Diesel Cycle Efficiency Calculator
Compute the ideal thermal efficiency of a compression-ignition (diesel) engine from its compression ratio and cutoff ratio. Ideal for engineering students and engine developers evaluating how fuel injection timing and cylinder geometry affect performance.
About this calculator
The diesel cycle models compression-ignition engines with four processes: isentropic compression, constant-pressure heat addition (combustion), isentropic expansion, and constant-volume heat rejection. Unlike the Otto cycle, combustion occurs at constant pressure over a finite crank-angle range, captured by the cutoff ratio r_c = V₃/V₂ (volume at end of combustion divided by volume at start). Thermal efficiency is: η_th = [1 − (1/r^(γ−1)) × (r_c^γ − 1) / (γ × (r_c − 1))] × 100, where r is the compression ratio, r_c is the cutoff ratio, and γ = 1.4. As r_c → 1 the formula reduces to the Otto efficiency, confirming that shorter combustion duration (less fuel) improves efficiency. Higher compression ratios (14–25 for diesels) give diesel engines an inherent efficiency advantage over gasoline engines.
How to use
Example: compression ratio r = 18, cutoff ratio r_c = 2.5, γ = 1.4. Step 1 — Compute r^(γ−1) = 18^0.4 = e^(0.4 × ln 18) = e^(0.4 × 2.890) = e^1.156 ≈ 3.177. Step 2 — Compute r_c^γ = 2.5^1.4 = e^(1.4 × 0.916) = e^1.282 ≈ 3.604. Step 3 — Numerator of bracket: 3.604 − 1 = 2.604. Step 4 — Denominator: 1.4 × (2.5 − 1) = 2.1. Step 5 — η = [1 − (1/3.177) × (2.604/2.1)] × 100 = [1 − 0.3148 × 1.240] × 100 = [1 − 0.3904] × 100 ≈ 61.0 %. Enter your engine's values to evaluate other configurations.
Frequently asked questions
How does the cutoff ratio affect diesel cycle efficiency?
The cutoff ratio r_c represents how far the piston travels during constant-pressure combustion — effectively how much fuel is burned per cycle. A higher cutoff ratio means more fuel is injected and combustion extends further into the power stroke, which reduces efficiency because heat is added at progressively lower pressures. For a fixed compression ratio of 18, increasing r_c from 1.5 to 3.0 drops ideal efficiency from about 67 % to 58 %. This is why modern common-rail diesel engines use precisely timed short injection pulses to keep the cutoff ratio small and maximize efficiency while meeting power targets.
Why are diesel engines more efficient than gasoline engines at similar displacement?
Diesel engines operate at much higher compression ratios (14:1–25:1) compared to gasoline engines (9:1–12:1), which directly raises cycle efficiency. They are not throttle-controlled, eliminating pumping losses at part load. Diesel fuel also has approximately 10–15 % higher energy density per litre than gasoline. Combined, these factors give modern diesel cars and trucks brake thermal efficiencies of 42–48 %, versus 30–40 % for the best gasoline engines. Large marine and stationary diesel engines can exceed 50 % brake efficiency — the highest of any heat engine in wide commercial use.
What are realistic compression and cutoff ratios for modern diesel engines?
Automotive direct-injection diesel engines typically use compression ratios between 14:1 and 18:1; older indirect-injection designs ran up to 23:1 to aid cold starting. Cutoff ratios at full load range from about 2.0 to 3.5 depending on the load and injection strategy. At light load, cutoff ratios near 1.2–1.5 are common, which is why diesels are most efficient at part load — a key advantage for fuel economy in urban driving. Heavy-duty truck engines and marine two-stroke diesels may use higher cutoff ratios at peak torque but compensate with very high compression ratios to maintain efficiency.