96 EKMAN. ON DEAD-WATER. [norw. pol. exp. 



ciably altered (from 14 to 13.8 dm. per second) 1 , and the change of water has 

 no effect on the vessel. If now the wind gradually slackens, the velocity of 

 the vessel diminishes slightly more than it would have done under ordinary 

 circumstances (because the vessel must to a greater and greater extent generate 

 diverging boundary-waves), and is 12 dm. per second, when the propelling 

 force has fallen to 021 ton. But if the wind slacken a very little more, 

 the velocity of the vessel drops right down to 4 3 dm. per second (0.86 knot); 

 the reason is that with decreasing velocity the resistance due to boundary- 

 waves begins to increase more than the frictional resistance decreases, and 

 particularly, when it has fallen below 7'3 dm. per second, large transverse 

 boundary-waves are created and contribute towards the resistance — the vessel 

 has taken dead-water. If the wind now recovers its initial strength, the 

 only effect is that the vessel has her velocity increased a little (to 4'7 dm. 

 per second), but she still lies in dead-water, and consumes her energy of 

 propulsion upon large boundary-waves. Only if the wind freshens still 

 more, so that the propelling force gets the better of the maximum resistance 

 0'29 ton, is her velocity at once increased from 6 to 15'6 dm. per second 

 (full 3 knots); and the large boundary-waves simultaneously disappear — 

 the vessel has got free from the dead-water. 



A vessel may evidently get into dead-water or get rid of it, even if the 

 wind is not altering. The vessel may for instance move in a brackish surface- 

 layer on the top of salt water, at a speed at which she is still insensible to 

 dead-water. If the vessel enters a more and more fresh, surface-layer, or if 

 the thickness of the latter alters suitably, its effect upon the resistance is in- 

 creased (as will be shown in the next section of this chapter), and particularly, 

 the maximum resistance represented by the top point of the resistance-curve 

 and the minimum resistance at a somewhat higher velocity, are increased. 

 When the minimum resistance (which in the above example was 0"21 ton) is 

 large enough to get the better of the force of propulsion, the velocity is at 



For the sake of simplicity, it is supposed for the present, that the curves in Fig. 8, 

 PI. VI, are exactly correct, although their determination (as well as the applicability 

 of Froude's rule) was to a great extent only approximate. Especially is it assumed, 

 that the resistance is always the same at the same velocity, although it actually de- 

 pends also on the manner in which the vessel is set in motion (see p. 75). The 

 errors which these suppositions involve, are of no importance, as far as our present 

 qualitative discussion is concerned. 



