Landing Gear Layout

Landing Gear Layout (vehicle-design/sizing/landing-gear-layout)

Use when the task is laying out a tricycle landing gear arrangement against the center-of-gravity envelope: the tipback angle at the aft CG limit, the tail strike clearance angle at rotation about the main gear contact, the lateral turnover angle from the wheel track, and the nose gear static load fraction band across the CG travel, closing with the main gear position check that gates the configuration. This leaf implements the arrangement geometry with deterministic stdlib trigonometry and statics, with fixed rotation and station conventions so the outputs are reproducible. It pairs with vehicle-design/sizing/landing-gear-sizing, which sizes the strut loads and landing energy once the layout is fixed, and takes the CG travel limits as given inputs from vehicle-design/mass-properties/cg-envelope.

Domain quick reference

Pinned conventions: stations x are measured in metres aft of a fuselage datum, the ground plane is z = 0 at the tire contacts with the static deflection, rotations are nose-up about the main gear contact point, and all angles are returned in degrees. The aircraft is level on the ground in the reference attitude, and the aft CG limit sits forward of the main gear contact by the margin d = x_mg - x_cg_aft.

• Tipback angle: rotating nose-up about the main gear contact by the tipback angle brings the aft CG onto the vertical through the contact; beyond that attitude the vertical CG line passes aft of the contact and gravity rolls the aircraft onto its tail. The rotation obeys tan(theta_tip) = (x_mg - x_cg_aft) / h_cg, so theta_tip = atan((x_mg - x_cg_aft) / h_cg). The angle grows with the aft-CG margin and vanishes when the aft CG reaches the contact station. This is the standard tipback check from common conceptual design methodology (name and paraphrase only).
• Tail strike clearance: the tail cone lowest point at station x_tail and height h_tail_contact above the ground descends during the rotation as z(theta) = h_tail_contact * cos(theta) - a * sin(theta) with the horizontal arm a = x_tail - x_mg, which vanishes at tan(theta_ts) = h_tail_contact / a. The rotation attitude is tail-strike limited when theta_ts sits below the tipback angle, the transport-typical ordering.
• Lateral turnover, main gear pair: rolling about the line joining the two main gear contacts, tan(theta_lat) = h_cg / (track / 2) = 2 * h_cg / track.
• Lateral turnover, tricycle diagonal: rolling about the diagonal line joining the nose gear contact and the nearer main gear contact, the perpendicular ground-plane distance from the CG vertical to the diagonal is d_perp = (x_cg - x_ng) * (track / 2) / sqrt(wheelbase^2 + (track / 2)^2) with wheelbase = x_mg - x_ng, and theta = atan(d_perp / h_cg). The diagonal arm is shorter than the half track, so the tricycle angle is the lower, binding lateral check at a forward CG.
• Nose gear static load fraction: the moment balance about the main gear contact gives P_n / W = (x_mg - x_cg) / (x_mg - x_ng); the nose gear carries more when the CG is forward, so the aft CG limit gives the lower fraction and the forward CG limit the upper one. The fraction is dimensionless and layout-level only; strut loads are never computed here.
• Typical bands used by the verdicts: nose gear fraction 5-20 % of the total weight (NOSE_FRACTION_MIN to NOSE_FRACTION_MAX), lateral turnover 40-50 deg for transports, and ROTATION_REF_DEG = 10.0 deg as the typical transport unstick rotation reference.
• FAR-25 and CS-25 frame the transport landing gear arrangement context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the arrangement geometry: the nose gear station x_ng, the main gear station x_mg, the tail cone lowest point station x_tail and contact height h_tail_contact, the CG height h_cg, the main gear wheel track, and the CG travel limits with the aft limit x_cg_aft forward of x_mg (otherwise the module raises ValueError).
2. Tipback angle check at the aft CG limit: run tipback_angle(h_cg, x_mg, x_cg_aft) and read the nose-up rotation about the main gear contact at which the aircraft would tip onto its tail.
3. Tail strike clearance at rotation: run tail_strike_clearance_angle(h_tail_contact, x_tail, x_mg) and compare it with the tipback angle; when the tail strike angle sits below the tipback angle the rotation attitude is tail-strike limited. Reference ROTATION_REF_DEG for the rotation margin print.
4. Lateral turnover checks from the wheel track: run lateral_turnover_angle(h_cg, track) for the simplified main gear pair check, then lateral_turnover_tricycle_angle(h_cg, x_cg, x_mg, x_ng, track) at the forward CG limit for the nose-to-main diagonal refinement, which binds when it sits below the main-pair value.
5. Nose gear load fraction band across the CG travel: run nose_gear_static_load_fraction(x_cg, x_mg, x_ng) at the forward and aft CG limits and compare each limit fraction against NOSE_FRACTION_MIN and NOSE_FRACTION_MAX for the band verdicts.
6. Main gear position check and close: confirm both CG travel limits sit inside the nose-to-main station pair with a positive aft margin, carry the angles and the fraction band verdicts into the layout gate, and run the deterministic contract test scripts/test_landing_gear_layout.py.

Worked example

Transport-class aircraft: W = 60000 kg, wheelbase 15 m with the nose gear at x_ng = 3 m and the main gear at x_mg = 18 m from the datum, CG travel from the forward limit x_cg_fwd = 14 m to the aft limit x_cg_aft = 16.5 m, CG height h_cg = 2.8 m, main gear track = 6.5 m, tail cone lowest point at x_tail = 30 m at h_tail_contact = 3.5 m above the ground.

• Nose fractions: fwd = (18 - 14) / 15 = 0.266667 (26.6667 %) and aft = (18 - 16.5) / 15 = 0.1 (10.0 %); on the 60000 kg weight the nose gear carries 16000 kg at the forward CG limit and 6000 kg at the aft CG limit.
• Tipback angle: the aft CG sits d = 1.5 m forward of the main gear contact, so theta_tip = atan(1.5 / 2.8) = 28.1786 deg (tipback_angle(2.8, 18.0, 16.5)).
• Tail strike clearance: arm a = 12 m, theta_ts = atan(3.5 / 12) = 16.2602 deg (tail_strike_clearance_angle(3.5, 30.0, 18.0)), giving a 6.2602 deg margin against the 10.0 deg unstick rotation reference. Tail strike precedes tipback (16.2602 < 28.1786), so rotation is tail-strike limited, matching transport practice.
• Lateral turnover: the simplified main gear pair check gives theta_lat = atan(2 * 2.8 / 6.5) = 40.7462 deg (lateral_turnover_angle(2.8, 6.5)), inside the 40-50 deg transport band. The tricycle diagonal check at the forward CG gives d_perp = 11 * 3.25 / sqrt(15^2 + 3.25^2) = 2.32908 m and theta = atan(2.32908 / 2.8) = 39.7567 deg (lateral_turnover_tricycle_angle(2.8, 14.0, 18.0, 3.0, 6.5)), marginally below the main-pair value as the binding lateral case.
• Verdicts: the aft CG fraction of 10.0 % sits inside the 5-20 % typical band (True); the forward CG fraction of 26.6667 % sits above it (False) and flags the arrangement, because with the forward CG limit 4 m ahead of the main gear the nose gear is over-weighted and the main gear station or the forward CG limit must move before the layout closes. The lateral turnover angle sits inside the 40-50 deg band (True).

Verification

• Confirm tipback_angle(2.8, 18.0, 16.5) returns 28.1786 deg and that doubling the aft-CG margin at fixed h_cg doubles tan(theta_tip).
• Confirm tail_strike_clearance_angle(3.5, 30.0, 18.0) returns 16.2602 deg and that the rotation margin against ROTATION_REF_DEG is 6.2602 deg.
• Confirm lateral_turnover_angle(2.8, 6.5) returns 40.7462 deg and lateral_turnover_tricycle_angle(2.8, 14.0, 18.0, 3.0, 6.5) returns 39.7567 deg, below the main-pair value.
• Confirm nose_gear_static_load_fraction returns 0.266667 at the forward CG limit and 0.1 at the aft CG limit, that the two fractions complement the main gear share to 1, and that the aft CG limit sits inside the 5-20 % typical band while the forward CG limit sits above it.
• Confirm repeated calls return identical scalars and that every non-positive height, non-positive track, aft CG limit at or behind the main gear station, tail station at or forward of the main gear station, and CG station outside the nose-to-main pair raises ValueError rather than returning a plausible number.

Pitfalls

• Using the aft CG at or behind the main gear station: the nose gear fraction goes to zero or negative and the tipback arrangement is statically tipped; the logic raises ValueError on x_cg_aft >= x_mg.
• Reading the simplified main-pair lateral angle as the binding check: the tricycle diagonal arm is shorter than the half track, so at a forward CG the diagonal angle (39.7567 deg in the worked example) sits below the main-pair value (40.7462 deg) and is the binding lateral case.
• Taking the mid-wheelbase fraction as the band check: the nose gear carries more when the CG is forward, so the band verdict must be taken at the forward and aft CG limits, not at a single station.
• Treating the layout geometry as the strut load split: the nose fraction here is dimensionless and layout-level only; the strut loads and landing energy for a given wheelbase belong to vehicle-design/sizing/landing-gear-sizing.
• Using exact float equality on computed sums: tan and atan round-trip only to machine precision, so verification uses tolerances (assertAlmostEqual with a delta or math.isclose).

Related leaves

• vehicle-design/sizing/landing-gear-sizing: the strut weight split and landing energy demand for a given wheelbase once the layout is fixed.
• vehicle-design/sizing/landing-gear-retraction-sizing: the retraction mechanism sized after the arrangement exists.
• vehicle-design/sizing/tire-sizing: tire selection from the per-tire load.
• vehicle-design/mass-properties/cg-envelope: the CG travel band from longitudinal stability, taken as a given input here.

Behavior contract (gate 3)

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

python3 scripts/test_landing_gear_layout.py

The test covers the worked-example layout contract (tipback 28.1786 deg, tail strike 16.2602 deg with a 6.2602 deg rotation margin, lateral 40.7462 deg, tricycle diagonal 39.7567 deg at the forward CG limit, nose gear load fraction 0.266667 forward and 0.1 aft), the tangent doubling identities for the aft-CG margin, the tail contact height and the wheel track, the vanishing-angle limits at the contact stations, the nose fraction complement to 1 and the mid-wheelbase 0.5 identity, the band verdicts against NOSE_FRACTION_MIN and NOSE_FRACTION_MAX, the main gear position check, determinism of repeated calls, degree and dimensionless return types, and ValueError rejection of every non-physical input class.

Compliance

• Standards referenced, not reproduced: FAR-25 and CS-25 are transport airworthiness standards (ecfr.gov and easa.europa.eu); the arrangement relations above are standard conceptual design methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.