The Otto Cycle: The Four Strokes Behind Every Petrol Engine

Four strokes, four idealised processes

The Otto cycle, named after Nikolaus Otto, who built the first practical four-stroke engine in 1876, is the idealised thermodynamic model behind every petrol (gasoline) engine on the road. A piston repeats four strokes inside a cylinder: intake draws in an air-fuel mixture, compression squeezes it, combustion ignites and rapidly burns it, and expansion lets the hot gas push the piston back down and deliver work, before exhaust clears the cylinder and the cycle repeats. The idealised cycle used to analyse it strips this down to four clean thermodynamic processes on a pressure-volume diagram, treating the working fluid as a fixed quantity of ideal gas rather than tracking the actual intake and exhaust of fresh mixture.

Two of the four processes are adiabatic — fast enough that essentially no heat has time to escape through the cylinder walls — and two are treated as happening at constant volume, because the piston's position barely moves during the brief instant combustion or exhaust venting takes compared to the full stroke.

Walking the P-V diagram

On a pressure-volume diagram, the ideal Otto cycle traces a closed loop through four legs, and the area enclosed by that loop is exactly equal to the net work the engine delivers per cycle:

1 -> 2   adiabatic compression     piston rises, gas compressed, no heat exchanged
2 -> 3   constant-volume heating   spark ignites mixture; pressure spikes, volume ~fixed
3 -> 4   adiabatic expansion       hot high-pressure gas pushes piston down (power stroke)
4 -> 1   constant-volume cooling   exhaust valve opens, pressure drops back to intake level

net work per cycle  =  area enclosed by the 1-2-3-4-1 loop on the P-V diagram

In a real engine the closed loop is actually a five-stroke path once intake and exhaust strokes are drawn in (a low, roughly flat loop at the bottom of the diagram representing pumping the fresh charge in and the spent gas out), but that pumping loop contributes comparatively little work and is usually left out of the idealised analysis so the thermodynamics of compression, combustion and expansion stay in focus.

Why efficiency depends only on the compression ratio

Working through the first law for each of the four legs of an ideal-gas Otto cycle, most of the details cancel out and leave a strikingly simple result: the thermal efficiency depends on nothing but the compression ratio r (the ratio of cylinder volume before compression to cylinder volume after compression) and the working gas's heat-capacity ratio γ (about 1.4 for air):

r = V1 / V2          (compression ratio, typically 8-12 for petrol engines)
gamma ~ 1.4          (heat capacity ratio of air)

eta_Otto = 1 - r^(1 - gamma) = 1 - 1/r^(gamma - 1)

  r =  8   ->  eta ~ 0.56
  r = 10   ->  eta ~ 0.60
  r = 12   ->  eta ~ 0.63     (diminishing returns as r grows)

The intuition matches the maths: compressing the mixture further before ignition means the adiabatic expansion afterward has more room to run and pulls proportionally more work out of the hot gas before it has to be exhausted at a lower temperature. Real engine designers push compression ratio up for exactly this reason — it is one of the cheapest ways to improve fuel efficiency.

The wall that stops the ratio climbing forever: knock

Compression ratio cannot simply be raised without limit, because compressing the unburned mixture harder also heats it more, and past a certain point the still-unburned fuel-air mixture ahead of the advancing flame front becomes hot and pressurised enough to spontaneously ignite on its own, before the flame front from the spark plug ever reaches it. This uncontrolled secondary ignition — knock, or detonation — produces a sharp, damaging pressure spike and an audible metallic pinging, and left unchecked it can crack pistons and blow head gaskets. Higher-octane fuels resist this kind of self-ignition better, which is exactly why high-compression and turbocharged engines are designed to run on premium fuel: the octane rating is a direct measure of how much compression (or boost) the fuel can tolerate before knock sets in.

Real engines fall well short of the ideal number

The idealised Otto-cycle efficiency assumes instantaneous, perfectly reversible combustion, zero friction, and no heat lost through the cylinder walls or exhaust — none of which is true of a real engine. Combustion actually takes a finite number of crank-angle degrees to complete rather than happening at one fixed volume; a meaningful fraction of the fuel's chemical energy is conducted away as waste heat through the cylinder walls and out through the cooling system and exhaust rather than doing mechanical work; friction between the piston rings, bearings and other moving parts eats more still; and pumping the intake and exhaust gases in and out costs work too. Add all of that up and a typical production petrol engine achieves a real-world thermal efficiency in the roughly 25–35% range, well below the 55–65% the idealised r-and-γ formula alone would predict for a normal compression ratio — the gap between ideal-cycle theory and real-engine practice is itself one of the most active areas of internal-combustion engineering.

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