Yim 



waves. Although the stern problem in the non-viscous fluid is exactly the same 

 as the bow problem, it should be studied separately due to the large influence of 

 viscosity, wakes, propellers, etc. Because of these influences, the bow waves 

 are more important in practice than the stern waves. The humps and hollows of 

 the curve of the wave resistance due to a ship without a bulb may be applied to 

 that for the ship with the bulb without any considerable error. The bulb has an 

 effect of smoothing out the humps and hollows of the resistance curve to a con- 

 siderable extent (Yim 1962) in the vicinity of the designed speed or for larger 

 speeds. Pien (1962) seems to have obtained this effect using the principle of 

 wave cancellation by distributed singularities rather than concentrated ones. 

 Naturally, a ship with a bulbous bow would have much the better performance if 

 it has a better stern. At the present time, shapes like the transom stern seem 

 to attract the interest of many naval architects for high speed ships. 



The higher order effect and the influence of viscosity are extremely difficult 

 to analyze, yet they should and will be gradually exploited in the near future. 

 The theoretical study on the seaworthiness of the bulbous ships remains to be 

 done, although it is known from experiments that bulbous bows are still effective 

 in waves. 



ACKNOWLEDGMENT 



This work was kindly sponsored by the Office of Naval Research, Depart- 

 ment of the Navy under Contract No. Nonr-3349(00), NR 062-266. Thanks are 

 due to Mr. M. P. Tulin for his helpful discussions. 



NOTATION 



a = Length of run of wedge strut 



a^ = Coefficients of polynomial representing source distribution for 

 a ship 



h^ = Coefficients of polynomial representing concentrated singularity 

 distributions for a bulb 



B = Beam 



f(x,z) = Ship hull form 



f'H'f^L - Froude numbers with respect to draft and length respectively 



g = Acceleration of gravity 



H = Draft of ship 



H^ ~ Struve function 



l<o = kH/V^ 



1094 



