PROPULSION OF VESSELS 241 



and cut-off when towing or having the resistance of the vessel 

 increased by other means, than will be developed under the 

 same engine conditions but running free. The reason for this 

 is explained in the following discussion, in which for the sake 

 of simplicity two convenient assumptions have been made 

 that are not absolutely correct in practice. These assumptions 

 are that the horsepower of an engine varies directly as the 

 number of revolutions, the mean effective pressure remaining 

 the same, and that the speed of the vessel varies directly as" 

 the number of revolutions. 



Consider a paddle-wheel steamer running free, with its 

 engine developing its greatest horsepower possible. Since 

 the turning effort of the engine depends on only the mean 

 effective pressure in the cylinders, it is independent of the 

 revolution so long as the throttle position, boiler pressure, 

 and cut-off remain the same. This turning effort, when 

 exerted at the circumference of the effective diameter circle 

 tangentially to the same parallel to the surface of the water, 

 is the total force tending to propel the vessel forwards, and 

 is resisted by an opposing force, which is the resistance of 

 the vessel. Let the engine be started and assume that it is 

 making its greatest turning effort. The resistance being less 

 than the forward force, the vessel moves forwards under the 

 influence of a forward accelerating force equal to the differ- 

 ence between the total forward force and the resistance. As 

 the vessel gathers headway, the resistance increases; this 

 means that the difference between the forward and the resist- 

 ing force, that is, the accelerating force, decreases until the 

 total forward force and total resistance have become equal, 

 when the vessel continues at a uniform speed. Let the resist- 

 ance be increased either by the vessel picking up a tow, by a 

 head-wind or head-sea, by encountering an adverse current, 

 or by a combination of these circumstances. The conditions 

 remaining the same as before at the engine, the turning effort, 

 that is, the total forward force, is the same; but, as the initial 

 resistance is increased, the initial difference between the total 

 forward force and the total resistance is smaller than in the / 

 first case. This means that a smaller accelerating force is 

 available with an increased resistance, and consequently the 



