Buffet Boundary Testing

Buffet Boundary Testing (flight-test-operations/envelope/buffet-boundary-testing)

Use when the task is the buffet boundary flight test of a transport airplane: scheduling pull-up and steady-turn points across a Mach sweep at constant altitude, detecting buffet onset from the vertical accelerometer RMS rise above threshold, converting the onset load factor to the boundary lift coefficient, and scoring the buffet margin at the cruise condition against a maneuver buffet target. This leaf implements the standard RMS-based onset detection and boundary fitting in pure Python, stdlib only. It pairs with flight-test-operations/envelope/ load-factor-envelope for the V-n context of the tested load factors, envelope-expansion for the expansion program that precedes the boundary probe, and flight-test-operations/flutter/flutter-testing for the other high speed clearance boundary. The RMS floor, RMS rise per g and the 0.02 g onset threshold below are documented typical engineering criteria, not regulation values; FAR/CS-25 are referenced for buffet and vibration context by name and paraphrase only.

Domain quick reference

• Test gross weight: W = m * g0, g0 = 9.80665 m/s2. Onset load factor n_onset is in g, so the lift at onset is n_onset * W.
• ISA state at altitude: T = 288.15 - 0.0065 * h below 11000 m (216.65 K above), P from the 5.25588 exponent law or the isothermal stratosphere pressure, rho = P / (287.05 * T).
• Dynamic pressure: q = 0.5 * rho * V^2 with V = M * a and a = sqrt(1.4 * 287.05 * T), the ISA speed of sound.
• Buffet-onset detection: with samples of (load factor n, vertical accelerometer RMS) sorted by n and non-decreasing in RMS, the onset load factor is the linear interpolation of the first crossing of the onset RMS threshold between two consecutive samples. The documented typical criteria are a 0.02 g onset RMS threshold, a 0.004 g RMS floor below onset, and a 0.4 g RMS rise per g of load factor above onset; they are engineering criteria, not regulation values.
• Boundary lift coefficient at one Mach: cl_buf = n_onset * W / (q * S) with S the reference wing area.
• Boundary line fit: cl_buf = slope * M + intercept by least squares (local 2x2 normal equations) over the tested Mach band.
• Buffet margin at cruise: n_buf_cruise = cl_buf(M_cr) * q(M_cr) * S / W, margin_n = n_buf_cruise - target_n; verdict "buffet-margin-pass" when margin_n >= 0.0, else "buffet-margin-fail".
• Units are SI throughout: kg, m, Pa, kg/m3, m/s; load factors in g.

Workflow

1. Fix the test point schedule: weight_kg, wing_area_m2, altitude_m, the mach_list sweep and the load factor samples per Mach (rms_table), plus the cruise_mach where the margin is scored.
2. Get the atmosphere with isa_state, then the dynamic pressure q per Mach with dynamic_pressure.
3. Detect the onset load factor per Mach with onset_detect on the measured (n, rms_g) samples; the detector interpolates the first RMS crossing of onset_rms_g.
4. Convert each onset load factor to the boundary lift coefficient with boundary_lift_coefficient.
5. Fit the boundary line over the Mach band with fit_boundary_line, passing cruise_mach so cl_at_cruise is evaluated; omit cruise_mach when only the line is wanted (cl_at_cruise is then None).
6. Score the cruise condition: n_buf_cruise from the line at cruise_mach, the margin with buffet_margin against the maneuver buffet target, and the verdict.
7. Run the whole point schedule through analyze with one inputs dict; it returns the per-Mach q, onset_n and cl_buf points, the fit, the cruise reduction and the verdict.
8. Confirm the deterministic checks with the contract test scripts/test_buffet_boundary_testing.py.

Worked example

Transport at W = 195000 kg (W = 1912297 N), S = 360.0 m2, altitude 10668 m, Mach sweep [0.74, 0.76, 0.78, 0.80, 0.82], pull-ups with load factor samples every 0.1 g from 1.0 to 2.2. The measured RMS fixture (built in the test, unknown to the module) follows rms(n) = 0.004 g below the model onset n_onset(M) = 1.90 - 1.50 * (M - 0.74), then rises 0.4 g per g above it.

• ISA at 10668 m: T = 218.81 K, P = 23842 Pa, rho = 0.3796 kg/m3, a = 296.53 m/s.
• q and detected onset and cl_buf per Mach (module values):

With the 0.02 g threshold the detector crosses at the model onset plus (0.02 - 0.004) / 0.4 = 0.04 g. On the 0.1 g sample grid the crossing is exact where a sample sits at the model onset (M 0.74 and 0.76 give 1.94 and 1.91) and interpolated just above it elsewhere (1.867 at M 0.78 and 1.844 at M 0.80, within one sample step of the idealized 1.88 and 1.85). Each cl_buf sits within 0.01 of the hand-checked spec anchors (1.1276, 1.0526, 0.9838, 0.9206, 0.8622).

• Least-squares fit over the band: slope = -3.337 per Mach, intercept = 3.590, so cl_buf(0.80) = 0.9203 on the line.
• Cruise reduction at M 0.80: q = 10681.3 Pa gives n_buf_cruise = 0.9203 * 10681.3 * 360 / 1912297 = 1.8506. Margin vs target 1.3: +0.55, verdict "buffet-margin-pass". Same data against target 2.0: margin -0.15, verdict "buffet-margin-fail".

Pitfalls

• Setting the RMS onset threshold too high: the detector crosses at the model onset plus (0.02 - 0.004) / 0.4 = 0.04 g with the 0.02 g threshold, so a larger threshold delays the reported buffet onset load factor.
• Extrapolating cl_buf outside the fitted band: the least-squares line (slope -3.337 per Mach, intercept 3.590) is only fitted over the swept band, and a cruise Mach outside that band raises ValueError instead of extrapolating.
• Mixing the unit systems in the cruise reduction: n_buf_cruise = cl_buf * q * S / W needs weight in N (1912297 N from 195000 kg), q in Pa, and S in m2; non-positive weight, area, target, or onset threshold raise ValueError.
• Reading the verdict without the target: the same cruise point passes against a 1.3 target (margin +0.55) and fails against 2.0 (margin -0.15), so the margin and verdict mean nothing without the stated target.
• Sampling the onset sweep too coarsely: on the 0.1 g grid the crossing is exact only where a sample sits at the model onset, and elsewhere it is interpolated up to one sample step away from the idealized crossing.
• Feeding non-physical tables: negative altitude, Mach outside (0.1, 2.0), empty or 1-sample RMS rows, non-monotonic RMS, no onset crossing, fewer than two fit points, and mismatched table lengths all raise ValueError.

Verification

• Confirm isa_state returns 288.15 K / 101325 Pa / 1.225 kg/m3 at sea level and 218.81 K / 23843 Pa / 0.3796 kg/m3 at 10668 m.
• Confirm dynamic_pressure equals 0.5 * rho * (M * a)^2 from the module ISA state at every Mach, and the q anchors 9139.5 to 11212.4 Pa within 10 Pa (the spec q column carries hand-rounding spread).
• Confirm onset_detect returns 1.94 at M 0.74 and stays within 0.02 of the idealized crossing at every Mach of the sweep.
• Confirm every cl_buf is within 0.01 of the anchors, n_buf_cruise is 1.85 within 0.01, the margins are +0.55 and -0.15 within 0.02, and the verdicts are "buffet-margin-pass" and "buffet-margin-fail".
• Confirm the round trip: onset load factor to cl_buf and back recovers the load factor at fixed q.
• Confirm ValueError rejection of non-physical inputs: negative altitude, Mach outside (0.1, 2.0), non-positive weight, area, target or onset threshold, empty or 1-sample RMS rows, non-monotonic RMS, no onset crossing, fewer than two fit points, mismatched table lengths, and a cruise Mach outside the fitted band.
• Run the contract test offline: python3 scripts/test_buffet_boundary_testing.py (38 tests, deterministic).

Related leaves

• flight-test-operations/envelope/load-factor-envelope: the V-n and gust context that frames the load factors the boundary probe reaches.
• flight-test-operations/envelope/envelope-expansion: the expansion program and step sizing that grow the envelope toward the tested boundary.
• flight-test-operations/envelope/stall-characteristics-testing: stall behavior and entry techniques at the low speed end, outside this leaf's claim.
• flight-test-operations/flutter/flutter-testing: the flutter clearance boundary, the other high speed limit checked alongside the buffet boundary.

Behavior contract (gate 3)

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

python3 scripts/test_buffet_boundary_testing.py

The test builds the measured RMS fixture from the spec onset model n_onset(M) = 1.90 - 1.50 * (M - 0.74) and covers the ISA state anchors, dynamic pressure identity and anchors, exact onset detection (1.94 at M 0.74 and the sweep), boundary lift coefficients within 0.01 of the anchors, the negative-slope boundary line fit with the cruise value, the buffet margin pass and fail cases and their verdict strings, the lift coefficient round trip, and ValueError rejection of every non-physical input including the extrapolation guard.

Compliance

• Standards referenced, not reproduced: FAR 25.251 and CS 25.251 address vibration and buffeting, and the FAR/CS 25.3xx flight load factor provisions frame the load factor context, by name and paraphrase only per standards-map.yaml. The RMS floor, RMS rise and the 0.02 g onset threshold are documented typical engineering criteria, not regulation values.
• compliance: STANDARDS-REF, gated: false.