Engine Sizing

Engine Sizing (vehicle-design/sizing/engine-sizing)

Use when the task is sizing the propulsion for a transport aircraft: sea level static thrust from the design thrust to weight ratio and the takeoff gross weight, thrust lapse with altitude, installed takeoff thrust, cruise and top of climb thrust margin, SFC fuel flow, engine weight, and the thrust split across the number of engines.

Domain quick reference

• Sea level static thrust: T_SL = (T/W) * W, with T/W the design thrust to weight ratio and W the takeoff gross weight in newtons. A 500000 N transport at a 0.25 design ratio needs 125000 N of sea level static thrust; this is the engine selection design point.
• ISA density ratio: sigma = (1 - L * h / T0) ** (g0 / (R * L) - 1) in the troposphere, with L = 0.0065 K/m, T0 = 288.15 K, and the exponent g0 / (R * L) - 1 = 4.255879. Sigma is 1.0 at sea level, about 0.601 at 5000 m, 0.337 at 10000 m, and 0.297 at the 11000 m tropopause.
• Thrust lapse with altitude: T(h) = T_SL * sigma ** m, with m the thrust lapse exponent. High bypass turbofans retain altitude thrust well, m near 0.7; a turbojet lapses closer to the density ratio itself, m near 1.0. At 11000 m a 125000 N engine with m = 0.7 still delivers about 53446 N, versus 37134 N with m = 1.0.
• Installed takeoff thrust: T_TO = T_SL * (1 - loss), with the installation loss covering intake, nacelle, and bleed, typically 0.02 to 0.04 for a padded turbofan installation.
• Cruise thrust required: T_req = W / (L/D), the drag the engines must overcome in level cruise. A 500000 N aircraft at 18 to 1 needs about 27778 N.
• Thrust margin: available / required. The margin is 1.0 when the thrust exactly meets the demand; the top of climb check keeps it above 1.0 so the aircraft can hold the climb condition at altitude.
• Top of climb: the thrust available at the top of climb altitude (sigma ** m lapse applied to T_SL) against W_TOC / (L/D)_TOC. An undersized engine shows a margin below 1.0 and the sea level thrust must grow.
• Specific fuel consumption: 1 lb/(lbfh) equals 2.8325e-5 kg/(Ns), so 0.5 lb/(lbfh) is about 1.4163e-5 kg/(Ns). Fuel flow is mdot = SFC * T, about 0.3934 kg/s at the cruise thrust point, roughly 1416 kg/h.
• Engine weight: W_eng = T_SL / (T/W)_eng with the engine thrust to weight ratio near 5 for a modern turbofan (4 to 6 is the typical band). A 125000 N total at ratio 5 weighs 25000 N, about 2549 kg.
• Thrust split: T_per = T_total / N across N engines. The per engine thrust is the entry to the engine catalogue; matched_engine_count returns the smallest whole number of catalogue engines that covers the demand.
• FAR-25 (14 CFR Part 25) and CS-25 set the certification context: the climb gradients of FAR 25.121 and CS 25.121, including the one engine inoperative cases, are among the thrust sizing drivers; the lapse and margin formulas above are common conceptual sizing practice.

Workflow

1. Set the design point: takeoff gross weight W and design thrust to weight ratio, then compute the sea level static thrust with sea_level_static_thrust.
2. Apply the installation loss with takeoff_thrust to get the installed takeoff thrust, the thrust available at the start of the takeoff roll.
3. Lapse the thrust to the design altitude with thrust_at_altitude, using the ISA density ratio from isa_density_ratio and the lapse exponent that matches the engine class (0.7 high bypass turbofan, 1.0 turbojet).
4. Compute the cruise thrust required with cruise_thrust_required and the margin with thrust_margin; check the top of climb with top_of_climb_margin and grow T_SL if the margin falls below 1.0.
5. Estimate the cruise fuel flow with fuel_flow from the SFC, using sfc_from_lb_per_lbf_hr when the catalogue quotes English units.
6. Size the engines: engine_weight from the engine thrust to weight ratio, thrust_per_engine for the chosen number of units, and matched_engine_count when the catalogue engine must cover the demand.
7. Close the loop: feed the engine weight and thrust back into the takeoff gross weight estimate and re-run until the design ratio and the top of climb margin are both met.

Pitfalls

• Using the aircraft thrust to weight ratio as the engine thrust to weight ratio: T/W of the aircraft is the design demand, T/W of the engine is a measure of engine technology; the two differ by an order of magnitude (0.25 versus 5).
• Lapsing with the density ratio directly for a high bypass turbofan: m = 1.0 underpredicts the altitude thrust by a third at 11000 m; use m near 0.7 for high bypass engines.
• Forgetting the installation loss: uninstalled sea level static thrust overstates the takeoff thrust; apply the 0.02 to 0.04 loss before checking the takeoff constraint.
• Checking the cruise margin at the wrong weight: the top of climb check must use the weight and lift to drag ratio at the top of climb, not the sea level takeoff values.
• Mixing fuel flow units: SFC in lb/(lbf*h) must be converted before it multiplies a newton thrust, or the fuel flow comes out off by three orders of magnitude.
• Sizing the engine for cruise alone: the takeoff and top of climb constraints usually bind; the sea level static thrust must satisfy all three, and the binding condition sets the size.
• Treating engine weight as a constant: engine weight scales with the sea level static thrust through the engine thrust to weight ratio, and a heavier engine feeds back into the takeoff gross weight and the design thrust demand.
• Confusing this leaf with the matching chart: ws-tw-trade computes the required aircraft level T/W from takeoff distance, climb gradient, and cruise constraints; this leaf turns that requirement into an engine: sea level static thrust, lapse, installed thrust, margin, SFC, and weight.

Behavior contract (gate 3)

The engine sizing math is exercised by the gate 3 contract test: scripts/test_engine_sizing.py against scripts/engine_sizing_logic.py (stdlib unittest, offline). Run: python3 scripts/test_engine_sizing.py

Compliance

• Standards referenced, not reproduced: FAR-25.121 and CS-25.121 frame the climb gradient certification basis that drives thrust sizing (including the one engine inoperative gradients), and FAR-25.101 and CS-25.101 set the general performance basis; the lapse, margin, SFC, and weight formulas above are common conceptual sizing methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.