Frame and Form

Second post about the documentary Man On Wire (here the first) with which we complete the story of Phelippes Petit and his feat of walking across the twin towers on a wire suspended over 400 meters. In this second post will make a short analysis of deformations and forces of the cable used and the physical concepts behind the tightrope walkers acobracias.

Man On Wire - bracing, - ©2008 Jean-Louis Blondeau / Polaris Images

In normal situations the funambulistas Additional cables can use the main cable brace. These bracing, normally placed in the midpoint anchored to the ground and have the function of reducing the oscillations created by walking the tightrope.

In the case of the twin towers that option was not possible due to the height of buildings. For this reason and in order to reduce lateral movement of the cable was chosen for a asymmetric bracing in plan like the one shown above and below.

The curve describing a cable subjected only to its own weight is called Catenary. The horizontal component of cable force at the supports is not negligible and is critical to determine the arrow of cable. The greater strength is the arrow on the lower cable on the midpoint.

Victory Dance - © 2008 Jean-Louis Blondeau - All Rights Reserved

For example, a cable like that used by Philippe Petit weighs approximately q =0.04 kN/m ( 4 Kg/m), if you want to limit the maximum deflection of the cable under its own weight to the value of f_CAT = 0.5 m horizontal force at the supports would be H_CAT= 25 kN (2500 Kgs).

Assuming that the change in cable length is negligible and without taking into account the dynamic effects the arrow of the cable under the weight of a person 70 it en kg F_PP=0.9 m at the midpoint. Assuming an overlap of effects, the total strain would be f_TO = 0.5 0.9 m = 1.4my the total horizontal force would be H_TO= 50 kN (5000 Kgs).

Deformation of the cable unbraced

As mentioned previously a way of limiting this arrow and increase the stiffness of the cable is using struts. Assuming that the struts used by Philippe Petit vain reduce cash in the third central section, deformation caused by the tightrope walker would 0.2my the total 0.7m. or saying it other way, half of you would have if not to use braces. This reduction of the deformed wire and hence horizontal forces at the supports evidence that this feat was rehash thanks to the good structural design.

WTC - August 7, 1974 - © 2008 Jean-Louis Blondeau - All Rights Reserved

Philippe Petit in the documentary mentioned that in addition to vertical and horizontal motion suffers a major cable rotation along its guideline. The asymmetrical struts help greatly to reduce this torque as dangerous to the tightrope.

An essential element of fonambulistas technique is the use of poles. These serve two important functions to increase stability Acrobat. On the one hand to Flectar its own weight due to the pole lowers the center of gravity of the person raising the period of oscillation and making more stable balance tightrope as it occurs in the classical problem of the compound pendulum.

The other advantage of using the pole lies in the increased value of Moment of Inertia the axis of the cable. This way is more difficult than turning on the tightrope cable guideline.

Visits, models and simulations are tools used by structural designers in the process of analysis and structure definition. It is interesting to see how they apply in this documentary of the same tools to a priori situations so far removed from the sheet of paper. This together with the capacity for synthesis of Philippe Petit and company to define the problem at hand makes the design of the deed itself is a work of art in itself.

Meta-Information:

Static Yarn, the theoretical principles of statics thread as the Professor of the UPM D. José M. Goicolea.

Tentetieso, explanation of the physical principles behind the classic toy.

The catenary curve, interactive website that explores the different theoretical approaches to the problem of defining the catenary curve.

Tensile Structures, The cables are in some ways the simplest of textile coverings.

Photos: Jean Louis Blondeau