Landing Gear Height Sizing

Landing Gear Height Sizing (vehicle-design/sizing/landing-gear-height-sizing)

Use when the task is selecting the vertical landing gear geometry of a tricycle-gear aircraft at the conceptual level: solving the static ground line from the ground clearance constraints, setting the main and nose gear heights that level the cabin waterline over the wheelbase, and reporting the clearance margins and the height verdict. This leaf implements a closed-form trigonometric model in pure Python, stdlib only. It pairs with vehicle-design/sizing/landing-gear-layout, which takes the solved gear heights as given inputs to its tipback, tail strike clearance angle and lateral turnover angle checks, and with vehicle-design/mass-properties/ cg-envelope, the source of the CG travel band that fixes the design CG used in the static load share check.

Domain quick reference

• Body frame at the level attitude: stations x in metres aft of the fuselage datum, z in metres positive up from the main gear attach plane, the horizontal plane through the main gear attach point.
• Clearance of a hard point during a nose-up rotation theta about the main gear contact: c(theta) = (H_gl + z_body) * cos(theta) - (x_point - x_mg) * sin(theta). At the level attitude (theta = 0) the clearance is H_gl + z_body.
• Required ground line from one point at one attitude: H_gl >= clearance_req / cos(theta) + (x_point - x_mg) * tan(theta) - z_body. The single closed form holds at theta = 0 and at any rotation angle in the design band.
• Static ground line: H_gl = max over all hard points and all required attitudes of the required ground line. The tail cone lowest point with a rotation clearance is typically the aft binding case; a nacelle or propeller point forward of the main gear contact binds at the level attitude.
• Gear heights: main gear height = H_gl (the main gear is vertical, contact directly below the attach point); nose gear height = H_gl + z_na. The attach heights differ by exactly z_na, so the cabin waterline is level over the wheelbase.
• Tail contact height of the solved geometry: h_tail_contact = H_gl + z_tail. The layout sibling relation tan(theta_ts) = h_tail_contact / (x_tail - x_mg) gives the tail strike angle of the solved geometry and the rotation margin theta_ts - theta_rot.
• Propeller disc lowest point body height: z_hub - radius.
• Nose gear static load share at the design CG from the wheelbase moment balance: P_n / W = (x_mg - x_cg) / (x_mg - x_ng); the main gear share complements it to 1. Feasibility only: the design CG must sit strictly between the contacts.
• Units are SI: m, deg, dimensionless fractions. All angles enter through math.radians via the module constant DEG2RAD.
• FAR-25 and CS-25 frame the transport landing gear context; the relations above are standard conceptual design methodology (Raymer, Gudmundsson, Sadraey, Torenbeek, landing gear chapters), summary-only, never reproduced.

Workflow

1. Fix the wheelbase and hard point geometry: nose gear station x_ng, main gear station x_mg, and the body height z_body, station and required clearances of every hard point (tail cone, nacelle, propeller) that constrains the ground line.
2. Solve the static-ground-line with static_ground_line over the hard points and the design rotation attitude, which returns H_gl and the binding point name.
3. Derive the main and nose gear heights with gear_heights from H_gl and the nose gear attach offset z_na.
4. Report the achieved clearance and margin of every hard point at both attitudes with clearance_at_attitude and clearance_margin.
5. Evaluate the tail strike margin of the solved geometry with tail_strike_angle_deg on the solved tail contact height h_tail_contact = H_gl + z_tail, and compare it against the design rotation attitude.
6. Check the nose gear static load share at the design CG with static_load_share, confirming the CG sits strictly inside the wheelbase.
7. Issue the height verdict: every required margin is non-negative and both gear heights are positive, confirmed by the contract test scripts/test_landing_gear_height_sizing.py.

Worked example

Reference aircraft: twin-turboprop utility transport (King Air 350 class scale, representative conceptual geometry). Nose gear contact at x_ng = 1.40 m, main gear contact at x_mg = 7.40 m (wheelbase 6.00 m), design CG at x_cg = 6.80 m. Design rotation attitude 10.0 deg about the main gear contact. Nose gear attach point 1.00 m below the main gear attach plane (z_na = -1.00 m). Tail cone lowest point at x_tail = 12.40 m (5.00 m aft of the main gear contact) with body height z_tail = -0.45 m and a required rotation clearance of 0.25 m. Propeller disc lowest point from a hub center body height of 0.10 m and a disc radius of 1.15 m (z = -1.05 m) at station 4.90 m with a required level clearance of 0.20 m. Nacelle lowest point at z = -0.60 m, station 5.30 m, with a required level clearance of 0.15 m and a required rotation clearance of 0.15 m.

• Required ground lines: tail cone level 0.450000000000 m, tail cone rotation 1.585491556514 m, propeller level 1.250000000000 m, nacelle level 0.750000000000 m, nacelle rotation 0.382027332295 m. The tail cone rotation constraint governs: H_gl = 1.585491556514 m.
• Main gear height h_mg = H_gl = 1.585491556514 m. Nose gear height h_ng = H_gl + z_na = 0.585491556514 m. Height difference h_mg - h_ng = 1.000000000000 m, exactly -z_na.
• Tail contact height h_tail_contact = H_gl + z_tail = 1.135491556514 m at arm a_t = 5.00 m. Tail strike angle theta_ts = 12.794763238232 deg, a rotation margin of 2.794763238232 deg over the 10.0 deg design rotation.
• Margins: tail rotation margin 0.000000000000 m (the governing constraint binds exactly), propeller level margin 0.335491556514 m, nacelle level margin 0.835491556514 m, nacelle rotation margin 1.185180898483 m.
• Static load share: nose share (7.40 - 6.80) / 6.00 = 0.100000000000, main share 0.900000000000, sum 1.000000000000. Both gears carry positive load.
• Height verdict: every required margin is non-negative and both gear heights are positive, so the height verdict is clearance-ok.

Verification

• Confirm static_ground_line on the worked points returns H_gl = 1.585491556514 within 1e-9 with binding point "tail cone lowest point".
• Confirm gear_heights(1.585491556514, -1.00) returns main_gear_height 1.585491556514, nose_gear_height 0.585491556514 and height_difference 1.000000000000 within 1e-9.
• Confirm the tail rotation clearance recomputed from H_gl equals 0.25 m within 1e-9 (identity I1, the binding constraint round trip), and that the tangent algebra identities I2 and I3 hold within tolerance.
• Confirm tail_strike_angle_deg(1.135491556514, 5.00) returns 12.794763238232 deg within 1e-6 and the rotation margin is positive.
• Confirm static_load_share(6.80, 7.40, 1.40) returns 0.100000000000 within 1e-12 and complements the main share to 1.
• Confirm every ValueError rejection: negative clearance requirements, rotation angle outside (0, 25] deg, wheelbase not positive, empty point list, non-positive ground line, non-positive nose gear height, and non-positive propeller radius.
• Run the contract test offline: python3 scripts/test_landing_gear_height_sizing.py (34 tests, deterministic).

Related leaves

• vehicle-design/sizing/landing-gear-layout: takes the solved gear heights as given inputs to the tipback angle, tail strike clearance angle and lateral turnover angle checks; this leaf is the inverse of its tail strike identity.
• vehicle-design/sizing/landing-gear-sizing: sizes the static strut loads, the nose and main gear CG load split and the shock absorber stroke once the heights and layout are fixed.
• vehicle-design/mass-properties/cg-envelope: the CG travel band source for the design CG used in the static load share feasibility check.
• vehicle-design/sizing/propeller-sizing: the propeller diameter and blade count selection, and the installation clearance check of a given hub height, downstream of the height this leaf solves.

Pitfalls

• Solving the ground line from the level attitude only: a point clear at the level attitude can still strike the ground during rotation, since every aft hard point drops as (H_gl + z_body) * cos(theta) - (x_point - x_mg) * sin(theta); the tail cone rotation requirement governs the worked example at 1.585491556514 m against its 0.450000000000 m level requirement.
• Treating a forward point's rotation clearance as binding: a point forward of the main gear contact (arm x_point - x_mg negative) rises during rotation, so its level-attitude clearance is the binding case, not its rotation clearance (identity I6 in the contract test).
• Confusing the small-angle rise with the exact rise: the tangent rise (x_tail - x_mg) * tan(theta_rot) understates the exact rise h_tail_contact - c_tail by c_tail * (1/cos(theta_rot) - 1), about 1.5% of the exact rise at 10 deg in the worked example (identity I3); use the exact cosine and sine form for the ground line solve, not the tangent approximation.
• Feeding the layout sibling's tail strike angle formula the wrong contact height: this leaf solves h_tail_contact = H_gl + z_tail as an output; the layout sibling's tail_strike_clearance_angle takes h_tail_contact as a given input. Do not reuse a contact height from another aircraft configuration.
• Skipping the static load share feasibility check: a solved geometry with positive gear heights and clearance margins can still be infeasible if the design CG does not sit strictly between the nose and main gear contacts; static_load_share raises ValueError in that case rather than returning a share outside [0, 1].

Behavior contract (gate 3)

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

python3 scripts/test_landing_gear_height_sizing.py

The test covers the worked static-ground-line solve and its per-constraint required ground lines, the gear height derivation and the leveling identity, the achieved clearance and margin of every hard point at both attitudes, the tail strike angle and rotation margin of the solved geometry, the static load share and its complement, the propeller low point, the closed-form identities I1 through I6, the level-attitude round trip, determinism of repeated solves, module constant fixity, and ValueError rejection of every non-physical input listed in the spec validation list.

Compliance

• Standards referenced, not reproduced: 14 CFR Part 25 and CS-25 frame the transport landing gear context; the height-selection relations above are standard conceptual design methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.