Otto, Diesel, Dual, Atkinson & Miller Cycles
The idealised air-standard cycles behind every petrol and diesel engine — and the Atkinson/Miller tricks modern engines borrow for efficiency.
A petrol engine and a diesel both burn fuel in a cylinder, yet their efficiency differs by ten percent — a gap traceable to how each draws its heat-addition line on the p-V diagram.
The full thermodynamic cycle theory — first law, ideal-gas relations, the meaning of thermal efficiency — is owned by the Material & Energy Balances course. Here we apply those results to the engine-specific cycles and focus on what changes between them: how heat is added and how the compression and expansion strokes relate.
Three ways to add heat
All piston engines share the same skeleton — intake, compress, add heat, expand, exhaust — but the heat-addition step differs. The Otto cycle (the idealised petrol/gasoline engine) adds heat at constant volume: the fuel burns so fast the piston barely moves while pressure spikes. The Diesel cycle adds heat at constant pressure: fuel is injected and burned progressively as the piston descends, holding pressure roughly steady while volume grows. The dual cycle blends both (a constant-volume spike then a constant-pressure tail) and is the most realistic idealisation of modern direct-injection engines. These differences shift where the heat-addition line sits on the p-V diagram and hence the cycle's efficiency and peak pressure.
Atkinson and Miller: over-expand for efficiency
Both Otto and Diesel expand the gas back down only to the compression-start volume. But if you could expand it further, you'd extract more work from the same heat — raising efficiency. The Atkinson cycle does exactly that by closing the intake valve late, so the effective compression ratio is smaller than the expansion ratio. Less charge is compressed, but the full stroke is used to expand. The penalty is lower power density (less air per cycle), which is why the Atkinson cycle shines in hybrids: the electric motor fills the torque gap, and the engine runs efficient Atkinson for fuel economy. The Miller cycle achieves the same over-expansion by closing the intake valve early (or late) and pairs it with a supercharger or turbo to recover the lost charge — a higher-tech route to similar efficiency gains.
Hybrid engines are almost universally Atkinson-cycle, and you can hear it: they feel gutless off the line because the reduced charge makes low-end torque weak. That weakness is exactly what the electric motor covers with instant torque. The engine then settles into its efficient Atkinson band for steady cruising, where the over-expansion pays off. The engine-plus-motor combination is not just additive power — the motor exists partly to mask the Atkinson cycle's weakness so the engine can run at high efficiency most of the time.
- η_Otto = 1 − 1/r^(γ−1) = 1 − 1/10^0.4
- 10^0.4 = 2.512
- η = 1 − 1/2.512 = 1 − 0.398 = 0.602
- η = 1 − 1/8^0.4 = 1 − 1/2.297 = 1 − 0.435 = 0.565 (56.5%)
- Lower compression ratio than the r=10 example ⇒ lower ideal efficiency.
Check your understanding
- Otto adds heat at constant volume, Diesel at constant pressure, dual blends both — all on a p-V loop whose area is net work
- Ideal Otto efficiency = 1 − 1/r^(γ−1) rises with compression ratio (the engine-design lever, knock-limited)
- Atkinson/Miller over-expand (expansion ratio > compression ratio) to extract more work — efficient but weak, ideal for hybrids
- Hybrid engines mask the Atkinson cycle's low-end weakness with electric motor torque