Landing Ground Loads

Landing Ground Loads (structures/loads/landing-ground-loads)

Use when the static reaction sets of the certification landing and ground handling conditions must be resolved for an aircraft structure: the parked and level-landing split between the nose and main gear, the braked-roll deceleration with all brakes on the main gear, the tail-down condition with the nose gear unloaded, and the one-wheel asymmetric level landing. This leaf implements the reaction statics in pure Python, stdlib only, and reports the critical condition for each gear station that gates a landing loads check. The limit vertical inertia load factor is an input chosen from the certification basis; the in-flight air load conditions of the same load survey live in the companion loads-pack leaf and are not computed here. It pairs with vehicle-design/sizing/landing-gear-sizing, which carries these reaction loads into the gear component sizing.

Domain quick reference

• Geometry: a is the distance from the nose gear to the CG, b the distance from the CG to the main gear, wheelbase = a + b. Static reactions R_nose = W * b / (a + b) and R_main = W * a / (a + b); the two reactions sum to the weight W (round-trip identity).
• Weight: W = m * g0 with g0 = 9.80665 m/s^2 (G0). A mass in kg enters through weight_force; every other function takes the weight W in N.
• Level landing: the static reactions scaled by the limit vertical inertia load factor LF: nose = LF * W * b / (a + b), main = LF * W * a / (a + b), total = LF * W. N_LEVEL_DEFAULT = 2.5 is the typical input value; the certification value is a caller choice.
• Braked roll: all brakes act on the main gear. The main reaction is evaluated at the ground-roll load factor (default 1.0): F_brake = friction * R_main and deceleration_g = F_brake / W = friction * a / (a + b) in g units, a pure number. At the worked example 0.8 * 0.8 = 0.64 exactly.
• Tail-down condition: nose gear unloaded, the entire vertical reaction sits on the main gear: R = W * LF.
• One-wheel condition: asymmetric level landing from a lateral CG offset y over the track t: loaded side reaction R = W * LF * (0.5 + y / t), valid for y in [0, t/2]; a CG outside the track half width is non-physical for this condition.
• Friction is a dimensionless braking coefficient in [0, 1]; the load factor, distances and track are SI (N, m), deceleration is in g.
• FAR 25.471 to 25.511 style ground conditions frame the reaction statics above; summary-only, reference-only per standards-map.yaml.

Workflow

1. Convert the mass to a weight force with weight_force, or take the weight W directly.
2. Split the parked load with static_reactions (nose and main gear).
3. Scale to the limit condition with level_landing_reactions at the chosen limit vertical inertia load factor.
4. Evaluate the braked roll with braked_roll using the braking friction coefficient (main gear reaction, brake force, deceleration in g).
5. Take the tail-down reaction with tail_down_reaction when the nose gear is unloaded.
6. Take the asymmetric case with one_wheel_reaction at the lateral CG offset and the track.
7. Call landing_loads_summary for the full per-station set; the critical main reaction is the maximum of the main gear values (level landing, braked roll, tail down, one wheel) and the critical nose reaction the maximum of the nose values.
8. Confirm the deterministic checks with the contract test scripts/test_landing_ground_loads.py.

Worked example

Transport: mass 60 000 kg (W = 588 399 N), nose gear to CG a = 8 m, CG to main gear b = 2 m, limit load factor 2.5, braking friction 0.8, lateral offset 0.1 m, track 5.0 m.

• Static: R_nose = 588 399 * 2 / 10 = 117 679.8 N, R_main = 588 399 * 8 / 10 = 470 719.2 N; the pair sums to 588 399 N exactly.
• Level landing at 2.5: nose = 294 199.5 N, main = 1 176 798.0 N (inside the 1.10e6 to 1.25e6 N bound), total = 1 470 997.5 N.
• Braked roll (load factor 1.0): main reaction 470 719.2 N, brake force 0.8 * 470 719.2 = 376 575.4 N, deceleration 0.64 g; the identity deceleration_g = friction * a / (a + b) = 0.8 * 0.8 holds to float precision.
• Tail down: R = 588 399 * 2.5 = 1 470 997.5 N on the main gear.
• One wheel: R = 588 399 * 2.5 * (0.5 + 0.1 / 5) = 764 918.7 N (inside the 0.72e6 to 0.81e6 N bound).
• Summary with lateral_offset 0.1 m: static nose 117 679.8 N, static main 470 719.2 N, level nose 294 199.5 N, level main 1 176 798.0 N, brake force 376 575.4 N, deceleration 0.64 g, tail down main 1 470 997.5 N, one wheel main 764 918.7 N. Critical main is the tail-down value 1 470 997.5 N and critical nose the level nose value 294 199.5 N.

Pitfalls

• Feeding mass where weight is expected: every function past weight_force takes the weight W in N (m * g0); passing kilograms divides every reaction by gravity.
• Swapping the CG arms: a is nose-gear-to-CG and b is CG-to-main- gear, so the nose reaction W * b / (a + b) uses the FAR arm and the main reaction W * a / (a + b) the near arm; swapping them puts the parked load on the wrong gear.
• Using the static reaction for a dynamic condition: the level landing, tail-down and one-wheel cases scale by the limit vertical inertia load factor, and the certification value is a caller choice (2.5 typical), not a module constant.
• Forgetting the braked-roll identity: with all brakes on the main gear the deceleration is friction * a / (a + b) (0.64 g in the worked example), so a friction value near 1 does not mean a 1 g stop.
• Placing the CG outside the track half width: the one-wheel condition is only valid for a lateral offset y in [0, t/2]; a CG beyond that is non-physical and raises ValueError.
• Sizing one station only: the critical main reaction is the maximum over level landing, braked roll, tail down and one wheel (the tail-down 1 470 997.5 N in the worked example), so the summary's per-station max, not any single condition, gates the gear check.

Verification

• Confirm static_reactions(588399.0, 8, 2) returns nose 117 679.8 N and main 470 719.2 N and that the sum equals the weight (1e-6 relative checks).
• Confirm level_landing_reactions scales the static set by the load factor and that the total equals W * load_factor.
• Confirm braked_roll deceleration equals friction * a / (a + b) (1e-9 relative) and the brake force equals friction times the main reaction.
• Confirm one_wheel_reaction at lateral offset 0 returns W * LF * 0.5 exactly and that the worked example value 764 918.7 N lies in 0.72e6 to 0.81e6 N.
• Confirm the summary picks the tail-down value as critical main and the level nose as critical nose.
• Confirm every non-positive weight, a, b, load factor and track, and every friction outside [0, 1] or lateral offset outside [0, track/2] raises ValueError.
• Run the contract test offline: python3 scripts/test_landing_ground_loads.py (32 tests, deterministic).

Related leaves

• structures/loads/random-vibration-analysis: dynamic response methods for the vibration qualification of the same structure, the dynamic complement to this static reaction set.
• structures/loads/shock-response-spectrum: transient response spectra used for shock qualification cases around the ground conditions.
• vehicle-design/sizing/landing-gear-sizing: gear component sizing counterpart that carries these reaction loads into the structure design.
• vehicle-design/sizing/brake-energy-sizing: braking energy sizing for the rejected takeoff case that pairs with the braked-roll check.

Behavior contract (gate 3)

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

python3 scripts/test_landing_ground_loads.py

The test covers the worked example contract (static 117 679.8 N / 470 719.2 N, level main 1 176 798 N inside 1.10e6 to 1.25e6 N, brake force 376 575.36 N, deceleration 0.64 g, tail down 1 470 997.5 N, one wheel 764 918.7 N inside 0.72e6 to 0.81e6 N), the exact identities (static Wb/(a+b) and Wa/(a+b), reaction sum equals weight, decel = frictiona/(a+b), one-wheel offset 0 equals WLF*0.5), boundary cases (friction 0 and 1, offset at track half), ValueError rejection of every non-physical input, and determinism.

Compliance

• Standards referenced, not reproduced: the FAR 25.471 to 25.511 style ground conditions are summarized as standard reaction statics above (summary-only, reference-only per standards-map.yaml); the limit load factor is an input, never asserted as a regulation quote.
• compliance: STANDARDS-REF, gated: false.