Design of Low-Resistance Hull Forms 



of the residuary resistance ? If so, it means that boundary layer thickening can 

 have a net beneficial effect, a very surprising result. 



Of course, the increase in wave -pattern resistance when the propeller is 

 running might be due, not to a mere suppression of separation, but rather to an 

 induction by the screw, over the stern bulb, of low pressures such as would oc- 

 cur in potential flow. It appears from Figs. 13b and 13c that there is little effect 

 on wave height at the stern, but a very small change of local wave height could 

 be associated with a relatively large change in pressure drag. For this latter 

 reason it cannot be accepted as conclusive proof in favour of Guilloton's theory 

 (2) that he demonstrates good agreement between theory and experiment re- 

 garding the wave profiles along the side of the model. 



Guilloton's theory does, however, suggest an alternative explanation of the 

 discrepancy between the residuary resistances of the model run in the different 

 directions. As mentioned above, a given source distribution should have the 

 same wave drag run in either direction. According to either Michell's theory 

 or to Inui's theory the same hull run in opposite directions corresponds to the 

 same source distribution, but this is not so for Guilloton's theory. (I cite Guil- 

 loton's method rather than other potentially more exact methods of taking ac- 

 count of the distortion of the free surface because these latter methods have not 

 so far been developed to the point of being practicable for application, whereas 

 Guilloton's method is practicable.) If, then, Inui's theory is valid, the discrep- 

 ancies in Fig. 12 must be attributed to viscosity, but they need not be if Guillo- 

 ton's theory is more correct. On the other hand even Guilloton's theory predicts 

 that a hull of minimum wavemaking should be symmetrical about the centre line. 

 The bulb-aft model has such a low wave resistance that it is hard to imagine 

 that its effective hydrodynamic shape (including boundary layer displacement 

 effects) can be far from an optimum, unless this is such that some kinds of 

 large departure from the ideal shape can be tolerated without much increase of 

 resistance. 



If then we fall back on viscous effects as representing probably at least 

 part of the explanation, it seems important to develop a theoretical treatment of 

 them. Of course Havelock (10), Wigley (11), Emerson (12), and Inui (1) have 

 attempted to do this, but their methods lack a strong theoretical justification. 

 More satisfactory in principle is the method of Wu (13), but its development to 

 take proper account of the three-dimensional, turbulent nature of the boundary 

 layer would be difficult. However, the following arguments suggest, in support 

 of Havelock's intuition (10), that probably only the local boundary -layer thicken- 

 ing near the stern is of any significance. Hogben's experimental measurements 

 (14) show that the mean displacement thickness on a mathematical-form model 

 with parabolic waterlines varies roughly linearly with distance from the bow till 

 quite near the stern, where there is a rapid increase. Let us therefore consider 

 a central-plane source distribution whose density S is defined by 



/ 2x\ 



S = AV 1 - — +AVe, 0<x<L, 0<z<D, 



where e = o for x < X. If X= such a distribution defines, according to the 

 Michell approximations, a body of the shape shown in Fig. 14a, with parabolic 



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