338 APPLIED SCIENCE 



The forces required to accelerate the piston and the connecting 

 rod may now be calculated as follows : 



For the piston. If M be the mass of the piston and piston rod 

 in Ibs., the force in Ibs. is 



M <Px 



When this quantity is negative, the force acts towards the centre of 

 the crank shaft. 



For the connecting rod. The motion may be looked at as a 

 translation of the whole rod in the direction of motion of the piston, 

 combined with a rotation of the rod about the crosshead. Hence 

 the force producing acceleration is the resultant of three compo- 

 nents : Fj, the force required for the linear acceleration in the 

 direction of motion of the piston ; F 2 , the force required for rotation 

 about the crosshead at the angular velocity which the rod has at 



FIG. 66. 



the instant under consideration. This acts towards the centre of 

 rotation, and is equal and opposite to the so-called ' centrifugal 

 force ; ' and, lastly, F 3 , the force required to give the rod the angular 

 acceleration which it has at the given instant. 



Let M' be the mass of the connecting rod in Ibs., and G its centre 

 of mass, distant 1 from the crosshead B ; also let k be its radius of 

 gyration about B. Then the first component mentioned above, or 

 F,,is 



Mt ,J2~ 

 \M vO 



~g dP' 



and acts through G parallel to the path of the piston. 

 The second component, F 2 , is 



( V> 



(Note. In Figs. 55 and 56 the engine has been represented as seen from 

 behind, if the engine in the previous figures be considered as viewed from the 

 front.) 



