# Thread: Forces on Hammock stand guylines/stakes...

1. ## Forces on Hammock stand guylines/stakes...

To help with those who are playing with such ideas as some shown the stand discussions here is some design calculations. (I'm sure we can get some checking of my math too...)

This goes with this image

Basic premise is as follows. Each force applied to the pole can be broken down into components that act parallel to the ground (perpendicular to the pole) and parallel to the pole.

Now the calculations!!!

We start with the weight/tension on the hammock line (Hammock Line Tension). The vertical component of this (HLV) has to be half the weight of the person (plus the hammock) otherwise they fall. Lets make that half weight, W. The angle from horizontal of the suspension line is going to be A.

HLV = W
HLH = (HLV/sin A)*cos A = (W/sin A)*cos A = W/tan A

Ok now we want to know the guy line forces, for this we have to assume there is a pre-tension on the top line of TL.

GLH = HLH + TL = (W/tan A) + TL

This has to be true other wise the pole is falling one way or the other. Also you'll note that when the weight is zero then, GLH = TL (that is TL is just the pre-tension in the top line before anyone gets in the hammock, and that we want this to be as small as possible to reduce our stresses on the system.)

The tension on an imaginary (single) guy line coudl eb written as GLT. This GLT is found from the value of GLH.

GLT = GLH/cos B = ((W/tan A) + TL)/cos B

from this we get the vertical portion.

GLV = GLT *sin B =(((W/tan A) + TL)/cos B)*sin B
= ((W/tan A) + TL)*tan B

The compression force on your pole is

Compression force = GLV + HLV
= W + (((W/tan A) + TL)*tan B)

Moving on to tension in the guy lines as shown in the top view. Here we have the half angle between the guy lines shown as C (in the plane of the lines). And we have the tension they have to exert together as GLH... individually that component is going to be called HGLT.

HGLT = GLH/2 = ((W/tan A) + TL)/2

The tension in each guy line is:

TGuyline=(HGLT/cos B)/cos C = ((W/tan A) + TL))/cos B /cos C.

I'll follow-up with a second post where I do an example with numbers.

2. OK now for "real" numbers.

If we assume a weight of person and hammock of 200lbs (for easy math) then the half weight W is 100lbs.

Also assuming angles in degrees of A=30, B=60 and C=30.

So
HLV = 100 lbs,

HLH = 100/(tan 30) = 100*(1.732)= 173.2 lbs

We can work it with TL = 0lbs, 1lbs and 10lbs to show the effect it has.

With T=0, GLH = 173.2
T=1, GLH = 174.2
T=10, GLH = 183.2

then we work out GLV, for T=0, GLV = 300lbs
T=1, GLV = 301.7 lbs
T=10, GLV = 317.3 lbs

The compression force on the pole is = HLV+GLV

For T=0, its = 400
T=1, its = 401.7
T=10 its = 417.3

The tension on an individual guyline = (GLH/2)/cos B/cos C ...

For T=0, Tguyline = (173.2/2)/cos 60/cos 30 = 200 lbs
T=1, Tguyline = (174.2/2)/cos 60/cos 30 = 201.2 lbs
T=10, Tguyline = (183.2/2)/cos 60/cos 30 = 211.5 lbs

************************************************** *

If we were to use the same weights and use T=10 and A=30, B and C = 45 we'd get.

HLH =173.2 lbs
GLH = 183.2 lbs
GLV = 183.2 lbs

Pole compression = 283.2 lbs

Tguyline = 183.2 lbs

As you can see the angles make a BIG difference and explain why simple tent pegs won't hold.

3. man, that's more than i can handle.

Rapt, thanks for taking the time to look into this.

basically what you are saying is that pole compression is reduced by placing the stakes farther away from the pole.

compression is also reduced by moving the stakes farther from eachother as well?

and, the sag angle of the hammock effects compression as well? more hammock sag, less compression?

for everyone who doesn't know what the hell we are talking about:

i pm rapt and schrochem about suggestions about the right size pole to use for my stand.

idea: two alum poles connected by a ridgeline, and supported on the other side by 2 guylines that go to yard screws. poles will hopefully be collapseable.

i made half of one this weekend (tree was other half) it worked great, i am planning a better version, and wanted to know how small the poles could reasonably be.

should be a very light and portable stand though. i'll post pics when it's done.

4. ## fly the not-so-friendly skies

Originally Posted by warbonnetguy
man, that's more than i can handle.

Rapt, thanks for taking the time to look into this.

basically what you are saying is that pole compression is reduced by placing the stakes farther away from the pole.
true

compression is also reduced by moving the stakes farther from eachother as well?
not true. TGuyline increases as C increases (meaning the stakes are farther apart). As TGuyline increases, so does the compression on the pole.

Tguyline increases as C increases for the same reason that it decreases as you move the stakes farther away from the pole. You are using the guyline to counter the horizontal force at the top of the pole, and the more the guyline "looks" horizontal at the top and aligned with the top line, the less force has to be on it to counter the force on the top line. Moving the stakes away from the pole makes the line more flat. Moving the stakes away from each other pulls the guyline away from being centered on the top line.

and, the sag angle of the hammock effects compression as well? more hammock sag, less compression?

true, modulo the correction above.

A result of the correction is that the closer the stakes are together, the smaller the compression is....in the limit the stakes are immediately next to each other. This suggests some stability issues, but there is this curious piece of evidence as well.

One way to formulate the problem of "what is the minimum distance between stakes I need" would be to figure the left-to-right force that occurs when someone gets into the hammock. Then the tension on the guylines is working also to counter force in that direction---and as you might imagine then wider is better.

I've wished for a hammock stand that is compact enough to bring on an airplane as carry-on luggage (not that I'm flying anywhere with a hammock stand, I'm just using that as an all-too-familiar-to-me volume that is "small"). If you get this working, it could met that criteria. Not that the ATA is going to let me onto an airplane with stakes rugged enough to hold this....

Grizz

5. thanks grizz, i noticed the leaning effect when the stakes were connected by a single piece, the line would slide through the attachment point an would allow it to lean, very strange feeling. by using two lines individually tied to the pole, the pole cannot lean, leans more or less depending on how close or apart the stakes are i guess. as long as it doesn't move more than a few inches either way, it should work fine, and it did. the no stretch lines lessened this too i imagine.

i think it will be pretty darn light. for a stand anyway.

7. Thinking about your engineering problem, which is essentially the excessive guy line tension and resulting excessive pole compression (GLV), it's essentially down to the way the Hammock line forces (HLH) are exerted. If one could hypothetically eliminate the horizontal component GLH and the top line force TL, then GLV -> half the suspended weight.

If you replaced the top line with a third pole, you would achieve this. If you made this of thick walled aluminium tubing (or even a three bar cross-braced member) you could store the vertical poles inside.

Essentially, I am describing a "queenpost truss" bridge.

8. I forgot to mention that with the drastic reduction of the guy line tension, these should be redesigned to provide side stability, not lengthwise stability. (You need two lines per pole.

Also, if you decide to continue with your original design and need to increase the holding power of the guy line anchors, you can do what the suspension bridge engineers do: divide the tension over multiple anchors. Unlike the engineers, you can't individually pretension each anchor line, but there is an old trick to handle dynamic tensioning - lacing. You terminate your guy line in a ring and then lace another line with two or three anchors (tent pegs or lawn screws) through the ring, so that the load is evenly distributed between each anchor point. This is the same principle as lacing shoes.

9. yes, thats essentially what i did with the two stakes at first, i just used one line, and threaded through. then i switched to individual lines due to the rope being able to run freely through the ring and allowing the pole to lean left and right. the two yard screws seem to be plenty strong though, and the soil was soft.

10. Reasonable limits for some of the variables. Ideally you'd want the system to work with the worst possible combination of these.

C between 0 and 45; The one the reduces tension the most is not necessarily the "best" one here since its going to be wobbly (notwithstanding Grizz's link) So worst case here would be 45.

A between 20 and 45; worst case here is 20

B between 45 and 30; worst case is 45, but even 30 isn't bad. Line lengths to meet 30 and 45 for C are 17' from pole to stake.

W= 175 lbs (this is the half weight and since most hammocks are rated for not more than 350 lbs and many for less I think this is pretty reasonable.)

Once you have your compression load then calculate the buckling limit as given in this thread in posts 638 and 640. Using that formula assumes that the hammock webbing is right at the top of the post. When you get your size, go for a tube wall that's twice as thick to allow for a safety margin.

If you intend to hang lower down you'll have to do a pure bending analysis also. Perhaps a choice for the subject of another thread.

But this should get you started...

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