Otto Cycle Efficiency (Compression Ratio)

The air-standard Otto cycle says something remarkable: the thermal efficiency of a spark-ignition engine depends on nothing but its compression ratio. Not fuel, not speed, not displacement, not how much heat you add. At $r = 8$ with $\gamma = 1.4$ the answer is $1 - 8^{-0.4} = 56.5\%$, and at $r = 10$ it is 60.2%. Every engineering student meets that result and immediately asks why real petrol engines manage 25 to 35%, which is the right question.

Part of the gap is honest thermodynamics that the air-standard model throws away: real combustion is not instantaneous and not at constant volume, heat leaks into the coolant, exhaust gas leaves hot, and $\gamma$ for a hot combustion mixture is nearer 1.3 than 1.4. Recompute at $\gamma = 1.3$ and the $r = 8$ figure falls to 48%. The rest is pumping work, friction and part-load throttling, none of which appear anywhere in the equation.

The reason nobody simply raises the compression ratio is knock. Squeeze the charge harder and the end gas ahead of the flame front gets hot enough to autoignite, which produces the metallic rattle and, sustained, holes in pistons. Fuel octane rating is precisely a measure of resistance to this, and it is the ceiling that has held petrol engines near $r = 10$ for decades. Diesels dodge it entirely by compressing air alone and injecting fuel at the top, which is why they run at 16 to 22 and why they are more efficient. Direct injection and variable valve timing have lately pushed petrol engines to 12 or 13, which is worth a few real points of efficiency.