Piston Engine Cycle

Piston Engine Cycle (propulsion/reciprocating/piston-engine-cycle)

Use when the task is a reciprocating four-stroke aircraft powerplant operating-point analysis for general-aviation propulsion: the air-standard Otto cycle thermal efficiency, the four-stroke indicated and brake power from the mean effective pressure bookkeeping, and the brake specific fuel consumption and thermal efficiencies from the fuel flow. This leaf implements the standard textbook air-standard Otto cycle and PLAN indicated-power method in pure Python, stdlib only. It pairs with propulsion/turboprop/free-turbine and propulsion/turboprop/turboprop-cycle for the other aircraft prime-mover classes and with propulsion/engine-airframe for installed-behavior bookkeeping once the powerplant side is fixed.

Domain quick reference

• Air-standard Otto thermal efficiency: eta = 1 - 1/r^(gamma-1), with r the compression ratio (r > 1) and gamma the specific-heat ratio (gamma > 1, air-standard default 1.4). This is the ideal efficiency ceiling of the spark-ignition cycle, not a real-cycle prediction.
• Isentropic compression temperature ratio: T2/T1 = r^(gamma-1); the efficiency identity eta = 1 - 1/(T2/T1) holds exactly.
• Four-stroke indicated power (SI): P_i = IMEP * V_d * (rpm/60)/2, with IMEP in Pa and V_d in m3. One power stroke occurs per two crankshaft revolutions, so the revolution rate halves in the bookkeeping; the bar/L convention gives the identical value.
• Brake power: P_b = P_i * eta_m, with eta_m the mechanical efficiency in (0, 1]; eta_m = 1.0 returns the indicated power exactly.
• Brake specific fuel consumption (family shaft-power convention): BSFC = m_dot_fuel * 3600 * 1000 / P_b in kg/(kW h), also reported in lb/(hp h) through the exact unit bridge KG_PER_KWH_PER_LB_PER_HP_HR.
• Thermal efficiencies on the fuel lower heating value: eta_i = P_i / (m_dot_fuel * LHV); eta_b = P_b / (m_dot_fuel * LHV) = eta_m * eta_i. The air-standard eta_otto is the ideal ceiling and sits above eta_b for any real point.
• Volumetric fuel flow: V_dot = m_dot_fuel / rho_fuel, reported in m3/s, L/h and US gal/h.
• Reference-only general-aviation band verdict: brake thermal efficiency against 0.25 to 0.30 and BSFC against 0.40 to 0.55 lb/(hp h), published bands for carbureted and fuel injected four-stroke aircraft engines. The verdict reports the point's position and never enforces it.
• Units are SI throughout except the two reporting conversions (hp, lb/(hp h), L/h, US gal/h) that the module carries as named outputs.

Workflow

1. Fix the operating point: compression ratio and gamma, then compute the air-standard Otto cycle thermal efficiency with otto_efficiency and the isentropic compression temperature ratio with isentropic_temperature_ratio.
2. Compute the four-stroke indicated power from the indicated mean effective pressure, the displacement and the crankshaft speed with indicated_power.
3. Compute the brake power at the mechanical efficiency with brake_power.
4. Compute the brake specific fuel consumption with brake_specific_fuel_consumption, convert it to lb/(hp h) with bsfc_lb_per_hp_hr, and round-trip back to the fuel flow with fuel_flow_from_bsfc when checking a reported BSFC.
5. Compute the indicated and brake thermal efficiencies on the fuel lower heating value with indicated_thermal_efficiency and brake_thermal_efficiency.
6. Compute the volumetric fuel flow in m3/s, L/h and US gal/h with volumetric_fuel_flow.
7. Get the reference-only general-aviation band verdict with ga_band_verdict, reporting the point's position without enforcing it, or call piston_engine_cycle once for the full single-point summary dict that chains steps 1 through 7.
8. Confirm the deterministic checks with the contract test scripts/test_piston_engine_cycle.py.

Worked example

Lycoming O-320 class general-aviation four-stroke flat-four at a cruise rating: compression ratio r = 8.5, gamma = 1.4 (air standard), IMEP = 9.5e5 Pa (9.5 bar), displacement V_d = 5.4e-3 m3 (5.4 L), crankshaft speed 2700 rpm, mechanical efficiency eta_m = 0.85, fuel flow m_dot = 7.6e-3 kg/s avgas at the reference density 720 kg/m3 and LHV 43.5 MJ/kg.

• Ideal cycle: eta_otto = 1 - 1/8.5^0.4 = 0.5751531234, within 0.1 percent of the published 0.575 anchor; the isentropic compression temperature ratio is T2/T1 = 8.5^0.4 = 2.3537892242, and eta = 1 - 1/(T2/T1) holds exactly.
• Indicated power: P_i = 9.5e5 * 5.4e-3 * (2700/60)/2 = 115425.0 W = 154.7875 hp.
• Brake power: P_b = 115425.0 * 0.85 = 98111.25 W = 131.5694 hp, about 82 percent of a 160 hp class rating at the cruise point.
• BSFC: 7.6e-3 * 3600 * 1000 / 98111.25 = 0.2788671024 kg/(kW h) = 0.4584538370 lb/(hp h), inside the published 0.40 to 0.55 lb/(hp h) band.
• Thermal efficiencies on LHV: eta_i = 115425.0/(7.6e-3 * 43.5e6) = 0.3491379310; eta_b = 98111.25/(7.6e-3 * 43.5e6) = 0.2967672414 = eta_i * eta_m exactly, inside the published 0.25 to 0.30 GA brake-thermal-efficiency band and below the ideal eta_otto (0.2968 < 0.5752), as it must be.
• Volumetric fuel flow: V_dot = 7.6e-3/720 = 1.0555555556e-05 m3/s = 38.0 L/h = 10.0385 US gal/h, a realistic avgas cruise burn for this power class.
• Band verdict: eta_b_position "inside" and bsfc_position "inside" with enforced False.

Verification

• Confirm otto_efficiency(8.5, 1.4) returns 0.5751531234287552, within 0.1 percent of the published 0.575 anchor.
• Confirm indicated_power(900e3, 4.0e-3, 2700.0) returns 81000.0 W and brake_power(81000.0, 0.85) returns 68850.0 W.
• Confirm the isentropic identity: 1 - 1/isentropic_temperature_ratio( 8.5, 1.4) equals otto_efficiency(8.5, 1.4).
• Confirm fuel_flow_from_bsfc round-trips the fuel flow used to build a BSFC value to better than 1e-15 kg/s.
• Confirm every non-positive or non-finite IMEP, displacement, rpm, power, fuel flow, density or LHV raises ValueError, and every mechanical efficiency at or below 0 or above 1 raises ValueError.
• Confirm ga_band_verdict never raises for an out-of-band point; it only rejects non-finite or non-positive inputs.
• Run the contract test offline: python3 scripts/test_piston_engine_cycle.py (35 tests, deterministic).

Related leaves

• propulsion/turboprop/free-turbine: the turboshaft power-turbine prime-mover slot, the shaft-power alternative to this reciprocating engine.
• propulsion/turboprop/turboprop-cycle: propeller (Froude) efficiency and shaft-power-to-thrust bookkeeping once a prime mover, turbine or reciprocating, delivers shaft power.
• propulsion/engine-airframe: installed thrust and drag bookkeeping for the airframe integration once the powerplant operating point is fixed.

Pitfalls

• Reading the air-standard Otto efficiency as the achievable brake thermal efficiency: eta_otto (0.5752 in the worked example) is the ideal cycle ceiling; the real point's eta_b (0.2968) sits well below it because of heat transfer, combustion, pumping and mechanical losses the air-standard cycle does not model.
• Forgetting the two-revolutions-per-power-stroke factor: the four-stroke indicated power formula divides by two after the rpm/60 conversion (one power stroke per two crankshaft turns); omitting it doubles the indicated power.
• Treating the BSFC bands as a pass/fail gate: ga_band_verdict and piston_engine_cycle carry enforced: False and never raise for an out-of-band point; the bands are a published reference range for carbureted and fuel injected engines, not a certification limit.
• Mixing the BSFC reporting units: the module's native BSFC is kg/(kW h); the lb/(hp h) figure is a separate conversion through KG_PER_KWH_PER_LB_PER_HP_HR, not a unit-label swap on the same number.
• Applying this leaf to gas-turbine, turboshaft or turboprop powerplants: the Otto cycle, IMEP bookkeeping and BSFC bands here are specific to reciprocating four-stroke engines; shaft-power turbine cycles belong to propulsion/turboprop/free-turbine and propulsion/gas-turbine-cycle.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_piston_engine_cycle.py

The test covers the air-standard Otto cycle efficiency and isentropic temperature ratio at the worked-example compression ratio, the limits as compression ratio and gamma approach one, the four-stroke indicated power receipt target and its linear scaling with rpm and displacement, the brake power receipt and worked-example targets, the brake specific fuel consumption and its lb/(hp h) conversion with the round trip back to fuel flow, the indicated and brake thermal efficiencies and their ordering against the ideal Otto efficiency, the volumetric fuel flow in three reporting units, the reference-only band verdict at an inside and an artificial out-of-band point, the full piston_engine_cycle single-point summary dict and its determinism, and ValueError rejection of every non-physical input.

Compliance

• Standards referenced, not reproduced: 14 CFR Part 33 (far-33, Airworthiness Standards for Aircraft Engines) historically covers reciprocating and turbine aircraft engines; the relations above are standard air-standard-cycle and PLAN-bookkeeping engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.