Presets
Playback
Line and anchors
Span and pretension set how the line sags; the line type sets its stiffness EA.
Walker
Mass, position and gravity. Press Walk to cross the line, Bounce to excite it.
Layers
Model checks
The science
Model
A pretensioned elastic line of span L is stretched between two rigid anchors. Its free (unstretched) length is L0 = L / (1 + T0 / EA), so the empty line carries the pretension T0. The walker is a point load W = m g at a material point at fraction a of the free length. The line is two straight segments of length l1 = sqrt(x^2 + d^2) and l2 = sqrt((L - x)^2 + d^2), where x is the horizontal position and d the sag. Each segment carries the tension Ti = EA (li - li0) / li0.
Equilibrium
Horizontal: T1 x / l1 = T2 (L - x) / l2. Vertical: (T1 / l1 + T2 / l2) d = W. In the middle of the line this gives T = W l / (2 d) ~ W L / (4 d): the smaller the sag angle, the larger the tension. A sag of one twentieth of the span multiplies the body weight by about 5 at each anchor. The same state minimises the total potential energy Pi = sum EA eps_i^2 l_i0 / 2 - W d, which the page uses as an independent check.
Bounce
The vertical stiffness at equilibrium is k = dFv / dd with Fv = (T1 / l1 + T2 / l2) d. The bounce is a damped oscillation y'' + 2 zeta w y' + w^2 y = 0 with w = sqrt(k / m) added to the quasi-static sag. A tighter line and a lighter walker give a higher frequency. The page integrates the nonlinear line force with RK4 and compares the measured period with 2 pi / w.
What is simplified
The line mass is neglected (its own sag is below a centimetre for these loads). The walker is a point mass: the real weight shift, the swing of the feet and the hysteresis of nylon webbing are not modelled, and the anchors and trees are rigid. Webbing stiffness values are typical orders of magnitude, not product data. The walker animation is cosmetic; the line state is the exact solution of the equations above.
What to try
- Walk to the middle and compare the anchor load with the body weight: it is several times larger.
- Raise the pretension: the sag falls but the anchor load rises. The tension-sag graph shows the trade-off.
- Switch to a steel cable or the Moon preset and watch the bounce frequency change.
- Press Bounce and compare the frequency readout with the oscillation in the time graph.