Ram Air Turbine Sizing

Ram Air Turbine Sizing (vehicle-design/sizing/ram-air-turbine-sizing)

Use when the task is sizing the emergency ram air turbine (RAT) rotor at the conceptual level from the required emergency power at a fixed emergency airspeed. The model is the wind-power relation P = 0.5 rho V^3 A Cp with a fixed design overall power coefficient that absorbs the blade, ducting and machine efficiency losses, so the swept area follows directly from the load and the flight condition. This leaf implements the standard wind-power rotor sizing method in pure Python, stdlib only. The required emergency power P_req is an input supplied by vehicle-design/sizing/aircraft-electrical-load-analysis; the emergency hydraulic side of the installation is covered by vehicle-design/sizing/hydraulic-system-sizing. RAT machine details (embedded generator and control laws) are empirical and out of scope.

Domain quick reference

• Wind-power relation: P = 0.5 * rho * V^3 * A * Cp, with P the extracted power in W, rho the air density in kg/m3, V the airspeed in m/s at the fixed emergency condition, A the rotor swept area in m2 and Cp the overall power coefficient.
• Required swept area: A = P / (0.5 * rho * V^3 * Cp). Sizing the area at the emergency speed means a fixed emergency descent speed anchors the condition (the classic anchor is a minimum controllable descent speed); the density defaults to ISA sea level.
• Rotor disk diameter: D = sqrt(4*A/pi). A round disk sweeps the full circle of radius D/2.
• Design power coefficient: Cp = 0.10 fixed for the emergency RAT, including efficiency and losses; the ideal actuator-disk upper bound (Betz limit) is 16/27 = 0.592593 and physical inputs must stay below it.
• Round-trip check: feeding the sized area back through 0.5 * rho * V^3 * A * Cp must return the required power exactly; the margin is available power minus required power.
• Stowage verdict: PASS when the disk diameter fits within the stowage diameter limit of the installation bay, else FAIL.
• Units are SI throughout: W, m/s, kg/m3, m2, m.
• FAR 25.1351 frames the emergency electrical and essential power context (reference-only); the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the emergency condition: the required emergency power P_req in W (from the electrical load analysis input) and the emergency airspeed V in m/s at which the RAT must deliver it.
2. Keep the defaults (ISA sea level density 1.225 kg/m3, design power coefficient 0.10) or pass explicit rho and cp values to rat_swept_area.
3. Compute the required swept area with rat_swept_area(P_req, V) and the rotor disk diameter with disk_diameter(area).
4. Run the round-trip power check with rat_available_power(area, V): it must equal P_req within numerical tolerance; the margin is the difference.
5. Get the fit verdict in one call: rat_sizing_summary(P_req, V, max_stowage_diameter_m) returns the area, diameter, available power, margin and the PASS/FAIL stowage verdict dict.
6. Confirm the deterministic checks with the contract test scripts/test_ram_air_turbine_sizing.py.

Worked example

Reference installation: the emergency RAT must supply 5000 W at the fixed emergency descent speed of 100 m/s at ISA sea level with the design power coefficient 0.10.

• Swept area: A = 5000 / (0.5 * 1.225 * 100^3 * 0.10) = 5000 / 61250 = 0.081633 m2 (module output 0.081632653 m2).
• Disk diameter: D = sqrt(4 * 0.081633 / pi) = 0.322394 m, about 322.4 mm (module output 0.322394 m).
• Round-trip power: 0.5 * 1.225 * 100^3 * 0.081633 * 0.10 = 5000.00 W exact, so the margin is 0.00 W.
• Stowage verdict: diameter 0.322394 m against the 0.40 m bay limit gives PASS; against a 0.30 m limit the same rotor gives FAIL.
• Scaling sanity: doubling the airspeed to 200 m/s at the same area multiplies the available power by 2^3 = 8 to 40000 W.

Verification

• Confirm rat_swept_area(5000, 100) returns 0.081633 m2 within 1e-6 and disk_diameter gives 0.3224 m within 1e-4 (322.4 mm class rotor).
• Confirm the round trip: rat_available_power(rat_swept_area(P, V), V) equals P within 1e-6 for any positive power, and the disk identity A = pi * D^2 / 4 holds.
• Confirm the scaling law: doubling V at fixed area multiplies the available power by 8, and the required area scales as 1/V^3.
• Confirm the stowage verdict flips from PASS to FAIL as the limit drops below the 0.3224 m diameter (PASS at 0.40 m, FAIL at 0.30 m).
• Confirm every non-positive power, airspeed, density, coefficient, area and stowage limit raises ValueError, and a coefficient at or above the Betz bound 0.592593 (for example 0.60) is rejected.
• Confirm the summary dict keys are exactly area_m2, diameter_m, available_w, margin_w, stowage_verdict, and that repeated calls are deterministic.
• Run the contract test offline: python3 scripts/test_ram_air_turbine_sizing.py (29 tests, deterministic).

Related leaves

• vehicle-design/sizing/aircraft-electrical-load-analysis: supplies the required emergency power P_req that is the input here.
• vehicle-design/sizing/hydraulic-system-sizing: the hydraulic power side of the emergency installation architecture.
• vehicle-design/sizing/bleed-air-system-sizing: engine bleed pneumatic extraction, the unrelated alternative air power source.

Pitfalls

• Sizing on the emergency airspeed alone: the swept area is extremely sensitive to the speed (A goes as 1/V^3), so a low anchor speed can demand a rotor that will not fit the bay; always run the stowage verdict against the installation limit.
• Confusing the round-trip power with the installed capability: the wind-power relation returns the power at the sized condition, not the rated machine output; the margin is available minus required at that condition.
• Feeding a power coefficient at or above the Betz bound: Cp = 0.60 is physically impossible for a wind-driven rotor and the module rejects it, so keep the design value at or below the overall 0.10 default.
• Deriving the load here: P_req comes from the electrical load analysis leaf; this leaf only converts that requirement into rotor geometry.
• Treating the RAT as a machine model: embedded generator and control behavior are empirical and out of scope; the power coefficient is the fixed design abstraction for those losses.

Behavior contract (gate 3)

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

python3 scripts/test_ram_air_turbine_sizing.py

The test covers the 5000 W worked example (area 0.081633 m2 within 1e-6, diameter 0.3224 m within 1e-4, round-trip power 5000.00 W within 1e-6), stowage verdict PASS at 0.40 m and FAIL at 0.30 m, V^3 and linear power scaling, the area and diameter round-trip identities, module defaults (ISA sea level density, 0.10 coefficient, Betz 16/27), summary dict structure and determinism, and ValueError rejection of non-positive power, airspeed, density, coefficient, area and stowage limit plus coefficients at or above the Betz bound.

Compliance

• Standards referenced, not reproduced: FAR 25.1351 is cited for the emergency electrical and essential power context (reference-only per standards-map.yaml); the wind-power sizing relations above are standard engineering methodology, summary-only.
• compliance: STANDARDS-REF, gated: false.