speed and the body oscilla- 

 tion is considered to be the most important factor to be investigated. 



2. Although an improvement of the analytical prediction at 



493 



