# Real cycles of thermal engines

The actual cycle of a thermal engine is the one that reflects the effective conditions of its operation. These conditions are identified with the diagram of average pressures in the cylinder in correspondence to the different positions of the piston. The pressure shown in a mean pressure diagram is the so-called average pressure indicated.

The indicated diagram is the graph that represents this cycle.

## Simplified operation of the indicator

The indicator is a device used to obtain the indicated diagram of a thermal engine cycle.

In the indicator of the indicated diagram, a small cylinder provided with a piston retained by a spring communicates with the combustion chamber of the motor cylinder by means of a tube. The piston rod acts on a system of levers that form an amplifying quadrilateral. The longest lever arm of the quadrilateral is provided at its end with a stylet.

The drawing below shows schematically how the diagram indicated by the indicator is drawn. The schematic apparatus serves to show how an indicated diagram is obtained, but it is not feasible in practice. The indicators are, in fact, more complicated devices, which are used by specialized technicians.

The pressure of the gases is transmitted through the cylinder. The pressure acts on the piston and, overcoming the loading of the spring, moves the piston to a length proportional to the value of the pressure. The stylus traces, therefore, vertically a line of length proportional to the pressure acting on the piston. As all the indicating device is fixed to the motor piston, the stylet moves linearly with it, and its horizontal position corresponds at each point to that of the motor piston.

The curve traced by the stylus is, therefore, referred to two coordinate axes. The abscissas represent the spaces covered by the piston and, therefore, the volumes. The ordinates represent the pressures.

### Example for a four-cycle otto-cycle thermal engine

Suppose that the engine is an Otto engine ( spark ignition engine) and that it is a 4-stroke engine. Also, we will assume that the operating conditions are approximately theoretical.

We slide the piston from the top dead center (P.M.S.) to the bottom dead center (P.M.I.) and vice versa, with the valve open. We assume that the piston does not offer any resistance to the passage of gas. The pressure in the cylinder remains equal to the atmospheric pressure. During this movement the stylet traces a horizontal segment A-A, of length equal to the stroke of the piston. The drawn segment represents the pressure diagram for the suction and exhaust phases.

The valve is then closed during the compression stroke. The stylet describes curve A-B. At the end of the compression stroke, the combustion is verified and, consequently, a sudden increase in pressure occurs which makes the stiletto line almost vertical B-C. Subsequently, during the expansion run, the stylet describes curve C-D. Shortly before finishing the expansion stroke, the exhaust valve opens, the pressure drops to a value very close to atmospheric and, therefore, the stylet traces the small, almost vertical feature, D-A.

## Comparison of two real cycles of Otto engine and diesel engine

Below we show the representation of two typical real cycles of Otto engine and diesel engine of equal unit displacement.

To facilitate the comparison between the two real cycles, the diagrams have been drawn superimposed. The axis of the pressures for the Otto cycle, as a consequence of the volume difference Vc of the combustion chamber. In fact, with equal unit displacement Vp, the compression ratio of the diesel engine being higher than that of the Otto engine, the volume Vc of the combustion chamber is smaller.

The surface 1 2 6 1 '1 represents the negative work due to pumping in the suction and exhaust phases. The surface 2 3 4 5 6 2 represents positive work. Its difference is useful work. By dividing the area corresponding to the useful work carried out by the fluid, by the length of the stroke, or by the displacement Vp according to the scale chosen for the abscissa axis, the value of the indicated average pressure (pmi) is obtained.

If we wish to evaluate the difference of useful work between the theoretical cycle and the indicated cycle, we will establish the comparative relation between the corresponding surfaces. By dividing the surface of the indicated cycle by the respective one of the theoretical air cycle, the indicated yield is obtained.

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Last review: November 22, 2017