Control Force Flight Test

Control Force Flight Test (flight-test-operations/stability/control-force-flight-test)

Use when the task is reduction of the measured longitudinal control force records of a flight test: calibrating the force transducer, fitting the stick force gradient versus calibrated airspeed, the stick force per g from pull-ups, the breakout force and the centering check. This leaf reduces the measured FORCE side of the pitch control; the position side (elevator angle trim curves and neutral points) belongs to its sibling flight-test-operations/stability/static-stability- flight-test. Pull (aft) forces are positive, push forces negative. All fits are ordinary least squares computed with pure stdlib closed-form sums (no numpy), deterministic and offline.

Domain quick reference

• Calibration: least-squares fit of applied load y (lbf) against recorded counts x, y = a x + b with slope a = Sxy/Sxx and intercept b = y_mean - a x_mean over the closed-form sums Sxx = sum((x - x_mean)^2), Sxy = sum((x - x_mean)(y - y_mean)). The fitted line converts every recorded count to force during the test day.
• Stick force gradient: fit measured stick force (pull positive, lbf) against calibrated airspeed (KCAS) from a level-speed sweep. A positive slope (pull force increases with speed) is the stable convention and gives the verdict stable-gradient; a zero or negative slope gives unstable-gradient.
• Stick force per g: fit measured pull force against load factor from pull-up maneuvers at constant speed; the slope is the force per g, the load the pilot must pull for each additional g.
• Breakout force: from the push-pull hysteresis of the control, width = pull - push and breakout = width / 2, the half-width force that must be overcome before the control moves.
• Centering check: margin = limit - residual on the residual control position after release; verdict centered when the margin is non-negative, else exceeds-limit.
• Regression identities: on noise-free points the calibration reproduces the applied loads (predicted equals known), and a perfectly linear sweep returns r2 = 1.0.
• FAR-25 frames the certification context (reference-only); the relations above are standard engineering methodology, summary-only.

Workflow

1. Calibrate: call calibrate_force_transducer(known_lbf, counts) with the applied loads and the recorded counts from the ground calibration, and keep slope_lbf_per_count and intercept_lbf for the whole test day.
2. Reduce the speed sweep: stick_force_gradient(speeds_kts, forces_lbf) returns the gradient slope_lbf_per_kt, intercept, r2 and the verdict stable-gradient or unstable-gradient.
3. Reduce the pull-ups: force_per_g(load_factors, forces_lbf) returns slope_lbf_per_g (the force per g), intercept and r2.
4. Extract the breakout: breakout_force(push_lbf, pull_lbf) returns the hysteresis width and the half-width breakout force.
5. Run the centering check: centering_check(residual_deg, limit_deg) returns the margin and the centered or exceeds-limit verdict.
6. Combine the full reduction with control_force_report(...), which returns every sub-result plus the calibrated force at any requested predict count.
7. Confirm the deterministic checks with the contract test scripts/test_control_force_flight_test.py.

Worked example

Reference transport pitch-force flight test, pull positive:

• Calibration: 20 lbf applied at 1230 counts, 60 lbf at 3250 counts. calibrate_force_transducer returns slope 0.019802 lbf/count and intercept -4.35644 lbf; the calibrated force at 2100 counts is 37.2277 lbf.
• Speed sweep: V = 120, 130, 140, 150 KCAS with Fe = -3.8, -1.6, 0.5, 2.9 lbf. stick_force_gradient returns slope 0.222 lbf/kt, intercept -30.47 lbf, r2 0.99927, verdict stable-gradient.
• Pull-ups: n = 1.0, 1.5, 2.0, 2.5 g with Fe = 1.2, 7.4, 14.3, 20.8 lbf. force_per_g returns slope 13.14 lbf/g, intercept -12.07 lbf, r2 0.99962.
• Breakout: push -4.2 lbf, pull 6.4 lbf gives hysteresis width 10.6 lbf and breakout force 5.3 lbf.
• Centering: residual 0.42 deg against a 0.50 deg limit gives margin 0.08 deg, verdict centered.

Pitfalls

• Extrapolating the force calibration beyond its two points: the transducer is calibrated at 20 and 60 lbf (slope 0.019802 lbf/count, intercept -4.35644 lbf), and fewer than 2 calibration points or negative counts raise ValueError.
• Interpreting the gradient sign without the maneuver: the speed sweep gives slope 0.222 lbf/kt with verdict stable-gradient, and a reversed sweep returns unstable-gradient - the sign of the gradient carries the stability claim.
• Reading the pull-up fit as a speed effect: force_per_g fits the load factor pull-ups (slope 13.14 lbf/g), a different quantity from the speed gradient, so lbf/g and lbf/kt values are not comparable.
• Passing a push that is not more negative than the pull: the breakout comes from the push -4.2 lbf and pull 6.4 lbf pair (hysteresis width 10.6 lbf, breakout 5.3 lbf), and pull not greater than push raises ValueError.
• Judging centering without the residual margin: a 0.42 deg residual against the 0.50 deg limit gives margin 0.08 deg and verdict centered, so the margin, not the raw residual, is the pass criterion; negative residuals and non-positive limits raise ValueError.
• Fitting gradients on too few points: fewer than 3 points for the gradient and per-g fits, and length mismatches, raise ValueError.

Verification

• Confirm calibrate_force_transducer([20, 60], [1230, 3250]) returns slope 0.019802 lbf/count and intercept -4.35644 lbf, and that the predicted loads at the calibration counts equal the applied loads to 1e-9 (regression identity).
• Confirm stick_force_gradient on the sweep returns slope 0.222 lbf/kt, r2 0.99927 and verdict stable-gradient, and that a reversed sweep returns unstable-gradient.
• Confirm force_per_g returns 13.14 lbf/g with r2 0.99962.
• Confirm breakout_force(-4.2, 6.4) returns breakout 5.3 lbf, and that centering_check(0.42, 0.50) returns margin 0.08 deg, centered.
• Confirm ValueError rejection: fewer than 2 calibration points, fewer than 3 points for the gradient and per-g fits, length mismatches, negative counts, non-positive speeds, pull not greater than push, negative residual, non-positive limit.
• Run the contract test offline: python3 scripts/test_control_force_flight_test.py (35 tests, deterministic).

Related leaves

• flight-test-operations/stability/static-stability-flight-test: the position-side sibling; this leaf is the measured force complement.
• flight-test-operations/stability/lateral-directional-stability- flight-test: the lateral axis sibling.
• flight-mechanics/stability-control/control-surface-effectiveness: the analytic design prediction boundary.

Behavior contract (gate 3)

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

python3 scripts/test_control_force_flight_test.py

The test covers the calibration worked values to 1e-6 with the applied load regression identity to 1e-9 and zero residual on a third collinear point, the gradient worked slope and r2 with the reversed unstable verdict, the force per g worked slope and r2, the breakout half-width including the symmetric case, the centering margin with the exceeds-limit case, the combined report keys and prediction at 2100 counts, run-to-run determinism, and ValueError rejection of every non-physical input in the validation list.

Compliance

• Standards referenced, not reproduced: FAR-25 (14 CFR Part 25) frames the certification context for the transport-class control force flight test; the reduction relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.