Cruise Performance Flight Test

Cruise Performance Flight Test (flight-test-operations/performance/cruise-performance-flight-test)

Use when you must plan and reduce a cruise performance flight test that measures fuel flow versus Mach number at constant altitude to build the flight-test range performance curve: schedule the level cruise test points across a Mach sweep with stabilized fuel-flow runs, correct each measured fuel flow from the test weight to the reference weight with the square-root weight correction, convert the corrected fuel flow and the true airspeed into the range performance of each point, fit a quadratic curve of range performance versus Mach by ordinary least squares, and read off the maximum range cruise Mach and the long range cruise speed. This leaf reduces MEASURED fuel-flow runs from a dedicated cruise test; the analytic neighbors flight-mechanics/performance/specific-range and breguet-range compute cruise results from models instead, and level-acceleration-test and engine-flight-test cover the other performance flight tests.

Domain quick reference

• ISA speed of sound: a = sqrt(gamma * R * T), gamma = 1.4, R = 287.05 J/(kg K); T = 288.15 - 0.0065 h below 11 km and T = 216.65 K in the isothermal stratosphere. True airspeed: V = M * a.
• Square-root weight correction: Wf_corr = Wf_measured * sqrt(W_ref / W_test). This is a documented engineering approximation valid for small weight differences at constant Mach and altitude, where induced drag dominates the cruise drag balance; it removes the test-weight effect so all runs reduce to one reference weight.
• Range performance at a point: rp = V_tas / Wf_corr (distance per unit fuel mass).
• Curve fit: rp(M) = c2M^2 + c1M + c0 fitted by ordinary least squares (normal equations, 3x3 Gaussian elimination inside the module; no external solver).
• Maximum range cruise Mach: M_mrc = -c1 / (2*c2), the parabola vertex, reported only when c2 < 0 (downward-bowed data).
• Long range cruise Mach: the larger root of c2M^2 + c1M + c0 = LRC_FRACTION * rp_max with LRC_FRACTION = 0.99, the faster Mach at which range performance falls to 99 percent of its maximum. It must sit above M_mrc (ordering verdict "lrc-faster").
• Units are SI throughout: m, s, kg, kg/s, m/s.

Workflow

1. Build the test card with plan_test_matrix: the Mach sweep at the cruise altitude, one stabilized run per Mach, with a linear test-weight ramp from the start weight to the end weight across the sweep (each run burns fuel).
2. Fly the level stabilized runs and record wf_measured_kg_s, w_test_kg and altitude_m per point at each Mach.
3. Correct every measured fuel flow to the reference weight with corrected_fuel_flow (weight_correction_factor gives the factor).
4. Convert each point with range_performance using the true airspeed from tas_from_mach (isa_speed_of_sound for the altitude).
5. Reduce the whole set with reduce_cruise_test(points, w_ref) to get the point table, the fitted coefficients, max_rp_mach, max_rp, lrc_mach, residuals, and the reduction verdict.
6. Confirm the ordering with verify_speed_ordering(max_rp_mach, lrc_mach): the long range cruise speed is the faster 99 percent point.
7. Confirm the deterministic checks with the contract test.

Worked example

Reference W_ref = 200000 kg at 10668 m (a = 296.51 m/s), seven stabilized runs across the Mach sweep 0.72 to 0.84 with test weights ramping 209000 kg down to 197000 kg. The measured fuel-flow table is built from an exact quadratic model rp(M) = 90 - 6000*(M - 0.8)^2, so the reduction recovers it exactly.

• At M = 0.80, W_test = 201000 kg: V = 0.8 * 296.51 = 237.21 m/s, the model gives rp = 90, Wf_corr = 237.21 / 90 = 2.6357 kg/s, and the correction factor sqrt(201000 / 200000) = 1.00250, so Wf_measured = 2.6423 kg/s. corrected_fuel_flow(2.6423, 201000,
  200000. returns 2.6357 kg/s.
• reduce_cruise_test on the fixture returns max_rp_mach = 0.800000 (within 1e-6), max_rp = 90.0, coefficients c2 = -6000.0, c1 = +9600.0, c0 = -3750.0 (within 1e-3), since 90 - 6000*(M - 0.8)^2 = -6000M^2 + 9600M - 3750. Vertex M = -9600 / (2 * -6000) = 0.8.
• Long range cruise: solve -6000M^2 + 9600M - 3750 = 0.99 * 90 = 89.1; discriminant 21600, roots 0.78775 and 0.81225, so lrc_mach = 0.81225 (exact fitted root 0.812247), the larger root. verify_speed_ordering(0.8, 0.81225) = "lrc-faster".
• Residuals are all below 1e-9 (noise-free parabola) and the verdict is "maximum-found".
• Sanity case: range performance linear in Mach gives c2 near zero and a "no-maximum" verdict with no reported vertex or LRC Mach.

Pitfalls

• Comparing raw fuel flows across runs at different test weights: the reduction works on flows corrected to W_ref with the sqrt(W_test / W_ref) factor (2.6423 kg/s at 201000 kg reduces to 2.6357 kg/s at 200000 kg), so un-corrected values mask the Mach trend.
• Reading the LRC Mach as the smaller parabola root: solving the 0.99 * max equation gives roots 0.78775 and 0.81225, and lrc_mach is the larger root 0.81225, the faster cruise point.
• Reporting a maximum where none exists: when range performance is linear in Mach the quadratic coefficient goes to zero and the verdict is "no-maximum" with no vertex or LRC Mach reported, not a fitted corner.
• Fitting on too few or duplicate points: fewer than 3 points and duplicate Mach values raise ValueError, as do negative altitude or Mach, non-positive weights, non-positive fuel flow, and Mach outside (0.3, 1.0).
• Forgetting the speed-of-sound basis of the reduction: V = M * a uses the local speed of sound (296.51 m/s at 10668 m, 340.29 m/s at sea level), so a wrong a shifts every specific-range point.
• Trusting the vertex without the residual check: on the noise-free fixture the fit recovers the exact model (residuals below 1e-9) and the verdict is "maximum-found"; real data needs the same verdict logic rather than an eyeballed peak.

Verification

• Confirm isa_speed_of_sound returns 340.29 m/s at sea level and 296.51 m/s at 10668 m (within 0.1).
• Confirm corrected_fuel_flow(2.6423, 201000, 200000) returns 2.6357 kg/s within 1e-3 and that range_performance(237.21, 237.21/90.0) returns 90 within 1e-6 (the exact-model round trip).
• Confirm the reduction recovers vertex 0.8, max 90, coefficients -6000/9600/-3750, and the LRC root 0.81225, with residuals below 1e-9.
• Confirm the round trip: measured flow built as Wf_corr * sqrt(W_test/W_ref) reduces back to exactly Wf_corr at every point.
• Confirm every non-physical input raises ValueError: negative altitude or Mach, non-positive weights, non-positive fuel flow, fewer than 3 points, duplicate Mach, Mach outside (0.3, 1.0).
• Run the contract test offline: python3 scripts/test_cruise_performance_flight_test.py (35 tests, deterministic).

Related leaves

• flight-mechanics/performance/specific-range: analytic range performance and fuel economy calculation, the model counterpart of this measured-data reduction.
• flight-mechanics/performance/breguet-range: analytic cruise range from the Breguet equation.
• flight-test-operations/performance/level-acceleration-test: the accelerated level flight test that shares the cruise condition.
• flight-test-operations/performance/engine-flight-test: installed thrust and fuel flow verification at altitude.
• flight-test-operations/performance/climb-performance-flight-test: the climb side of the performance flight test campaign.

Behavior contract (gate 3)

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

python3 scripts/test_cruise_performance_flight_test.py

The test covers the ISA speed of sound anchors at 0 m and 10668 m, the true airspeed conversion, the weight correction factor and its inverse round trip, the worked-example corrected fuel flow anchor, the range performance conversion, the full fixture reduction (vertex 0.8, max 90, coefficients -6000/9600/-3750, LRC root, residuals below 1e-9, point-table entries, verdicts), the linear-data no-maximum sanity case, the test-card weight ramp from plan_test_matrix, the fixture inverse-build consistency, and ValueError rejection of non-physical inputs.

Compliance

• Standards referenced, not reproduced: FAR 25 and CS 25 frame the cruise performance context for transport category airplanes (performance and flight test data requirements); the relations above are standard flight-test engineering methodology, summary-only per standards-map.yaml. No verbatim regulatory text.
• compliance: STANDARDS-REF, gated: false.