69 



For general analysis of resistance properties in shoal water, the 

 ratio h/L is more characteristic than the draft -depth ratio H/h. As usual, 

 Taylor's representation of the matter*'"' based on F and h/L is superior to 

 others. 



Within the validity of the theory (H/h small) H/h is a parameter 

 whose changes cause only moderate deviations from corresponding deep water 

 phenomena when h/L is kept constant. Hence, it is in principle disadvantage- 

 ous to link up wave effects with the draft H instead of the length L. 



d. Besides the critical speed defined by v = ^gh, another critical 

 speed V (the speed of maximum resistance) is sometimes used; we prefer to re- 

 strict the terminology "critical speed" to v = V§h- 



The maximum wave resistance occurs at a speed v_ < Vgh, the differ- 

 ence Vgh - V increasing with increasing h/L. 



e. The maximum wave resistance in shoal water for a given displacement 

 does not seem to depend much on the ship form. This can be inferred (within 

 the validity of the theory) as follows: The speed of maximum resistance in 

 shoal water corresponds to an extremely high speed in deep water; but in the 

 latter case, displacement is decisive and the resistance is nearly independ- 

 ent of form. 



f . When h/L becomes large, say of the order of unity, so that F, crit- 

 ical corresponds to P ~ 1 , the difference between deep and shallow water re- 

 sistance is not too large. This is the reason why resistance tests with mod- 

 els of high-speed ships yield useful results for deep water, although they may 

 run in the range of the critical speed. 



The motion of a ship in a canal can be treated by the methods of 

 engineering hydraulics. A clever application was made by Kreitner;-''^ he ex- 

 plained supercritical conditions by analogy with the hydraulic jump and gave 

 information on the average speed of flow of the water around a ship in a canal. 

 The study of motions in a canal, besides its immediate practical application to 

 canal and river shipping, also has a bearing on foundations of model testing. 



In a canal the speed for maximum resistance occurs somewhat earlier 

 than in shoal water of unlimited breadth. 0. Mueller tries to explain this 

 fact by introducing an empirical Proude number^^ 



^-vsV^^-^hl^F^ 1"! 



vgH 

 substituting the hydraulic radius p. . = -^ for the depth h. 



