Presets
Playback
Span, cable and cabin
A counterweight keeps the horizontal cable tension constant; the cabin adds a point load that moves along the span.
Model checks
The science
What is modelled
A taut carrying cable with constant horizontal tension H under its own weight w per metre and a cabin weight P at distance a. The shape is the bending-moment diagram of a beam with the same loads, divided by H.
Equations
- Sag
y(x) = M(x) / HwithM(x) = w x (L - x) / 2 + P (L - a) x / Lfor x below a. - Vertical reactions
Vl = w L / 2 + P (L - a) / L,Vr = w L / 2 + P a / L. - Tension at a tower
T = sqrt(H^2 + V^2). - Extra cable length
8 d^2 / (3 L)for a parabola of sag d.
Checks run in the page
- Parabola against the exact catenary for self weight.
- Finite-difference cable with a nodal cabin load against the closed form.
- Force balance and end slopes.
- Cable length against the series.
Honest simplifications
Small-sag theory with level towers, constant horizontal tension, no rope stretch, no wind and no haul-rope or carriage dynamics. The 900 kN breaking load is an illustrative figure.
What to try
- Press Long span, light tension and see how sag grows as 1 / H.
- Press Heavy cabin, high tension to see a stiff cable carry a heavy load.
- Watch the tower tensions swap as the cabin crosses the middle.