The Otto and Diesel cycles, explained

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Two ways to add the heat

Both cycles compress air isentropically, add heat, expand isentropically and reject heat at constant volume. The difference is the heat addition. In the Otto cycle the spark ignites the mixture at top dead centre and the pressure jumps before the piston can move: constant volume. In the Diesel cycle fuel is injected into air already hot from compression and burns while the piston moves down: roughly constant pressure, up to the cutoff point.

The compression ratio r is the cylinder volume at bottom dead centre divided by the volume at top dead centre. The cutoff ratio r_c is how far the cylinder volume grows while fuel is still burning. With r_c equal to 1 the Diesel formula reduces exactly to the Otto one.

Why diesels win anyway

At equal r, the Diesel bracket is always greater than 1, so the Diesel cycle is less efficient. But a petrol engine compresses fuel and air together, and above a compression ratio of roughly 10 to 12 the mixture can ignite on its own before the spark: knock. A diesel compresses only air, so it has no knock limit and runs compression ratios of about 14 to 22.

Real engines reach well under these ideal figures, because of heat loss to the walls, friction, finite combustion time and pumping losses. The ideal cycles are still the right tool for comparing designs and seeing which way a change moves efficiency.

A worked number

With γ = 1.4, an Otto cycle at r = 10 has an ideal efficiency of 1 − 1/10^0.4 ≈ 1 − 0.398 = 60.2 per cent.

A Diesel cycle at r = 18 with r_c = 2: 1/18^0.4 ≈ 0.315, and the bracket is (2^1.4 − 1)/(1.4 × 1) ≈ 1.171, so η ≈ 1 − 0.315 × 1.171 ≈ 63.2 per cent. An Otto cycle at the same r = 18 would reach 68.5 per cent, but no petrol engine can run that compression ratio without knocking.

Common mistakes

• Comparing Otto and Diesel at the same compression ratio and concluding the Diesel is worse. They never run at the same ratio.
• Using the pressure ratio in place of the volume ratio r.
• Treating the ideal efficiency as what an engine delivers. Real engines lose a large share to heat transfer and friction.