MECH9761 Chap.2 Otto and Diesel Cycle Efficiency
Otto and Diesel Cycle Efficiency
This chapter reads the Otto and Diesel air-standard cycles through their pressure-volume paths and efficiency equations. The Otto model adds heat at constant volume; the Diesel model uses constant-pressure heat addition and a cutoff ratio. The key comparison holds compression ratio fixed first, then restores the higher ratio and different loss structure of real compression-ignition engines.
Limiting checks connect the algebra back to the diagram: efficiency should rise with compression ratio, and the Diesel expression should approach the Otto limit as cutoff ratio approaches one.
What this chapter covers
- 01
Pressure-volume loop area as ideal net cycle work
- 02
Constant-volume heat addition in the Otto model
- 03
Constant-pressure heat addition in the Diesel model
- 04
Compression ratio and specific-heat ratio effects
- 05
Diesel cutoff ratio and its efficiency penalty
- 06
Air-standard ceilings compared with brake efficiency
Worked example · free
Calculate an Otto-cycle efficiency
- +1Use eta = 1 - 1 divided by r to the power gamma minus one.
- +1Compute 10 to the power 0.4 = 2.512.
- +1Eta = 1 - 1/2.512 = 0.602, so the ideal efficiency is 60.2%.
Key terms
- Otto Cycle
- An air-standard spark-ignition model with ideal constant-volume heat addition.
- Diesel Cycle
- An air-standard compression-ignition model with ideal constant-pressure heat addition.
- Cutoff Ratio
- The cylinder-volume ratio across the constant-pressure heat-addition part of the ideal Diesel cycle.
- Air-Standard Efficiency
- The thermal efficiency predicted under ideal-gas cycle assumptions without real combustion or mechanical losses.
- Pressure-Volume Work
- Boundary work represented by the integral of pressure with respect to changing cylinder volume.
- Compression Ratio
- Maximum cylinder volume divided by clearance volume for the ideal cycle model.
- Isentropic Process
- An ideal reversible adiabatic process used to model compression or expansion.
- Constant-Volume Heating
- Ideal heat addition with unchanged cylinder volume and a corresponding pressure rise.
- Constant-Pressure Heating
- Ideal heat addition while volume increases and pressure remains fixed.
- Specific-Heat Ratio
- The ratio of constant-pressure to constant-volume specific heat used in ideal-cycle exponents.
Otto and Diesel Cycle Efficiency FAQ
Why is the ideal Otto cycle better at one fixed compression ratio?
At a cutoff ratio above one, the Diesel-cycle correction factor increases the subtracted term in its efficiency equation. With compression ratio and specific-heat ratio fixed, that makes the ideal Diesel result lower than the Otto result. This is a model comparison, not a production-engine fuel-economy claim.
Why can a real diesel engine still use less fuel?
Production compression-ignition engines use substantially higher compression ratios, which raises their theoretical efficiency potential. They also control load mainly through fuel quantity rather than a restrictive throttle, reducing pumping loss at part load. Real heat transfer, friction, combustion duration and after-treatment still affect the measured result.
What does the area inside a pressure-volume loop mean?
The signed area enclosed by the cycle is net boundary work. High-pressure expansion produces positive work while compression consumes work. In a real engine, the intake and exhaust loop can subtract pumping work. A plotted loop therefore connects thermodynamic path shape to cycle output.
What physical role does cutoff ratio play?
Cutoff ratio measures the volume change during ideal constant-pressure heat addition in the Diesel model. A larger value represents heat addition continuing farther into expansion. It enters the efficiency correction because the timing and path of energy addition influence how much expansion remains available to recover work.
Why must ratio definitions be written first?
Compression ratio and cutoff ratio compare different state volumes. Writing their definitions prevents a state-number swap and makes the pressure-volume sketch auditable. The formula is then tied to a physical interval rather than memorised as a sequence of symbols whose numerator and denominator can be reversed.
How can the formula be checked quickly?
Increase compression ratio while holding other inputs fixed and verify that efficiency rises. Move cutoff ratio toward one and verify that the Diesel correction approaches the Otto limit. Also require a final value between zero and one. These checks diagnose bracket, exponent and ratio-entry errors.
Why is brake efficiency lower than the ideal result?
The air-standard model omits finite combustion duration, heat transfer, gas exchange and mechanical friction. Brake output is measured after those processes have acted. A comparison should identify which boundary each efficiency belongs to instead of subtracting one number from another without a consistent engine condition.
Exam move
Memorise neither formula in isolation. Sketch the heat-addition path, define compression and cutoff ratios, and then write the equation. Practise one Otto and one Diesel calculation with every intermediate factor shown. For comparison questions, use a two-stage conclusion: fixed compression ratio first, then the higher real diesel ratio and pumping-loss difference.
End each result by saying whether it is ideal, indicated or brake efficiency. Redraw both loops without notes and point to the heat-addition segment before touching a calculator. Recalculate one case after changing only compression ratio, then another after changing only cutoff ratio. Explain the direction of each change from the graph.
Finally, substitute a cutoff ratio close to one to test whether the Diesel expression approaches the expected limit.
