A prototype application in development (beta version)
Here comes the plot!
This application is still under development while a thorough evaluation against real measurements is ongoing. Until testing and tuning are completed, any values extracted from this simulator must be considered with caution, it should not be assumed that the resulting estimates are accurate enough. Therefore, as for now, no judgements regarding rigging practices and safety in highlining should be made based on this application. In its present form, the application is released only for collecting your ideas and suggestions on how to improve it. Constructive criticism and your feedback are very welcome.
Very soon an article will get published presenting the equations behind this application. Then, there will be improvements. Also, a similar but more advanced application will be used in collaboration with the ISA for assisting safety evaluation of highline rigs upon request (e.g. for certain public events). Everything is based on Flask and Python. Time dependent simulations are coming, too. The plan is to have a web site dedicated to slackline science, also hosting the work of others (articles, applications, experiments, presentations and a small forum for discussing emerging topics). The HTML code does not support cellphones and tablets, but soon it will.
All models are in simulacra, that is, simplified reflections of reality that, despite being approximations, can be extremely useful. Here, highline backup falls are simulated assuming linear elastic behavior for the backup line and the leash. An experimental study (article currently in review) has shown that the assumption of a constant modulus is acceptable for polyester and nylon webbing in a range of strain rates. In a real backup fall there are various aspects that are very difficult to determine and simulate. An example can be the details of the taping applied, or the exact way of falling. Models simplify reality for the benefit of studying and understanding what is more important and what is not.
The basic dynamical concept behind this simulator is the conservation of mechanical energy. Namely, during the fall of the the body, its gravitational potential energy is converted to kinetic energy and finally to elastic energy stored in the webbing and the leash. It is assumed that all kinetic energy is eliminated when the body reaches the lowest point of its trajectory, in effect implying a completely vertical trajectory. It is possible to wave this condition, yet there is little benefit in doing so, especially considering that such a trajectory results in the maximum peak forces and the maximum vertical displacement for a given rig, which are most often the question.
The backup fall is supposed to happen exactly at the midpoint, which is another assumption made for the benefit of simplicity. In reality, falling way off the center can cause severe frictioning between the leash ring and the backup line. This will absorb energy. At the same time the body will acquire horizontal velocity, thus further softening the fall. Though, there is a danger of reaching high temperatures, which will not be assessed here.
On the right side the boxes accept values for a number of variables. More options will be added as the complexity of the application builds up. For the moment there are from top to bottom: m: the mass of the slackliner, accepted range: 0–100 kg. D: the horizontal distance from anchor to anchor: accepted range: 15–300 m. L: the unstretched length of the backup line between the anchors, accepted range: D–1.15D. ρ: the relative excess length, REL = 100(L-D)/D, accepted range: 0–15%. Obviously, knowing L determines ρ and vice versa, thus, to ensure consistency, only one of the two (either one) is accepted as input. Example: D=200m and ρ=5% give L=210m. S: the mainline sag at the midpoint and the level from which the body falls, accepted range: 0–Se, where Se is the sag at the level of backup engagement (see below). d: the leash length (body to line distance), accepted range: 0–2m. E: the stretch (relative elongation) of the backup line at 10kN (%), the accepted range is kept wide to account also for dynamic ropes: 1–40%. N: the number of taping points (integer) between the anchors, accepted range: 0–50. It should be noted that N is not considered in the dynamics of the fall, though it helps visual learning as the aspect ratio of the plot is 1:1 and the angles shown are true angles. Moreover, the displayed curves are true catenaries, therefore setting N=0 gives the curve of the free hanging backup.
At the bottom right of the plot a number of the computed variables are shown: θ: the angle corresponding to Se. Se: the sag at the backup engagement. Sm: the maximum sag of the backup line (when the body comes to a rest rest). Tm: the maximum tension of the backup line and the peak force seen by the anchors. Lm: the maximum tension of the leash and the peak force seen by the body. Em: the maximum relative elongation of the backup line (corresponding to Sm). φ: the maximum angle (called floor-angle) also corresponding to Sm. τ: the duration of the deceleration phase of the body.
(1) Τhe ratio Lm/Tm is determined by the angle φ, which in turn depends strongly on ρ. So, keep your ρ as low as possible so as to avoid critical values of Lm (anything larger than 4-5kN can be seriously harmful). Low stretch webbings induce higher forces, particularly on short highlines. Try it!
(2) The duration of the deceleration phase (the total time until rest in which the leash force exceeds the weight of the body) is a critical parameter for your safety. Even for moderate values of Tm (say 2-3kN), a very short τ is indicative of likely trouble because the body does not have the time to adjust to the forces exerted. Short lines are more susceptible to short fall durations (τ), hence use only stretchy webbings (or climbing ropes) for backup in short highlines and keep the excess length to a minimum (ρ < 4%).
(3) Setting d=0 and keeping ρ and the ratio S/D constant, one can see, as predicted by theory, that decreasing the anchor-to-anchor distance (D) does not affect the peak forces, the maximum elongation and the floor angle (Tm, Lm, Em, φ), but it does affect τ (which gets smaller). When d>0, as in reality, the peak forces increase as D gets smaller. The conclusions are yours.
(4) ISA recommends avoiding in all circumstances anchor forces (Tm) exceeding 12kN. You judge for your selves.
Built with Python via the Flask framework.
© Panos Athanasiadis, Bologna, Italy, 2018.