ashfordeOU Landing Performance (flight-mechanics/performance/landing-performance)
Use when the task is landing performance analysis: reference approach speed, flare geometry, air distance over the landing obstacle, ground roll, and stopping distance from the stall speed, weight, braking coefficient, and reverse thrust.
Domain quick reference
- Stall speed from wing loading: V_s = sqrt(2 * (W/S) / (rho * Cl_max)), with wing loading W/S in N/m^2 and density rho in kg/m^3; this is the landing-configuration stall speed the approach speed is built on.
- Reference approach speed: V_APP = 1.3 * V_s. FAR 25.125 and CS 25.125 use 1.3 times the stalling speed in the landing configuration as the reference landing speed; 1.23 is the minimum tied to the stall-speed definition used in the demonstrated distance.
- Touchdown speed: V_TD = 0.95 * V_APP (transport convention). The airplane flares and touches down below the approach speed but still well above the stall speed.
- Flare radius: R = V_APP^2 / (g * (n - 1)), with load factor n near 1.2 in a normal transport landing and g = 9.80665 m/s^2.
- Flare height: h_f = R * (1 - cos(gamma)), the height lost while rotating the flight path from the approach angle gamma down to the flare (gamma = 3 degrees on a standard glideslope).
- Flare distance: s_f = R * sin(gamma), the horizontal travel during the flare arc from flare start to touchdown.
- Air distance over the 50 foot obstacle: s_air = (h_obs - h_f) / tan(gamma) + s_f, with h_obs = 15.24 m (50 ft) per FAR 25.125; the straight segment at the approach angle down to the flare height plus the flare arc.
- Landing ground roll: s_g = V_TD^2 / (2 * a), constant deceleration a in m/s^2 from the touchdown speed to a full stop.
- Force balance on the ground roll: a/g = mu * (1 - L/W) + D/W + T_rev/W, with mu the braking coefficient, L/W the lift ratio (unloaded wheels reduce braking friction), D/W the drag ratio, and T_rev/W the reverse thrust ratio. A firm touchdown with weight on the wheels gives L/W near zero.
- Certified landing field length: FAR 25.125 requires the landing distance measured from 50 feet above the runway to a full stop to be multiplied by 1.67 for the published field length (the same 1.67 factor applies to the dry-runway demonstration; wet-runway and contaminated-runway operations apply the operator's additional margins).
- Stopping time: t = V_TD / a under constant deceleration.
Workflow
- Establish the landing configuration stall speed with stall_speed from the wing loading, density, and Cl_max (flaps and gear down).
- Build the reference approach speed with approach_speed using the 1.3 factor, then the touchdown speed with touchdown_speed using the 0.95 factor.
- Size the flare: flare_radius from the approach speed and load factor, then flare_height and flare_distance from the approach angle.
- Estimate the air distance over the 50 foot obstacle with air_distance (obstacle height 15.24 m is the FAR 25.125 default).
- Compute the ground roll: mean deceleration from average_deceleration (braking coefficient, lift, drag, and reverse thrust ratios), then ground_roll_from_forces, or use ground_roll_distance directly with a measured deceleration.
- Sum the phases with landing_distance and apply the certification factor with certified_landing_distance for the published field length; check the runway demand with required_braking_coefficient when the stop distance is fixed.
Pitfalls
- Using the approach speed instead of the touchdown speed in the ground roll: the ground roll runs from V_TD, not V_APP, and the difference is a squared-speed effect on the stopping distance.
- Forgetting the 1.67 certification factor: the demonstrated landing distance is not the published field length; FAR 25.125 applies the 1.67 multiplier.
- Ignoring lift unloading during the roll: with L/W near zero the full weight sits on the wheels and mu works at full value; a model that carries L/W through the roll weakens the braking friction and lengthens the distance.
- Treating the flare as a straight segment: the flare is a circular arc at load factor above 1; a straight-line model understates the air distance.
- Using an obstacle height at or below the flare height: the obstacle must be crossed before the flare arc completes, and air_distance rejects that geometry.
- Applying a braking coefficient that cannot be met: required_braking_ coefficient sizes the friction demand for a target stop distance, and a wet or contaminated runway supports far less than the dry 0.4 to 0.5 range.
- Confusing takeoff ground roll with landing ground roll: takeoff accelerates with thrust minus rolling friction; landing decelerates with braking friction plus drag plus reverse thrust. The two models are not interchangeable.
- Mixing kg and N: weights and thrusts must be in newtons (mass * g0) when they enter the force ratios, or the deceleration and distances come out wrong.
Behavior contract (gate 3)
The landing performance math is exercised by the gate 3 contract test: scripts/test_landing_performance.py against scripts/landing_performance_logic.py (stdlib unittest, offline). Run: python3 scripts/test_landing_performance.py
Compliance
- Standards referenced, not reproduced: FAR-25.125 (US government work, public domain) and CS-25.125 (free EASA download) frame the landing distance certification basis; the approach speed factor, flare geometry, and ground roll force balance above are common flight-mechanics methodology, summary-only per standards-map.yaml.
- compliance: STANDARDS-REF, gated: false.