# Real Cycle Effects > Use when you must compute the real-cycle gas turbine performance with component losses: the compressor exit temperature and the turbine exit temperature from the pressure ratio and the component-efficiency (isentropic-efficiency) of each machine, the real-cycle thermal efficiency of the non-ideal Brayton cycle, the actual-SFC from the efficiency and the fuel lower heating value, and the efficiency penalty from the combustor pressure-loss. Produces the actual station temperatures, the real-cycle efficiency, the actual-SFC, and the pressure-loss penalty in SI units that gate the engine cycle assessment. Trigger: real cycle, component efficiency, isentropic efficiency, pressure loss, combustor loss, actual SFC, off-ideal Brayton. - Skill: `ashfordeou/real-cycle-effects` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/real-cycle-effects` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/real-cycle-effects/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Web & Frontend - License: Apache-2.0 - Author: ashfordeOU (https://skillmd.com/u/ashfordeou) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/ashfordeou/real-cycle-effects --- # Real Cycle Effects (propulsion/gas-turbine-cycle/real-cycle-effects) Use when the task is a non-ideal gas turbine (Brayton) cycle: the compressor and turbine isentropic efficiencies, the combustor total-pressure loss, the real thermal efficiency, and the actual specific fuel consumption. This leaf is the lossy follow-on to the ideal gas-turbine-cycle leaf: the ideal relations are recovered at eta_c = eta_t = 1 with no pressure loss. ## Domain quick reference Units are SI throughout: temperatures in kelvin, pressure ratio dimensionless, gamma = 1.4 and cp = 1005 J/(kg K) air-standard values, LHV in J/kg. - Compressor with isentropic efficiency eta_c: T2s = T1 * PR**((gamma-1)/gamma), and the actual exit temperature T2 = T1 * (1 + (PR**((gamma-1)/gamma) - 1)/eta_c). Example: T1 = 288.15 K, PR = 20, gamma = 1.4, eta_c = 0.85 give T2s about 678 K and T2 about 747 K. The compressor work per kg is w_c = cp * (T2 - T1). - Turbine with isentropic efficiency eta_t: T4s = T3 / PR**((gamma-1)/gamma), and the actual exit temperature T4 = T3 - eta_t * (T3 - T4s). Example: T3 = 1500 K, eta_t = 0.88 give T4s about 637 K and T4 about 741 K. The turbine work per kg is w_t = cp * (T3 - T4). - Real thermal efficiency with the actual temperatures: eta_th = (T3 - T4 - T2 + T1)/(T3 - T2) = (w_t - w_c)/q_in; cp cancels. The example gives eta_th about 0.40 against the ideal cycle value 1 - PR**((1-gamma)/gamma) of about 0.575. - Specific fuel consumption: SFC = 3600/(eta_th * LHV) with LHV in J/kg, the cycle-basis value in kg/(kN*s) at the reference effective velocity V_ref = 3.6 m/s (the 3600 factor is the hourly scaling of the classic SFC = 3600/(eta * LHV) form). For a real engine scale with the effective jet velocity: SFC_T = 1000 * V_eff/(eta_th * LHV) in kg/(kN*s) with V_eff in m/s (typical 500 to 700 m/s for a turbojet); the example gives SFC about 2.1e-4 kg/(kN*s) on the cycle basis and SFC_T about 3.5e-2 kg/(kN*s) at V_eff = 600 m/s. - Combustor total-pressure loss: PR_eff = PR * (1 - loss_frac) with loss_frac the fractional loss (typical 0.02 to 0.06). The compressor still sees the full PR; the turbine sees PR_eff, so T4s (and T4) rise and the real efficiency falls. Example: a 5% loss at PR 20 cuts eta_th from about 0.399 to about 0.388, roughly one percentage point; the penalty grows at higher pressure ratio. - Sensitivity verdicts: d(eta_th)/d(eta_c) > 0 and d(eta_th)/d(eta_t) > 0 - improving either component efficiency always raises the real cycle efficiency, and the gains flatten as the cycle approaches the ideal limit; d(eta_th)/d(loss) < 0 - any combustor pressure loss lowers efficiency. At PR 20 the turbine efficiency is the stronger lever in the example. ## Workflow 1. Fix the inlet temperature T1, the turbine inlet temperature T3, the pressure ratio, gamma, the compressor efficiency eta_c, and the turbine efficiency eta_t; add the combustor loss fraction if the burner pressure loss matters. 2. Compute the actual compressor exit temperature with compressor_exit_temperature(t1, pressure_ratio, gamma, eta_c). 3. Compute the actual turbine exit temperature with turbine_exit_temperature(t3, pressure_ratio, gamma, eta_t). 4. Compute the real thermal efficiency with real_thermal_efficiency(t1, t2, t3, t4) using the ACTUAL temperatures. 5. Compute the actual SFC with sfc_from_efficiency(eta_th, lhv) and, when the effective jet velocity is known, the thrust SFC with sfc_thrust(eta_th, lhv, v_eff). 6. Apply the combustor loss with pressure_loss_penalty(pr, loss) or cycle_efficiency_with_losses(...) and compare against the lossless case to size the penalty. 7. Run efficiency_sensitivity() to report which component efficiency dominates at the design point. ## Pitfalls - Passing eta_c or eta_t above 1: non-physical (the exit would be colder than isentropic); the module raises ValueError. - Using the ideal (isentropic) temperatures in the real efficiency: T2 and T4 must be the actual lossy station temperatures, and cp cancels only when both work terms use the same cp. - Mixing units: temperatures in kelvin, never Celsius; LHV in J/kg, not kJ/kg or MJ/kg, or the SFC shifts by factors of 1000. - Quoting the efficiency as a percent in the SFC formula: eta_th is a fraction (0.4), not 40. - Forgetting the combustor loss: the turbine sees PR_eff, not the full pressure ratio, and the loss compounds at high PR. - Reading the cycle-basis SFC as a thrust SFC: the 3600/(eta*LHV) value carries the reference effective velocity; the thrust value needs V_eff, or the answer is off by an order of magnitude. - Treating the sensitivity verdicts as exact: the derivative signs are robust, the magnitudes move with the design point. - Treating any of this as a certification requirement: FAR-33 sets the certification context for aircraft engines; the component efficiencies and loss fractions are assessment inputs, and the relations above are common cycle assessment practice. ## Behavior contract (gate 3) The real-cycle relations are exercised by the gate 3 contract test: scripts/test_real_cycle_effects.py against scripts/real_cycle_effects.py (stdlib unittest, offline). Run: python3 scripts/test_real_cycle_effects.py ## Compliance - Standards referenced, not reproduced: FAR-33 is US government work (public domain); the component efficiency and pressure-loss relations are common cycle assessment methodology, summary-only per standards-map.yaml. - compliance: STANDARDS-REF, gated: false.