Ideal Thermodynamic Cycles
The Otto and Diesel cycles are idealized models of the processes inside reciprocating internal combustion engines. By treating the working fluid as an ideal gas undergoing reversible processes, we derive elegant efficiency expressions that capture the essential physics: higher compression means higher efficiency. These air-standard cycles serve as the theoretical ceiling against which real engine performance is benchmarked.
The P-V Diagram
The pressure-volume diagram is the fundamental visualization tool for engine cycles. The area enclosed by the cycle represents net work output per cycle. In the Otto cycle, the tall, narrow shape of constant-volume heat addition creates high peak pressures. In the Diesel cycle, the constant-pressure heat addition produces a wider loop with lower peak pressure but potentially more total work at high loads.
Compression Ratio: The Master Variable
Compression ratio is the single most important design parameter for engine efficiency. Increasing r from 8 to 12 boosts Otto cycle efficiency from 56% to 63%. But real engines face knock limits (Otto) or peak pressure limits (Diesel) that constrain maximum r. Modern gasoline engines use direct injection, cooled EGR, and variable compression to push these boundaries, achieving real efficiencies approaching 40%.
From Theory to Practice
The gap between ideal and real efficiency — typically a factor of 1.5–2× — arises from irreversibilities: heat loss through cylinder walls, friction in bearings and piston rings, incomplete combustion, pumping work to move air through the engine, and exhaust energy that escapes unrecovered. This simulation shows the ideal cycle while highlighting where real-world losses erode performance, helping engineers identify the most impactful areas for improvement.