parabola formula question

[Ramblinrev]

The side arc in the bridge hammock is an absolute must structurally. While it may not add to the overall strength, it is vital to the form, shape and hang of the bridge hammock. The bridge hammock is called such because it takes it's design inspiration from a suspension bridge. The arc serves to allow the forces to distribute such that they are evenly loaded and maintain a flat surface for the bed. The depth of the arc is variable and has been played with over a lot of trials. I have not kept up with the developments in recent bridge hammock technology, but when I was making them I know there was lot of experimenting going on with the best depth v length v width.

[GrizzlyAdams]

no one wants to bother a Grizz...

So. Two points. One theoretical and of interest only to pointy heads such as myself. A perfect cable with uniform diameter and density hanging from eqi-height towers assumes the shape of a catenary curve. However, attach load to that curve, such as in a suspension bridge, the curve changes slightly and becomes a parabola. Word. The mathematics of how the curve carries the load along the cable and to the towers depends on it. So cut a parabola and hold your head up among pointy heads. But remember that the load-carrying analysis assumes that load is uniformly distributed, and unless you have the shape and uniform density of a railroad tie, in practice that ain't what's happening on the curve.

Second point, practical. Experience shows that pure catenary or parabolic curves aren't necessary at all. Solutions that involve bending flexible poles work just fine.

Conclusion...don't sweat the details on the suspension curve. Set the depth, find a convenient way to make a continuous curve that doesn't change abruptly, and you're golden.

back to my cave now

[thematt]

no one wants to bother a Grizz...

So. Two points. One theoretical and of interest only to pointy heads such as myself. A perfect cable with uniform diameter and density hanging from eqi-height towers assumes the shape of a catenary curve. However, attach load to that curve, such as in a suspension bridge, the curve changes slightly and becomes a parabola. Word. The mathematics of how the curve carries the load along the cable and to the towers depends on it. So cut a parabola and hold your head up among pointy heads. But remember that the load-carrying analysis assumes that load is uniformly distributed, and unless you have the shape and uniform density of a railroad tie, in practice that ain't what's happening on the curve.

Second point, practical. Experience shows that pure catenary or parabolic curves aren't necessary at all. Solutions that involve bending flexible poles work just fine.

Conclusion...don't sweat the details on the suspension curve. Set the depth, find a convenient way to make a continuous curve that doesn't change abruptly, and you're golden.

back to my cave now

TIL that a catenary curve is the physical representation of a hyperbolic cosine function. I could see it was a hyperbolic but was too lazy to look up the definitions. I just had to see the proof to understand things.

I am fairly heavy, around 240 pounds right now. Have you found that the suspension cable in the bridge deforms a lot under this weight? If so would it be beneficial to model the curve as elastic? Really I'm just asking because I think it's fun to get a solid understanding and to have fun, read over complicate, the design of a hammock.

[GrizzlyAdams]

TIL that a catenary curve is the physical representation of a hyperbolic cosine function. I could see it was a hyperbolic but was too lazy to look up the definitions. I just had to see the proof to understand things.

I am fairly heavy, around 240 pounds right now. Have you found that the suspension cable in the bridge deforms a lot under this weight? If so would it be beneficial to model the curve as elastic? Really I'm just asking because I think it's fun to get a solid understanding and to have fun, read over complicate, the design of a hammock.

I had some fun thinking about non-parabolic curves in this ancient post.

[krshome]

BTY Thanks for the #'s Grizz. Sometimes its just easier to ask the master.

[RePete]

I am not a pointy head. I do have a question though regarding catenary and parabola curves as they apply to the hammock. If the hammock is made with a catenary curve will it not be a parabola once you are in it just the same as the cables on any suspension bridge are a catenary until the deck is attached? It took me a bit of google searching and reading things I do not understand to come to this thought. I do not ask to challenge anyone only to seek clarification as to weather I understand correctly. If I do understand correctly then I am really confused as to why starting with a parabola is an advantage over starting with a catenary that will be a parabola as soon as I am in it. If I totally missed on my conclusions the please dismiss my comments and just tell me I am not correct for I am not likely to understand a pointy headed reply. :-)

[thematt]

I am not a pointy head. I do have a question though regarding catenary and parabola curves as they apply to the hammock. If the hammock is made with a catenary curve will it not be a parabola once you are in it just the same as the cables on any suspension bridge are a catenary until the deck is attached? It took me a bit of google searching and reading things I do not understand to come to this thought. I do not ask to challenge anyone only to seek clarification as to weather I understand correctly. If I do understand correctly then I am really confused as to why starting with a parabola is an advantage over starting with a catenary that will be a parabola as soon as I am in it. If I missed on my conclusions the please dismiss my comments and just tell me I am not correct for I am not likely to understand a pointy headed reply. :-)

It is my understanding that a catenary curve is what you get when a rope hangs only under its own weight. Think about power lines, those are an example of a catenary curve. Once weight is applied to the curve it shifts to a parabola, which looks very similar but is mathematically different. Grizz, did I get that right? Please forgive any typos I'm at work replying from my phone.

[GrizzlyAdams]

Point scored. A cat curve reforms to a parabola under UNIFORM load. But load is not uniform, and (referring to a previous quote of mine cited earlier in the thread) practically the difference between a cat curve and parabola with the shallowness of these curves is in within the error of drawing the curve, cutting it, rolling in the webbing. And the parabola is way easier to code up.

[DivaB]

no one wants to bother a Grizz...

So. Two points. One theoretical and of interest only to pointy heads such as myself. A perfect cable with uniform diameter and density hanging from eqi-height towers assumes the shape of a catenary curve. However, attach load to that curve, such as in a suspension bridge, the curve changes slightly and becomes a parabola. Word. The mathematics of how the curve carries the load along the cable and to the towers depends on it. So cut a parabola and hold your head up among pointy heads. But remember that the load-carrying analysis assumes that load is uniformly distributed, and unless you have the shape and uniform density of a railroad tie, in practice that ain't what's happening on the curve.

Second point, practical. Experience shows that pure catenary or parabolic curves aren't necessary at all. Solutions that involve bending flexible poles work just fine.

Conclusion...don't sweat the details on the suspension curve. Set the depth, find a convenient way to make a continuous curve that doesn't change abruptly, and you're golden.

back to my cave now

OMG!!!! Between you and Ramblinrev, I think I finally get it!! I wasn't doing this DIY because I was making it harder than it needed to be. Can someone please forward me my pointy head cap now??

Dang, I'm book marking this!

[DivaB]

Ok....opps, was left with too much time to think (like an entire 15 seconds) If your built like an overweight giraffe....theoretically speaking of course, is your depth still going to be 6" to 6.5"? Out of what width fabric? Lets pretend the height of the person is almost 6'? We won't discuss weight.

Hold onto the pointy cap just a little longer. I'm close though, real close