High Angle Of Attack Testing

High Angle of Attack Testing (flight-test-operations/envelope/high-angle-of-attack-testing)

Use when the task is the high angle of attack (HiAOA) flight test: the post-stall and deep stall test envelope, angle of attack sensor position error calibration, stall warning margin assessment, and departure and spin entry resistance judgment. This leaf covers the envelope beyond the stall boundary and the instrumentation calibration that makes the AoA data meaningful; the stall boundary test matrix, warning onset verification, and recovery demonstration at the stall are the stall-characteristics-testing leaf.

Domain quick reference

• HiAOA envelope: the angle of attack region from the stall angle through the post-stall range up to the maximum tested AoA, including the deep stall region where the aircraft can settle into a stable stalled attitude with the nose above the horizon. Each configuration and center of gravity condition is probed at the warning angle, the stall angle, post-stall steps, and the deep stall point.
• AoA position error: the local flow direction at the sensor differs from the free stream because of fuselage upwash and downwash and the sensor mounting position, so the indicated AoA carries a bias and a scale error. The correction relates indicated AoA to a reference AoA measured by an independent method.
• Reference methods: a tower fly-by gives a reference by flying at constant speed past a tower-mounted sighting baseline, and a trailing cone trailed behind the aircraft gives reference static pressure from which the flow angle is derived; both are used to calibrate the installed AoA sensor over the test range.
• Calibration model: corrected = bias + scale * indicated, fitted by least squares over the calibration points, with the residual spread judging the quality of the fit before the correction is applied to the flight data.
• Stall warning margin (FAR 25.201 / CS-25.201 context, paraphrased): the stall demonstration must show the stall break and the warning onset, and the warning must be distinct and must begin ahead of the stall with margin; in AoA terms the margin is the difference between the stall angle and the warning onset angle, compared with the required margin of the test program.
• Departure resistance (FAR 25.203 / CS-25.203 context, paraphrased): at and beyond the stall the aircraft must show no excessive pitch-up and no uncontrollable rolling or yawing; the departure resistance index scores the observed roll-off, yaw divergence, and pitch-up against reference levels.
• Spin entry resistance: with pro-spin controls applied at the high AoA points, the aircraft must resist entering autorotation; the observed roll-off and yaw rate against the allowed limits, plus the recovery altitude loss and turn count, give the verdict.

Workflow

1. Build the HiAOA test matrix with build_test_matrix(configs, cg_conditions, warning_aoa_deg, stall_aoa_deg, max_aoa_deg, post_stall_step_deg): the matrix covers the warning onset, the stall angle, the post-stall progression, and the deep stall point for every configuration and c.g. condition.
2. Calibrate the AoA sensor with aoa_least_squares_calibration(indicated_aoas, reference_aoas) from the tower fly-by or trailing cone data, then correct every flight AoA with apply_aoa_correction(indicated_aoa_deg, calibration).
3. Compute the observed stall warning margin with stall_margin_deg (stall_aoa_deg, warning_aoa_deg) and judge it with stall_margin_verdict(stall_aoa_deg, warning_aoa_deg, required_margin_deg).
4. Score the departure behavior with departure_resistance_index(roll_off_deg, yaw_divergence_deg, pitch_up_deg) at each post-stall point.
5. Judge spin entry resistance with spin_entry_resistance_verdict(roll_off_deg, yaw_rate_deg_s, max_roll_off_deg, max_yaw_rate_deg_s) and the recovery with spin_recovery_verdict(altitude_loss_m, altitude_loss_limit_m, turns_to_recover, turns_limit).

AoA position error calibration model

The installed sensor reports an indicated angle alpha_i that differs from the true (reference) angle alpha_r by a position error that is well modeled over the test range as

alpha_r ~= bias + scale * alpha_i

with scale near 1 and bias in degrees. The least squares fit minimizes the sum of squared residuals r_k = alpha_r,k - (bias + scale * alpha_i,k) over the calibration points, giving

scale = cov(alpha_i, alpha_r) / var(alpha_i)
bias  = mean(alpha_r) - scale * mean(alpha_i)

The residual root mean square and the maximum absolute residual (aoa_least_squares_calibration outputs) show how well the linear model holds; a large residual at the ends of the range warns that the sensor position error is nonlinear there and the correction should not be extrapolated beyond the calibrated AoA range.

Worked example

Tower fly-by calibration over five points: indicated [6.0, 8.0, 10.0, 12.0, 14.0] deg versus reference [8.2, 10.1, 12.0, 13.9, 15.8] deg. The fit returns scale 0.95 and bias 2.5 deg, so corrected = 2.5 + 0.95

• indicated: 10.0 deg indicated corrects to 12.0 deg, matching the reference. Residuals are near zero over the range, so the correction is accepted.

Stall margin: with stall at 15.5 deg and warning onset at 12.0 deg the margin is 3.5 deg; against a required margin of 2.0 deg the verdict is ok. A warning onset at 14.0 deg would leave only 1.5 deg and would fail the same requirement.

Departure resistance: roll-off 4 deg, yaw divergence 2 deg, pitch-up 1 deg give penalty 0.5 * 4/20 + 0.3 * 2/10 + 0.2 * 1/10 = 0.18, index 0.82, rated high. Roll-off 20 deg with yaw divergence 10 deg and pitch-up 10 deg give index 0.0, rated low.

Pitfalls

• Extrapolating the AoA correction beyond the calibrated range: the position error is linear only over the calibration points, so the deep stall points must stay inside the calibrated AoA range or the correction is carried outside its validity.
• Calibrating with a single reference point: the least squares fit needs at least two points with varying indicated AoA, otherwise neither bias nor scale can be separated.
• Confusing the stall angle with the stall warning onset angle: the warning margin is the difference between the two, and a warning that fires at or after the stall break carries no margin at all.
• Judging departure resistance from one axis only: roll-off alone misses yaw divergence and pitch-up, and the index combines all three motions.
• Testing the deep stall point without pro-spin control checks: the spin entry resistance verdict only means something when the aircraft is probed with pro-spin controls at the high AoA points.
• Using uncorrected AoA for the stall margin: the margin verdict is only valid on corrected AoA, otherwise a sensor bias of several degrees hides or fakes the margin.
• Passing negative angles, empty configuration lists, or non-finite data to the logic functions; the module raises ValueError instead of returning a meaningless matrix or verdict.

Behavior contract (gate 3)

The calibration fit, correction, stall margin, departure resistance, spin entry resistance, recovery, and test matrix logic is exercised by the gate 3 contract test: scripts/test_high_angle_of_attack_testing.py against scripts/high_angle_of_attack_testing_logic.py (stdlib unittest, offline). Run:

python3 scripts/test_high_angle_of_attack_testing.py

Compliance

• Standards referenced, not reproduced: FAR-25 is US government work (public domain) and CS-25 is a free EASA download; the HiAOA envelope practice, AoA calibration methods, stall margin, and departure resistance checks are common flight test methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.