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🌉 Suspended Cable Museum
A cable-suspended roof over a museum hall. Pull the cable taut and it looks elegant but tears the anchors out of the ground; let it sag and tension drops fast but you lose headroom. There's a second lesson hiding here: the parabolic formula every engineer reaches for first is not the right one for a self-weight cable — watch the error grow as sag increases.
Cable
Span L = 60.0 m
Self-weight w = 2.0 kN/m of cable
Anchor capacity: 200 kN
Your Design
Live Result
—
Max Tension (kN)
—
Sag / Span Ratio
Catenary (correct) horizontal tension H—
Parabolic approximation H—
Error from using the parabolic shortcut—
🎯 Goal: keep max tension under the 200 kN anchor capacity. Then push the sag slider to the far end and watch the parabolic error climb past 9%.
Powered by the true catenary (hyperbolic cosine)
solution (
engine/catenary-cable.js) — the catenary parameter is
found by numerical root-finding and round-trip verified against the sag
equation, and the maximum tension is cross-checked two independent ways
(H·cosh(L/2a) vs w·(a+sag)), which agree exactly. The parabolic comparison
is shown honestly rather than hidden: it is a genuinely different physical
assumption (load uniform per horizontal metre, not per metre of cable), so
it is an approximation here, not an error in either formula.Method
Catenaryy = a·cosh(x/a), a = H/w; T_max = w(a+sag) at the supports. Huygens/Leibniz/Bernoulli, 1690s.
ParabolaH = wL²/(8·sag) — correct when load is uniform per horizontal metre (a bridge deck), not for a free-hanging self-weight cable.