Rotorcraft Autorotative Descent

Rotorcraft Autorotative Descent (flight-mechanics/performance/rotorcraft-autorotative-descent)

Use when you must estimate the power-off autorotative descent performance of a single-rotor helicopter after engine failure: the descent rate that the airframe reaches in a steady autorotative glide, before any flare. This leaf pairs with flight-mechanics/performance/rotorcraft-hover-performance (which owns the hover power terms at zero rate), with flight-mechanics/performance/rotorcraft-vertical-climb-performance (the climb-only momentum leaf that does not descend) and with flight-mechanics/performance/rotorcraft-forward-flight-performance (the speed-dependent level-flight power split whose minimum feeds this energy method). It implements the empirical energy method in pure Python, stdlib only.

Context: the wave-31 review declined a momentum-theory autorotation model because momentum theory is inapplicable in the vertical-descent vortex-ring and windmill transition range (Leishman receipts). This leaf is the empirical reopen: it never evaluates momentum theory in descent and uses the energy balance W*V = P_min together with the flight-test-validated empirical correlation of NASA TM 78452 (Talbot and Schroers 1978, "A Simple Method for Estimating Minimum Autorotative Descent Rate of Single Rotor Helicopters", NTRS 19780012170, public domain). The correlation is a least-squares fit through measured minimum-descent-rate data of multiple single-rotor helicopters and is deterministic with pinned coefficients.

Domain quick reference

All quantities are SI (N, W, m/s). Module constants are the public-domain NASA values: M0_TALBOT_MPS = 2.30 m/s (intercept), M1_TALBOT = 0.66 (slope), G0 = 9.80665 m/s^2.

• Energy method (the paper's simple method): V = P_min / W follows from the steady-descent energy balance W*V = P_min, where P_min is the minimum level-flight power and W the weight. The paper documents that this overestimates the measured minimum descent rate.
• Empirical correlation (NASA TM 78452 eq. 14): V_est = M1_TALBOT * OmegaR * (C_PMIN / C_T) + M0_TALBOT_MPS, with OmegaR the rotor tip speed and C_PMIN / C_T the minimum power coefficient over thrust coefficient ratio.
• Power-based entry: in level flight T = W, so OmegaR * C_PMIN / C_T = P_min / T = P_min / W and V_est = M1_TALBOT * P_min / W + M0_TALBOT_MPS. The tip speed cancels in level flight but is still validated as an input for dimensional consistency.
• Unit conversion: ft/min = m/s * 60.0 / 0.3048, so 8.233 m/s converts to about 1621 ft/min, inside the published single-rotor measured minimum-descent band of roughly 1500-2000 ft/min.
• Validity: steady minimum-rate autorotative glide of a single main rotor helicopter; not the vortex-ring vertical-descent regime.
• Scope: this leaf never evaluates momentum theory in descent, does not model vortex-ring state or vertical zero-airspeed descent, and does not cover fixed-wing spin autorotation (the stalled-wing autorotative band is owned by flight-mechanics/stability-control/spin-recovery).

Workflow

1. Fix the operating point: weight W (N), minimum level-flight power P_min (W), rotor tip speed OmegaR (m/s). P_min comes from the level flight power curve, e.g. the output of the rotorcraft-forward-flight-performance leaf.
2. Get the energy-balance sink rate with energy_method_sink_rate(P_min, W) = P_min / W. Treat this as the conservative upper estimate.
3. Get the empirical estimate with talbot_min_descent_rate_from_power(P_min, W, OmegaR); the power entry is valid because T = W in level flight.
4. When power coefficients are on hand, cross-check with talbot_min_descent_rate_mps(cp_min, c_t, OmegaR); both entries must agree to 1e-9.
5. Bundle the assessment with autorotative_descent_assessment(W, P_min, OmegaR): it returns energy_method_sink_rate_mps, talbot_min_descent_rate_mps, talbot_min_descent_rate_ft_per_min, power_to_weight_ratio_mps and the fixed validity_note.
6. Confirm the deterministic checks with the contract test scripts/test_rotorcraft_autorotative_descent.py.

Worked example

UH-1H-scale helicopter: W = 42270 N, P_min = 380000 W, rotor tip speed OmegaR = 208 m/s. Real module outputs:

• energy_method_sink_rate(380000, 42270) = 8.9898 m/s, within the 8.5-9.5 m/s bound and equal to the power-to-weight ratio 380000/42270 m/s.
• talbot_min_descent_rate_from_power(380000, 42270, 208) = 8.2333 m/s, within the 7.5-9.0 m/s bound.
• talbot_min_descent_rate_ft_per_min = 1620.7 ft/min, about 1621 ft/min (m/s * 60 / 0.3048).
• Cross-entry consistency: the power entry and the coefficient entry talbot_min_descent_rate_mps(cp_min, 1.0, 208) with cp_min = P_min / (W * OmegaR) agree to 1.8e-15, below the 1e-9 threshold.
• The empirical estimate 8.2333 m/s sits below the energy-balance estimate 8.9898 m/s, as expected: the correlation intercept of 2.30 m/s scales the pure energy balance down to the measured minimum-descent band.

Verification

• Confirm energy_method_sink_rate(380000, 42270) returns 8.9898 m/s and that talbot_min_descent_rate_from_power(380000, 42270, 208) returns 8.2333 m/s, with the empirical value below the energy value for the worked case.
• Confirm the ft/min conversion identity: talbot_min_descent_rate_ft_per_min equals talbot_min_descent_rate_mps * 60.0 / 0.3048, and 8.233 m/s converts to about 1621 ft/min.
• Confirm the cross-entry identity: talbot_min_descent_rate_from_power equals talbot_min_descent_rate_mps with cp_min / c_t = P_min / (W * OmegaR) to 1e-9.
• Confirm every non-positive weight, power and tip speed, c_t <= 0 and negative cp_min raises ValueError, and that the assessment dictionary contains exactly the five documented keys with the fixed validity_note.
• Confirm determinism: identical inputs give identical floats run to run (no RNG).
• Run the contract test offline: python3 scripts/test_rotorcraft_autorotative_descent.py (34 tests, deterministic).

Pitfalls

• Quoting the energy-balance sink rate as the predicted descent rate: P_min/W overestimates the measured minimum descent rate by design (the paper documents it), so treat energy_method_sink_rate as the conservative upper bound and the Talbot correlation as the estimate.
• Applying the correlation outside its validity: it is fit to steady minimum-rate autorotative glide of single main-rotor helicopters and is not valid in the vortex-ring vertical-descent regime or for fixed-wing autorotation (spin recovery owns that band).
• Using the power entry without level flight: the power-based entry relies on T = W in level flight, so P_min must be a level-flight minimum power; a power from another flight state breaks the OmegaR*C_PMIN/C_T = P_min/W identity.
• Assuming the coefficient entry needs c_t = 1.0 only: the two entries agree to 1e-9 only when cp_min/c_t = P_min/(W*OmegaR); passing an arbitrary cp_min with c_t = 1.0 silently violates the cross-entry identity.
• Unit slips: all inputs are SI (W in N, P_min in W, OmegaR in m/s) and the ft/min output is m/s * 60 / 0.3048; mixing knots or kg-force shifts the sink rate off the measured 1500-2000 ft/min band.
• Non-positive weight, power or tip speed (and c_t <= 0, negative cp_min) raise ValueError by contract.

Related leaves

• flight-mechanics/performance/rotorcraft-vertical-climb-performance: the climb-only momentum leaf that does not descend.
• flight-mechanics/performance/rotorcraft-hover-performance: the hover state at zero descent rate.
• flight-mechanics/performance/rotorcraft-forward-flight-performance: the level-flight power split that supplies P_min.
• flight-mechanics/stability-control/spin-recovery: fixed-wing autorotation is a different regime.
• flight-test-operations/performance/rotorcraft-performance-flight-test: flight-test reduction of rotorcraft performance, not to be confused with this analytic estimate.

Behavior contract (gate 3)

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

python3 scripts/test_rotorcraft_autorotative_descent.py

The test covers the UH-1H-scale worked example (energy sink rate within 8.5-9.5 m/s, empirical rate within 7.5-9.0 m/s and about 1621 ft/min), the empirical-below-energy ordering for the worked case, the cross-entry consistency of the power-based and coefficient-based correlation entries to 1e-9, the exact assessment dictionary keys and fixed validity note, the pinned module constants (M0 = 2.30 m/s, M1 = 0.66, G0 = 9.80665), determinism run to run, and ValueError rejection of non-positive weight, power, tip speed, c_t and negative cp_min.

Compliance

• Standards referenced, not reproduced: FAR-29 is named reference-only per standards-map.yaml. NASA TM 78452 (public domain, NTRS 19780012170) is named in the body with its energy method and correlation coefficients; the relations above are summary-only standard engineering methodology, not reproduced text.
• compliance: STANDARDS-REF, gated: false.