# Wall strength and tension on rope-pulley system

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1. Apr 21, 2015

### melodica

Hello,
My friend needs to transfer construction objects across a pond, came up with this idea of tying a rope between the pond and a big tree then transfer objects through a pulley, I'd like to know how to calculate the tension and will the thin concrete wall withstand the load? Here a diagram.
http://i304.photobucket.com/albums/nn192/melodic27/pulley wall_zpshceuf5ah.jpg

The crossing length is 20 meters, the starting point of rope is tied to a big tree, 0.5 meters higher than the point at destination.
The person and rope in purple is to make sure the pulley does not move to faster than, to give a constant velocity of 1 meters per second.
I also have no data of how much shear stress the wall can handle.

If need clarification you are welcomed to ask.

Thank you very much.

2. Apr 21, 2015

### tech99

These systems are very good, but ...the tension in the guide wire can be many times more than the weight being carried. The weight causes the guide wire to dip at the centre, and then there is a triangle of forces, which is easily worked out. If you try to pull the guide wire straight, the tension will be enormous. If you decide how much force the concrete wall can take, then the weight being carried will be several times smaller than this. Of course, if you allow too much dip, the weight will hit the water. It is a good idea with systems like this to monitor the guide wire tension with a dynamometer or to use a pulley block, with weights such as water bags, to create a known tension. If using a dynamometer, put a loose chain across it to act as a preventer in case of a failure.

[Mentor's note: edited to fix the quotes]

Last edited by a moderator: Apr 22, 2015
3. Apr 21, 2015

### sophiecentaur

The tension in the rope will depend very much on the amount of sag that you can permit. I(There will always be some sag, whatever tension you put on the rope!) f you need only 0.5m in 20m then that will require a lot of tension.
A simple way to estimate the order of magnitude of the tension would be to draw a diagram (accurate scale) with a straight line from start to finish and two lines to show the shape of the rope with a load on it at about half way. The tension at that position will be about W/(2 SIN(θ)) where W is the load and θ is the angle between the rope and the straight route from A to B. If you are prepared to have a large sag then the tension can be reduced but, of course, the zip wire will not carry the passenger right to the end.
For your model, you are talking about a very small angle θ and the Sin will be around 1/20, giving 0 times as much tension as the load. A 80kg man, hanging on the wire would have a weight of 800N and the tension would be 8kN!!!!. A single skin wall would be pulled over, for sure. You will notice that these systems nearly all use a bracing mechanism to provide the lateral strength (for example this link) Google zip wire images to see many examples. Also google zip wire design.

If you want kids to use it, in particular, then you have to consider health and safety. Sorry to bring it up but PF is very safety conscious.

4. Apr 22, 2015

### melodica

Thank you very much Tech99 and Sophiecentaur, substituting the weight to be 40 kg, I did the calculation on the worse case if one line is straight, and found that the tension is as huge as 8 kN, and needed to use some support for sure. The support is also drawn in the diagram.
Here is the free body diagrams of how I did the calculation for the tensions.

http://i304.photobucket.com/albums/nn192/melodic27/pullet FBD_zpsrvfbzzqt.jpg

So about wall strength I will use the beam bending calculation for fixed beam /shear strength of given wall material.

5. Apr 22, 2015

### sophiecentaur

For the wall fixing, I would personally not rely on it at all and use the sort of triangular sheerlegs that the zip wires all seem to use. The wall would be convenient to locate it against but there is a problem with mixing resilient and rigid structures (i.e. using a frame and a wall) in that the wood can move a bit before providing its force so the total force could well be acting on the wall unless you attach your wire directly to the wood and not the wall and allow some movement in the mounting.

6. Apr 22, 2015

### OldEngr63

Unless you are prepared to deal with extremely large forces, you better plan on lots and lots of sag. This will reduce the forces, but at the expense of making it more difficult to move the load.

7. Apr 23, 2015

### sophiecentaur

Which is why all the zip wires you see in kids' play areas have very high legs on them. I get the feeling that it is unlikely to find the ideal anchor points naturally occurring at either end of a randomly chosen route.
It's also important do have some natural slowing down at the end of the ride. There must be some significant 'uphill' near the bottom end.