Hydropneumatic Suspension Strut

What is modelled

A sprung mass m rests on a hydropneumatic strut. A gas volume behind a floating piston acts as a spring; oil displaced by the rod passes through a metering orifice, giving a damper force that grows with the square of the velocity. A sine road (or a one-off bump) moves the base.

Equations

• Gas: p = p0 (V0 / (V0 - A c))γ, force A (p - patm), linear stiffness k = γ p A² / V, natural frequency f = (1/2π) √(k/m).
• Orifice: Δp = (ρ/2) (Ah v / (Cd Ao))², force Ah Δp sign(v), plus linear seal damping.
• Motion: m a = Fgas + Fdamp + Fstop - m g, solved with RK4 at 240 Hz (implicit fallback for very stiff damping).

Checks run in the page

• Static compression against the root of A (p(c) - patm) = m g.
• Small free oscillations against f = (1/2π) √(γ p A² / (V m)).
• Energy balance: work from the road minus heat in the damper equals the change of stored energy.

Honest simplifications

One degree of freedom, a constant polytropic exponent (no heat exchange model, no oil compressibility or gas dissolution), a turbulent orifice with a fixed discharge coefficient, and no tyre or wheel mass. It is a teaching model, not a suspension design tool.

• Choose Resonance and watch the mass amplitude exceed the road amplitude near the natural frequency.
• Choose Over-damped: the small orifice makes the strut stiff and passes bumps through.
• Press Trigger bump with the road off (set the amplitude to 0) and watch the energy graph.