396 HYDRAULICS AND ITS APPLICATIONS 



form at all velocities, and are similar for similar bodies. Also, as pointed 

 out by Mr. Froude, and subsequently confirmed by experiment, this holds for 

 partially submerged bodies in spite of the effect of gravity on the vertical 

 displacements, if the similar bodies move with velocities proportional to 

 V I), where D is the ratio of their linear dimensions. Assuming then, 

 as appears to be approximately true, that the height of the waves is 

 proportional to v*, and that their breadth is proportional to their height, 

 we have their mass proportional to v 4 , and the energy of formation to 

 v 6 . This energy is largely dependent on the form and relative length of 

 entrance and run of a ship, and every vessel would appear to have some 

 limiting speed beyond which any increase is accompanied by an altogether 

 disproportionate increase in wave-making resistance. Mr. Scott Russell 

 states that this limit is somewhat less than that corresponding to the 

 length of the wave which the ship tends to form, which length depends 



FIG. 180. 



on the length of entrance and run, and gives the following formula L for 

 the maximum velocity obtainable without abnormal resistance : 



V 1-03 Vi + La. 



Where V = velocity in knots; LI and L 2 are lengths of entrance and run 

 in feet. 



He also states that LI should not be less than '562 F 2 

 Li '375 V\ 



Thus for a speed of 10 knots, LI + L 2 > 93'7 feet. 

 20 Li 

 30 L! 



While agreeing fairly well with observed results, more recent investiga- 

 tions 2 point to the incompleteness of this rule, and indicate that the 

 length of the middle body of a ship also affects the wave resistance. 



Eddy formation, apart from that due to skin friction, is largely confined 



1 " Transactions Inst. Naval Architects," vols. 1 and 2. 



2 - Transactions Inst. Naval Architects," 1881. 





