Rotorcraft Height Velocity Diagram Test

Rotorcraft Height-Velocity Diagram Test (flight-test-operations/performance/rotorcraft-height-velocity-diagram-test)

Use when you must reduce the FAR 29 rotorcraft height-velocity (dead-man-curve) demonstration flight test from the hover and low-speed engine-failure runs (requirement named and framed only). Each demonstration starts at 20 to 200 ft AGL at 0 to 40 KTAS, the engine fails at hover or low speed, and the rotorcraft must be recognized, autorotation established, and a flare and landing completed before the touchdown sink exceeds the safe limit. This leaf reads measured marks and baro/radar altitude traces only: the recognition delay, the time to establish autorotation, the height lost before the flare and the recovery altitude the flare consumes, the touchdown verdict per demonstration, the reduced height-velocity boundary per speed, the measured avoid-region map over the (height, speed) grid and the per-speed clearance verdict against the predicted height-velocity diagram. The steady autorotative sink rates and the predicted boundary table are quoted inputs from the flight-mechanics autorotative-descent analytic leaf, never re-derived. It pairs with flight-test-operations/performance/ rotorcraft-autorotation-flight-test, which owns the steady-descent demonstration side (least-squares sink-rate regression over the steady window, rotor-RPM checks, recovery to re-established level flight); a passing high-start demonstration of this leaf keeps any brief steady segment as flown and stops its reduction at the flare-initiation mark.

Domain quick reference

• Recognition delay: tau_r = t_reaction - t_failure, the trace time of the first control input minus the trace time of the engine-failure event mark. The worked record shows 0.5 to 1.0 s across 0 to 40 KTAS.
• Recognition-phase height loss with allowance: h_rec + v_sink_end * allowance, the measured height lost over the recognition window plus the additional sink during the declared 1.0 s reaction time allowance. Module constants: SAFE_TOUCHDOWN_FPM = 600.0 ft/min (10 ft/s) and REACTION_ALLOWANCE_S = 1.0 s.
• Establishment time: t_estab = t_flare - t_reaction, from the first control input to the flare-initiation mark. The flare duration is the contact time minus the flare mark.
• Height-loss split: h0 = h_lost_to_flare + h_recovery, the height lost from the starting height to the flare-initiation mark plus the flare recovery altitude above the touchdown altitude (0 ft for a touchdown); the split identity holds on every marginal passing demonstration.
• Touchdown verdict: PASS when the measured touchdown sink rate is at or below the declared 600 ft/min limit, inclusive at the limit.
• Boundary reduction at one speed: the linear crossing of the touchdown-sink-versus-starting-height line through the bracketing pair (highest FAILING starting height, lowest PASSING starting height) at the sink limit: h_b = h_fail + (h_pass - h_fail) * (limit - s_fail) / (s_pass - s_fail). With the reaction allowance the published boundary rises by v_sink_end * allowance, 6.0 ft in the worked record.
• Avoid-region map: one cell per (height AGL, speed KTAS) grid point, AVOID strictly below the reduced boundary at that speed (inside the dead-man-curve region), SAFE at or above it.
• Clearance: margin = predicted - measured, PASS when the measured avoid region does not extend above the predicted height-velocity diagram (margin >= 0, inclusive).
• Units are ft AGL, KTAS, seconds and ft/min throughout; the reduction is deterministic stdlib arithmetic on measured marks and traces, never a stochastic model.

Workflow

1. Fix the demonstration record: the speed KTAS, the starting height in ft AGL, and the baro/radar altitude-loss-versus-time trace from the engine-failure event mark to the touchdown with the first control input mark and the flare-initiation mark.
2. Measure the engine-failure recognition delay with recognition_delay(t_reaction_s, t_failure_s): the first-control-input trace time minus the engine-failure mark time.
3. Measure the establishment and flare times: the time to establish autorotation and set up the flare with time_to_establish_autorotation(t_flare_s, t_reaction_s), and the flare duration as the touchdown time minus the flare mark.
4. Split the measured height loss with height_lost_to_flare(h_start_ft, h_flare_ft) (the recognition and establishment losses together, read off the trace) and flare_recovery_altitude(h_flare_ft, h_contact_ft): on a marginal pass the split sums to the starting height.
5. Give the touchdown verdict of the demonstration with touchdown_verdict(touchdown_sink_fpm): PASS at or under 600.0 ft/min, inclusive.
6. Apply the declared reaction time allowance to the recognition-phase height loss with recognition_loss_with_allowance(h_rec_measured_ft, sink_end_recognition_fps): the measured loss plus the sink during the 1.0 s allowance, the read used for the published boundary.
7. Interpolate the height-velocity boundary height at each speed with interpolate_boundary_height(fail_h0_ft, pass_h0_ft, fail_sink_fpm, pass_sink_fpm): the linear crossing through the highest FAILING and lowest PASSING demonstration pair at the sink limit, then apply step 6 for the boundary with the reaction allowance.
8. Build the measured avoid-region map over the (height, speed) grid with build_avoid_map(heights_ft, speeds_kt, boundary_ft): AVOID strictly below the reduced boundary at each speed, SAFE at or above it.
9. Judge the clearance against the predicted height-velocity diagram with clearance_verdict(measured_boundary_ft, predicted_boundary_ft) at each speed: PASS when the measured avoid region does not extend above the predicted boundary (margin >= 0), and report the margins and verdicts that gate the height-velocity demonstration.
10. Confirm the deterministic checks with the contract test scripts/test_rotorcraft_height_velocity_diagram_test.py.

Worked example

Representative single-rotor rotorcraft height-velocity demonstration record, speeds 0, 10, 20, 30, 40 KTAS over the 20 to 200 ft AGL sweep (grid 20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, 200 ft). Per-speed measured parameters: recognition delay 0.6 to 1.0 s, recognition-window end sink 6.0 ft/s, steady autorotative sink 33.0 ft/s easing to 28.0 ft/s across the speeds (quoted from the flight-mechanics autorotative-descent sink model), establishment times 2.2 to 1.7 s, declared minimum flare altitudes 28.0 down to 14.0 ft.

• Hover column (0 KTAS) over the sweep: from 20 ft contact at 1.901 s at 1318.3 ft/min FAIL; 30 ft 2.310 s 1619.1 FAIL; 40 ft 2.654 s 1872.2 FAIL; 50 ft flare at 5.3 ft, 2.968 s 1801.8 FAIL; 60 ft flare at 15.3 ft, 3.342 s 1405.3 FAIL; 70 ft flare at 25.3 ft, 3.877 s 838.6 FAIL; 80 ft flare at 30.1 ft, 4.542 s 300.0 PASS; 90 ft and above PASS. The verdict flips between 70 ft (FAIL) and 80 ft (PASS).
• Passing 80 ft hover demo reduced marks: recognition delay 0.60 s, time to establish autorotation 2.357 s (the flare mark sits about 0.16 s after establishment, past the brief unreduced steady segment), contact 4.542 s, flare duration 1.585 s; the time identity 0.60 + 2.36 + 1.585 = 4.542 s holds.
• Per-speed boundary from the bracketing pairs (highest FAIL height and sink, lowest PASS height and sink, reduced boundary, boundary with the 1.0 s allowance): 0 KTAS 70/838.6 and 80/300.0 to 74.430 ft (80.430 with allowance); 10 KTAS 80/751.7 and 90/300.0 to 83.358 (89.358); 20 KTAS 70/1151.4 and 80/502.7 to 78.500 (84.500); 30 KTAS 60/829.0 and 70/300.0 to 64.329 (70.329); 40 KTAS 40/1182.3 and 50/300.0 to 46.600 (52.600). The reduced dead-man-curve boundary rises from 74.430 ft at hover to the knee at 83.358 ft near 10 KTAS and falls to 46.600 ft at 40 KTAS as recoverable translational energy grows.
• Marginal-pass split identity at every speed: 80 ft hover gives 49.877 + 30.123 = 80.0 ft; 10 KTAS at 90 ft 54.497 + 35.503 = 90.0 ft; 20 KTAS at 80 ft 48.000 + 32.000 = 80.0 ft; 30 KTAS at 70 ft 45.938 + 24.062 = 70.0 ft; 40 KTAS at 50 ft 34.465 + 15.535 = 50.0 ft; residual 0.00e+00 at every speed.
• Measured avoid-region map: 60 cells, 27 AVOID and 33 SAFE, per speed 6, 7, 6, 5, 3 AVOID cells below the 74.4, 83.4, 78.5, 64.3 and 46.6 ft boundaries: the avoid region tops out near the 10 KTAS knee and shrinks as speed adds recoverable energy.
• Clearance against the predicted height-velocity diagram (96.855, 104.055, 103.110, 92.428 and 80.522 ft, quoted input from the flight-mechanics sink model in the standard energy reduction): measured with allowance 80.430, 89.358, 84.500, 70.329 and 52.600 ft, margins 16.424, 14.697, 18.610, 22.098 and 27.922 ft, PASS at every speed: the demonstration data show a tighter dead-man-curve region than the conservative analytic prediction.

Verification

• Confirm recognition_delay(0.6, 0.0) = 0.6 s on the hover record and the mark-subtraction identity on any valid pair.
• Confirm recognition_loss_with_allowance(1.8, 6.0) = 7.8 ft with the default allowance and equals 1.8 ft with allowance_s = 0.
• Confirm time_to_establish_autorotation(2.957, 0.6) = 2.357 s on the marginal hover pass mark.
• Confirm the split identity on every marginal passing demonstration: height_lost_to_flare + flare_recovery_altitude equals the starting height to float noise, and the time identity recognition delay plus establishment time plus flare duration equals the failure-to-touchdown time.
• Confirm touchdown_verdict passes at 300.0 and exactly 600.0 ft/min and fails at 600.1 ft/min.
• Confirm interpolate_boundary_height(70.0, 80.0, 838.6, 300.0) = 74.430 ft lies strictly inside the bracket and rises exactly 6.0 ft with the reaction allowance, and the per-speed ordering 74.430 < 83.358 > 78.500 > 64.329 > 46.600 reproduces the dead-man-curve knee near 10 KTAS.
• Confirm build_avoid_map over the worked grid yields 60 cells with 27 AVOID and 33 SAFE and marks a cell AVOID exactly when the height is strictly below the reduced boundary at that speed.
• Confirm clearance_verdict passes all five worked speeds with the quoted margins and passes inclusively when predicted equals measured.
• Confirm every non-physical input raises ValueError across the nine functions (26 offending-input cases in the contract test), and that repeated calls are identical.
• Run the contract test offline: python3 scripts/test_rotorcraft_height_velocity_diagram_test.py (34 tests, deterministic).

Related leaves

• flight-test-operations/performance/rotorcraft-autorotation-flight-test: the steady-descent demonstration reduction (least-squares sink-rate regression over the steady window, rotor-RPM checks, altitude lost to a recovery ending in re-established level flight), the high-altitude complement fenced by regime and framing.
• flight-mechanics/performance/rotorcraft-autorotative-descent: the analytic power-off sink model whose steady sink rates and predicted height-velocity diagram enter this leaf as quoted inputs.
• flight-mechanics/performance/rotorcraft-vertical-climb-performance: hover-axis climb prediction, out of scope here (every record of this leaf descends to a touchdown).

Pitfalls

• Regressing the steady segment: a passing high-start demonstration carries a brief steady autorotation segment between establishment and the standard flare (about 0.16 s on the marginal hover pass). This leaf stops its reduction at the flare-initiation mark, keeps the segment as flown, and never fits it or runs rotor-RPM checks; those belong to the steady-descent demonstration leaf.
• Measuring the wrong height loss: the boundary identity requires the measured height loss plus the recovery altitude to equal the starting height on the marginal pass. Losses must be read from the baro/radar trace between the failure mark and the touchdown, never from the generator-side or analytic models.
• Applying the allowance twice: the published boundary already carries the 1.0 s reaction allowance (the measured boundary plus 6.0 ft in the worked record); judging clearance against the predicted diagram must compare like for like, the measured boundary with the allowance against the predicted boundary.
• Interpolating without a verdict flip: the boundary is only defined through a FAIL to PASS pair; if the highest failing demonstration sits at or under the limit or the lowest passing one above it, the height sweep must extend further, and the module raises ValueError rather than extrapolating.
• Treating the predicted diagram as measured data: the predicted height-velocity boundary is an input table from the analytic sink model, quoted not re-derived; this leaf only subtracts it for the clearance margin.
• Reproducing standard text: FAR 29 frames the height-velocity demonstration requirement by name only, no rule text is reproduced.

Behavior contract (gate 3)

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

python3 scripts/test_rotorcraft_height_velocity_diagram_test.py

The test covers the full reduction workflow of the SKILL.md: the recognition delay on the worked hover record and its mark-subtraction identity, the recognition-phase height loss with and without the reaction allowance, the establishment and flare times on the marginal hover pass mark, the height-loss split with the flare and recovery altitudes, the PASS or FAIL touchdown verdict at and around the inclusive 600 ft/min limit, the hover column reduction over the whole 20 to 200 ft sweep (verdict flip between 70 and 80 ft, touchdown sinks within 0.05 ft/min of the quoted values), the sampled-trace reduction and its time identity, the marginal-pass split and time identities at every speed, the per-speed height-velocity boundary reduction with the dead-man-curve knee near 10 KTAS and the exact 6.0 ft allowance rise, the measured avoid-region map counts and strict-below region rule over the 60-cell grid, the per-speed clearance margins and verdicts against the predicted height-velocity diagram, the 26-case ValueError suite across the nine functions, determinism of repeated calls, and the stdlib-only, no-randomness module discipline.

Compliance

• Standards referenced, not reproduced: FAR 29 is named and framed only (it frames the rotorcraft height-velocity demonstration requirement); the reduction relations above are standard flight-test engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.