How Is Speed Calculated on a Zip Line?

[oferar]

Hello. I want to build a small zip line. Basically it is a steel cable anchored in two points with a different height in each anchor. Then you travel along the cable from the highest anchor to the lowest with the help of a pulley to reduce friction.
I found that the cable form a Catenary curve, there are ways to figure the maximum force at each of the anchors, but could not find out how to find the speed at each point of the cable. Basically the cable’s angle should work the speed, but also the cable tension should influence the speed. Do you know how can this speed be calculated or estimated, assuming frictionless displacements, etc?

Tanks very much.
Regards;
Fernando.

 

[NascentOxygen]

http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif Hi, oferar!

This sounds an interesting analysis. though quite beyond me. But will the tension be such that the load (i.e., the person) will distort the original catenary shape significantly? It so, I think this is going to add a major complication to the analysis in that the shape will be in constant change as you travel along.

Good luck, https://www.physicsforums.com/images/icons/icon14.gif and keep safety uppermost!

 

[oferar]

http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif Hi, oferar!

This sounds an interesting analysis. though quite beyond me. But will the tension be such that the load (i.e., the person) will distort the original catenary shape significantly? It so, I think this is going to add a major complication to the analysis in that the shape will be in constant change as you travel along.

Good luck, https://www.physicsforums.com/images/icons/icon14.gif and keep safety uppermost!

Thanks, yes, the shape of the curve will be modified all the time. Seems that if the weight of the cable is not taken into account, I’ll move through an elliptic path, and the cable will form a triangle.

 

[OldEngr63]

As a first shot at this, I would suggest using an energy based approximation to the motion. The exaction motion, including cable weight, is likely to be extremely complicated, but neglecting the cable weight, it may be that an energy approach will be forth coming.

 

[alphy]

Hello Fernando,

I would recommend approaching this problem using the basic principles of physics. The speed of the zip line can be calculated using the equation v = √(2gh), where v is the speed, g is the acceleration due to gravity (9.8 m/s²), and h is the height difference between the two anchor points. This equation assumes that there is no friction or other external forces acting on the system.

However, in reality, there will be some friction and tension in the cable, which will affect the speed. To account for this, you can use the equation v = √(2gh/(1+μ)), where μ is the coefficient of friction. This equation takes into account the frictional forces and will give you a more accurate estimation of the speed.

Additionally, you can also use the equations for calculating the tension in the cable at each point, which can then be used to determine the speed. The tension in the cable will vary along the catenary curve, with the highest tension being at the lowest point of the curve.

I would also recommend conducting experiments or simulations to test the speed of the zip line under different conditions, such as varying weights and cable lengths, to get a more precise understanding of the speed.

I hope this helps in your project. Best of luck!

Regards,