# Diesel Cycle > Use when you must compute the operating point of a reciprocating compression-ignition aircraft powerplant: the air-standard Diesel cycle thermal efficiency from the compression ratio, the specific-heat ratio and the cutoff ratio of the constant-pressure heat-addition model, the isentropic compression temperature ratio and state temperatures, the four-stroke indicated power from the indicated mean effective pressure, displacement and crankshaft speed, the brake power at the mechanical efficiency, and the brake specific fuel consumption from the fuel flow and the brake power on Jet-A. Produces the single-point summary dict with the ideal Diesel cycle efficiency, the state temperatures, indicated and brake power, BSFC in both units, thermal efficiencies, volumetric fuel flow and the reference-only compression-ignition band verdict, the bands reported and never enforced. Trigger: diesel-cycle, air-standard-diesel-cycle, compression-ignition, cutoff ratio, jet-a-fuel-cycle. - Skill: `ashfordeou/diesel-cycle` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/diesel-cycle` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/diesel-cycle/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: AI & ML - License: Apache-2.0 - Author: ashfordeOU (https://skillmd.com/u/ashfordeou) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/ashfordeou/diesel-cycle --- # Diesel Cycle (propulsion/reciprocating/diesel-cycle) Use when the task is a reciprocating compression-ignition aircraft powerplant operating-point analysis, an aircraft diesel: the air-standard Diesel cycle thermal efficiency under the constant-pressure heat-addition model, the four-state temperature bookkeeping and heat addition, the four-stroke indicated and brake power from the mean effective pressure bookkeeping, and the brake specific fuel consumption and thermal efficiencies on Jet-A. This leaf implements the standard textbook air-standard Diesel cycle and PLAN indicated-power method in pure Python, stdlib only. It pairs with propulsion/reciprocating/piston-engine-cycle for the spark-ignition Otto cycle prime mover, 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 Diesel thermal efficiency (constant-pressure heat addition): eta = 1 - (1/r^(gamma-1)) * ((rc^gamma - 1)/(gamma * (rc - 1))), with r the compression ratio (r > 1), gamma the specific-heat ratio (gamma > 1, air-standard default 1.4) and rc the cutoff ratio (1 < rc <= r; heat addition must end before bottom dead center). This is the ideal efficiency ceiling of the compression-ignition cycle, not a real-cycle prediction. - Isentropic compression temperature ratio: T2/T1 = r^(gamma-1); the state bookkeeping continues T3 = T2 * rc (constant-pressure heat addition 2 to 3) and T4 = T1 * rc^gamma (isentropic expansion 3 to 4 to V4 = V1, closed form). The temperature-form identity eta = 1 - (T4 - T1)/(gamma * (T3 - T2)) holds exactly. - Constant-pressure heat addition per kg of air: q_in = cp * T2 * (rc - 1); the cutoff-ratio identity rc = 1 + q_in/(cp * T2) is the exact inverse. - As rc approaches 1 the Diesel efficiency approaches the same-r constant-volume Otto ceiling 1 - 1/r^(gamma-1), showing the two air-standard cycles share a common limit; for any rc above 1 the Diesel efficiency sits below that ceiling. - 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 Jet-A 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_diesel 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 compression-ignition band verdict: brake thermal efficiency against 0.3262 to 0.3806 and BSFC against 0.35 to 0.42 lb/(hp h), published bands for compression-ignition aircraft engines of the Centurion/AE300 class. The verdict reports the point's position and never enforces it. - Units are SI throughout except the reporting conversions (hp, lb/(hp h), L/h, US gal/h) that the module carries as named outputs. ## Workflow 1. Fix the compression-ignition operating point: compression ratio, cutoff ratio and gamma, then compute the air-standard Diesel cycle thermal efficiency with diesel_efficiency and the isentropic compression temperature ratio with isentropic_temperature_ratio. 2. Compute the four-state temperature bookkeeping with cycle_state_temperatures (or the individual compression_temperature, cutoff_temperature and expansion_temperature steps) and the constant-pressure heat addition with heat_addition_j_per_kg, round-tripping to the cutoff ratio with cutoff_ratio_from_heat_addition when checking a reported heat addition. 3. Compute the four-stroke indicated power from the indicated mean effective pressure, the displacement and the crankshaft speed with indicated_power. 4. Compute the brake power at the mechanical efficiency with brake_power. 5. 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. 6. Compute the indicated and brake thermal efficiencies on the Jet-A lower heating value with indicated_thermal_efficiency and brake_thermal_efficiency. 7. Compute the volumetric fuel flow in m3/s, L/h and US gal/h with volumetric_fuel_flow. 8. Get the reference-only compression-ignition band verdict with ci_band_verdict, reporting the point's position without enforcing it, or call diesel_cycle once for the full single-point summary dict that chains steps 1 through 8. 9. Confirm the deterministic checks with the contract test scripts/test_diesel_cycle.py. ## Worked example Centurion/AE300-class compression-ignition aircraft diesel at a cruise rating: compression ratio r = 17, cutoff ratio rc = 2.2, gamma = 1.4 (air standard), inlet temperature T1 = 288.15 K, IMEP = 1.8e6 Pa (18 bar), displacement V_d = 2.0e-3 m3 (2.0 L), crankshaft speed 2300 rpm, mechanical efficiency eta_m = 0.86, fuel flow m_dot = 3.9e-3 kg/s Jet-A at the reference density 800 kg/m3 and LHV 43.2 MJ/kg. - Ideal cycle: eta_diesel = 1 - (1/17^0.4) * ((2.2^1.4 - 1)/(1.4 * 1.2)) = 0.6136842121239982; the isentropic compression temperature ratio is T2/T1 = 17^0.4 = 3.1058435015977315. - State bookkeeping from T1 = 288.15 K: T2 = 894.9488049853862 K, T3 = T2 * 2.2 = 1968.8873709678498 K, T4 = T1 * 2.2^1.4 = 868.9811925471146 K, and the constant-pressure heat addition q_in = 1005 * T2 * (2.2 - 1) = 1079308.258812376 J/kg (about 1.08 MJ per kg of air); the temperature-form identity 1 - (T4 - T1)/(1.4 * (T3 - T2)) reproduces eta_diesel exactly, and the cutoff-ratio identity rc = 1 + q_in/(cp * T2) round-trips to 2.2 exactly. - Cutoff-ratio sensitivity at this compression ratio: rc = 2.0 gives 0.6230571224158052 and rc = 2.5 gives 0.600330985397127, so a longer constant-pressure heat addition costs efficiency at fixed r, the compression-ignition signature. As rc approaches 1 the efficiency approaches 0.6780262755, the same-r constant-volume ceiling. - Indicated power: P_i = 1.8e6 * 2.0e-3 * (2300/60)/2 = 69000.0 W = 92.53052418205692 hp. - Brake power: P_b = 69000.0 * 0.86 = 59340.0 W = 79.57625079656896 hp. - BSFC: 3.9e-3 * 3600 * 1000 / 59340.0 = 0.23660262891809908 kg/(kW h) = 0.3889716002062689 lb/(hp h), inside the published 0.35 to 0.42 lb/(hp h) compression-ignition band. - Thermal efficiencies on LHV: eta_i = 69000.0/(3.9e-3 * 43.2e6) = 0.40954415954415957; eta_b = 59340.0/(3.9e-3 * 43.2e6) = 0.3522079772079772 = eta_i * eta_m exactly, inside the published CI brake-thermal-efficiency window 0.3261878583333333 to 0.3805525013888889 and below the ideal eta_diesel (0.35221 < 0.61368), as it must be. - Volumetric fuel flow: V_dot = 3.9e-3/800 = 4.875e-06 m3/s = 17.55 L/h = 4.636219518885506 US gal/h. - Band verdict: eta_b_position "inside" and bsfc_position "inside" with enforced False. ## Verification - Confirm diesel_efficiency(17.0, 2.2, 1.4) returns 0.6136842121239982, and that efficiency falls as the cutoff ratio grows at fixed compression ratio (0.6230571224 at rc 2.0, 0.6003309854 at rc 2.5). - Confirm isentropic_temperature_ratio(17.0, 1.4) returns 3.1058435015977315 and compression_temperature(288.15, 17.0, 1.4) returns 894.9488049853862 K. - Confirm heat_addition_j_per_kg and cutoff_ratio_from_heat_addition round-trip the cutoff ratio to better than 1e-13 relative. - Confirm indicated_power(1.8e6, 2.0e-3, 2300.0) returns 69000.0 W and brake_power(69000.0, 0.86) returns 59340.0 W. - 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 compression ratio, cutoff ratio, gamma, temperature, IMEP, displacement, rpm, power, fuel flow, density or LHV raises ValueError, that every mechanical efficiency at or below 0 or above 1 raises ValueError, and that a cutoff ratio above the compression ratio raises ValueError. - Confirm ci_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_diesel_cycle.py (deterministic, no network). ## Related leaves - propulsion/reciprocating/piston-engine-cycle: the spark-ignition Otto cycle reciprocating prime mover, the constant-volume heat-addition sibling of this constant-pressure Diesel cycle at the same station. - 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 Diesel efficiency as the achievable brake thermal efficiency: eta_diesel (0.6137 in the worked example) is the ideal cycle ceiling; the real point's eta_b (0.3522) sits well below it because of heat transfer, combustion, pumping and mechanical losses the air-standard cycle does not model. - Confusing the cutoff ratio with the compression ratio: rc = V3/V2 = T3/T2 describes the constant-pressure heat-addition stroke and must satisfy 1 < rc <= r; passing a cutoff ratio above the compression ratio raises ValueError because the heat addition cannot outlast the power stroke back to bottom dead center. - 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 and brake-thermal-efficiency bands as a pass/fail gate: ci_band_verdict and diesel_cycle carry enforced: False and never raise for an out-of-band point; the bands are a published reference range for compression-ignition aircraft 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 spark-ignition, gas-turbine, turboshaft or turboprop powerplants: the constant-pressure Diesel cycle, IMEP bookkeeping and CI bands here are specific to compression-ignition reciprocating engines; the Otto cycle belongs to propulsion/reciprocating/piston-engine-cycle and 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_diesel_cycle.py The test covers the air-standard Diesel cycle efficiency at the worked-example compression and cutoff ratios, the cutoff-ratio sensitivity ordering and the limits as the cutoff ratio approaches the same-r Otto ceiling and as gamma or compression ratio approach one, the four-state temperature bookkeeping and the temperature-form and heat-rejection-form efficiency identities, the constant-pressure heat addition and its cutoff-ratio round trip, 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 Diesel 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 diesel_cycle single-point summary dict and its determinism, and ValueError rejection of every non-physical input including a cutoff ratio above the compression ratio. ## Compliance - Standards referenced, not reproduced: 14 CFR Part 33 (far-33, Airworthiness Standards for Aircraft Engines) historically covers reciprocating and turbine aircraft engines, including certified compression-ignition aircraft diesels; the relations above are standard air-standard-cycle and PLAN-bookkeeping engineering methodology, summary-only per standards-map.yaml. - compliance: STANDARDS-REF, gated: false.