# Hanging cable (catenary)

• joel_f
In summary, the conversation discusses determining the tension a in the equation of a hanging cable with known length and end points. The equation involves a horizontal translation h and the weight of the cable is not important for a computer simulation. It is possible to find a numerical approximation for a based on the given information and an equation involving the distance between end points and the length of the cable. There is also a question about whether this method would work for end points of unequal height and if the equation used is correct for this type of catenary. Lastly, there is a question about solving for tension in a scenario where the force acting on the cable is not equally distributed, such as a fish on a fishing rod or a cable with increasing density towards one end

#### joel_f

hi~
i need to determine the tension a in the equation of the hanging cable y=acosh(x-h)/a+k with a known length and known location of end points. i figured out how to determine the horizontal translation h but i need a in order to do it and to have the complete equation.

this is for a computer simulation where the weight of the cable is not important. this is why i condensed tension in the formula down to a. if the weight is a requirement then it can be set, in which case i would need to find the horizontal force acting on the cable.

is it possible to find the tension with the given information?

The length of the cable L is given by $$y=2a\mbox{sinh}\left(\frac{d}{2a}\right)$$, where d is the distance between the end points of the cable (I assumed they were at equal heights based on your equation). You can get a numerical approximation of a from this equation after substituting in the known values of d and L.

would this work for end points of unequal height? am i using the wrong equation for the catenary of this type?

Check this out.

Hello benorin,

I hope you will still get this. I very much liked your extensive answer of the problem.

What if you would replace the force acting on the cable from being gravity to drag. In other words what if the force is not equally distributed. Like a fish on a fishingrod swimming around the fisherman, or a cable with increasing density towards one end.

Can this be solved?

Regards,
Seuren