240 PROPULSION OF VESSELS 



fuller. Furthermore, the value of k should be smaller for 

 relatively high speeds than for low speeds, for vessels of the 

 same form and displacement. Prof. W. F. Durand states that 

 -a speed may be considered as relatively high or low if the 

 speed exceeds the numerical value of the square root of the 

 length of the vessel in feet, or falls below it. Thus, if a vessel 

 is 64 ft. long, V64 = 8, a speed of 10 knots would be considered 

 as relatively high, while a speed of 5 knots would be considered 

 as relatively low. For small boats, if the speed is given in 

 statute miles per hour, the values of k range between 150 and 

 225, and for speeds given in knots, between 100 and 150, 

 according to Prof. W. F. Durand. 



Relation of Horsepower and Revolutions. The speed of a 

 ship fully under way is about directly proportional to the 

 number of revolutions made by the engine. But the power 

 required to turn the propelling instrument varies as the cube 

 of the number of revolutions, or, what is the same thing, as 

 the cube of the speed. Hence, it is possible to find, approx- 

 imately, the power developed by an engine for any given 

 number of revolutions per minute, any other horsepower and 

 the corresponding revolutions per minute being known by the 

 use of the formula 



in which Hi = required indicated horsepower; 



Ri = revolutions per minute at required power; 



H = given indicated horsepower; 



R = revolutions corresponding to the horsepower H. 

 In practice, the horsepower calculated by this formula will 

 not always correspond to that actually used, as found by the 

 indicator diagram. This is due to the fact that the efficiency 

 of the machinery is not necessarily the same at all speeds. 

 As a general rule, the engine will be at its maximum efficiency 

 at some certain speed, and will have a lower efficiency at a 

 higher or lower speed. The speed at which the engine is at 

 its best efficiency can be found only by actual trial. 



Reduction of Horsepower When Towing. It is a well-known 

 fact among marine engineers that an engine will develop a lower 

 horsepower with a given boiler pressure, throttle position, 



