Newman and Tuck 



Table 1 

 Rational Linear Theories for Oscillatory Surface Ships 



Nomenclature: B = beam, T = draft, k = wavelength, 

 CO = radian frequency. 



indicate this situation by the designation "fat ship theory"; this approach has the 

 advantage that no assumptions are made concerning the hull geometry, but 

 closed form solutions are not obtainable, and moreover the theory is restricted 

 to zero speed by the requirement that the disturbance of the free surface be 

 small. 



The thin ship model, which is most familiar in wave resistance theory, has 

 been applied to ship motions in longitudinal (head or following) waves and both 

 first- and second-order theories have been developed; criticisms are first that 

 conventional ships are not thin (B/T is usually greater than one), secondly that 

 the first order theory contains an unbounded resonance in pitch and heave while 

 the second order theory is extremely complex, and thirdly that the use of this 

 model for oblique wave motions results in a lifting- surface type of integral 

 equation. 



The flat ship was proposed in order to overcome the objections of the thin 

 ship, but its analysis is still incomplete, and one may note that it suffers from 

 drawbacks similar to the thin ship, but with the vertical and transverse modes 

 reversed. 



The strip theory and slender ship theory are based upon identical geomet- 

 rical assumptions, namely that the beam and draft are both small compared to 

 the ship's length; intuitively this assumption seems reasonable for conventional 

 ships. They differ however, in regard to the additional characteristic length of 

 the problem, namely the length of the incident waves. The strip theory, which 

 assumes two-dimensional flow in transverse planes at each section of the ship, 

 is rational only if the wavelength is small compared to the ship length. If this 

 is the case, interference between the bow and stern will be negligible, since 

 they are many wavelengths apart, and the three-dimensional hydrodynamic 



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