HD Animation: Thermodynamics of the Four-Stroke Petrol Engine

Explanations

The current state is marked in a PV diagram. A PV diagram (pressure-volume diagram) is used to visualize the state of a gas, in this case the air-fuel mixture inside the cylinder of an internal combustion engine. The four strokes are color-coded in the PV diagram.

The ignition timing is also shown. The ignition timing is the moment when the air-fuel mixture in the cylinder is ignited.

If the engine speed is changed (by accelerating), the ignition occurs earlier. This is because the speed of combustion is always constant. By shifting the ignition timing, it is ensured that the flame front hits the piston at exactly the right moment.

This relationship between engine speed, ignition timing, and flame front position ensures optimal engine performance.

The flame front spreads in the cylinder at an almost constant speed. To ensure that the maximum pressure acts on the piston at the optimal moment, the ignition timing must be adjusted depending on engine speed. At low speeds the ignition occurs later, at high speeds earlier. Even a few degrees of deviation can cause the engine to produce less power or burn inefficiently. Modern engine control units correct the ignition timing up to hundreds of times per second.

The Four Strokes in Detail

Each working cycle of a four-stroke Otto engine consists of four consecutive strokes. During one complete cycle, the crankshaft rotates twice (720°).

1st Stroke: Intake

The piston moves from top dead centre (TDC) to bottom dead centre (BDC). The intake valve is open, the exhaust valve is closed. The downward movement creates a partial vacuum in the cylinder, drawing in an air-fuel mixture. In the PV diagram, this stroke shows an increase in volume at approximately constant (atmospheric) pressure.

2nd Stroke: Compression

Both valves are closed. The piston moves from BDC to TDC, compressing the mixture. Volume decreases while pressure and temperature rise sharply. The typical compression ratio of an Otto engine ranges from 8:1 to 12:1. In the PV diagram, this stroke appears as a rising curve from right to left.

3rd Stroke: Power

Shortly before top dead centre, the spark plug ignites the compressed mixture. Combustion produces high pressure and high temperature. The expanding gases push the piston downward – this is the only stroke that produces mechanical work. In the PV diagram, a steep pressure rise (combustion) is followed by a declining expansion curve.

4th Stroke: Exhaust

The exhaust valve opens. The piston moves from BDC to TDC, pushing the burnt gases out of the cylinder. In the PV diagram, this stroke runs at slight overpressure from right to left, until the residual gas is expelled and a new cycle begins.

The Ideal Otto Cycle

The idealised Otto cycle describes the thermodynamic process in an Otto engine under simplified assumptions. It consists of four changes of state:

1. Isentropic compression (1→2): The gas is compressed without heat exchange. Pressure and temperature rise.
2. Isochoric heat addition (2→3): Heat is added at constant volume (modelling combustion). Pressure rises sharply.
3. Isentropic expansion (3→4): The hot gas expands without heat exchange, performing work.
4. Isochoric heat rejection (4→1): Heat is rejected at constant volume (modelling the gas exchange). Pressure falls.

The thermal efficiency of the ideal Otto cycle depends only on the compression ratio \( \varepsilon \) and the heat capacity ratio \( \kappa \):

\[ \eta_{\text{th}} = 1 – \frac{1}{\varepsilon^{\kappa – 1}} \]

For a compression ratio of \( \varepsilon = 10 \) and \( \kappa = 1.4 \) (diatomic gas), the ideal efficiency is approximately 60%. In practice, the actual efficiency is considerably lower – the section Energy Balance and Efficiency explains why.

Ideal vs. real: The real cycle – as shown in the animation – deviates from the ideal: combustion does not occur instantaneously, there are heat losses through the cylinder walls, and the gas exchange (intake/exhaust) creates flow losses. The PV diagram in the animation therefore shows rounded curves instead of the sharp corners of the idealised process.

Ignition Timing and Engine Knocking

As the animation shows, the ignition timing must be adjusted to match the engine speed. But what happens when the ignition timing is not set optimally?

Ignition Too Early

If the mixture is ignited too early, the maximum combustion pressure reaches the piston before it has passed top dead centre. The piston is loaded against its direction of motion – this costs power and can cause mechanical damage.

Ignition Too Late

With ignition too late, the piston has already passed TDC and is moving downward before combustion reaches its peak. The pressure rise comes too late, the work output is reduced, and some of the heat is lost unused with the exhaust gases.

Engine Knocking

Particularly critical is so-called knocking (also known as detonation). This occurs when the remaining unburnt mixture ignites spontaneously before the regular flame front arrives – triggered by high pressure and temperature. Pressure waves are created that audibly reflect off the cylinder walls (the characteristic “knocking” sound). Persistent knocking can severely damage pistons, bearings and the cylinder head.

Modern engine control units use knock sensors that respond to the characteristic vibrations and immediately retard the ignition timing when knocking is detected.

Otto vs. Diesel Engine Comparison

Both engine types are four-stroke internal combustion engines, but they differ in several key aspects:

The diesel engine achieves its higher efficiency through a significantly greater compression ratio. However, it is heavier and produces more nitrogen oxides, which makes exhaust aftertreatment more complex.

History and Everyday Relevance

The history of the four-stroke Otto engine goes back to the 19th century and is closely linked to industrialisation and the development of the automobile.

• 1862: French engineer Alphonse Beau de Rochas describes the four-stroke principle for the first time in theory.
• 1876: Nicolaus August Otto builds the first practical four-stroke engine in Cologne, Germany – the “Otto engine”. It is considered a milestone in the history of technology.
• 1886: Carl Benz and Gottlieb Daimler use the Otto engine for the first automobiles.
• 20th century: Further development through fuel injection, electronic ignition and catalytic converter technology. The Otto engine becomes the most widely produced engine in the world.

Where do we encounter the Otto engine today? In cars and motorcycles, in lawn mowers and chainsaws, in emergency generators and boats. It is estimated that over one billion Otto engines are in use worldwide. Even though electric vehicles are gaining importance, the Otto engine will remain relevant in many applications for decades to come – especially where high energy density in a small space is required.

Energy Balance and Efficiency

Not all the energy contained in the fuel is converted into mechanical work. A typical Otto engine has an effective efficiency of 25 to 35%. The remaining energy is lost as heat:

• Exhaust heat (~30–35%): The hot combustion gases leave the cylinder at temperatures of 600–900 °C, carrying a significant portion of the energy away.
• Cooling losses (~25–30%): Heat is transferred through the cylinder walls and cylinder head to the cooling system.
• Friction losses (~5–10%): Mechanical friction between pistons, bearings and the valve train consumes energy.
• Other losses (~5%): Driving auxiliary components (alternator, water pump, oil pump) and incomplete combustion.

Efficiency can be improved through various measures: higher compression ratios, direct injection, variable valve timing, turbocharging and downsizing. Modern turbocharged direct-injection Otto engines achieve effective efficiencies of up to 40% – significantly more than just a few decades ago.

Glossary

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Overview and Download

Contributors

C. Hein, S. Rikowski

Sources

• Idea and initial concept: Tamara Riehle
• Technical drawing of the engine: based on Ulrich Rapp (http://www.ulrich-rapp.de/stoff/fahrzeug/motor/index.htm)
• Authoring tool (control elements included): Adobe Animate