Propeller Range

Propeller Range (flight-mechanics/performance/propeller-range)

Use when the task is the cruise range of a propeller or turboprop aircraft from the propeller Breguet equation: power specific fuel consumption (PSFC), propeller efficiency, lift to drag ratio and the initial and final masses. This is the propeller branch of the Breguet range family; the jet side of the family (flight-mechanics/performance/ breguet-range) never takes a propeller efficiency, and the endurance leaf (flight-mechanics/performance/breguet-endurance) already carries the propeller branch on the endurance side, so the range side is completed here. It pairs with the engine-side leaf propulsion/turboprop/turboprop-cycle, which evaluates PSFC and propeller efficiency from slipstream velocities; this leaf turns those engine metrics into an aircraft cruise range. Does NOT do: jet transport cruise range from thrust specific fuel consumption (breguet-range); endurance of either propulsion type (breguet-endurance); specific air range (specific-range); required thrust for the cruise condition (thrust-required); engine-side PSFC or propeller efficiency from slipstream velocities (turboprop-cycle).

Domain quick reference

• Propeller Breguet range equation for still-air cruise range R:

  R = (eta_p / (c_p * g0)) * (L/D) * ln(m0 / m1)

  with eta_p the propeller efficiency, c_p the power specific fuel consumption in kg/(W s), g0 = 9.80665 m/s^2 the standard gravity, L/D the lift to drag ratio, m0 the initial (start of cruise) mass and m1 the final mass, all masses in kg.

• Units: PSFC in kg/(W s), range in meters (divide by 1000 for kilometers). There is no cruise speed term: the propeller relation is an energy bookkeeping on the shaft fuel flow, so the efficiency enters the numerator and the PSFC the denominator.

• Unit conversion: 1 lb/(hp h) = 0.45359237 / (745.6999 * 3600) kg/(W s); a pounds per horsepower hour PSFC is multiplied by that factor with psfc_lb_per_hp_h_to_kg_per_w_s.

• Final mass from the fuel fraction f: m1 = m0 * (1 - f), the form used when the fuel plan is stated as the burned fraction of the initial mass.

• Range analysis sits in the FAR-25 transport performance context for cruise fuel planning of propeller and turboprop aircraft.

Workflow

1. Fix the operating inputs: propeller efficiency eta_p in (0, 1], the power specific fuel consumption c_p, lift to drag ratio L/D, initial mass m0 and final mass m1. When the PSFC arrives in pounds per horsepower hour, run step 1's unit conversion with psfc_lb_per_hp_h_to_kg_per_w_s to get c_p in kg/(W s).
2. When the fuel plan is a burned fuel fraction, derive the final cruise mass with final_mass_from_fuel_fraction: m1 = m0 * (1 - f).
3. Form the cruise range with propeller_range (or propeller_range_km for kilometers directly), evaluating the propeller Breguet equation on the mass ratio m0/m1.
4. Run the physical sanity gate: eta_p must sit in (0, 1], c_p and L/D positive, and 0 < m1 < m0 so ln(m0/m1) stays positive; confirm the range scales linearly with the propeller efficiency (eta_p 0.9 against the 0.8 reference) and halves when the PSFC doubles.
5. Package the result with range_report, which returns the report dict with the range_m and range_km keys, and cross check that the kilometers figure equals the meters value divided by 1000.
6. Close with the deterministic offline checks in the contract test scripts/test_propeller_range.py.

Worked example

A turboprop transport cruises at L/D = 12 with propeller efficiency eta_p = 0.80 and PSFC c_p = 0.55 lb/hp/h, from m0 = 11,500 kg to m1 = 10,000 kg.

• Unit conversion (workflow step 1): psfc_lb_per_hp_h_to_kg_per_w_s (0.55) = 9.293126e-8 kg/(W s), within the 9.293e-8 anchor.
• Cruise range (workflow step 3): propeller_range(0.80, 9.293126e-8, 12, 11500, 10000) = 1.4722367e6 m = 1472.24 km, within 1 km of the 1472.2 km anchor.
• Efficiency scaling (workflow step 4): eta_p 0.9 raises the range to 1656.27 km (0.9/0.8 * 1472.24), within 2 km of the 1656 km anchor.
• Fuel fraction (workflow step 2): final_mass_from_fuel_fraction (11500, 1500/11500) = 10,000 kg exactly; the range computed through the fuel fraction profile equals the direct m0/m1 form.
• Report (workflow step 5): range_report returns {"range_m": 1472236.70, "range_km": 1472.24}, exactly the two documented keys.

Verification

• Confirm propeller_range(0.80, 9.293126e-8, 12, 11500, 10000) returns 1.4722367e6 m and that doubling the propeller efficiency doubles the range while doubling the PSFC halves it.
• Confirm the range vanishes toward zero as the final mass approaches the initial mass (the ln(m0/m1) factor collapses).
• Confirm final_mass_from_fuel_fraction(11500, 1500/11500) returns 10,000 kg and the fraction round trips: (m0 - m1) / m0 = f.
• Confirm range_report returns exactly the keys range_m and range_km and that range_km equals range_m / 1000.
• Confirm every non-physical input raises ValueError: propeller efficiency 0, above 1 or negative; PSFC zero or negative; L/D zero; initial or final mass not positive; final mass at or above the initial mass; fuel fraction 1, above 1 or negative; negative PSFC in the unit conversion.
• Run the contract test offline: python3 scripts/test_propeller_range.py (35 tests, deterministic).

Related leaves

• flight-mechanics/performance/breguet-range: jet transport cruise range from speed and thrust specific fuel consumption, the jet side of the same family.
• flight-mechanics/performance/breguet-endurance: endurance of both propulsion types, where the propeller branch already exists.
• flight-mechanics/performance/specific-range: specific air range for fuel planning at a fixed flight condition.
• flight-mechanics/performance/thrust-required: the required thrust at the cruise condition that sets the L/D operating point.
• propulsion/turboprop/turboprop-cycle: engine-side PSFC and propeller efficiency from slipstream velocities, the inputs this leaf consumes.

Pitfalls

• Feeding a thrust specific fuel consumption or a cruise speed into the propeller equation: the propeller Breguet relation uses the power specific fuel consumption in kg/(W s) with the propeller efficiency in the numerator, and has no speed term.
• Leaving the PSFC in pounds per horsepower hour: 0.55 lb/hp/h must be converted to 9.293e-8 kg/(W s) before the range evaluation, or the range comes out wrong by the conversion factor.
• Inverting the mass ratio: m1 >= m0 makes ln(m0/m1) zero, negative or undefined, so the sanity gate rejects it.
• Using a fuel fraction of 1 or above: m1 = m0 * (1 - f) leaves no vehicle mass, so the derivation rejects the fraction outside [0, 1).
• Reporting a near-full-range burn as infinite: as m1 approaches m0 the log factor collapses and the range goes to zero, so a tiny fuel fraction gives a tiny range, not an unbounded one.

Behavior contract (gate 3)

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

python3 scripts/test_propeller_range.py

The test covers the worked example anchors (range 1.4722367e6 m and 1472.24 km within the spec bounds, PSFC conversion 9.293e-8 kg/(W s)), linear scaling with propeller efficiency and inverse scaling with PSFC, the fuel fraction derivation and its round trip, the fuel fraction profile against the direct mass ratio form, the near-zero range limit, the range report keys, determinism, and ValueError rejection of every non-physical input listed in the Verification section.

Compliance

• Standards referenced, not reproduced: FAR-25 is US government work (public domain); the propeller Breguet range relation is common range methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.