56 



c . Generally a suitable bulb improves bad forms by a greater absolute 

 amount than it does good ones, except in cases where the inneficiency of the 

 form is caused by features like an exaggerated t value. Reference is made to 

 Figure 15; there the good model 1370 could not be improved by a bulb, which, 

 applied to the bad model ^331 > proved to be quite effective. Theory suggests 

 the use of a bulb when rather full forms are driven beyond their limit of 

 economical speed. 



d. Generally a bulb uniformly distributed over the draft influences the 

 wave resistance of a normal form more than a submerged bulb (Figure 30a) pro- 

 vided the sectional-area curve of both bulbs Is the same. This can be easily 

 understood by the fact that wave effects, hence interference effects too, 



are stronger at the surface than near the bottom of the ship. In Wigley's 

 paper *■"■ a different statement is made; however, it seems to be due to the 

 rather abstract shape of the bulb used. Since the uniformly distributed bulb 

 cannot be used because of the spray formation, the submerged bulb is the only 

 practical solution. Probably the loss of efficiency mentioned above can be 

 compensated by a higher strength factor "a". 



e. In an- ideal fluid the optimum solutions are symmetrical with respect 

 to the midship ratios, i.e., bulbs should be fitted both at the bow and at the 

 stern. Obviously this deduction may be wrong for viscous flow. It has been 

 tried""'"^ on different models with the result that: 1) For higher Froude num- 

 bers, say F > 0.3 the symmetrical combination had nearly double the effect of 

 a bow bulb alone, and 2) a model with a stern bulb alone did not show any ad- 

 vantages compared with the normal form. The idea of a stern bulb may have 

 some merits with respect to the interaction between propeller and ship. 



In summary, the application of theory to bulb forms means a serious 

 violation of the assumptions on which Michell's integral is based. Neverthe- 

 less results are obtained which are useful for guidance in research and design 

 work . 



As for the cruiser stern, by fitting this type of afterbody the 

 total resistance of a model may be reduced at some Froude numbers while, for 

 other ones, the success may be negligible.*^ This dependence upon speed indi- 

 cates that at least one part of the beneficial effect is due to wave 

 interference. 



The phenomena involved can be investigated using a method proposed 

 by Havelock for calculating the Influence of viscosity on wave resistance 

 (page 63). Numerical computations are under way. Similar calculations can be 

 made when dealing with a possible influence of bossings on the wave resistance. 



