Hovercraft Cushion Balance

What is modelled

The craft floats when the cushion pressure times the cushion area equals its weight. Air escapes under the skirt through a gap of height h around the perimeter, as through a thin orifice, and the fan replaces it. If the craft rises the gap grows, the cushion pressure falls and it sinks back, so the gap settles where leakage equals fan flow.

Equations

• Cushion area A = π (w/2)(l/2), w = 6.6 m, l = 7.5 m; lift L = p A; required pressure preq = m g / A.
• Fan flow Q = π(D/2)² v, D = 1.8 m; fan power P = p Q / η.
• Gap leakage Q = Cd S h √(2p/ρ), with S the skirt perimeter (Ramanujan ellipse formula).
• Equilibrium gap h = Q / (Cd S √(2 preq/ρ)).
• Vertical motion m h″ = p(h) A - m g - c h′ with p(h) = min(pmax, ½ρ(Q/(Cd S h))²).

Checks run in the page

• Lift p A against the independent form p π w l / 4.
• Ramanujan perimeter against a numerical arc-length integral.
• The simulated settling height against the closed-form equilibrium gap.
• Jet kinetic power against p Q.

Honest simplifications

Single-plenum quasi-static cushion with a uniform gap, an ideal orifice with a constant discharge coefficient and no compressibility, no skirt flexure, no forward speed, waves or trim. The pressure slider is the highest pressure the fan can develop. A teaching model, not a hovercraft design tool.

• Press Light load and watch the craft rise higher and settle with a larger gap.
• Press Overloaded: the required pressure exceeds the fan rating and the craft stays on its skirt.
• Lower the discharge coefficient (a tighter skirt seal) and see the same fan lift the craft further.