"Tyrolese"

A tyrolese is an extremely simple way of going from one point to another over a natural obtacle. It is constructed with a cable attached at two points on oposite sides of the obstacle. The following example shows the values of the tension on the cable and the forces on the two fixed points F and G as a function of these parameters:

D     the distance (in meters) between the two fixed points F and G
H     the height of F (in meters) with respect to G.
L     the length of the cable (in m).
P     the weight suspended from the cable (in Kg).

In the example the elasticity of the cable is neglected, or more precissely, it is assumed that the lenght L includes the elongation of the cable.

The user is invited to study the values of the tension and the normal force (normal with respect to the vertical) on the fixed points F and G when the point P is dragged between them. Afterwards he or she is invited to vary the length of the cable and observe that the tension increases dangerously and the normal forces become very large when the cable is shortened. On the other hand, when the weight in P inceases the tension increases only slightly. This shows that the tension depends more on the length L of the cable than on the weight sustained. The user is also invited to study what happens when the height H or the distance D between F and G are changed. The conclusion is that the largest tension is reached when the weight is located at the mid point between F and G. When the cable is very tense, giving a little extra length to the cable goes a long way in diminishing the tension. This is recommended to avoid the attachments to break loose.

It is interesting to observe that the trajectory of P is an ellipse with focii at the fixed points F and G, because the sum of the distances from P to F and G is equal to the length L of the cable.

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	Ministerio de Educación, Cultura y Deporte. Año 2000