Diesel Cycle Efficiency Calculator

The Diesel cycle is the idealized thermodynamic cycle used to model a compression-ignition (diesel) engine, where fuel is injected into hot, highly compressed air and ignites without a spark, with combustion modeled as occurring at constant pressure rather than constant volume.

η = 1 − (1/r^(γ−1)) × (rc^γ−1)/(γ(rc−1)), where r is the compression ratio, rc is the cutoff ratio, and γ is the heat capacity ratio of the working gas.

Cutoff ratio rc is the ratio of cylinder volume at the end of constant-pressure combustion to the volume at the start of combustion, it measures how much the piston moves while fuel is still being injected and burning.

Diesel engines compress only air (not a fuel-air mixture), so they can safely use much higher compression ratios (typically 16-22) without risking the pre-ignition knock that limits gasoline (Otto cycle) engines to around 8-12.

At the exact same compression ratio, the Diesel cycle is actually slightly less efficient than the Otto cycle, because constant-pressure combustion is inherently less thermodynamically efficient than constant-volume combustion. Diesel engines instead gain their real-world advantage by running much higher compression ratios than are safe for gasoline engines.

As rc→1 (representing an infinitesimally short combustion period), the Diesel cycle efficiency formula approaches the Otto cycle efficiency formula exactly, since near-instantaneous combustion behaves like the Otto cycle's constant-volume assumption.

With a compression ratio of 20 and a cutoff ratio of 2 (representative values), the ideal Diesel cycle efficiency is about 64.7%, higher than a typical gasoline Otto cycle engine's ideal efficiency because of the diesel engine's much higher achievable compression ratio.

No, like all idealized thermodynamic cycles, the Diesel cycle assumes no friction, no heat loss, and instantaneous processes apart from the modeled combustion phase. Real diesel engines achieve considerably less than the ideal figure, though typically still more than a comparable real gasoline engine.

In a real diesel engine, fuel is injected gradually and burns progressively as the piston continues moving, roughly maintaining pressure during this phase, rather than burning nearly instantaneously (constant volume) as in a spark-ignited gasoline engine.

Yes, cutoff ratio increases with more fuel injected per cycle (higher load), since more fuel means a longer constant-pressure combustion phase and more piston travel before cutoff, this is one reason diesel engine efficiency varies meaningfully with operating load.