Rope Bridge Physics Simulator - 2D Cable Sag, Tension and Walker Load Profile

Presets

Speed

Live readouts

Graphs

Numerical checks

running...

How to use

The cable and deck are a chain of 40 elastic segments; colour shows tension relative to the break load (green low, red near failure). A walker crosses and its weight (plus a footstep ripple) loads the rope. Try: (1) Slack and sagging - more slack means a deeper sag but a much lower tension; (2) Taut rope - small sag, very high tension: the safety factor drops; (3) Group of 300 kg - read the safety factor; (4) Resonant gait - walking at the bridge's natural frequency with low damping builds up large swinging; (5) compare the simulated shape with the green catenary in the first graph. Space pauses, R rebuilds.

The science

Hanging cable. A flexible cable of weight per length w sagging under its own weight takes the shape of a catenary: y = a (cosh(x/a) - 1), a = H / w where H is the (constant) horizontal tension. For a span L and small sag s this is close to the parabola s = w L^2 / (8 H), so halving the sag doubles the horizontal force: tight ropes carry more load.

Tension at the anchors. The vertical reaction is half the total weight V = W/2 (symmetry), and T_end = sqrt(H^2 + V^2)

Moving load. A point load P at position x adds a kink in the cable: for a weightless taut cable the added sag is about P/(4H/L) at mid-span; the walker's step rhythm adds a periodic force P (1 + g sin 2 pi f t).

Natural frequency. Transverse waves on a taut rope travel at sqrt(H/mu), so the fundamental frequency is f1 = (1/2L) sqrt(H/mu) - when the stepping frequency equals it the response grows until damping balances the input, which is why soldiers break step on bridges.

Checks. (1) the end vertical reaction equals half the total weight to 1%; (2) mid sag matches the analytic catenary for the measured H within 3%; (3) end tension equals sqrt(H^2 + V^2); (4) an 80 kg walker at mid-span adds sag.

Simplifications. 2D in-plane motion only (no sideways sway or twist), planks as lumped mass, linear elastic cable with no creep or hysteresis, a single point-load walker with a sinusoidal gait force, viscous damping instead of real friction, and a pre-sagged rest shape with no pretension adjustment.