Engine cycles (A-level only)

AQA·Physics·3.11.2.4

Four-Stroke Petrol Engine Cycle

A petrol engine produces a power stroke by burning a compressed air–fuel mixture inside a cylinder. The resulting high-pressure gases push a piston, which moves through four strokes to complete one cycle. A stroke is one movement of the piston along the cylinder.

The four strokes

  1. Intake: The piston moves down, drawing an air–fuel mixture into the cylinder through the open intake valve.
  2. Compression: The valves are closed as the piston moves up, compressing the mixture. Near the end of the stroke, a spark ignites it.
  3. Power: Combustion raises the pressure in the cylinder. The high-pressure gases expand and push the piston down.
  4. Exhaust: The exhaust valve opens and the piston moves up, pushing the combustion products out of the cylinder.

The idealised Otto cycle

The Otto cycle is an idealised model of the petrol engine cycle. It represents the changes in the working gas on a pressure–volume diagram as four processes:

  1. Adiabatic compression: The gas is compressed without heat transfer. Its volume decreases and its pressure rises.
  2. Constant-volume heat addition: Heat is added while the volume stays fixed, causing the pressure to rise. This approximates the rapid combustion of the compressed mixture near the end of the compression stroke.
  3. Adiabatic expansion: The gas expands without heat transfer. Its volume increases and its pressure falls as it drives the power stroke.
  4. Constant-volume heat rejection: Heat leaves the gas while its volume stays fixed, causing its pressure to fall.

The ideal cycle models heat rejection as a constant-volume process; it does not represent the actual exhaust stroke as an identical process. In the engine, the exhaust stroke removes combustion products from the cylinder.

Diesel Engine Cycle

A diesel engine compresses air until it is hot enough to ignite fuel. Fuel is then injected into the hot air and burns. Combustion raises the gas pressure, and the expanding gases push the piston to produce the power stroke.

The four-stroke diesel cycle

  1. Intake: The piston draws air into the cylinder.
  2. Compression: The piston compresses the air, raising its temperature. Fuel is injected into the hot compressed air and ignites.
  3. Power: Combustion produces high-pressure gases that expand and push the piston, delivering useful work.
  4. Exhaust: The piston pushes the exhaust gases out of the cylinder.

Unlike a spark-ignition petrol engine, a diesel engine does not use a spark to ignite the fuel. Ignition follows injection into hot compressed air.

The ideal diesel cycle

The ideal diesel cycle is a simplified model of the changes in the gas. It represents compression and expansion as adiabatic processes: no heat is transferred between the gas and its surroundings during those stages. The model also includes two heat-transfer stages:

  • Constant-pressure heat addition: Heat is supplied while the gas expands, with its pressure held constant in the model. This idealises combustion as fuel is supplied.
  • Constant-volume heat rejection: Heat is removed while the gas volume remains fixed, returning the gas towards its initial state.

These ideal processes are not an exact description of the four physical strokes. In particular, constant-pressure heat addition does not mean that pressure stays exactly constant throughout combustion in a real diesel engine.

Engine Indicator Diagrams

An engine indicator diagram shows how the pressure of gas in a cylinder changes as the cylinder volume changes during an engine cycle. Pressure $$p$$ is plotted on the vertical axis and cylinder volume $$V$$ on the horizontal axis.

During compression, the volume decreases, so the path moves towards the left. During expansion, the volume increases, so the path moves towards the right. These paths, together with the other processes in the cycle, form a loop on the diagram.

Work from an indicator diagram

As the gas expands, it does work on the piston. During compression, work is done on the gas. The net area enclosed by the loop represents the net work done by the gas per cycle: expansion work minus compression work and any other work done on the gas. For a usual clockwise engine loop, this net work is positive.

An actual indicator diagram can also show work associated with intake and exhaust. Where these processes form a separate loop, their work must be included with its sign when finding the net work for the complete cycle. If pressure is measured in pascals and volume in cubic metres, the work is in joules.

Theoretical and measured indicator diagrams

A theoretical diagram predicts a cycle using idealised processes. A measured indicator diagram records the actual cylinder pressure against volume. Their paths and loop areas can differ because real combustion takes time and heat is transferred to the surroundings.

The loop area therefore gives the work for the particular theoretical or measured cycle shown. It does not automatically give the useful work delivered at the engine shaft: some work is lost, for example through friction.

Indicated power from the loop area

For identical cylinders, the net work per cycle is the same for each cylinder. Multiplying it by the number of cycles completed per second per cylinder and by the number of cylinders gives the indicated power:

Pindicated=(net area of p–V loop)(cycles per second per cylinder)(number of cylinders)P_{\mathrm{indicated}}=(\text{net area of }p\text{–}V\text{ loop})(\text{cycles per second per cylinder})(\text{number of cylinders})

A theoretical loop gives a prediction of indicated power; a measured loop gives indicated power from the recorded cycle. With work in joules and cycle rate in cycles per second, power is in watts.

In a four-stroke engine, each cylinder completes one cycle in two crankshaft revolutions. The cycles per second per cylinder are therefore half the crankshaft revolutions per second, not equal to them.

Other cycle diagrams can be interpreted in the same way: follow their labelled processes to identify the direction of each path and the net work represented by the loop.

Engine Power and Efficiencies

An engine receives chemical energy from fuel, develops power in its cylinders, and delivers useful power at its shaft. Comparing these rates shows how much of the fuel input becomes useful output.

The indicated power is the power developed in the cylinders. The brake power is the useful power delivered at the shaft. Brake power is lower because some of the power developed in the cylinders is used to overcome friction and other mechanical losses within the engine.

Fuel input and brake power

The rate at which fuel supplies chemical energy is the fuel input power:

Pinput=calorific value×fuel flow rateP_{\mathrm{input}}=\text{calorific value}\times\text{fuel flow rate}

The calorific value is the energy released per unit mass of fuel, and the fuel flow rate is the mass of fuel supplied per unit time. For example, using calorific value in $$\mathrm{J,kg^{-1}}$$ and flow rate in $$\mathrm{kg,s^{-1}}$$ gives input power in watts.

Brake power depends on the torque at the shaft and its angular speed:

Pbrake=TωP_{\mathrm{brake}}=T\omega

Here, $$T$$ is torque in newton metres and $$\omega$$ is angular speed in radians per second. The resulting brake power is in watts.

Indicated power and friction power

The difference between the power developed in the cylinders and the power delivered at the shaft is called friction power:

Pfriction=Pindicated−PbrakeP_{\mathrm{friction}}=P_{\mathrm{indicated}}-P_{\mathrm{brake}}

Thus, indicated power accounts for both the useful shaft output and the power used in overcoming the engine’s mechanical losses.

Engine efficiencies

Each efficiency compares a power output with the power supplied to the stage being considered:

ηthermal=PindicatedPinputηmechanical=PbrakePindicatedηoverall=PbrakePinput\begin{aligned} \eta_{\mathrm{thermal}}&=\frac{P_{\mathrm{indicated}}}{P_{\mathrm{input}}}\\ \eta_{\mathrm{mechanical}}&=\frac{P_{\mathrm{brake}}}{P_{\mathrm{indicated}}}\\ \eta_{\mathrm{overall}}&=\frac{P_{\mathrm{brake}}}{P_{\mathrm{input}}} \end{aligned}

Thermal efficiency is the fraction of fuel input power developed in the cylinders. Mechanical efficiency is the fraction of indicated power delivered at the shaft. Overall efficiency is the fraction of fuel input power delivered as brake power.

Multiplying the first two ratios cancels the indicated power, giving the overall efficiency:

ηoverall=ηthermalηmechanical\eta_{\mathrm{overall}}=\eta_{\mathrm{thermal}}\eta_{\mathrm{mechanical}}

An efficiency can be expressed as a fraction or multiplied by 100 to give a percentage.

A theoretical or measured indicated power can be combined with the corresponding fuel input and brake powers to calculate these efficiencies. An indicator diagram can help determine work developed in a cylinder, but it does not by itself provide all the quantities needed: the appropriate cycle rate is needed for indicated power, while fuel input and shaft output require additional information.