320 APPLIED MECHANICS a 
represent the resistance reduced to the crank pin. In the upper part of 
Fig. 498, LMN is a straight line parallel to OX, while in the lower part 
LMN is-a curved line. In each case the work done by the effort is 
- represented by the area between the effort curve and the base, and the 
work done on the resistance is represented by the area between the 
resistance line and the base. It will be noticed that the points 
A, B, C, D, E, and F are the points where the effort is equal to the 
resistance. 
Let K denote the kinetic energy in the moving parts when the crank 
pin is at A, then while the crank pin moves from A to B the work done 
by the effort is greater than that required by the resistance by the 
amount represented by the area a,, and therefore the kinetic energy in 
the moving parts when the crank pin reaches B is K+a,. Again, while 
the crank pin moves from B to C the work done by the effort is less than 
that required by the resistance by the amount represented by the area a,, 
and therefore the kinetic energy in the moving parts when the crank pin 
reaches C is K+a,—a,. Similarly, the values of the kinetic energy in the 
moving parts when the crank pin reaches D, E, and F are, K + a, — a) + dg, 
K +a, — @,+4, —a,, and K +a, —- a,+4@,—4@,+4; respectively. Between 
O and X the velocity of the crank pin will be a maximum at that point 
where the kinetic energy of the moving parts is greatest, and the velocity 
will be a minimum at that point where the kinetic energy is least. 
The difference between the kinetic energy of the moving parts at the 
points of maximum and minimum speed is called the fluctuation of energy. 
The ratio which the fluctuation of energy bears to the work done per 
cycle is called the coefficient of fluctuation of energy. In an ordinary steam- | 
engine the cycle takes place in one revolution, while in an internal com- 
bustion engine working on the Otto cycle, the cycle covers two revolutions 
of the crank shaft. 
Referring to Fig. 498, suppose that OX represents the distance 
travelled by the crank pin during one cycle, and suppose that F is the 
point of maximum speed, and C the point of minimum speed, Let the 
area between the effort curve and the base equal a, then the fluctuation 
of energy is represented by a,—a,+4;, and the coefficient of fluctuation 
of energy is equal to “3— “47s “12 wa 
279. Fluctuation of Energy in Gas-Engines.—In a single-cylinder, 
single-acting gas-engine working on the ‘‘ Otto cycle,” the operations 
performed during a cycle are as follows :— 
First Stroke.—The piston moves outwards, and draws in the charge of 
air and gas. This is the charging or suction stroke. 
Second Stroke.—The piston moves inwards and compresses the charge. 
This is the compression stroke. 
Third Stroke.—The compressed charge is ignited, an explosion takes 
place, and the piston is driven outwards by the expansive force of the 
products of combustion. This is the working stroke. 
Fourth Stroke.—The piston moves inwards and expels the products 
of combustion. This is the exhaust stroke. 
The indicator diagram is shown in Fig. 499, but the suction and 
exhaust pressures are shown exaggerated for the sake of clearness. 
Fig. 500 shows the diagram as continuous on a four-stroke base. 
