Oleo-Pneumatic Landing Strut

What is modelled

One main-gear strut supports a share of the aircraft mass. At touchdown the piston is pushed up into the cylinder at the sink speed. A sealed nitrogen chamber acts as a polytropic gas spring; oil forced through an orifice gives damping that grows with the square of the compression speed. Together they must stop the sink motion within the stroke without exceeding a sensible load.

Equations

• Gas spring p = p0 (V0 / (V0 - A s))n, force Fg = (p - patm) A, n = 1.35 for a fast compression.
• Orifice damping Fd = ρ A³ v |v| / (2 Cd² Ao²) on compression; rebound is damped less (0.3 x).
• Motion m s″ = (1 - λ) m g - Fg - Fd, where λ is the wing lift as a fraction of weight.
• Load factor nz = Fpeak / (m g); energy ½ m v0² + (1 - λ) m g smax = ∫ F ds.

Checks run in the page

• Static compression from the gas law against a numerical solve.
• The orifice pressure drop from Bernoulli against F_d / A.
• Energy balance at maximum stroke.
• A half time step changes the peak stroke by less than half a percent.

Honest simplifications

The 3D page is a mechanism viewer and has no strut solver, so the geometry and numbers here (piston area 80 cm², 0.40 m stroke, 4.5 L gas volume) are illustrative, not those of a real aircraft. The tyre, the unsprung mass, the metering pin and the oil compressibility are ignored. Not an aircraft design or certification tool.

• Press Hard landing: the strut bottoms out and the load factor spikes.
• Press Soft pre-charge and see the stroke grow while the peak load falls.
• Increase the orifice size and watch the damping fall and the gas spring do the work, with more bounce.