Catenary curve

[paulmcz]

I am wondering if anybody ever seen a LISP routine that draws a 'catenary' (hanging chain) curve? I am looking for program that takes coordinates of the two anchoring points and length of the chain and then draws the curve.
Anyone?
Paul.

[peter]

I looked into the formula's for catenary curves and found that it requires more information than the three parameters you listed. I think you could solve for the curve if you added one more parameter. The unit weight per length of the catenary. This affects the amount of sag. The lighter the cable the more like a parabola it becomes. I found a few cool sights on the internet that showed the formula's.

Maybe we could create a routine to do this. Do you want it to draw the curve in 3d space or just 2d? Do you have the unit weight of your chain/cable?

Peter Jamtgaard

[Ed Jobe]

I have one I found for doing cables. I'll post it later when I dig it up.

[Ed Jobe]

Here it is.

[paulmcz]

Peter,
Thanks for your reply.
Here is the situation:
I have 2 different chains here. One is a jewelry chain, weighing almost nothing and the other is an industrial ball chain, several times heavier. They both have the same length and are suspended from the same 2 points, yet they both form identical curve.
You see, this is about crystal chains, those you could see on large custom made chandeliers. Single chains themselves do not weigh much. Let’s say 1unit of weight per 1 inch of length. Because of cost, the length, or number of crystals in each chain is very important to know at the time of design.
2 suspension points are usually given and are very rarely in the same elevation.
This is all I have to work with.
I am trying to figure it out for some time now but so far I couldn’t get anywhere.
Watching these 2 chains on the wall in front of me and reading all kinds of info on the web made me think that it probably doesn’t matter how heavy the chain is. It, at least, looks like it if you see it with naked eye.
For now, I usually simulate the situation in real world and then, trace the curve from piece of paper. Especially when there are changes, it would be handy to have a routine drawing the curve in full scale on the screen. 2D curve would be just fine.
If you have an idea of how to approach this problem, I’d really appreciate your help.
Thanks again,
Paul.

[QUOTE=peter]I looked into the formula's for catenary curves and found that it requires more information than the three parameters you listed. I think you could solve for the curve if you added one more parameter. The unit weight per length of the catenary. This affects the amount of sag. The lighter the cable the more like a parabola it becomes. I found a few cool sights on the internet that showed the formula's.

Maybe we could create a routine to do this. Do you want it to draw the curve in 3d space or just 2d? Do you have the unit weight of your chain/cable?

[paulmcz]

Ed,
Thanks for the routine. It works fine but as I mentioned before, I need to start with the length of the chain and 2 susp. points. I don’t know the tension. It is just a hanging chain. Tension is very close to weight of the chain.
Thank you,
Paul.

[soorajedu]

Ed

I have tried your routine but i failed to get a catenary because of the unknown unit system. Can u give the unit system which used in your routine?

Thanking you
S

[Ed Jobe]

First of all, I didn't write it. I got it off the internet. However, it sounds like you haven't set the units in your dwg. Use the UNITS command.

[soorajedu]

I have gone through your Lisp routine, but i could not trace out the unit system used for the routine. Can you please tell me the units for the Tension of cable and the cable weight for the attached routine?

[gisdude]

I have a question regarding units. I set up my model space to be inches, and I assume this is what the routine calls for? It seems like it works out ok.

[cwake]

I have a question regarding units.
It's been a while since I looked at Catenary, but linear units wouldn't affect the routine posted above. Think of it as plotting a mathematical function where the x units (horizontal) and the y units (vertical) are the same unit of measurement. There is no option to distort the horizontal to vertical scale in the function, so it wouldn't change anything. It's just x units long by y units high.
And since my understanding of catenary theory is that you use the same unit for both the tension in the cable and the mass per unit length that too would cancel out, because the function uses a ratio of the two. i.e. kg and kg, or Newtons and Newtons, or lbs and lbs.
Of course if you had 3 points on the curve you could calculate the catenary constant from them without tension and unit mass.