The inevitable swing

Who has stood, has fallen and swung. It is a law behind which there is no sorcery. The equations of motion in three-dimensions are highly nonlinear and impossible to solve analytically, yet numerical methods can do the trick on the fly. One needs only to assume (attention here) that the leash ring is fixed on the mainline and cannot slide. This assumption is perfectly valid in a wide range around the center of the highline, but it collapses when the leash fall occurs at the vicinity of the anchors (leash ring sliding towards the center). Energy dissipation occurs via a number of processes, including webbing visco-elasticity, aerodynamic friction, inelastic deformation of the human body and friction in the leash knots. Given that these processes are hard to simulate, a simple drag proportional to the body speed is used. This choice, although imperfect, is tuned to have a minimal effect on the peak forces occurring in the first bounce.

The pretension T refers to the free line, though ignoring its own weight. Hence, the accuracy of the simulator gradually drops as the weight of the webbing becomes significant compared to the body weight (say beyond 200 m). The non-dimensional fractional distance measures the distance from the nearest anchor scaled by the anchor-to-anchor distance. Namely, on a highline with D\(=\)100 m, a value of δ\(=\)0.3 corresponds to a distance of (δD) 30 m from one of the anchors. When the leash fall does not happen exactly at the midpoint, for a vertical displacement of the leash ring, the additional relative elongation of the webbing towards the near anchor is larger than that towards the far anchor, and so the webbing tension increases unequally at the two sides. Moreover, the line angle is different, too. Consequently, there is an asymmetry causing always a non purely vertical motion. Even if (x,y)\(=\)(0,0) and (u,v)\(=\)(0,0), the trajectory of the body will be purely vertical only for δ\(=\)0.5 (midpoint).

One can run the simulator for a first time with a given pretension and assess what is the equilibrium mainline sag (s\(=\!|z_{end}|-\)d). Then, to simulate a leash fall from the walking position at the same point (δ) along the highline, one simply needs to set: z\(=-\)s\(+\)1 with (x,y)\(=\)(0,0) and (u,v)\(=\)(0,0). The added unity is supposed to represent the vertical distance of the center of mass of the body in respect to the leash ring.

Built with Python via the Flask framework.
© Panos Athanasiadis, Bologna, Italy, 2018.