Bridge Hammock

[GrizzlyAdams]

Got back from family adventures involving lakes, trails, state park rangers, and the headwaters of the Mississippi. Had a nap in v0.1, brought a yardstick. Some relevant measurements

webbing to webbing at the midsection : 22"
webbing at midsection down more or less straight to hips (before the body bends the fabric around : 14"

webbing at shoulder down more or less straight to shoulder blades (before the body bends the fabric around : 19".

These will be useful in making more precise compression estimates, just thought I'd get them recorded.

I took out the spreader bars, make sure there was a rescue team standing by, and got into the hammock. Now the gap between webbing at the center is 14". I was able with one arm to push out the side to 21". So there wouldn't be any problem pulling the side out at the center with stakes, with or without lowered spreader bars.

Having the spreader bar lowered by 12" makes for very little headroom. I'll want to rethink the placement of that.

Grizz

[schrochem]

I'm going through more 'visual' alterations and need some help with a knot.
I plan to use webbing on the edges, but then use rope on the upper suspension 'triangle.'
Since I'm using a Cinch Buckle for my tree attachment, I'd like to try something different. Right now I have each rope attaching to the buckle. Well the forces kind of move those bits around and they can slide up the side making the webbing hard to loosen.
So I was thinking of tying the two ropes together and using a single rope tied to that knot and then to the buckle. Is that clear?
So my question is what knot would you use to tie the two lines together? They are super duper important to keep my butt off the ground
I was looking through the animated knots and thought maybe the double fisherman's, or maybe just an overhand knot with both ropes?
Any recommendations or other ideas on how to handle this would be apppreciated.

[GrizzlyAdams]

I'm going through more 'visual' alterations and need some help with a knot.
I plan to use webbing on the edges, but then use rope on the upper suspension 'triangle.'
Since I'm using a Cinch Buckle for my tree attachment, I'd like to try something different. Right now I have each rope attaching to the buckle. Well the forces kind of move those bits around and they can slide up the side making the webbing hard to loosen.
So I was thinking of tying the two ropes together and using a single rope tied to that knot and then to the buckle. Is that clear?
So my question is what knot would you use to tie the two lines together? They are super duper important to keep my butt off the ground
I was looking through the animated knots and thought maybe the double fisherman's, or maybe just an overhand knot with both ropes?
Any recommendations or other ideas on how to handle this would be apppreciated.

sure seems to me like the ropes ought to migrate to opposing corners, maybe it's the knots you use? On my rings I use a "full turn" (which is really twice around) cinched off with 2 half hitches. On the rings they stay put, regardless of how the rings might twist with the webbing.

I would minimize the number of knots involved, 'cause knots reduce the strength of the rope in the region of the knot.

Grizz

[GrizzlyAdams]

climbed back into v0.1 in spreaderless mode. The gap between the webbing at my shoulders is 14". I could push them apart to 21" with my arms (understood I have no significant upper body strength, and the angle here is bad). Beyond that it requires quite a push. But the force needed will be lessened if the center is staked out first. My main hope continues to be that hiking poles work as lowered spreader bars, without the special mods and gizmos that TeeDee cooked up to make his work.

I re-evaluated the head room w/o spreaders. It's fine. I'll continue to think about this in terms of dropping the spreader bar 12" down.

Unrelated, but answering an old danging question of Scott's : the length of my suspension ropes at the foot end is 37", at the head end is 41". The only part of this that was concious design was to use the longer ropes at the head end (whose longer spreader bars make for greater compression). I think that at time I cut cord I was aiming for around 36". Maybe it was late, I dunno.

Grizz

[schrochem]

Well, it's almost time for me to start over and make the next version.
After reading Grizz' Guide I got pretty fired up to plot it out.
Here's what I plan to do.
1) 90" length of 1.9oz using grizz' curve
2) the suspension will be 1/2" tubular webbing. I think I'm going to dump the corner rings. Instead I'll just transition the webbing to 1/8" spyderline. That will then connect to a cinch buckle, that will connect to the tree with 1" polyster webbing. Since the corner rings are gone, I 'm going to sew in some D-rings in the bartacks of the webbing to use for the adjusting layer. I'm going to reinforce the corners and probably install grommets. Basically, I'm going to be moving the spreaders down to these reinforced corners and attaching them somehow.....
3)I'll probably use 3/32" spyderline for the ridgeline.
4)I'm going to go ahead and sew then ends on. I'll either use 1.1oz ripstop or noseeum. If it's 1.1, I might make a window out of noseeum then have a flap to close it.
5)The bugnet will just be on top. One long side will be sewn to the hammock body. The other long side will be a two way separating zipper. The two short sides will be velcro over the ridgeline. The net will be able to come off the top by three sides, with the last side still attached.
6)I will have an adjustable underlayer made from 1.1 or noseeum. Most likely 1.1 and held snug against the hammock. This will make a double layer hammock and should be good against bottom attack. If not permithrin. I have also considered making this layer out of a neat sheet. This will expand the temperature range a little as well.
7)I'll sew two tabs on the head end and use 3/32 spdyderline to lift it for lounging.
8)I plan to incorporate a gear loft as well.
9)The only other thing is a second ridgeline. I'm going to sew up the main body and then work with and decide on the second ridgeline before doing the end caps or the netting.

The only other thing I'd like to do if find a way to hang/test inside the house....

[GrizzlyAdams]

With TeeDee's posts gone, I thought it would be good to recreate the analysis describing compression forces on the spreader bar, particularly to create a point of comparison with a new analysis of compression force with the lowered spreader bar.

This post does that, and works out a compression analysis for the lowered spreader bar.

So be warned, this is mostly math, and mostly for reference, the permanent record, and a hard-core remedy for insomina. I will reveal the punch line though, which is that the lowered spreader bar method could reduce compression force significantly.


Recreating the Old Analysis

Let's go back and think again about the original way of doing things. In the figure below, Joe the Hammock Crash Test Dummy lies in the hammock, and induces an angle beta between the suspension lines and the ridge-line. The compression analysis is done in a two-dimensional plane that contains the suspension lines, this plane lies at angle beta to the plane z=0. The key reason for identifying this angle is that when we view the weight force vectors we really have to work with their geometric projection into this plane. That projection amounts to dividing the magnitude by sin(beta).



The figure below looks directly down on this plane.



We're assuming that half of Joe's weight W is accounted for at each end. The upper triangle is of the suspension lines and ring buckles; the dark black line is the spreader bar. alpha is the angle between the spreader bar and suspension line. The projection of force (W/4)/sin(beta) on the suspension line towards the ring buckle has magnitude (W/4)/( sin(beta) sin(alpha) ). The compression force is the geometric projection of this force vector onto the horizontal, e.g.

cos(alpha) (W/4)/( sin(beta) sin(alpha) ) = cot(alpha) (W/4)/sin(beta)

where cot(alpha) = cos(alpha)/sin(alpha), a.k.a. the cotangent function.

There is also compression force on the spreader bar from the webbing that is transmitting the weight. In my earlier analyses I was thinking in terms of the hammock fabric transmitting the force, and considering angles that the fabric body formed with the spreader bar. For this set-up that's wrong. The force to be considered is at the webbing, transmitted through the webbing, and we need to consider angles formed by the webbing. TeeDee may or may not have been saying that in his analysis; his explanations were terse.

The lower portion of the diagram illustrates how the body of the hammock is pulled in towards the center by Joe's weight. Angle gamma is a function of the slope of the tangent of this curve at the corner. Since the slope is change in y over change in x, with the x-axis being down the longitudinal axis of the hammock that makes tan(gamma) equal to change in x over change in y, e.g., cot(gamma) is the slope of the tangent line. The analysis of this compression is entirely similar and symmetric to that due to the suspension lines, and gives a compression component of cot(gamma) (W/4)/sin(beta). The total compression force (on one end of the spreader bar) is the sum of these two components :

total compression on one end = (cot(alpha) + cot(gamma) ) (W/4) / sin(beta)

Let's now get a feel for what these formulae imply. Angle beta is essentially the same angle as gets bandied about when worrying about the force on suspension ropes, and so beta=30 degrees is a pretty good working number. This makes sin(beta) = 0.5. If the suspension lines have the same length as the spreader bar, then alpha = 60, and cot(alpha) = 0.57.

In my hammock I measured a distance of 22" between webbing lengths, at the center of the hammock, when I'm in it. With a 36" spreader bar this means that the hammock body curves in by 7" on each side. Now if I assume that that curve is itself a parabola, I can determine p in the parabolic equation y = p*x^2, choosing coordinates so that y=0 at x=0, making y=7 at x=(L/2)---here L is the hammock length---so that

p = 7*4/(L*L).

To get cot(gamma) I need the slope of the line tangent to the curve in the webbing at x=L/2. That's the derivative of the curve at x=L/2 (yeah! calculus at last!), which happily is also cot(gamma)

cot(gamma) = 2*p*(L/2) = 56/L .

So for example, my latest bridge hammock has L=90", making cot(gamma) = 0.62.

Adding the two compression components, we can estimate the (one-ended) compression on a spreader bar as

(cot(alpha) + cot(gamma) ) (W/4) / sin(beta) = (0.57+0.62) (W/4) / 0.5 = 0.595 W .

Of course, the full compression force comes from both sides, so this figure is doubled.

Compression on Lowered Spreader Bar

[ the rest of this post was edited 27 August 2007 and completely replaces the older (incorrect I think) lower spreader bar analysis ]


Now we consider lowering the spreader bar, as HC4U saw in a vision. I've been working on a scheme where on each side of the hammock, in the interior, we put a length of webbing that is parallel to the ground and passes just under the lowest point of the suspension cut. Put loops in the ends of that webbing. Afix that webbing to the hammock body by sewing, or by snaps. The fabric at the edge near the loops will need re-enforcing. A hiking pole/spreader bar hangs from those loops, and another bit of cord passes from loop, straight back to the tree from to which the suspension is attached at this end, around the tree and back to the webbing on the other side. (one could use tree huggers here, and on each side attach a line from webbing loop to tree hugger loop on the corresponding side). Observe that this is distinct from the lines that suspend the hammock, the tree is now being used twice, once high to bear the weight, once low to bear the load of the body-separating tension. A line from tree, through hammock, and out to a tree again ought to be parallel with the ground, when there's someone in the hammock.



Now to get the force needed to pull the hammock body apart when someone is in it, we need to tighten up these lines. I'll call the total force applied pulling on one side (e.g. from tree to tree) F. This force is stored as deformation (stretching) of the lines and webbing, like a spring. So now when there's someone in the hammock the force diagram looks like this



The diagram looks a lot like the one for the normal spreader bars. The key differences are the (unknown) force F, and that the lines go out to around the tree. tau will be strictly greater than alpha; but will vary from situation to situation. If I take the spreader bar to be 28", the tree to be 4' away with a diameter of 1', then ordinary trig works out cot(tau) = 8/48 = 0.167.

We can use the same approach to estimate cot(delta) as we did to estimate gamma. Here though, S is, say, 28" inches (to give the same shoulder squeeze) rather than 36", while m is 22" as before. This means the parameter p' in the assumed parabolic shape is p' = 3*4/(L*L), so

cot(delta) = 2*p'*(L/2) = 12/L

where again L=90" in my hammock, making cot(delta) = 0.1333.


All this put together says that lowering the spreader bar and making it 28" rather than 36" (which, according to the analysis in this post, yields the same shoulder squeeze as with the 36" spreader in the old position), and under the other modeling assumptions gives a (one-sided) compression force 0.3*F, as compared with 0.595*W using the raised spreader bar.

The unknown here is the force F needed to bring the middle apart to 22". Experience suggests that it is significant, this analysis shows that if it is as much as W, then the compression on the lowered spreader bar is still half of what it is raised.

Grizz

[schrochem]

Grizz, good to see you keeping up with the analysis.
I'll check your math later

There is something I was wondering about earlier but had forgotten about it. How do all these forces change if the width of the hammock increases?
Instead of 60", say 70,80 or 90" ??
This of course would require sewing two pieces together to achieve that, but I don't think that would be an issue if the seam was made around the thighs or knees, since most of the forces are downward and not side to side.
Sewing two pieces together pretty much allows us to have any dimensions we want...

[schrochem]

[actually, I want to try an idea I have for a bridge hammock stand first].

Grizz

Do share!
I was wondering how it would hang with the longer triangular suspension lines. it seems on the typical stand it might hang too low.....

[GrizzlyAdams]

Do share!
I was wondering how it would hang with the longer triangular suspension lines. it seems on the typical stand it might hang too low.....

patience, grasshopper. I want to see if it works first before committing a stupid idea to the eternal memory of the internet

Grizz

[GrizzlyAdams]

...
There is something I was wondering about earlier but had forgotten about it. How do all these forces change if the width of the hammock increases?
Instead of 60", say 70,80 or 90" ??
This of course would require sewing two pieces together to achieve that, but I don't think that would be an issue if the seam was made around the thighs or knees, since most of the forces are downward and not side to side.
Sewing two pieces together pretty much allows us to have any dimensions we want...

There are places in the analysis where particular lengths are used for computing particular compression values, these will be affected.

Putting those aside, imagine the effect of increasing the fabric width. If you don't increase the spreader bar width also, all you are doing is making it harder to get in and out, and are also increasing shoulder squeeze (because the angle of the fabric from shoulder to ridgeline gets more vertical.)

But of course you weren't thinking about not increasing the spreader bar length. And of course as you increase the spreader bar width you correspondingly lengthen the suspension lines to keep the same compression forces induced by those lines.

Your hope I imagine is that you can reduce the squeeze about your body by increasing fabric width. However, once the fabric body is tall enough along your body to keep you in, the squeeze of the hammock on you is a function of the angle of the fabric from the body to the spreader bar (or webbing, in the middle), not the length of the fabric. You'll have the same squeeze at the bottom of a 5 foot trough of fabric as you do from a 2.5 foot trough if that angle is the same.

What I think you're after then is achieved by increasing the spreader bar width, regards of the fabric width. You can compensate for compression due to suspension lines by increasing their length, but the other component (due to the webbing) is going to increase. Referring back to angle gamma in this post, I did a quick check and found that for a fixed hammock length, cot(gamma) increases as a linear function of the spreader bar width; this means that the overall compression increases linearly as the spreader bar increases, even if you increase the length of the suspension lines.

One thing you could do with a wider body hammock is share it with someone else. That would be, ah, cozy. The Bridge is ideal for spooning, but beyond that I'm having a hard time imagining two people being comfortable. I don't have any experience with multiple bodies a in traditional hammock to compare with though.

Grizz