73 



of research. Again, the difficulty arises of how to find the shape of the 

 body generated by the assumed concentrated singularities. 



A rather general method due to Kotchine^* may be mentioned, devel- 

 oped with the idea of obtaining all the force components due to free surface 

 effects. Kotchine's elegant expressions have not yet led to new results for 

 the wave resistance, but they have proved to be useful when calculating verti- 

 cal forces. 



Finally, reference must be made to the work of R. Guilloton. Two 

 new basic ideas may be distinguished in his publications (References 15, l6 



and 17): 



a. The improvement of resistance calculations over those based on 



Michell's potential only, mentioned before. 



b. The use of resistance calculations based on a second approximation 

 to the velocity potential valid for forms with fuller section (flat bottom). 



Both methods of calculation are characterized by the use of wave 

 profiles and of the pressure distribution due to wave motion. An original 

 approach based on finite differences leads to solutions for an arbitrary ship 

 form with finite draft. 



Figure 36 'indicates how far Guilloton' s method is superior to 

 Michell's integration of the pressure 

 distribution from a physical point of 

 view; while the latter is confined to 

 the underwater part of the form only, 

 Guilloton extends it over the proper 

 limits. Objection can be made that 

 Guilloton' s procedure is liable to lead 

 to errors of computation, since the 

 result is arrived at by evaluating quan- 

 tities which are relatively small dif- 

 ferences of other quantities, themselves 

 known with only limited accuracy. This 

 question can only be decided by actually 

 performing calculations, and the present 

 author has not to date had the opportun- 

 ity of carrying out such work. However, 

 Guilloton' s method of evaluating wave 

 profiles and the wave pressure exceeds as 



to rigor all the proposals hitherto made; hence, it must be considered as a 

 fundamental work intended to base the computation of wave resistance on an 

 evaluation of the complete flow pattern. 



Figure 36 - Pressure Distribution 



Over a Section due to the Motion 



of a Ship, Following Michell 



and Guilloton 



