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In-Flight Menagerie

'shame, shame, to have lived scenes from a woman"s magazine'

Monday, July 04, 2005

Funicular Wind Tunnel

I believe a funicular system can be physically modeled at a reduced scale, and that such a model would benefit EcoSystems and other suspended-cableway groups. Just as a wind tunnel attempts to match Reynolds numbers to create correlations to full-scale functionality, I believe the relevant variables of funicular systems could be matched in a scale model. Maybe we could even made some dimensionless numbers from empirical testing. I see a look-up table being created.

I don't think this is a new idea. I read on the web - and can't recall now where it was - that Cathedral designers hundreds of years ago would hang weights from wires to estimate the shape their arches should take.

The principle reference for this post is from brantacan.co.uk. It states that in a funicular system, "the relevant parameters are the length, diameter, density and Young's modulus of the material, and the curvature of the shape when hung."

After reading the Brantacan web site, I got excited that a numerical model could be made in Matlab or Excel to model how variations in the EcoSystems design would affect cable tension. I ran into a roadblock as soon as I thought more about how trolley wheel size affects tension. A trolley wheel is not a point load, and the larger the wheel diameter, the more distributed are the forces. Maybe a parabolic distribution of force across the wheel diameter would be good - parabolic is in my mind from the pieces I've read about Hertzian Contact Stresses and how they distribute.

I haven't thought a great deal on how to solve the wheel-force-distribution problem, because I don't think a numerical model is entirely necessary. EcoSystems already has bridges that work, and banana plantations have decades of overhead-cableway experience. What we're looking for are answers to how variations in the current funicular setup will affect tension.

So if a small wire - say a guitar wire - were matched reasonably to a AISI 1045 11mm cables for [1] density and [2] Young's Modulus, and a sample span in the office had a comparable [A] length to [B] wire diameter ratio to a real bridge, then useful data could possibly occur.

The extent to which AISI 1045 11mm cables deviate from 'the line of zero bending moment' in >40m spans, versus how much a guitar wire deviates from 'the line of zero bending moment' is a good question. I bet that if the wire looks long and skinny with a long span, we're doing well and can make the assumption our curve will follow 'the line of zero bending moment'.

I think that if the reader [A] follows along with the Hanging With Galileo link to understand the angle of deflection of a cable is directly related to its tension, and [B] reads and understands the entire Brantacan series on funiculars, keeping in mind there is a continue button at the bottom of lots of the pages, then one could build a scale model bridge to experiment with configurations and limitations of EcoSystem's bridges.


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