Thoughts On The Bridge Hammock Cat Cuts.

[headchange4u]

I have fabric on the way that I am going to use on my first attempt at making a Bridge hammock. I was sitting here this morning playing around with lVleph's Excel program (via blackbishop's directions for making a cat cuttarp) for making the cat cut curves.

I have decided that I am going to shoot for a finished hammock that will be 84" (~7') long and I will be using fabric that is about 60" wide. Using lVleph's program I have been fooling around with the sag inch/ft measurement which basically influences the depth of the cat cut.

At 1" sag/ft the deepest part of the cat cut is going to be 5 1/8" per side which means that the narrowest part of the hammock (the middle part) is going to be about 49-50". If you go with a 2" sag/ft the deepest part of the cat cut is 10 1/8" per side which means you the narrow part of the hammock will be somewhere around 40" and with a 3" sag/ft you are looking at about 30". etc etc

I'm sure the depth of the cat cut is definitely going to influence how easy it is to get in and out of the hammock because a lower sag in/ft is going to make higher sides of the hammock to climb over to get in. On the other hand I would not think you would want your sag in/ft to be to high because a really narrow middle section might make moving around or lying in the fetal position difficult. I'm thinking that the depth of the cat cut may also have some influence or how the hammock lays and hangs. Is the depth of the cat cut also going to influence the forces on the edges of the hammock?

Any thoughts?

[GrizzlyAdams]

I have fabric on the way that I am going to use on my first attempt at making a Bridge hammock. I was sitting here this morning playing around with lVleph's Excel program (via blackbishop's directions for making a cat cuttarp) for making the cat cut curves.

I have decided that I am going to shoot for a finished hammock that will be 84" (~7') long and I will be using fabric that is about 60" wide. Using lVleph's program I have been fooling around with the sag inch/ft measurement which basically influences the depth of the cat cut.

At 1" sag/ft the deepest part of the cat cut is going to be 5 1/8" per side which means that the narrowest part of the hammock (the middle part) is going to be about 49-50". If you go with a 2" sag/ft the deepest part of the cat cut is 10 1/8" per side which means you the narrow part of the hammock will be somewhere around 40" and with a 3" sag/ft you are looking at about 30". etc etc

I'm sure the depth of the cat cut is definitely going to influence how easy it is to get in and out of the hammock because a lower sag in/ft is going to make higher sides of the hammock to climb over to get in. On the other hand I would not think you would want your sag in/ft to be to high because a really narrow middle section might make moving around or lying in the fetal position difficult. I'm thinking that the depth of the cat cut may also have some influence or how the hammock lays and hangs. Is the depth of the cat cut also going to influence the forces on the edges of the hammock?

Any thoughts?

I can't speak---yet---on how easy or hard it will be move around in a narrower hammock. But soon, I'm hoping, soon. The spyderline needs to be delivered, and the hammock I've sewn needs not to rip to shreds when I get into it.

But I can tell you that I've looked at the equations for force on the ropes. A shallower sag has more force. But if you're using stuff that handles loads above 1000 lbf you shouldn't have any problem.

Since I know how much HC4U in particular likes the math part, let me explain .....

nah. I put pointers to relevant source material in another post for those who really care. Bottom line rule of thumb---if you reduce the sag by a factor of two, the increase in force is no larger than a factor of 2. The increase is actually quite a bit less, but that rule is easy to remember.

Grizz

[TeeDee]

I have fabric on the way that I am going to use on my first attempt at making a Bridge hammock. I was sitting here this morning playing around with lVleph's Excel program (via blackbishop's directions for making a cat cuttarp) for making the cat cut curves.

I have decided that I am going to shoot for a finished hammock that will be 84" (~7') long and I will be using fabric that is about 60" wide. Using lVleph's program I have been fooling around with the sag inch/ft measurement which basically influences the depth of the cat cut.

At 1" sag/ft the deepest part of the cat cut is going to be 5 1/8" per side which means that the narrowest part of the hammock (the middle part) is going to be about 49-50". If you go with a 2" sag/ft the deepest part of the cat cut is 10 1/8" per side which means you the narrow part of the hammock will be somewhere around 40" and with a 3" sag/ft you are looking at about 30". etc etc

I'm sure the depth of the cat cut is definitely going to influence how easy it is to get in and out of the hammock because a lower sag in/ft is going to make higher sides of the hammock to climb over to get in. On the other hand I would not think you would want your sag in/ft to be to high because a really narrow middle section might make moving around or lying in the fetal position difficult. I'm thinking that the depth of the cat cut may also have some influence or how the hammock lays and hangs. Is the depth of the cat cut also going to influence the forces on the edges of the hammock?

Any thoughts?

First off - they are not catenary curves on the ends of the hammock. A lot of people are mistaken in thinking they are catenary arcs.

They are parabolic - think suspended-deck suspension bridge with the hammock occupant the road bed. The threads of the fabric act as the vertical cables on a suspended-deck suspension bridge. You can go ahead and use the cat cuts, but I don't think it will support you as well as the parabolic arcs.

The parabolic arcs are lots easier to make than the catenary arcs. You don't need to make all those measurements and connect the dots.

Just get a good flexible rod, fiberglass or carbon fiber or AL tent poles work very well. I used fiberglass chimney brush handles, 2 4' sections coupled together to make an 8' rod. You can get them at Lowes for about $4 per section.

Mark out the end points, fix the rod at the end points and then flex the rod to the desired shape. Use a marker of some sort, a Sharpie works good, to trace the rod on the material and cut and you are done.

A great parabolic arc.

Note that the head end of the arc is steeper than the foot end to accommodate the extra weight there. You have to adjust the center point where you pull the rod to get that.

[GrizzlyAdams]

First off - they are not catenary curves on the ends of the hammock. A lot of people are mistaken in thinking they are catenary arcs.

They are parabolic - think suspended-deck suspension bridge with the hammock occupant the road bed. The threads of the fabric act as the vertical cables on a suspended-deck suspension bridge. You can go ahead and use the cat cuts, but I don't think it will support you as well as the parabolic arcs.

The parabolic arcs are lots easier to make than the catenary arcs. You don't need to make all those measurements and connect the dots.

Just get a good flexible rod, fiberglass or carbon fiber or AL tent poles work very well. I used fiberglass chimney brush handles, 2 4' sections coupled together to make an 8' rod. You can get them at Lowes for about $4 per section.

Mark out the end points, fix the rod at the end points and then flex the rod to the desired shape. Use a marker of some sort, a Sharpie works good, to trace the rod on the material and cut and you are done.

A great parabolic arc.

Note that the head end of the arc is steeper than the foot end to accommodate the extra weight there. You have to adjust the center point where you pull the rod to get that.

If you hang a chain from equi-height end points, it forms a catenary curve due to gravity on its own weight. If you suspend a load that is much heavier than the chain, uniformly along the chain, then that same chain re-forms into the shape of a parabola. So if the webbing/spectra weight were much larger than the weight of the hammock fabric, and if climbing into the hammock has the occupant's weight distributed uniformly along its length, then you'd be justified in forming up a catenary curve, knowing that under load it will do what it needs to do.

BUT the weight of the hammock is not insignificant relative to the weight of the webbing/spectra, so the catenary curve isn't really appropriate.

Having said that, it is not true either that an occupant's load is distributed evenly long the hammock, and this assumption is at the basis of analysis of suspension bridges and the supporting parabolic cables.

I don't think the curve TeeDee gets by his method is rigorously parabolic, at least not for a parabola like those in suspension bridges. Parabolas are defined as a set of points equi-distant from a given point and a straight line one which that point lays. If that straight line is vertical (as it is with suspension bridges) and the parabola opens "up", then the parabola is symmetric around its minimum, which is geek-talk for saying that if you look at the curve 2 feet to the right of it's lowest point, that's at the same height as the curve 2 feet to the left. Works for 2 feet, or 1 feet, or 3.1415926536 feet .... . The method TeeDee documented, for example in this picture looks to me to be setting the curve height the same at the stacks of pineapple cans, but these are a different distance from the low point of the curve. These are points of asymmetry with respect to the horizontal distance from the minimum, so the curve is not symmetric.

Machts nicht. Whatever that curve is, it works.

I can add experimental validation that accounting for the non-uniform distribution of weight is critically important. TeeDee did it by applying the force on his rod at a non-centered point. I'm just back from the garage where I was hanging my first effort at a bridge hammock. While I knew I should have shifted the center of my parabola (and mine was a measured one), I didn't, mostly because I didn't know how far to shift it. The only way I hung flat was when I shifted my body so that about 3/4 of my legs weren't in the hammock at all! So this is a detail that really matters. (Bridge hammock version 0 for me was my first sewing project, and I some got some good experience that will help with other projects.. I count it a success that I got in and out of the hammock for a couple of hours without having seams tear. On to Version 0.1. Love that $1 bin at Walmart's ).

Grizz

[blackbishop351]

I agree with the analysis - the parabola is the correct shape for this application - but not the reasoning I guess. A tarp and the bridge hammock require two different curves because the curves have to satisfy two different sets of demands. Simple as that, really.

[Coffee]

Not to start this argument, but a suspension bridge or cable stay bridge has a catenary shape and not a parabola. A parabola is close, but does not account for the real world effects of gravity and all that math.

I would go cat if you have the choice. Although the parabola shape is really close. In the end is it different enough to notice a difference. Probibly not.

[Just Jeff]

Why not hang a rope from each end of the fabric, then hang the fabric on the wall at an angle instead of horizontally...so the lowest point of the rope is towards the head end rather than at the center.

I know that's not all geeky with formulas (formulae?) and stuff...but would it work good enough?

[warbonnetguy]

hey griz, is the added force resulting from the shallower curve an increase to the force applied to the webbing only, or does it increase the force to the fabric as well?

hey blackbishop, you mentioned the different sets of demands with regards to a tarp edge. is there really an advantage to using a true caternary on a tarp edge as opposed to a parabolic curve. i have always used parabolic curves on my tarp designs.

speaking of a parabolic curve generator, i use easton alum. tent pole with seamless joints, really easy to trace this way, and i drilled holes in the end, so i can run string from on end to the other (like a archery bow) the length of the string and thus the amount of curve is adjustable by using a plastic clamp. this makes adjusting and fine tuning the curve a cinch.

this is a very interesting topic, its cool to hear discussion in actual scientific terms even if i don't understand 100%. it is still very informative and intriguing, as this is cutting edge stuff.

[blackbishop351]

hey blackbishop, you mentioned the different sets of demands with regards to a tarp edge. is there really an advantage to using a true caternary on a tarp edge as opposed to a parabolic curve. i have always used parabolic curves on my tarp designs.

I'm just working from really general principles - I haven't worked out the math, and I'm sure I'll get called on that - but it seems there's a difference in the physical situation. On a bridge, the force vectors are all parallel along the vertical support cables, but with different magnitudes because of the pilings at the ends of the suspended section. On a tarp, you want totally uniform force to generate a planar surface. The parabolic curve seems the right solution to the first situation, while the catenary is definitely the solution to the second. But like I said, I haven't worked out the math, and may not. I'm pretty busy.

One thing I may work on, though, is whether a purposefully flexed material like a tent pole actually forms a true parabola. I'm not convinced on that as easily as I am on the heavy rope forming the catenary like Jeff mentioned.

[GrizzlyAdams]

Not to start this argument, but a suspension bridge or cable stay bridge has a catenary shape and not a parabola. A parabola is close, but does not account for the real world effects of gravity and all that math.

Hey HE-
best wishes on your thru-hike.

I think about this engineering stuff when I run, with all the free time you have on trail you can think about it too.

You're a like a modern day Galileo, with a twist. He thought that a chain hanging free (under gravity and all that math) would be a parabola. But according to Wolfram (also know in the biz as "Mr. Wizard")

In 1669, Jungius disproved Galileo's claim that the curve of a chain hanging under gravity would be a parabola

Here's a very readable article on why suspension bridges are parabolas and not catenary curves.

I would go cat if you have the choice. Although the parabola shape is really close. In the end is it different enough to notice a difference. Probibly not.

Considering that our the weight of our bodies laying in hammocks is not uniformly distributed, I suspect too that in practice the difference between parabolic and catenary is not important.

so you've got other things to do than mess with curves. Carry on, and good luck on your hike.

Grizz