Climb Performance Flight Test

Climb Performance Flight Test (flight-test-operations/performance/climb-performance-flight-test)

Use when the task is climb performance flight testing: the rate of climb measurement from timed steady climb segments, the weight and density corrections of the measured rate, the service and absolute ceiling determination, the time to climb, and the climb gradient checks against the certification requirement.

Domain quick reference

• Test technique: the sawtooth climb, a series of timed climb segments over measured pressure altitude blocks at a constant indicated airspeed and a fixed power setting, with the outside air temperature recorded per block; or a continuous climb sampled at altitude steps. The airplane is trimmed, the configuration is fixed, and the segment is straight.
• rate_of_climb_from_pressure_altitude: ROC = (h2 - h1) / t * 60 in ft/min from the pressure altitude change over the segment time. Worked: 2000 ft gained in 60 s gives 2000 ft/min.
• geometric_roc_from_pressure_roc: h_geo_dot = h_p_dot * T_amb / T_ISA(pressure altitude); at the same pressure the geometric altitude rate exceeds the pressure altitude rate by the ambient over ISA temperature ratio. Worked: 2000 ft/min at 10000 ft pressure altitude with OAT 15 C (ISA there is -4.8 C) gives 2147.7 ft/min.
• density_altitude_ft: sigma = delta(pressure altitude) * T0 / T_amb, then the altitude where the ISA density ratio equals sigma. Worked: 10000 ft pressure altitude with OAT 15 C gives a 12248 ft density altitude; on the ISA day at 10000 ft (OAT -4.8 C) the density altitude equals the pressure altitude.
• Corrections of the measured rate: the weight correction weight_corrected_roc, ROC_ref = ROC_meas * W_test / W_ref, the specific excess power per unit weight scaling at constant true airspeed, the first order form valid when the drag is a small fraction of the thrust; the density correction density_corrected_roc, ROC_std = ROC_meas * (sigma_test / sigma_std)^(lapse_exp - 0.5), from the thrust lapse with sigma^lapse_exp and the true airspeed with sigma^-0.5 at constant indicated airspeed. Worked: 2000 ft/min at W_test 20500 lbf to W_ref 20000 lbf gives 2050 ft/min; sigma 0.9 with the 0.7 lapse exponent gives 1958.3 ft/min; the combined correction gives 2007.3 ft/min.
• Excess power model for planning: CL = W / (0.5 * rho0 * sigma * V^2 * S), CD = cd0 + k * CL^2, D = 0.5 * rho0 * sigma * V^2 * S * CD, T = T0 * sigma^0.7, ROC = (T - D) * V / W, climb_gradient_pct = 100 * (T - D) / W, the small angle form of the excess thrust over weight. Worked at sea level, 400 ft/s, W 20000 lbf, S 320 ft^2, cd0 0.022, k 0.0530, T0 6500 lbf: CL 0.329, CD 0.0277, D 1687 lbf, ROC 5775 ft/min, gradient 24.1 percent.
• Best rate of climb: best_rate_of_climb_fpm scans the true airspeed band at the test density and returns the maximum rate and the speed that achieves it. Worked for the synthetic light jet: 6289 ft/min at 516.8 ft/s (306 kt) at sea level, 5179 ft/min at 10000 ft, 4128 ft/min at 20000 ft.
• Ceilings: the service ceiling is the altitude where the best rate of climb decays to the threshold, 100 ft/min for jet aircraft in common usage, and the absolute ceiling is where it decays to zero. Worked: 56354 ft service ceiling and 57189 ft absolute ceiling; a 500 ft/min threshold lowers the service ceiling to 52980 ft.
• Time to climb: time_to_climb_min integrates dt = dh / ROC(h) over the best rate schedule with the trapezoid rule. Worked: 6.69 min from sea level to 30000 ft for the synthetic light jet (planning model only, the measured data drive the certification values).
• Gradient checks: gradient_from_roc gives the gradient from the measured rate and the true airspeed, and gradient_margin_pct the margin against the requirement. Worked at 10000 ft at the best rate speed with one of two engines inoperative: 2.70 percent, a margin of +0.30 percent against the 2.4 percent takeoff climb gradient requirement for a two-engine transport aeroplane (FAR-25.121 summary, reference-only; verify against the current regulation).
• Model caveat: the parabolic polar omits the compressibility drag rise, so predicted rates and ceilings run optimistic at high altitude; the flight test measures the actual values and the corrected measured data gate the assessment.

Workflow

1. Fly the sawtooth or continuous climb segments at the test configuration, recording pressure altitude, time, OAT, indicated airspeed, and weight per segment.
2. Compute the measured rate of climb with rate_of_climb_from_pressure_altitude from the pressure altitude change and the segment time.
3. Convert the pressure altitude rate to the geometric rate with geometric_roc_from_pressure_roc using the OAT and the segment pressure altitude.
4. Reduce each segment to the reference condition with corrected_rate_of_climb: weight_corrected_roc for the test weight and density_corrected_roc for the density altitude, using density_altitude_ft for the standard day reference.
5. Build the corrected rate of climb versus density altitude curve and locate the best rate speed with best_rate_of_climb_fpm per altitude block.
6. Determine the ceilings with service_ceiling_ft at the 100 ft/min threshold and absolute_ceiling_ft where the rate decays to zero, and the time to climb with time_to_climb_min.
7. Check the climb gradient with climb_gradient_pct and gradient_from_roc against the certification requirement, reporting the margin with gradient_margin_pct.
8. Report the corrected rate of climb, the ceiling altitudes, the time to climb, and the gradient margin for the climb test assessment.

Pitfalls

• Routing analytical climb questions here: computing the rate of climb from excess power without flight test data, service ceiling from a drag polar alone, and time to climb estimates belong to flight-mechanics/performance/climb-performance; this leaf is the flight test side: measurement from timed segments, corrections, and ceilings from the corrected data.
• Routing engine test questions here: engine systems checks, fuel flow, EGT margins, and engine thrust determination belong to engine-flight-test; the climb test consumes thrust, it does not determine the engine limits.
• Routing segment distance questions here: takeoff field length and the takeoff path segments belong to takeoff-distance-determination, landing distance and the approach climb segment to landing-distance-determination, and unpowered descent to glide-flight-test; this leaf covers the steady powered climb.
• Confusing the pressure altitude rate with the geometric rate: the temperature correction matters, 7 percent at 10000 ft with OAT 15 C in the worked case.
• Forgetting the weight and density corrections before ceiling determination: the measured rate at test weight and density does not give the reference ceilings directly.
• Mixing the ceiling definitions: the service ceiling threshold is commonly 100 ft/min for jets and differs for propeller aircraft; make the threshold explicit in service_ceiling_ft.
• Treating the planning model as the measured result: the parabolic polar without compressibility over-predicts the high altitude rate, so the measured and corrected data gate the assessment, not the model.
• Forming the gradient from the calibrated airspeed: the small angle form needs the true airspeed at the test density altitude.
• A zero or negative measured rate is not a climb: the segment must gain pressure altitude, and the time to climb integration requires a positive rate throughout the band.

Behavior contract (gate 3)

The climb measurement, correction, ceiling, and gradient logic is exercised by the gate 3 contract test: scripts/test_climb_performance_flight_test.py against scripts/climb_performance_flight_test_logic.py (stdlib unittest, offline). Run: python3 scripts/test_climb_performance_flight_test.py

Compliance

• Standards referenced, not reproduced: FAR-25 is US government work (public domain) and CS-25 is a free EASA download; climb performance flight testing is common methodology in the FAR 25.101 general performance, 25.115 climb, 25.119 landing climb, and 25.121 one-engine-inoperative climb context, summary-only per standards-map.yaml. Requirement values stated here are reference summaries, verify against the current regulation text.
• compliance: STANDARDS-REF, gated: false.