136 EKMAN. ON DEAD-WATER. [norw. pol. EXP. 



To calculate the greatest resistance by which the Fram could have been 

 held fast in the dead-water, let us assume first, that the fresh surface-layer 

 was 2'5 m. thick. The Fram's draught at that time, was 5 m. or more, say 

 5-1 or 5'2 m. aft. Her mean draught was then probably 4"9 m. According to 

 the rules given on pp. 132 — 133, we have therefore in Fig. 3 PI. XI to take 

 2-5 i— = 2'25 on the horizontal scale. The corresponding resistance given 

 by curve (1), is 0"87 ton, and curve (2) gives a velocity of - 8 m. per second. 

 The difference of specific gravity between the water-layers is assumed to be 

 0016. The displacement of the Fram with 4 - 9 m. mean draught is about 

 950 tons. The maximum dead-water resistance would consequently be 



n o 7 w 950 X 0-016 „.,, . 



87 X Or = 55 ton, 



and the corresponding velocity 



0-8 l/— — = 0' 6 m - P er second 

 r 30 4-4 r 



or 1"2 knots. As the Fram's speed, when not in dead-water, was at that 

 time 4"5 knots with the full force of the propeller (1 ton), the resistance at 

 1*2 knots in homogeneous water may have been (l , 2/4 - 5) 2 = 007 ton. The 

 whole resistance should then be - 55 + 0'07 = 0'62 ton only, and the ship 

 would consequently not be held in dead-water. 



As mentioned above, the depth of the surface-layer might, however, have 

 been as much as 5 m. or even a little more. Suppose it was 4 "5 in.; which 



would give nearly the greatest possible resistance. In Fig. 3, PL XI, we 



4-4 

 then have to take 4*5 j^ = 4 - 04, on the horizontal scale; the corresponding 



resistance given by curve (1), is P85 ton, and the velocity given by curve (2), 

 is 0'85 m. per second. Multiplying by the same factors as above, we obtain 

 a maximum dead-water resistance of 1*17 ton at a velocity of 1*3 knots. 

 The resistance in homogeneous water is at that speed 0'08 ton, and the 

 whole maximum resistance would consequently be about 125 ton, which is 

 more than sufficient to hold the Fram in dead-water. It may be remem- 

 bered, that this resistance 1'25 ton, denotes the propelling force necessary to 

 free the vessel from the dead-water, if the engine be stopped and after a 

 while given full speed again; while a still greater force would be necessary, 

 if this manoeuvre be not carried out. 



