Rotorcraft Forward Flight Performance Test

Rotorcraft Forward-Flight Performance Test (flight-test-operations/performance/rotorcraft-forward-flight-performance-test)

Use when the task is reducing a rotorcraft level-flight (forward flight) performance flight test from MEASURED data: measured main rotor torque and rotor speed samples converted to shaft power across a level-flight speed sweep, the measured power-required polar corrected to a reference weight and standard-day density with the induced and profile power split, the corrected polar fitted, and the characteristic speeds read off the fitted curve. Every input is a flight test measurement: torque, rotor speed, airspeed, gross weight, density. This leaf is the measured-data reduction counterpart to flight-mechanics/performance/rotorcraft-forward-flight-performance, which owns the analytic prediction of the forward-flight power-required curve from rotor geometry; it pairs the same way as the hover measured reduction pairs with the analytic hover model. It does NOT reduce hover or climb measured data (rotorcraft-performance- flight-test owns that) and does NOT touch fixed-wing cruise fuel flow.

Domain quick reference

• Shaft power from the torque sample: shaft_power: P = Q * omega for measured main rotor torque (Nm) at measured rotor speed (rad/s). Worked: 12,222 Nm at 27 rad/s gives 329,994 W (about 330 kW). A zero torque at positive rotor speed is a valid measured point (0 W).
• Density correction to standard day: density_correct_power: P_std = P * RHO_STD / rho_test, with RHO_STD = 1.225 kg/m3. Power required scales with 1/rho at fixed speed and weight. Worked: 330,000 W at rho 1.10 corrects to 367,500 W.
• Weight correction with the induced and profile split: weight_correct_power: P_ref = P * [ f_i * (W_ref/W_test)^1.5 + (1 - f_i) * (W_ref/W_test) ], f_i the induced fraction of the total power. The induced share scales with (W_ref/W_test)^1.5 (induced velocity ~ sqrt(W), induced power ~ W * v_i); the profile and parasite share scales linearly with weight (drag ~ weight at the same speed). At the reference weight the correction returns the measured power unchanged.
• Reference-condition chain: correct_to_reference applies the density correction first, then the weight correction at the standard-day power. At standard day AND reference weight the chain is identity.
• Polar fit: fit_power_polar fits P(V) = aV^2 + bV + c by quadratic least squares (normal equations, stdlib) over the sweep points; the hover anchor at zero airspeed is a valid sweep member. Fit is rejected when degenerate (a <= 0 on non-constant powers).
• Best-endurance speed: best_endurance_speed: V_ben = -b / (2*a), the polar minimum (minimum power-required point). Flat polar (a == 0) has no interior minimum: returns None.
• Best-range speed: best_range_speed: V_br = sqrt(c / a) from the tangent condition dP/dV = P/V, which reduces to a*V^2 = c. Returns None when c == 0.
• Maximum level-flight speed: max_level_speed: largest real root of aV^2 + bV + c = P_avail, D = b^2 - 4a(c - P_avail); Vh = (-b + sqrt(D)) / (2*a). None when D < 0 (available power below the polar minimum, no level flight). The + root is the high-speed intersection.
• Speed ordering: validate_speed_order checks V_ben < V_br < Vh (order only, None-safe). reduce_level_flight_sweep returns the computed Vh even beyond the measured band and sets vh_beyond_measured True so the report marks it an extrapolation.
• Sweeps run 4-40 points; arrays must be equal length.
• Units are SI throughout: Nm, rad/s, W, N, kg/m3, m/s.
• FAR 29 frames the airworthiness context (reference only); the relations above are standard rotorcraft flight-test reduction methodology, summary-only, and work only from measured data.

Workflow

1. Gather the measured test day: torque samples at the recorded rotor speed across the level-flight speed sweep, test gross weight, and the density from the test pressure altitude and outside air temperature; take the reference weight, the standard day and the maximum continuous available power from the flight manual.
2. Convert every torque sample to shaft power with shaft_power.
3. Correct each shaft power to the reference weight and standard day with correct_to_reference and the induced fraction split (weight_correct_power, density_correct_power).
4. Fit the corrected polar with fit_power_polar; keep the hover anchor (zero airspeed) in the sweep when it was measured.
5. Read the characteristic speeds off the fitted curve: best_endurance_speed, best_range_speed, and max_level_speed run against the maximum continuous available power.
6. Check the speed ordering with validate_speed_order (V_ben < V_br < Vh) and check vh_beyond_measured before quoting Vh in the report.
7. Run the whole sweep end to end with reduce_level_flight_sweep for the reduction dict, or run the convenience chain in place of steps 2-6.
8. Confirm the deterministic checks with the contract test scripts/test_rotorcraft_forward_flight_performance_test.py.

Worked example

Measured level-flight sweep of a light single-rotor helicopter at standard day (rho 1.225 kg/m3) at the reference weight (21,000 N), so the corrections are identity and the raw shaft powers carry the example. Hover torque 12.222 kN*m at 27.0 rad/s, then torque samples across V = [0, 12, 24, 36, 48, 60, 72] m/s at omega 27.0 rad/s (torque per point = power / 27.0). Running the module on the sweep:

• Shaft powers: [330000, 271400, 251800, 259400, 304200, 376000, 487000] W, each within +-2000 W of the listed value.
• Corrections: identity at standard day and reference weight, so the corrected powers equal the shaft powers.
• Fit: P(V) = 114.04V^2 - 6030.36V + 329300.0 (a in 100-130 W/(m/s)^2, b in -7000 to -5000 W/(m/s), c in 320000-340000 W).
• Best-endurance speed: 26.44 m/s (bound 23-30 m/s), polar minimum power 249.6 kW (about 250 kW).
• Best-range speed: 53.74 m/s (bound 48-58 m/s), above the best-endurance speed and inside the measured band; the tangent identity a*V^2 = c holds.
• Maximum level-flight speed at 470 kW maximum continuous power: 70.40 m/s (bound 66-74 m/s, about 137 kt), inside the measured band (top 72 m/s); Vh/V_br about 1.31 and speed_order.order_ok True, so no extrapolation flag (vh_beyond_measured False).
• Scale invariance: multiplying every measured power by a constant leaves both characteristic speeds unchanged (coefficients scale, ratios do not). At 560 kW available the computed Vh reaches 78.6 m/s, past the 72 m/s top of the band, and the flag vh_beyond_measured turns True.

Pitfalls

• Extrapolating Vh beyond the measured band: at 560 kW available the computed Vh reaches 78.6 m/s past the 72 m/s top of the band and the flag vh_beyond_measured turns True - the result is flagged, not silently quoted as a measured speed.
• Comparing corrected and raw powers across conditions: the corrections are identity only at the standard day and reference weight, so density_correct_power(330000, 1.10) gives about 367,500 W and every point must be reduced to the reference basis before fitting.
• Reading scaled coefficients as physical: multiplying every measured power by a constant scales the coefficients but leaves the best-endurance and best-range speeds unchanged to 1e-9, so the speeds, not the raw coefficients, carry the physical result.
• Fitting the polar from too few or too many points: fewer than 4 or more than 40 sweep points raise ValueError, as do torque < 0, omega <= 0, rho_test <= 0, power < 0, weight <= 0, induced fraction outside [0, 1], and negative airspeeds.
• Trusting a degenerate fit: a downward-curved polar (a <= 0 on non-constant powers) raises ValueError instead of reporting a minimum that does not exist.
• Mixing up the characteristic speeds: best-endurance speed is the polar vertex -b/(2a) (26.44 m/s), best-range speed satisfies the tangent condition a*V^2 = c (53.74 m/s), and Vh sits above both at the available-power root (70.40 m/s at 470 kW).

Verification

• Confirm shaft_power(12222, 27) returns about 330,000 W and that the sweep torques recover the listed powers within +-2000 W.
• Confirm the corrections are identity at standard day and reference weight, and that density_correct_power(330000, 1.10) returns about 367,500 W.
• Confirm the fitted coefficients sit in the magnitude bounds (a in 100-130, b in -7000 to -5000, c in 320000-340000) and reproduce the worked-example polar.
• Confirm best_endurance_speed equals -b/(2a) at the vertex, that best_range_speed satisfies a*V^2 = c with the tangent condition dP/dV = P/V to 1e-6, and that max_level_speed at an available power equal to the polar minimum returns the vertex speed (single root).
• Confirm every non-physical input raises ValueError: torque < 0, omega <= 0, rho_test <= 0, power < 0, weight <= 0, induced fraction outside [0, 1], fewer than 4 sweep points, more than 40 sweep points, array length mismatch, negative airspeed, and a degenerate downward-curved fit (a <= 0 on non-constant powers).
• Confirm scale invariance: multiplying every measured power by 2.0 leaves the best-endurance and best-range speeds unchanged to 1e-9.
• Confirm determinism: no RNG anywhere, run-to-run identical floats.
• Run the contract test offline: python3 scripts/test_rotorcraft_forward_flight_performance_test.py (27 tests, deterministic, passes in under 20 s).

Related leaves

• flight-mechanics/performance/rotorcraft-forward-flight-performance: the analysis sibling (momentum-theory prediction of the forward- flight power-required curve from geometry and weight); pair its predicted polar with the measured reduction here.
• flight-test-operations/performance/rotorcraft-performance-flight- test: the hover and vertical climb measured reduction sibling (torque-to-power, measured figure of merit, hover ceiling).
• flight-test-operations/performance/cruise-performance-flight-test: the fixed-wing fuel-flow reduction sibling (its quadratic range curve versus Mach, not rotorcraft polar data).
• flight-test-operations/performance/climb-performance-flight-test: the fixed-wing climb reduction sibling, sharing the weight and density correction conventions used here.

Behavior contract (gate 3)

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

python3 scripts/test_rotorcraft_forward_flight_performance_test.py

The test covers the worked-example anchors (shaft powers within +-2000 W of the listed values, identity corrections, fit coefficients in the spec magnitude bounds, best-endurance 26.44 m/s, best-range 53.74 m/s with the tangent identity, maximum level-flight speed 70.40 m/s at 470 kW), the closed-form identities (standard-day density identity, reference-weight identity, density scaling, induced-fraction endpoints 0 and 1, polar-minimum single root), the ValueError rejection of every non-physical input, scale invariance of the characteristic speeds, the vh_beyond_measured extrapolation flag, the exact reduction-dict keys, determinism, and the module constants.

Compliance

• FAR 29 frames the airworthiness context; it is referenced, not reproduced (no verbatim standard text appears here). The relations above are standard rotorcraft flight-test reduction methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.