318 APPLIED MECHANICS — 
the fluctuation of energy, which is discussed in the.next Article, and for 
this the length of the base is immaterial. 
Piston Effort Down Stroke 
% 
% 
=~he--- 
S 
= 
Curve 
of Crank i ae 
= fort: 
! 
an_} 
mr 
Tm 1 i \ : | 
Mat ae ae re 4 es | 
OO set 4 oe pes eben: RAE 1: BR bs Bea 
Fie. 495. 
The maximum crank effort can evidently be found from either the 
polar or rectangular curves. The maximum crank effort is also the 
maximum torque on the crank shaft, and this is of great importance ip 
designing the shaft. 
If T,, is the mean effort on the crank pin and P,, is the mean effort on 
the piston, during one revolution, then, since the work done at the crank 
pin is equal to the work done on the piston in the same time, friction 
being neglected, 
2P in 
fart = 2P kor orth rs: 
When there are two or more cranks on a shaft, the total turning 
effort on the shaft at any instant is the sum of the turning efforts on the 
separate cranks at that instant, and the total effort may be considered as 
acting on any one of the cranks. Hence a diagram of total turning effort 
may be constructed by adding to the ordinates of the effort diagram for 
one crank the corresponding ordinates of the 
effort diagrams for the other cranks, corre- 
sponding ordinates being those which show 
the efforts on the separate cranks at the same 
instant. 
Fig. 496 shows the relative positions of 
three cranks on the same shaft, and Fig. 497 
shows how the rectangular crank effort diagrams 
for these three cranks may be combined to give 
a total turning effort diagram. It will be 
observed in Fig. 497, that in order to bring 
the corresponding ordinates together the effort Fig. 496. 
diagrams for cranks No. 2 and No. 3 have been moved forward distances 
corresponding to the respective angles which these cranks would have to 
move through to overtake No. 1 crank. It is obvious that the crank 
