63 



Prom a theoretical point of view, the procedure leaves much to be 

 desired. The factor /S * Is assumed to be constant over the whole after half 

 of the ship, while the Influence of the viscous phenomena Is undoubtedly con- 

 centrated at the extreme end of the run, where the generation of waves Is most 

 heavily rescued by Its effect. Following Havelock, this fact alone explains 

 why the Influence of viscosity on the wave pattern Is so much more pronounced 

 for low Proude numbers. ^^ 



Havelock calls a third most promising step "an illustration of the 

 possible effect of boundary layer on wave resistance;" Small modifications 

 of the lines near the stern are made so as to obtain the required kind of 



77 



change in the calculated resistance curve. 



The displacement thickness* of the frlctional layer ( something of the 

 order of one-tenth of the boundary-layer thickness) is inappreciable, except 

 at the stern of the ship, where, because of the reduced girth and eventual 

 separation, a wider wake is created. 



Quantitative estimates of viscous effects on wave patterns appear 

 to be possible when an appropriate singularity distribution is found which 

 takes into consideration the influence of viscosity. 



With the kind permission of the Institution of Naval Architects, two 

 figures (Figures 33 and 3^+) are reproduced from a paper by Wlgley, which sum- 

 marize some important resistance results. The hulls Investigated belong to a 

 family (2,4,6); asymmetry is produced by adding a term ag(|'' - |^). 



The investigation is similar in purpose to the corresponding one in 

 the first part of this chapter, but more elaborate computations have been per- 

 formed. Instead of the resistance curves, differences in the resistance be- 

 tween appropriate models are plotted and experimental values are compared *'ith 

 results of calculations with and without viscosity correction. In Figure 33 

 the symmetrical basic Teddington Model 1970B sectional-area curve (2,4,6; 

 0.7; 2) is compared with an asymmetric model 2170A derived from 1970B by 

 shifting the center of buoyancy by 0.02L. 



When the full end of 2130A is leading, a reasonable agreement is ob- 

 tained between measured and calculated resistance without any viscosity cor- 

 rection. However, when the fine end is leading the concept of ideal fluid 

 breaks down, while the semleraplrical viscosity correction yields at least a 

 qualitative agreement . 



*The displacement thickness i* Is the amount of displacement by which the main stream is thrust away 

 from the body due to the slowing down in the boundaiy layer. The mathematical expression is 



■/' 



(1 -— )dy 



