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



It is often believed that the great resistance to a vessel in dead-water, 

 is felt only when the vessel reaches into the salt-water. This opinion, which is 

 not in accordance with the explanation of the phenomenon as an effect of 

 wave-generation, is not confirmed by the experiments. On the contrary, they 

 show that when the depth of the surface-layer is even twice as great as the 

 draught of the vessel, its effect upon the resistance is still very considerable, 

 the resistance being at certain velocities, four times as great as in homoge- 

 neous water, and the maximum resistance being only about 40 per cent smaller 

 than when the depth of the surface-layer is the same as the vessel's draught. 

 In the latter case its effect upon the resistance has its greatest value, as has 

 already been mentioned. On the other hand, the curves show, that when a 

 vessel pulled by a given force, is in dead-water, her velocity is, as a rule, 

 slowed down more, the thinner be the fresh-water layer. 



It would be useless to try to express the above mentioned experimental 

 results as a mathematical formula, it is better to use them, as they are given 

 in the diagrams. 



The resistance-curves in Fig. 1 PI. X clearly show their connection with 

 the maximum velocity of the boundary-waves. The latter quantity is represented 

 at the top of the figure, by a small circle containing a number indicating the 

 depth of the fresh-water layer in centimetres, and by a small pointer below in- 

 dicating the maximum wave-velocity. For instance, it is 5"35 cm./second in 

 the case of a 1 cm. fresh-water layer, 9'00 cm./second in the case of a 3 cm. 

 layer, and so on 1 . The velocity at which the dead-water resistance is a 

 maximum, cannot of course, be determined very accurately, although the 

 resistance-curves are drawn from the experiments as exactly as possible. Ac- 

 cording to the resistance curves, it is in most cases somewhat smaller than 

 the maximum wave-velocity; the ratio increases with decreasing depth of the 

 surface-layer, being - 7 or 0"75 if this is 9 or 13 cm., 0*9 if it is 3 cm., and 

 even above unity if it is only 1 cm. When the depth of the surface-layer 



1 The numbers are calculated according te equation (3) p. 43, and the finite depth of 

 the salt-water, is consequently taken into account. If the latter had been very deep, 

 the maximum wave-velocities would have been somewhat greater. The difference 

 would have been only 1 per cent for a 1 cm. surface-layer, but 7 per cent for a 5 

 cm. surface-layer and 20 per cent for a 13 cm. surface-layer. The relationship given 

 in Fig. 1 PI. X, between the resistance and the depth of the surface-layer, may there 

 fore be regarded as chiefly qualitative, as far as the greatest depths are concerned. 



