Attached mathcad 14 file analyzes zipline. It accepts three primary inputs. Horizontal span and vertical span are x&y distances between cable attach points. Max sag is variable to control tension. Forces are calculated for relaxed cable as well as for traversing load across span. Animation is provided at end to show traversing load. I'd like to disclaim all responsibility for injury or death resulting from use of this analysis.
Found error in calc's when noticed that right saddle angle did not change polarity when traversing along cable. Corrected formula for right saddle angle. It than affected force calc's which have also been updated. Rev2 file is attached. Glad I stated my disclaimer.
On 11/22/2009 5:02:32 PM, dickkeane wrote: >Found error in calc's when >noticed that right saddle >angle did not change polarity >when traversing along cable. >Corrected formula for right >saddle angle. It than >affected force calc's which >have also been updated. Rev2 >file is attached. Glad I >stated my disclaimer.
To make it work in Mathcad v11, you need to initialize mtrial and nloops. In addition, M11 doesn't like the first range variable definition in the animation section (has form 1,1..1)
Like usual, the project lacks a minimal abstract, no matter how it looks obvious or not. The catenary is a word but not a function in the real world of applications. The pure catenary is the "chainette" and it changes shape to a parabola in suspended bridges. In between, the function is as per the user best fit or best model. In this work sheet, an Hermite spline is concluded. It takes the shape of maybe not pure "chainette" but up to parabola (maybe not pure parabola either). From this concept and given some fixed parameters and an adjustable one, one can shape the resulting curve. Which based on the distributed load and the length will give a very plausible shape, shown by the two combined splines. I'm surprised the project does not start by a DE ? Maybe the two sagging functions could be plotted continuous ?
The animation is visually correct, except for the minor error noted in the post from the originator. Is there a more compact construct doing same ? The "Zspline" now makes sense as illustrated. OK, I toke Hermite as an example, but it could be any of the ones previously noted.
A zip-line (also known as a flying fox, zip wire, aerial runway, aerial ropeslide, death slide or tyrolean crossing) consists of a pulley suspended on a cable mounted on an incline. It is designed to enable a user propelled by gravity to traverse from the top to the bottom of the inclined cable, usually made of stainless steel, by holding on or attaching to the freely moving pulley. Zip-lines come in many forms, most often used as a means of entertainment. They may be short and low, intended for child's play and found on some playgrounds. Longer and higher rides are often used as a means of accessing remote areas, such as a rainforest canopy. Zip-line tours are becoming popular vacation activities, found at outdoor adventure camps or upscale resorts, where they may be an element on a larger challenge or ropes course
I have enjoyed the Zip-line indoor adventure ! I guess the "zspline" would do as well as Hermite.