34 EKMAN. ON DEAD-WATER. [norw. POL. EXP. 



at a uniform rate in open water. The physical reason for this is, shortly ex- 

 pressed, that under these suppositions the motion of the water depends only 

 on the actual velocity of the vessel; the vis viva of the water consequently 

 remains unchangeable, and as mechanical energy cannot, in a frictionless fluid, 

 be transformed into heat, no energy at all is communicated to the water by 

 the vessel. 



In actual practice the water has a free surface. The pressure of the 

 vessel against the water then causes a disturbance of level, which persists in 

 the form of waves. These gradually spread over all the sea behind the 

 vessel, and the vis viva of the water thereby continually increases. The work 

 necessary to generate this vis viva must be spent by the vessel and causes 

 a certain "wave-making resistance". 



Further, water is a viscous fluid, and this circumstance will in a twofold 

 way cause an alteration of the motion, and the addition of new causes of re- 

 sistance. Firstly, the water, flowing past the ship's sides, exerts on them a 

 sternward tangential stress — "frictional resistance". Secondly, the motion 

 which, though unstable, would theoretically take place in a perfect fluid, is 

 disturbed by the viscosity; the wake, which would otherwise be smooth and 

 even, becomes irregular and eddying, and the steady supply of energy required 

 for creating new eddies is a cause of resistance — "eddy making resistance". 



Elaborate experiments have been made for determining the relative im- 

 portance of each of these factors in contributing towards the sum-total of 

 resistance. The frictional resistance is found to be quite preponderant at low- 

 speeds, and even for fast vessels going at full speed, it amounts to nearly a 

 half of the whole. The eddy-making resistance is rated at about 10 per cent 

 of the former (in well-formed vessels), and the rest is wave-making resistance. 

 These numbers are under the supposition that the water is not shallow (see 

 the next section of this chapter). The frictional resistance is approximately 

 proportional to the square of the vessel's velocity. 



Tlie wave-making resistance is of special interest to us, because it is 

 the chief cause of the speed-reduction in "dead-water"; the following general 

 remarks, though referring particularly to wave-making resistance under ordi- 

 nary circumstances, are, with some modifications, applicable to the case of 

 a vessel moving in dead-water. 



