Otto Cycle Calculator (Efficiency, Temperatures, Pressures & MEP)
Air-standard Otto cycle: thermal efficiency from the compression ratio and γ, plus the temperature, pressure and volume at all four states, net work, heat rejected and mean effective pressure.
How it works
η = 1 − 1/r^(γ−1) · T₂ = T₁·r^(γ−1), P₂ = P₁·r^γ · T₃ = T₂ + q_in/cv, P₃ = P₂·T₃/T₂ · T₄ = T₃/r^(γ−1) · w_net = η·q_in · MEP = w_net / (v₁ − v₂), with v₁ = R·T₁/P₁ and R = cv(γ − 1)
The Otto cycle is the ideal model of a spark-ignition petrol engine: isentropic compression (1→2), heat addition at constant volume as the charge burns (2→3), isentropic expansion (3→4) and heat rejection at constant volume (4→1). Under the air-standard assumptions — air as an ideal gas with constant specific heats — the efficiency depends only on the compression ratio and γ, which is why higher-compression engines are more efficient (until knock limits them). Real engines reach roughly half to two-thirds of this ideal value. Equations follow Çengel & Boles, Thermodynamics: An Engineering Approach, chapter 9.
Worked example
With r = 10 and γ = 1.4, η = 1 − 1/10^0.4 = 1 − 0.3981 = 60.19%. Air enters at 27 °C (300.15 K) and 100 kPa: T₂ = 300.15 × 10^0.4 = 753.9 K and P₂ = 100 × 10^1.4 = 2,511.9 kPa. Adding 1,800 kJ/kg raises T₃ to 753.9 + 1,800/0.718 = 3,260.9 K. The net work is 0.6019 × 1,800 = 1,083.41 kJ/kg, 716.59 kJ/kg is rejected, and the mean effective pressure is 1,396.5 kPa.
Sources: Çengel & Boles — Thermodynamics: An Engineering Approach, Ch. 9 (Otto cycle) · NASA Glenn Research Center — Ideal Otto Cycle
Frequently asked questions
Why does a higher compression ratio give better efficiency?
Compressing the charge more raises the temperature at which heat is added relative to the temperature at which it is rejected, so a larger share of the heat becomes work. Efficiency rises from about 47.5% at r = 5 to 60% at r = 10 with γ = 1.4.
Why are real engines much less efficient?
Friction, heat loss to the cylinder walls, incomplete combustion, finite burn time, pumping losses and the drop in γ at high temperature all cut real brake efficiency to about 25–40%.
What is mean effective pressure (MEP)?
The constant pressure that, acting on the piston over the full stroke, would produce the same net work as the actual cycle. It lets engines of different sizes be compared.
How is the Otto cycle different from the Diesel cycle?
The Otto cycle adds heat at constant volume (spark ignition); the Diesel cycle adds it at constant pressure (compression ignition). At the same compression ratio the Otto cycle is more efficient, but diesels run at much higher ratios.
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Results assume the idealised textbook model stated above; real systems have losses and tolerances, so verify safety-critical values with measurements or a qualified engineer.