316 APPLIED MECHANICS 
square inch of piston, then p=, and at the. ends of the stroke 
2 
pa (1 £2), After’ the point of zero acceleration is passed, the 
acceleration is of course negative, or the accelerating force reverses. 
275. Correction of Piston Effort Diagrams for Inertia Forces.— 
From the beginning of the stroke of the piston up to the point of maxi- 
mum velocity, or zero acceleration, part of the effort on the piston, as 
determined in preceding Articles, is required to accelerate the piston and 
the other reciprocating parts, and that part is therefore not available at 
the cross-head for transmission to the crank pin. The work done by that 
part of the steam pressure which is not transmitted to the cross-head is 
stored up in the reciprocating parts as kinetic energy. After the piston 
has reached its point of maximum velocity its velocity diminishes, and 
the kinetic energy in the reciprocating parts is given out, appearing as 
work done at the cross-head. During the latter part of the stroke, there- 
fore, the effort due to the steam pressure is supplemented by the effort 
due to the retarding or negative accelerating force. 
The necessary correction of the piston effort diagram due to the inertia 
forces is made as shown in Figs. 492 and 493, where the full line diagram 
Se } 
‘ | 
TOP 4 
— a aif BOTTOM. 
Fig. 492. Fig. 493. 
on the straight base AB is the piston effort diagram due to the steam 
pressure, and AaOdB is the accelerating force diagram on the same base 
AB. The curve a’Cd’ is the curve got, say, by Klein’s construction (Art- 
261), and the curve aCé is obtained by altering the ordinates in the ratio 
of Aa’ to Aa. The length Aa is measured with the pressure or effort 
2 
rv: 1 : 
scale to represent p = “(i + a the accelerating force per square inch of 
piston at the beginning of the forward or “in” stroke. The curve aCd 
is the new base of the effort diagram. The corrected diagrams are shown 
constructed on straight bases below the others. 
It is evident that the forces due to the inertia of the reciprocating 
parts do not affect either the work done or the mean effort during a complete 
stroke. 
276. Crank Effort.—Referring to Fig. 494, if P is the effort on the 
