PISTON AND CRANK EFFORT DIAGRAMS 321 
____All the work delivered to the crank shaft during a cycle is delivered 
_ during the working stroke, and the work done in the cylinder during the 
other strokes comes from the fly-wheel. 
_ The fluctuation of energy is obtained from the’ rectangular crank 
x Fia. 499. F1a. 500. 
d effort diagram as in a steam-engine, but the diagram must be constructed 
7 for a complete cycle. The net work done on the useful resistance at the 
crank shaft and on the friction of the engine is represented by the shaded 
area in the working stroke in Fig. 500, minus the shaded areas in the 
other strokes. The maximum speed of the crank shaft is approximately 
at the end of the working stroke, and the minimum speed is approxi- 
mately at the beginning of that stroke. Hence the fluctuation of energy 
is approximately equal to the work done during the working stroke, 
‘ minus l-nth of the net work done during a cycle, where m is the number 
of strokes during a cycle. _ 
If the engine is governed on the “ hit or miss” principle, the governor 
acts by cutting off the gas, and there is no explosion and no effective work 
done for at least two revolutions after the completion of an effective cycle. 
The complete cycle then takes a number of revolutions, which is a simple 
multiple of two. 
” 280. Fly-wheels.—The function of a fly-wheel is to reduce the flue- 
; tuation of speed due to the fluctuation of energy during the period or 
cycle of the working of a machine. If over an interval the supply of 
energy toa machine is greater than the resistance requires, the moving 
parts increase in speed, and their kinetic energy therefore increases by 
an amount equal to the surplus energy ; and if over another interval the 
supply of energy is less than the resistance requires, the moving parts 
decrease in speed, and their kinetic energy therefore decreases by an 
amount equal to the deficiency in the supply of energy. In most cases 
where a fly-wheel is used it is usual to neglect the kinetic energy of all 
the moving parts other than the fly-wheel, so that over any interval the 
difference between the energy supplied and the energy required is equal 
to the change in the kinetic energy of the fly-wheel. 
If R is the radius of gyration of the fly-wheel, in feet ; v the velocity, 
in feet per second, of a point at a distance R from the axis; » the 
angular velocity in radians per second; N the speed in revolutions per 
minute ; W the weight of the wheel in lbs.; and K, its kinetic energy 
in ft.-lbs., then 
— We? _ yy 2 WR*w?_ yp 9 Wx 4a?R?N? _ yee 
K ee 39 M,w? = 2x 60% = MN?, 
where M,, M,, and M are constants for a given wheel. The kinetic 
x 
