Propeller Sizing

Propeller Sizing (vehicle-design/sizing/propeller-sizing)

Use when the task is sizing the geometric propeller for a given design point: the propeller diameter from the blade-tip constraint and the ground clearance, the blade count and chord from the solidity and the activity factor, the disk loading of the selected disk, and the operating point from the advance ratio. The output is the propeller geometry and its loading, not the evaluation of the engine that drives it.

Domain quick reference

• Units: forces in N, shaft power in W, speeds in m/s, rpm in revolutions per minute, densities in kg/m^3, lengths in m, disk area in m^2, angles in radians, Mach numbers and efficiencies unitless.
• Advance ratio: J = V / (n * D) with n = rpm / 60. Anchor: 70 m/s at 2200 rpm and 2.0 m diameter give J = 0.9545. The static point (V = 0) gives J = 0.
• Blade-tip constraint: the blade tip must stay below the local Mach limit. Anchor: 2200 rpm and 2.0 m diameter give 230.38 m/s at the tip, Mach 0.677 at a = 340.3 m/s, inside the common 0.85 limit with 0.173 margin.
• Diameter from the blade-tip bound: D = V_limit / (pi * n). Anchor: 2200 rpm with a 250 m/s bound gives 2.1703 m.
• Disk loading: T / A with A = pi * D^2 / 4. Anchor: 4000 N over a 2.0 m disk gives 1273.24 N/m^2.
• Static thrust (actuator disk momentum theory, loss-free): T = (2 * rho * A * P^2)^(1/3). Anchor: 150 kW over a 2.0 m disk at rho = 1.225 kg/m^3 gives 5573.99 N; the inverse relation returns the 150000 W.
• Solidity: sigma = B * c / (pi * D). Anchor: 3 blades of 0.25 m chord on a 2.0 m diameter give 0.11937.
• Activity factor (constant-chord summary of the blade loading integral): AF = B * (100000 / 16) * (c / D) * (1 - x_hub^4) / 4. Anchor: 3 blades, 0.25 m chord, 2.0 m diameter, hub fraction 0.15 give 585.64.
• Efficiency versus advance ratio (parabolic model): eta = eta_max * (1 - ((J - J_design) / J_design)^2) for J in [0, 2 * J_design], and 0 outside. Anchor: J_design = 0.9 and eta_max = 0.85 give 0.85 at the design point, 0.6375 at J = 0.45, and 0 at the static point.
• Ground clearance: the tip sits hub_height - D / 2 above the ground. Anchor: 2.0 m diameter at 1.6 m hub height gives 0.6 m of clearance, ok against a 0.2 m minimum; 3.0 m diameter gives 0.1 m, below the minimum.
• P-factor (first-order estimate): N_p = T * (D / 4) * sin(alpha). Anchor: 4000 N at 10 degrees angle of attack on a 2.0 m diameter gives 347.30 N m.
• In-flight thrust from the propulsive power: T = eta * P / V. Anchor: 150 kW at 70 m/s with eta = 0.8 gives 1714.29 N, below the 5573.99 N static thrust from the same power at the same diameter.
• FAR-25 (14 CFR Part 25) and CS-25 set the certification context for transport-category propeller installations (reference-only); the relations above are common conceptual sizing practice.

Workflow

1. Set the operating point: forward motion V, rpm, shaft power P, and the Mach limit at the cruise altitude.
2. Compute the advance ratio with advance_ratio to locate the operating point on the efficiency curve.
3. Size the diameter with diameter_from_tip_speed_limit against the blade-tip bound, then check the tip condition with tip_mach_check using the local speed of sound; reduce the rpm or the diameter until within_limit is True.
4. Check the ground clearance with ground_clearance_check; the tip must clear the ground in the static and takeoff attitudes.
5. Estimate the static thrust with static_thrust_estimate from the shaft power and the disk area, or invert the target with power_for_static_thrust when the requirement fixes the power.
6. Select the blade count and chord with solidity and activity_factor: more blades or more chord raise the loading capability at the cost of efficiency at the cruise point.
7. Evaluate the disk loading; a larger diameter lowers it and raises the propulsive efficiency, within the blade-tip bound and the ground clearance.
8. Estimate the P-factor yawing moment with p_factor_moment for the takeoff and climb attitudes, and the in-flight thrust with thrust_from_power_in_flight for the cruise point.
9. Hand the diameter, blade count, advance ratio, static thrust, and tip Mach margin to the sibling leaves: engine-sizing (shaft power matching), the turboprop cycle analysis (powerplant assessment), and the performance leaves (climb and takeoff distance).

Pitfalls

• Confusing this leaf with turboprop-cycle: turboprop-cycle evaluates the powerplant cycle and converts the shaft power into thrust and efficiency; propeller-sizing selects the geometric propeller (diameter, blade count, chord) against the blade-tip bound, the ground clearance, and the disk loading. The geometry sizing comes first, the cycle evaluation second.
• Confusing this leaf with engine-sizing: engine-sizing sizes the engine set and lapses its output with altitude; propeller-sizing converts the shaft power into propeller thrust. Do not size the gas generator here.
• Confusing this leaf with wing-planform-sizing: wing-planform-sizing sizes the wing geometry from the wing loading and the aspect ratio; the propeller constraints (blade-tip bound, ground clearance) apply to the propeller installation, not the wing. A wing geometry question belongs to the wing leaf.
• Treating the static thrust estimate as exact: actuator disk momentum theory ignores induced, profile, and installation losses; a real static thrust runs below the loss-free value, so size with margin.
• Ignoring the blade-tip bound at altitude: the speed of sound falls with altitude and temperature, so a tip condition that is safe at sea level may exceed the limit at cruise; check with the local speed of sound, not the sea level value.
• Sizing the diameter without the ground clearance: a large diameter that meets the blade-tip bound can still strike the ground in the takeoff attitude; run ground_clearance_check before fixing the diameter.
• Forgetting the static point: at J = 0 the propeller does no useful work and the efficiency is zero; the static thrust is the maximum available and drives the takeoff acceleration.
• Mixing units: rpm must be converted to revolutions per second before computing the advance ratio and the tip condition, and powers must be in W, not kW, in the actuator disk relations.
• Using the parabolic efficiency model outside its range: the model is a summary of the efficiency curve near the design point and returns zero beyond twice the design advance ratio; a blade element analysis supersedes it for detailed work.

Behavior contract (gate 3)

The advance ratio, tip condition and Mach check, disk loading, static thrust estimate and its power inverse, diameter from the blade-tip bound, solidity and activity factor, efficiency versus advance ratio, ground clearance check, P-factor moment, and in-flight thrust are exercised by the gate 3 contract test: scripts/test_propeller_sizing.py against scripts/propeller_sizing_logic.py (stdlib unittest, offline). Run: python3 scripts/test_propeller_sizing.py

Compliance

• Standards referenced, not reproduced: FAR-25 is US government work (public domain) and CS-25 is a free EASA download; the propeller sizing relations are common conceptual sizing methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.