Tuak and Taylor 



in agreement with (3,15). It is quite straightforward to show in a 

 similar manner that all of the shallow-water results of Section 3 are 

 reproduced in the corresponding limit, even when fore-and-aft 

 symnn.etry is not assumed. 



In carrying out this shallow- water limit, one may wonder 

 what happens to the "double-body" terms F?* and F^, The answer 

 is that they are of course quite independent of water depth and hence 

 nothing happens to them, and in principle they remain in the formulae. 

 However, when the depth is small the shallow-water terms formally 



dominate the total expression for 

 may be neglected. 



so that F, and F, 



J 



In Fig, 2 we present computed finite-depth sub-crltlcal sink- 

 age and super- critical trim for a ship with parabolic waterline and 

 section-area curves, a length of 600 ft, beam of 60 ft, draft of 20 ft, 

 and block coefficient 0,533, This geometry and size was chosen for 

 analytical convenience, but is not unlike a destroyer hull. The super- 

 critical trim was calculated directly from (4,17) by a single numeri- 

 cal quadrature (since this hull has fore-and-aft symmetry), whereas 

 the sub-critical sinkage required an extra numerical integration of 

 (4,10), and, furthermore, required separate estimation of the infinite- 

 fluid contribution F^ in (4,14). 



6.0 - 



- 2.0 -~ 



0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 



FROUDE NUMBER BASED ON DEPTH 



Fig. 2 Finite depth squat for a ship 600 ft long and 20 ft draft 



644 



