Help with Math, please

[MedicineMan]

recently told a friend that the lateral force (like applied to a tree or shelter) when hammocking can be much greater than body weight...he didnt believe it and said it was impossible.....
can someone provide the actual math/formulae/etc. that proves this?
thanks

[blackbishop351]

I wrote this up for the Yahoo Hammockcamping group a while ago.

[Wanderingson]

Dang,

I guess I need to go back to skewl to learn about the finer art of hammocking.

[Two Speed]

Medicine Man, you are absolutely correct, the forces applied by a taut hammock can be surprisingly high. It has to to with the catenary (sp?) curve that the hammock assumes. Youngblood did a good write up on the subject, and I believe he put a spreadsheet together that calculates the forces but I'm darned if I can find it right now.

Anyone know where that sucker's posted?

[Two Speed]

Blackbishop, just took a look at your document and it tracks with what I remember of the subject, which means you're probably dead on the money and my memory is failing me.

[Just Jeff]

Tell him it's trig - a force vector, where body weight is only one component of the vector.

Basically, the support rope is the hypoteneus of a triangle. Using the angle of the hammock support to true horizontal, calculate the force on the support (h) by

h = (.5 x user weight) / sin(support angle)

I think this formula only works if you convert the angle to radians, though.

So the tighter you hang your hammock, i.e. the more horizontal it is when weighted, the more force you put on the supports.

Youngblood's write-up is in the Files section at Yahoo hammockcamping.

[Touch of Grey]

Yes they are high indeed!

Another way to think of these things is this:

A 1 foot diameter pipe with 15 pounds of pressure applied to a fluid in it will exert 15 foot/pounds of pressure provided the end of the pipe is a solid wall.

That same 15 pounds of pressure applied to a fluid in a 1 inch pipe will exert (15 X 12 [12 inches in a foot] = 180) 180 pounds of pressure.

So these things having been said, and realizing that this is an over simplification for discussion purposes of course. The weight applied to a fixed diameter of rope exerts pressures rising or lowering based on diameter of the rope and the weight applied. I could do the math and be more exact but suffice it to say that Spectra being somewhere around a diameter of .125 (1/8 inch) with say my 255 lbs laying in it will exert (we'll do the long math here) 255 X 96 [8 eighths in an inch X 12 inches in a foot = 96] = 24480 foot pounds which you have to divide by two because you have to anchor points which share this load. Again this is measured at a single point right at the the tree (your figure-eight knot) and does not take into consideration that the webbing or straps distribute the load around the tree.

This while again not totally accurate like the formulas espoused by Just Jeff, BlackBishop and others is a laymans simplification and gets you in the ballpark for those who do not understand nor want to understand Trigonometric Functions (Sine, Cosine, Tangent, etc. of an angle stuff).

Numbers can explain it all! Unfortunately you have to know what you are looking at to understand it.

TOG

[MOWGLI]

The upshot to Youngbloods post was... you should not setup your hammock in a shelter. It places too much stress on the structure.

FYI, Youngblood is an Engineer by training.

[hammock engineer]

The big thing to consider in the equation is the angle. As the angle aproaches 45 degrees, the forces decrease. At 45 degrees you are only excerting half your body weight on the supports. So when in doubt pitch you hammock lossely. I remember talking about this in Hot Springs when a few people. BTW If I remember Youngbloods setup correctly, he was using that yellow rope if a 150 pound breaking strength to set up. He just had an extreme angle between the tree and his hammock.

[hopefulhiker]

It has been a while since I have taken physics but it seems to me that the Horizontal component of the force vector, unless someone is pulling on the rope, by the laws of conservation of energy, CANNOT exceed the vertical component of the whole kit and kabudal of the hammock, gear and person...
On the other hand, I did not take into account the little bit of potential energy that you get when you strectch the rope out,, Anyway I sticking with my tarp tent....

[SGT Rock]

Youngblood's spreadsheet file: http://f2.grp.yahoofs.com/v1/UNw2QuN...0web%20rev.xls

and an image of the file if you just want to look at it:

http://hikinghq.net/images/hammock/H...on_Diagram.jpg

http://hikinghq.net/images/hammock/H...ce_Diagram.jpg

[Critterman]

The total force on the trees in the same as the weight of your rig ( unless you bounce up and down ) however that weight is concentrated on the surfaceof the trees on the small area that your ropes contact the trees so the pressure ( pounds per square inch ) is high. If you stand with all your weight on one foot, the total weight of your body doesn't change but the pressure on your one foot is twice as high as when you stand on two feet. Same deal.

[hammock engineer]

I was thinking about this and came up with a little experiment to help show the forces.

Have one person stand 2 or 3 steps higher than you. Grab their hands and lean back.

Now have the person stand at the same level as you. Grab their hands and lean back.

If you don't kill each other trying any of this, you should see that using the same amount of weight you moved the other person more when you were standing at the same level.

[RockyTrail]

MM, tell your friend it works similar to a lever...the rope/angle geometry is a force multiplier just as the length of a lever is a force multiplier.

If that doesn't work, ask him to hang a clothesline with a shirt hanging on it, then try to tighten the clothesline until the cord is perfectly level and see how much force it takes on his hands. I guarantee it will take more pull than the shirt weighs!

[SGT Rock]

How about another idea for an experiment. Get two fish scales (the kind where you hang the fish off the bottom hook) and then tie them to two posts with a rope in the center, and on the middle of that rope put a carabineer. Now put a known weight in the center - something easy like a pound or two - the see what the scales read.

[Smee]

recently told a friend that the lateral force (like applied to a tree or shelter) when hammocking can be much greater than body weight...he didnt believe it and said it was impossible.....
can someone provide the actual math/formulae/etc. that proves this?
thanks

Here's the details:

http://www.whiteblaze.net/forum/vbg/...s&cutoffdate=1

[Just Jeff]

The total force on the trees in the same as the weight of your rig ( unless you bounce up and down ) however that weight is concentrated on the surfaceof the trees on the small area that your ropes contact the trees so the pressure ( pounds per square inch ) is high. If you stand with all your weight on one foot, the total weight of your body doesn't change but the pressure on your one foot is twice as high as when you stand on two feet. Same deal.

This is incorrect. I broke 550 cord twice when using it as a hammock support, and I don't weigh 1100 pounds. It's a force vector as described above.

Here's another exercise. Tie a 10' rope to a tree. Tie a gallon jug in the middle. Hold the other end and see if you can pull the rope until it's horizontal. Come on weakling...it's only a gallon of water!

The force exerted on the hammock support is measured in pounds (or Kilonewtons, actually) and is separate from the psi you're talking about.

Adding dynamic forces like bouncing increases it even more.

[Footslogger]

[quote=Just Jeff;268345]Here's another exercise. Tie a 10' rope to a tree. Tie a gallon jug in the middle. Hold the other end and see if you can pull the rope until it's horizontal. Come on weakling...it's only a gallon of water!
==============================================

You run into the same sort of physics when using the western style bear bag approach. A line is thrown over 2 trees (generally evergreens) a certain distance apart and the bear bag is attached to the end of the lines in the middle. Then comes the interesting part ...attempting to get the bear bag a reasonable distance off the ground by applying tension to/tying off the two ends. Amazing how difficult it can be to raise a 10 lb food bag 12 - 15 feet off the ground.

'Slogger

[Fiddleback]

Man! This brings back memories of H.S. physics and trig. As I remember, physics was second period and trig was 5th... The memory gets kinda fuzzy after that...

FB

[Hammerhead]

I don't have the mathmatical formula, but I do know from falling on my ass yesterday that a 200lb person in a hammock can snap a 4x4 fence post in half.