SOME RECENT DEVELOPMENTS IN 

 THEORY OF BULBOUS SHIPS 



B. Yim 



Hydroftautics, Incorporated 



Laurel, Maryland 



INTRODUCTION 



The history of the bulbous bow on ships may start in the early 19th century 

 with submerged rams on combatant vessels projecting forward along the water- 

 line at the stem, or with the projecting underwater hulls of many old French 

 warships built about the same time. Later, the British armored cruiser Levia- 

 than had such a projecting ram bow. D. W. Taylor suspected that this ram bow 

 played a definite part in the ships superior performance, and he based the par- 

 ent model for his famous Standard Series (D. W. Taylor 1911 or 1943) upon the 

 lines of Leviathan. Systematic bulb bow experiments were made by E. F. Eggert 

 in the early 1920's and the general data were reported upon by D. W. Taylor 

 (1923). It had been generally understood that the decrease of resistance due to 

 a bulbous bow is a wavemaking phenomenon, such as a decrease in bow wave 

 height due to a bulb wave. This understanding was more strongly supported 

 when Havelock (1928) calculated the surface wave due to a doublet immersed in 

 a uniform stream. A deeply submerged sphere is equivalent to a doublet. 

 Hence according to his calculation, a sphere moving through water at a constant 

 speed causes the surface wave to start with the trough just aft of the sphere. It 

 is natural to imagine that this trough has something to do with the bow wave 

 crest which is seen to start just aft of the bow in ordinary ships. However 

 there was also some other suspicion that the bulb effect is due to a change in 

 the effective ship length owing to the alteration by the bulb of the position of the 

 bow wave. This suspicion was removed by Wigley's mathematical and experi- 

 mental investigation (1936). He used Havelock's formula for wave resistance 

 (1934) in terms of the regular wave heights due to the ship hull and a point dou- 

 blet. He separated the wave resistance into three parts: the hull wave resist- 

 ance, the bulb wave resistance and the interference resistance of the hull and 

 bulb. The most favorable case occurred when the negative interference resist- 

 ance was largest. He derived the following six rules for the bulbous bow as the 

 conclusion of his investigation (W. C. S. Wigley, 1936): 



"(1) The useful speed range of a bulb is generally from V Vl = 0.8 to V x/L = 

 1.9 (or in Froude numbers based on ship length, from 0.238 to 0.563), V being 

 the speed in knots and L the ship's length in feet. 



(2) The worse the wavemaking of the hull itself is, the more gain may be 

 expected with the bulb and vice versa. 



1065 



