400 HYDRAULICS AND ITS APPLICATIONS 



coefficient of friction determined, the frictional resistance can now be 

 calculated for any speed, and the curve B B, of frictional resistances drawn. 



If now the horizontal scale be increased in the ratio V D : 1, and the 

 vertical scale in the ratio Z) 3 : 1, the curve A A serves as the total 

 resistance curve for the ship. Thus if the model is ^ the size of the 

 ship D = 12, the corresponding speeds of ship and model are in the 

 ratio A/32 : 1 = 3*461 : 1, and at this corresponding speed the resistances 

 are in the ratio 12 3 : 1 = 1728 : 1. 



If fresh water is used in the experimental tank the vertical scale is to 

 be increased again in the ratio of the densities of salt and fresh water, 

 while a further final correction is necessary because of the different 

 values of /for the ship and model. This is got over by calculating the 

 actual frictional resistance of the ship for her true length at various 

 speeds, and by setting the values thus obtained as ordinates downwards 

 from the curve B B, to form the curve C C. The true resistance of the 

 ship at any speed is then given by the corresponding vertical intercept 

 between A A and C C. 



The resistance at any given speed F,, is calculated from model observa- 

 tions at the corresponding speed F m , as follows : 



Total resistance of model (observed) = R m Ibs. 



Frictional,, (calculated) =f m S m V w ?.\\>*. 



.'. Wave-making and eddy resistance of ) _ ^ /. T7 n _ 1U 

 model 



.*. Wave-making and eddy resistance of ) _ ^ . 3 x 64 

 ship in salt water 62'4 ' 



fi4 



.-. Total resistance of ship = jj^ D S E +/, S 3 V s n . Ibs. 



A second method of carrying out tank experiments is due to Colonel 

 English, and has certain advantages. Suppose the resistance of a ship in 

 commission to be known at velocity FI, that of another proposed ship to 

 be determined at a velocity Fa. Make models of the two ships. Let 

 suffix 1 refer to existing ship ; suffix 2 to that to be built, and let 

 prefixes s and ra refer to ship and model respectively. 



Let * = < 1 ; * = i 2; and 



,F X a*l * V '2 



i.e., make m k and m l^ satisfy the conditions that 



If now the models be towed simultaneously, each attached to one of 





