The core Otto vs Diesel cycle difference is how heat is added: the Otto cycle adds heat at constant volume (spark-ignition petrol engines), the Diesel cycle adds heat at constant pressure (compression-ignition engines), and the Dual cycle adds heat partly at constant volume and partly at constant pressure. All three are idealised air-standard cycles used to model reciprocating internal-combustion engines, and they differ only in the heat-addition process — compression and expansion remain reversible adiabatic (isentropic) in each.
What are the three air-standard cycles?
Each cycle is built from four or five reversible processes acting on a fixed mass of air (the working fluid), with heat rejected at constant volume at the end:
- Otto cycle: isentropic compression → constant-volume heat addition → isentropic expansion → constant-volume heat rejection. Models petrol/spark-ignition (SI) engines.
- Diesel cycle: isentropic compression → constant-pressure heat addition → isentropic expansion → constant-volume heat rejection. Models compression-ignition (CI) engines.
- Dual (mixed/limited-pressure) cycle: isentropic compression → constant-volume heat addition → constant-pressure heat addition → isentropic expansion → constant-volume heat rejection. A more realistic model of modern high-speed CI engines.
How do the P-V diagrams differ?
On a pressure–volume (P-V) diagram, the heat-addition path is the visual signature of each cycle:
- Otto: heat addition is a vertical line (volume fixed, pressure rises sharply) — a near-instantaneous pressure spike at top dead centre.
- Diesel: heat addition is a horizontal line (pressure fixed, volume expands) as the piston begins its power stroke.
- Dual: heat addition is an L-shaped path — first a vertical constant-volume rise, then a horizontal constant-pressure segment.
On a temperature–entropy (T-s) diagram, all three show the same isentropic compression and expansion as vertical lines, while the heat-addition curves differ in slope.
What are the efficiency formulas?
Air-standard thermal efficiency depends on the compression ratio r = V1/V2 and the specific-heat ratio γ = cp/cv (about 1.4 for air). Efficiency η is dimensionless (a fraction, often expressed as a percentage).
- Otto: η = 1 − 1/r(γ−1)
- Diesel: η = 1 − (1/r(γ−1)) × [(ργ − 1) / (γ(ρ − 1))], where ρ is the cut-off ratio (V3/V2, the volume ratio during constant-pressure heat addition).
- Dual: efficiency lies between the two and depends on both the pressure ratio during constant-volume heating and the cut-off ratio ρ during constant-pressure heating.
The Otto formula has no cut-off-ratio term because all heat enters at constant volume. In the Diesel formula, the bracketed term is always greater than 1 (for ρ > 1), so it reduces efficiency relative to Otto at the same r.
Which cycle is most efficient?
The comparison depends on what is held constant:
- Same compression ratio: Otto > Dual > Diesel. Constant-volume heat addition extracts the most work per unit of heat at a given r.
- In practice: Diesel (CI) engines run at much higher compression ratios — typically 14:1 to 22:1 — because they compress air alone and avoid knock, whereas petrol (SI) engines are limited to roughly 8:1 to 12:1 by auto-ignition of the fuel-air mixture. The higher r lets real diesel engines achieve higher actual efficiency despite the cycle’s theoretical disadvantage.
| Feature | Otto Cycle | Diesel Cycle | Dual Cycle |
|---|---|---|---|
| Heat addition | Constant volume | Constant pressure | Constant volume + constant pressure |
| Engine type | Spark-ignition (petrol) | Compression-ignition | Modern high-speed CI |
| Ignition | Spark plug | Compression heat | Compression heat |
| Typical compression ratio | 8:1 to 12:1 | 14:1 to 22:1 | 14:1 to 22:1 |
| P-V heat-addition path | Vertical line | Horizontal line | L-shaped path |
| Efficiency at same r | Highest | Lowest | Intermediate |
| Key ratio in formula | r only | r and cut-off ratio ρ | r, pressure ratio, ρ |
How is this demonstrated and measured in a teaching lab?
Engineering colleges teach these cycles through both computation and hands-on measurement:
- Computed P-V plots: students calculate state points (P, V, T) at each corner of the cycle using the gas laws and isentropic relations, then plot the P-V and T-s diagrams to compare cycle areas (net work).
- Engine test rigs: a petrol or diesel engine coupled to a dynamometer lets students measure brake power, indicated power, fuel consumption, and brake thermal efficiency, then compare actual values against the air-standard ideal.
- Indicator diagrams: a pressure transducer and crank-angle encoder capture the real in-cylinder P-V loop, which students contrast with the idealised cycle to discuss losses.
- Calorimetry and heat balance: exhaust and cooling-water measurements let students draw up an energy balance and quantify where heat is rejected.
Scientico India, an ISO 9001:2015 and CE certified manufacturer and exporter of engineering and science laboratory equipment, supplies engine test rigs, cut-section models, and thermodynamics apparatus for these experiments. Explore the full range under Thermodynamics Lab Equipment.
Frequently Asked Questions
What is the main difference between the Otto and Diesel cycle?
The Otto cycle adds heat at constant volume (modelling petrol/spark-ignition engines), while the Diesel cycle adds heat at constant pressure (modelling compression-ignition engines). Compression and expansion are isentropic in both; only the heat-addition process differs.
Which is more efficient, the Otto or Diesel cycle?
For the same compression ratio, the Otto cycle is more efficient (Otto > Dual > Diesel). However, real diesel engines run at much higher compression ratios (14:1-22:1 versus 8:1-12:1 for petrol), so they often achieve higher actual efficiency in practice.
What is the cut-off ratio in the Diesel cycle?
The cut-off ratio (rho) is the ratio of cylinder volumes at the end and start of constant-pressure heat addition, V3/V2. It appears in the Diesel efficiency formula and, for any value above 1, reduces efficiency compared with the Otto cycle at the same compression ratio.
How does the Dual cycle combine Otto and Diesel?
The Dual (mixed) cycle adds heat in two stages: first at constant volume (like Otto), then at constant pressure (like Diesel). This more closely represents real high-speed compression-ignition engines, and its efficiency lies between the pure Otto and Diesel cycles at the same compression ratio.
What does the Otto cycle efficiency formula tell us?
The Otto efficiency, eta = 1 – 1/r^(gamma-1), shows that thermal efficiency rises with compression ratio r and the specific-heat ratio gamma (about 1.4 for air). It contains no cut-off-ratio term because all heat is added at constant volume.
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