Motion and Resistance of a Low-Waterplane Catamaran 



DISCUSSION 



J. N. Newman 



Massachusetts Institute of Technology 

 Cambridge, Massachusetts > U.S.A. 



(Discussion read by Professor Beck) 



Drs. Lee and Pien have applied up-to-date hydrodynamic 

 techniques to the prediction of catamaran motions and wave resistan- 

 ce, and while they have each experienced isolated cases of poor 

 agreement with experiments, the overall success in both problems 

 is quite striking. My remarks will be focused on the principal discre- 

 pancy experienced in the seakeeping portion of this paper; namely, 

 the substantial overprediction of pitch and heave, with forward speed, 

 at a critical wavelength. It seems clear that this is associated with 

 the presence of near-zero heave damping at zero forward speed, and 

 the use of the zero- speed hydrodynamic coefficients in a strip-theory 

 manner. This problem does not show up for conventional hull forms, 

 even when (zero-damping) bulbous sections are present locally such 

 as in the bow. But for a body such as Model 5266 where bulbous 

 sections are dominant, the total heave damping coefficient will be 

 more seriously affected and, in view of the strong coupling due to 

 forward speed, both the pitch and heave motions will be exaggerated 

 as shown in figure 8. 



To be more specific, let us consider the case of a thin-body 

 section, so that the explicit results of thin-ship theory are applica- 

 ble. Then it is known that the two-dimensional damping coefficient 

 for a section with offsets y =if (z) is proportional to the square 

 of the integral 



T 



/ 



-Kz df J 

 e — dz 



dz 



or to the Laplace transform of the hull slope in the vertical direction. 

 Here T is the ship's draft, and K is the wavenumber. Clearly, for 

 a bulbous form where df/dz changes sign, the above integral will 

 vanish for suitable combinations of the wavenumber and hull shape. 

 Now in three dimensions and with zero speed, the same conclusion 



541 



