Otto Cycle Compression Efficiency
Compression alone sets an ideal Otto engine’s efficiency, while the amount of heating sets how much work the cycle delivers.
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Otto Cycle Compression Efficiency
The Otto cycle models the ideal operation of a spark-ignition piston engine. It consists of two isentropic (reversible adiabatic) processes representing compression and expansion, and two isochoric (constant volume) processes representing heat addition and heat rejection.
worked-example
Consider an ideal air-standard Otto cycle with a compression ratio of r = 4, a heat capacity ratio of γ = 7/5, and a heat temperature multiplier of τ = 2. We start with state 1 at T_1 = 1, V_1 = 1.
r = 4, gamma = 7/5 = 1.4, tau = 2
State 1:
T1 = 1, V1 = 1
State 2 (Isentropic compression):
V2 = 1 / r = 1 / 4 = 0.25
T2 = T1 * r^(gamma - 1) = 1 * 4^(0.4) ≈ 1.7411011265922482
State 3 (Isochoric heat addition):
V3 = V2 = 0.25
T3 = tau * T2 = 2 * 1.7411011265922482 ≈ 3.4822022531844965
State 4 (Isentropic expansion):
V4 = V1 = 1
T4 = tau * T1 = tau = 2
Heat input (Qin) = Cv * (T3 - T2)
Since Cv = 1 in our normalized model,
Qin = 3.4822022531844965 - 1.7411011265922482 = 1.7411011265922482
Heat rejected (Qout) = Cv * (T4 - T1) = 2 - 1 = 1
Net Work (Wnet) = Qin - Qout = 1.7411011265922482 - 1 = 0.7411011265922482
Cycle Efficiency = Wnet / Qin = 0.7411011265922482 / 1.7411011265922482 ≈ 0.4256508225014825
Compression Efficiency Formula = 1 - r^(1 - gamma)
= 1 - 4^(-0.4)
= 1 - (1 / 1.7411011265922482)
≈ 0.42565082250148256experiment
Explore the interactive module to see how parameters affect the cycle:https://riano.app/module/otto-cycle-compression-efficiency
- Set Heat capacity ratio to "7/5" and Compression ratio to "4".
- Observe the cycle efficiency output.
- Change Heat temperature multiplier to "1". Note that the cycle collapses into a line with no net work, and efficiency is "Undefined no heat input".
limitations
The air-standard Otto cycle relies on several simplifying assumptions: the working fluid is treated as an ideal gas with constant specific heats, all processes are internally reversible, and the combustion and exhaust processes are replaced by simple heat transfer processes. Real engines experience friction, heat loss, and variable fluid properties, leading to lower actual efficiencies.
references
For further reading on the ideal Otto cycle, see the NASA Glenn Research Center's educational material on thermodynamics:
Experience it interactively
Adjust parameters, observe in real time, and build deep intuition with Riano’s interactive Otto Cycle Compression Efficiency module.
Try Otto Cycle Compression Efficiency on Riano →