Hydraulic Actuator Sizing

Hydraulic Actuator Sizing (vehicle-design/sizing/hydraulic-actuator-sizing)

Use when you must size a linear hydraulic actuator for an aircraft control or utility load: converting the required output load and the system pressure into the piston area and bore diameter with the pressure-margin factor and the mechanical efficiency, checking the rod-side annulus area for the retract direction, sizing the rod diameter from Euler column buckling over the extended rod length with the design factor, selecting the nearest preferred bore and rod diameters at or above the requirements, and estimating the actuator mass. This leaf implements the load-to-actuator chain in pure Python, stdlib only. It pairs with vehicle-design/sizing/hydraulic-system- sizing, which takes the piston area this leaf produces as the input for its system-level flow demand side; the actuator load that closes the surface side comes from vehicle-design/sizing/control-surface- sizing, and the specific gear mechanism force and stroke belong to vehicle-design/sizing/landing-gear-retraction-sizing. This leaf sizes the actuator structure itself, which no other leaf owns.

Domain quick reference

• Required piston area (extend direction): A = F_req * PRESSURE_MARGIN / (p * MECHANICAL_EFFICIENCY), with PRESSURE_MARGIN = 1.10 covering seal friction and dynamic effects on the required load and MECHANICAL_EFFICIENCY = 0.90 converting hydraulic to mechanical power, so the sizing runs on F_req * 1.1 / (p * 0.9).
• Bore diameter: D_b = sqrt(4 * A / pi), the circle formula applied to the required piston area.
• Annulus area: A_ann = pi/4 * (D_b^2 - D_r^2), the rod-side piston area that remains for the retract direction after the rod occupies the center of the bore.
• Retract capability: F_ret = A_ann * p * MECHANICAL_EFFICIENCY / PRESSURE_MARGIN. The margin load is divided back out, so F_ret compares directly with the required load; the actuator passes only when F_ret >= F_req.
• Rod column sizing (Euler): I_req = F_req * BUCKLING_FACTOR_OF_SAFETY
  • (END_FIXITY_K * L_rod)^2 / (pi^2 * MODULUS_ROD) with the factor of safety 2.0, pinned ends K = 1.0 and the steel modulus 205 GPa, over the extended rod length L_rod (the rod is a column at full extension); solid rod diameter D_r = (64 * I_req / pi)^0.25.
• Rod stress and margin: sigma = F_req / (pi/4 * D_r^2) must stay below STEEL_YIELD = 1100 MPa; the Euler critical load on the actual rod P_cr = pi^2 * E * I / (K * L_rod)^2 gives the buckling margin P_cr / F_req, which the sizing factor holds at or above 2.0.
• Preferred sizes: PREFERRED_BORES_MM = (25, 32, 40, 50, 63, 80, 100,
  125. mm and PREFERRED_RODS_MM = (12, 16, 20, 25, 32, 40, 50, 63) mm; select_preferred returns the first preferred size at or above the requirement so the selection never under-sizes.
• Mass estimate: m = ROD_DENSITY * [pi/4 * D_r^2 * L_s + 0.6 * pi/4 * (D_b^2 - D_r^2) * L_s] with ROD_DENSITY = 7850 kg/m3, the stroke L_s, and the documented 0.6 fill factor on the barrel annulus volume for the barrel wall, seals, gland and fittings.
• Units are SI throughout: N, Pa, m, m2, kg.
• FAR Part 25 (25.671 flight control actuation context) frames the certification setting; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the design point: the required actuator output load F_req (N), the system pressure p (Pa), the extended rod length L_rod (m) and the stroke L_s (m).
2. Convert the load into the required piston area with piston_area, which applies the 1.10 pressure margin and the 0.90 mechanical efficiency, then read the ideal bore with bore_diameter.
3. Select the production bore with select_preferred against PREFERRED_BORES_MM (at or above the ideal value).
4. Size the rod as a column with rod_buckling_diameter over the extended length at the factor of safety 2.0, then select the preferred rod with select_preferred against PREFERRED_RODS_MM.
5. Form the rod-side annulus with annulus_area(bore_pref, rod_pref) and check the retract direction with retract_capability: the annulus force at the system pressure must meet the required load.
6. Close the chain with actuator_review, which returns the piston area, ideal and preferred diameters, annulus area, retract capability, rod stress, buckling margin, mass and the pass/fail verdict in one dict; the annulus, stress, margin and mass use the preferred bore and rod, as in the worked example.
7. Confirm the deterministic checks with the contract test scripts/test_hydraulic_actuator_sizing.py.

Worked example

Aileron or flap actuator: F_req = 40000 N, system pressure 207 bar (20.7e6 Pa), extended rod length 0.35 m, stroke 0.20 m.

• Piston area: piston_area(40000, 20.7e6) = 40000 * 1.1 / (20.7e6 * 0.9) = 2.3618e-3 m2 (23.6 cm2), matching the spec anchor 2.361e-3.
• Bore: bore_diameter gives 54.84 mm (spec anchor 54.8 mm); select_preferred picks 63 mm from the bore list.
• Rod buckling: rod_buckling_diameter(40000, 0.35) = 17.72 mm (spec anchor 17.7 mm within 1 mm); select_preferred picks 20 mm.
• Annulus: annulus_area(0.063, 0.020) = pi/4 * (0.063^2 - 0.02^2) = 2.8031e-3 m2, within 1% of the spec anchor 2.807e-3.
• Retract capability: retract_capability(2.8031e-3, 20.7e6) = 47474 N (spec anchor 47530 N within 1%), above the 40000 N load, so the retract direction passes.
• Rod stress: 40000 / (pi/4 * 0.02^2) = 127.3 MPa, well below the 1100 MPa rod yield.
• Buckling margin on the preferred 20 mm rod: P_cr = 129.7 kN over 0.35 m, margin 3.24 against the factor of safety 2.0.
• Mass: actuator_mass(0.063, 0.020, 0.20) = 3.13 kg (rod 0.49 kg plus the 0.6-fill barrel annulus 2.64 kg), within 10% of the spec anchor.
• Review: actuator_review returns piston_area 2.3618e-3 m2, bore_mm 54.84, annulus_area 2.8031e-3 m2, rod_buckling_mm 17.72, bore_pref_mm 63.0, rod_pref_mm 20.0, retract_capability_N 47474, rod_stress_Pa 1.2732e8, buckling_margin 3.24, mass_kg 3.13 and verdict "pass".
• Counter-example: the same method at 30000 N over a 0.20 m rod picks a 50 mm bore with a 16 mm rod whose annulus gives only 29849 N of retract force, below the load, so the verdict is "fail"; the annulus must be rebalanced or the design point revisited.

Verification

• Confirm piston_area(40000, 20.7e6) returns 2.3618e-3 m2 and that bore_diameter of that area returns 54.84 mm (anchors 2.361e-3 m2 and 54.8 mm within tolerance).
• Confirm rod_buckling_diameter(40000, 0.35) returns 17.72 mm within 1 mm of the 17.7 mm anchor, and that doubling the rod length multiplies the required rod diameter by sqrt(2) (Euler length scaling identity) while doubling the load multiplies it by 2^0.25.
• Confirm select_preferred routes 54.84 mm to 63 mm and 17.72 mm to 20 mm (first preferred size at or above the requirement) and keeps an exact 63 mm requirement on 63 mm.
• Confirm retract_capability on the anchor annulus returns 47474 N, above the 40000 N load, and that it scales linearly with the annulus area.
• Confirm actuator_review on the worked example returns verdict "pass" with mass 3.13 kg (spec anchor within 10%) and that the 30000 N / 0.20 m case returns "fail" because the retract capability cannot cover the load.
• Confirm every non-positive load, pressure, length, stroke and area, every rod at or above its bore, and every requirement beyond the largest preferred size raises ValueError.
• Confirm the review dict keys are exactly the documented set and that repeated calls are deterministic.
• Run the contract test offline: python3 scripts/test_hydraulic_actuator_sizing.py (35 tests, deterministic).

Related leaves

• vehicle-design/sizing/hydraulic-system-sizing: the system-level partner that takes the piston area this leaf produces as the input for its flow demand side.
• vehicle-design/sizing/control-surface-sizing: computes the surface geometry and the actuator load that closes the surface side of the chain.
• vehicle-design/sizing/landing-gear-retraction-sizing: the gear mechanism force and stroke at its own linkage, a specific application rather than a general actuator sizing method.
• vehicle-design/sizing/spoiler-sizing: another surface that loads an actuator through its hinge line.

Pitfalls

• Sizing the bore on the raw load without the margin and efficiency: the piston area runs on F_req * 1.1 / (p * 0.9), so omitting either factor under-sizes the bore (2.3618e-3 m2 against 1.932e-3 m2 on the raw load in the worked example).
• Forgetting the retract direction: the rod occupies the center of the bore, so the annulus area, not the bore area, drives retraction; a heavily loaded actuator at the top of a size envelope can push more than it can pull back, and the review verdict exists to catch exactly that (29849 N of retract against a 30000 N load in the counter-example).
• Checking the rod only in compression stress: the rod is a column at full extension, so the Euler check over the extended length with the factor of safety 2.0 governs the diameter (17.72 mm), not the stress which passes at any reasonable size (127.3 MPa at 20 mm).
• Treating the ideal diameter as the production size: the selection steps to the first preferred size at or above the requirement (54.84 to 63 mm, 17.72 to 20 mm), and the annulus, stress, margin and mass all follow from the preferred pair.
• Sizing the mass on the full barrel volume: the documented 0.6 fill factor on the barrel annulus volume accounts for the wall, seals, gland and fittings, so the raw annulus volume overstates the mass by 40% before density is applied.

Behavior contract (gate 3)

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

python3 scripts/test_hydraulic_actuator_sizing.py

The test covers the worked-example contract (piston area 2.3618e-3 m2 and bore 54.84 mm within tolerance, rod buckling 17.72 mm within 1 mm, preferred selections 63 mm and 20 mm, annulus 2.8031e-3 m2 within 1%, retract capability 47474 N within 1% of 47530 N and above the load, rod stress 127.3 MPa below the 1100 MPa yield, mass 3.13 kg within 10%, verdict pass), the linearity of piston area and retract capability, the circle-formula inverse and Euler length and load scaling identities, the at-or-above preferred selection rule and its bounds, the annulus-too-small review failure at 30000 N, determinism of the review dict, exact dict keys, and ValueError rejection of non-positive load, pressure, length, stroke and area, rod at or above the bore, and requirements beyond the largest preferred size.

Compliance

• Standards referenced, not reproduced: far-25 (14 CFR Part 25, the flight control actuation context of 25.671 in which the sized actuator operates); the sizing relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.