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Old Oct 30th 2018, 11:25 AM   #1
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Winch pull force - Double Catenary Problem

Guys, I have a question and maybe you can help me. I will describe the scenario:

A winch should pull out the electrical cable configured as shown in the figure 1. In this configuration, two catenaries are present. I would know how to solve the problem if there was only one catenary. However, the presence of a second one is complicating me. Thus, the following doubt arise:

How to relate T_Catenary II (Figure 3) with T_Catenary (Figure 4) at the right end of the cable segment AB? (i.e, find an expression of T_Catenary = f(T_Catenary II, and, further, solve for F_winch.

Further information

1. The heights of the supports are the same.

2. Distance EF >> Distance FG (thus configuring the cable's tendency to "run" toward the spool if no force holds its left end.

3. The ratio of mass per length - w [kg / m] is known.

4. The winch pulling force must be small enough that, during the pulling, the cable maintains its initial configuration.

5. The spool has no rolling resistance (bearings with zero friction)

Hope to read your answers soon. Thank´s
Attached Thumbnails
Winch pull force - Double Catenary Problem-figure_1.jpg   Winch pull force - Double Catenary Problem-figure_2.jpg   Winch pull force - Double Catenary Problem-figure_3.jpg   Winch pull force - Double Catenary Problem-figure_4.jpg  
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Old Oct 31st 2018, 02:23 PM   #2
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Please clarify - is the support at F considered to be frictionless, so that the tension in the cable to the left of it is equal to the tension to the right? If the tension in the two catenaries is the same, the amount of "sag" in the short catenary will be much less than the "sag" in the long catenary, unlike what you show in your picture. Is your objective to derive the formula for the shape of the catenaries, based on the pulling force F and distance between the supports?

Last edited by ChipB; Oct 31st 2018 at 02:34 PM.
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