Landing Gear Retraction Sizing

Landing Gear Retraction Sizing (vehicle-design/sizing/landing-gear-retraction-sizing)

Use when you must size the landing gear retraction mechanism at the conceptual level: converting the gear weight acting ahead of the retract pivot into a retraction moment, that moment through the actuator arm into an actuator force with a design factor, the two fixed links of the four-bar linkage into an actuator stroke by the law of cosines between the down-locked and up-locked geometry, the same moment into down-lock and up-lock hold loads at their lock arms, and the wheel plus folded strut envelope against the bay dimensions into a stowage verdict. This leaf implements that chain in pure Python, stdlib only. It pairs with vehicle-design/sizing/landing-gear-sizing, which sizes the static strut demand at touchdown and stops before the mechanism, and with vehicle-design/sizing/hydraulic-system-sizing, which takes the actuator force computed here as the demand on the hydraulic power source.

Domain quick reference

• Retraction moment about the pivot: M = W * d, with W the gear weight (N) and d the gear CG arm (m) ahead of the retract pivot.
• Actuator force: F = K * M / r_act, with r_act the actuator attach arm and K the design factor, K = 1.5 default, never below 1. The design factor covers friction in the joints and mechanism inefficiency at the conceptual level.
• Linkage law of cosines: the pivot, the gear attach point and the actuator attach point form a triangle with fixed links a and b; the effective link length between the two attach points is L = sqrt(a^2 + b^2 - 2 a b cos(theta)) with theta in degrees inside (0, 180). L always lies between |a - b| and a + b for realizable geometry.
• Actuator stroke: stroke = L(down) - L(up), the change in effective link length when the gear travels from the down-locked to the up-locked angle. A non-positive stroke means the up-lock geometry is longer than the down-lock geometry and the actuator cannot retract the gear.
• Lock hold load: R = factor * M / r_lock at the lock arm, factor 1.0 default for the hold-load check; the gear moment is reacted by the over-center lock rather than by the actuator once locked.
• Stowage: the wheel diameter, wheel width and folded strut length must fit inside the bay length, bay width and bay depth; any violation fails the stowage check with a reason per dimension.
• Units are SI throughout: N, m, degrees. All angles enter the model through math.radians.
• FAR 25.729 frames the retraction system context (the gear must stay down in the event of a retraction system failure and up during flight); the relations above are standard engineering methodology, summary-only, not regulatory text.

Workflow

1. Fix the gear demand: gear weight W and its CG arm d ahead of the retract pivot (retraction_moment).
2. Choose the actuator attach arm and the design factor, then size the actuator force with actuator_force (K * M / r_act).
3. Fix the linkage: the two fixed links a and b of the four-bar triangle and the down-locked and up-locked angles (link_length for each position, or actuator_stroke directly for the stroke).
4. Check the stroke sign: a down angle smaller than the up angle, or equal geometry at both positions, raises ValueError because the actuator cannot retract the gear.
5. Size the lock mechanism: lock_reaction at the down-lock and up-lock arms with the hold-load factor.
6. Check stowage: stowage_check on the wheel diameter and width and the folded strut length against the bay length, width and depth.
7. Roll everything up with retraction_summary for the complete dict: moment, force, stroke, linkage, lock reactions and the stowage verdict.
8. Confirm the deterministic checks with the contract test scripts/test_landing_gear_retraction_sizing.py.

Worked example

Reference main gear: gear weight 14000 N with CG arm 1.10 m ahead of the retract pivot, actuator attach arm 0.35 m, design factor 1.5; four-bar links a = 0.55 m, b = 0.40 m; down-locked angle 85 deg, up-locked angle 8 deg; down-lock arm 0.80 m, up-lock arm 0.60 m; wheel 0.66 m diameter x 0.22 m wide; folded strut 2.80 m; bay 0.70 m x 0.30 m x 3.00 m. Module outputs:

• Retraction moment: M = 14000 * 1.10 = 15400.0 N m.
• Actuator force: F = 1.5 * 15400 / 0.35 = 66000.0 N (66.0 kN).
• Effective link lengths: L(down) = 0.6513 m at 85 deg, L(up) = 0.1637 m at 8 deg.
• Actuator stroke: 0.6513 - 0.1637 = 0.4876 m (about 488 mm).
• Down-lock hold load: 15400 / 0.80 = 19250.0 N.
• Up-lock hold load: 15400 / 0.60 = 25666.7 N.
• Stowage: 0.66 <= 0.70, 0.22 <= 0.30 and 2.80 <= 3.00, verdict PASS with an empty reason list.

Pitfalls

• Ignoring the stroke sign: the actuator stroke is L(down) - L(up), and a down angle below the up angle (or equal geometry at both positions) raises ValueError because the actuator cannot retract the gear - a non-positive stroke is a kinematic failure, not a sizing nuance.
• Skipping the design factor on the actuator: the force is K * M / r_act with K = 1.5 default and never below 1, covering joint friction and mechanism inefficiency; an undiscounted actuator force under-sizes the actuator and the hydraulic demand.
• Reading the lock loads off the actuator force: once locked, the over-center lock reacts the gear moment (R = factor * M / r_lock), not the actuator; the down-lock and up-lock hold loads use their own lock arms (19250 and 25666.7 N in the worked example).
• Sizing the mechanism without the stowage check: the wheel and folded strut envelope must fit the bay in every dimension, and the check reports a reason per failing dimension - a mechanism that retracts into a bay that cannot hold the gear is not sized.
• Misreading the linkage triangle: the effective length L = sqrt(a^2 + b^2 - 2 a b cos(theta)) always lies between |a - b| and a + b, and the angle must sit inside (0, 180) degrees; a link pair outside that geometry raises ValueError.
• Doing the static gear sizing here: the touchdown strut demand, nose and main CG split and shock absorber stroke belong to landing-gear-sizing; this leaf sizes the retraction mechanism for a gear that leaf already sized.

Verification

• Confirm retraction_moment(14000, 1.10) returns 15400.0 N m and that doubling the gear weight doubles the moment.
• Confirm actuator_force(15400, 0.35) returns 66000.0 N; doubling the design factor doubles the force and doubling the actuator arm halves it.
• Confirm link_length(1.0, 1.0, 60.0) returns 1.0 m (equilateral law of cosines) and link_length(1.0, 1.0, 90.0) returns sqrt(2); the even cosine identity makes the length at theta equal the closed form at -theta.
• Confirm actuator_stroke(0.55, 0.40, 85.0, 8.0) returns a 0.4876 m stroke and that a down angle below the up angle raises ValueError (up-lock not reachable).
• Confirm lock_reaction(15400, 0.80) returns 19250.0 N and the reaction is inversely proportional to the lock arm.
• Confirm stowage_check passes the nominal wheel and strut and fails with one reason for an oversize wheel and two reasons when the strut is oversize too.
• Confirm every non-positive weight, arm, link, angle or dimension, every angle outside (0, 180) degrees, and every design factor below 1 raises ValueError.
• Run the contract test offline: python3 scripts/test_landing_gear_retraction_sizing.py (35 tests, deterministic).

Related leaves

• vehicle-design/sizing/landing-gear-sizing: the static strut demand at touchdown, the nose and main gear CG split and the shock absorber stroke; it sizes the gear before the mechanism, this leaf sizes how the gear retracts.
• vehicle-design/sizing/tire-sizing: the wheel and tire dimensions used here as the stowage envelope inputs.
• vehicle-design/sizing/hydraulic-system-sizing: the hydraulic power source; it takes the actuator force computed by this leaf as its actuation demand.
• structures/loads/landing-ground-loads: the ground load cases that bound the gear structure the retraction mechanism carries.

Behavior contract (gate 3)

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

python3 scripts/test_landing_gear_retraction_sizing.py

The test covers the reference gear sizing contract (moment 15400 N m, actuator force 66000 N, link lengths 0.6513 and 0.1637 m, stroke 0.4876 m, lock reactions 19250 and 25666.7 N, stowage PASS), the scaling identities (weight, design factor, actuator arm, lock arm), the equilateral and sqrt(2) law-of-cosines closed forms with the cosine-even identity, the stroke sign guard, dict key contracts, determinism, and ValueError rejection of every non-physical input.

Compliance

• Standards referenced, not reproduced: FAR 25.729 is a regulatory requirement (retraction system context); the relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.