Hitchcraft for hammock tensioning

[Coffee]

Pretty impressive stuff. Being a lazy engineer I try to simplify things first until I get a very simple formula like: w*2*0.5=w
Of course, you might say that a black box may not be as comfortable as a hammock with a ridgeline. That's why engineers solve small problems one at a time while physicists are still trying to solve one big problem: how does the universe work?

The engineer in me does something like that too. I figure out the best I can easily what I need. Then throw a huge saftey factor on to it. That usually gets me to where I want to be. Then again, all my grad work is with bridges where everything is way over designed. With how light the spectra cord is now, I really don't think I am adding any extra weight.

[TeeDee]

Dear Hammock Physics 102 class,

A number of you have come to my office hours asking about Professor TeeDee's cryptic solution to midterm question number 42. Recall that the problem asks for you to give the tension on a ridgeline, given inclination angle alpha on the suspension ropes above the ridgeline, inclination angle beta on the suspension ropes below the ridgeline, and weight w. Professor TeeDee's solution is illustrated below



The key to understanding this solution is to think about the forces on the join point J where the ridgeline attaches to the suspension ropes.




Slightly abusing notation by reversing direction, the force F2 is the restorative force due to stretching, the force F1 is a force due to gravity on the hammock/user along the rope, and force P is the tension on the ridgeline. We know how to compute F2; we know that the force due to gravity is equal in magnitude to the restorative force on that line. Importantly, we know that in vector arithmetic P + F2 + F1 = 0; J is stationary, so the forces cancel.

Remember the geometry of vector addition : to compute F2+F1 we can draw vector F2, reposition a vector with the same length and angle as F1 at the head of F2, and the sum is the vector extending from F2's base to the head of the repositioned F1. This is illustrated below.



The first thing to note is that the direction of the vector F2+F1 has to be opposite to the direction of P. This is handy, because it means we can use right triangles in the analysis.

Now you need to recall some geometric identities, also illustrated in this picture, of angles equal to alpha and beta. You also need to recall a little bit of trigonometry, that says the length of the adjacent side is the cosine of the angle times the length of the hypotenuse. Knowing the length F2 and the angle alpha, we can compute the length of line segment ac; knowling length F1 and the angle beta, we can compute the length of line segment bc. The difference between lengths of ac and bc gives the length of ab, which is the magnitude of P, and is equal to Professor's TeeDee's solution.

Professor TeeDee reminds you all that the final exam will ask this same question, without giving you angles alpha and beta, only the spring constants and lengths of the suspension ropes and ridgeline.

Please note that June 15 is the last day you can drop this class without penalty. There are still plenty of spaces available in Professor JustJeff's popular survey course on Hammock Camping.

Hammock Physics 102 TA

Gee - you make it seem so easy - all I did was subtract the horizontal forces.

Your solution is better for the Freshman textbook though.

[GrizzlyAdams]

Gee - you make it seem so easy - all I did was subtract the horizontal forces.

and if you'd said that in your post, I wouldn't have understood what that implied. Still don't. Had to work it out from the few principles I know.

Your solution is better for the Freshman textbook though.

that's appropriate, seeing as my physics coursework was limited to the Introductory course. I remember spending a whole afternoon trying to work out why the equation for the differential cross-section in an Rutherford scattering experiment was correct. The smart guys just accepted the equation, knew when to use it, and got on with things.

it's been fun,
Grizz

[TeeDee]

and if you'd said that in your post, I wouldn't have understood what that implied. Still don't. Had to work it out from the few principles I know.

ahhhh -

bc = horizontal force due to person sitting in hammock

ac = horizontal force due to person sitting in hammock + horizontal force due to tension in structural ridge line

ac - bc = horizontal force due to tension in structural ridge line

I was looking at and visualizing the forces acting and that's what I saw while thinking about it at dinner. Then had to sit down and remember my trig and figure what ac and bc were and there I was. Looking at the forces acting is what finally convinced me that hitchcraft and BB351 were right - only one vertical force acting - occupant weight + hammock weight.

[GrizzlyAdams]

ahhhh -

bc = horizontal force due to person sitting in hammock

ac = horizontal force due to person sitting in hammock + horizontal force due to tension in structural ridge line

ac - bc = horizontal force due to tension in structural ridge line

I was looking at and visualizing the forces acting and that's what I saw while thinking about it at dinner. Then had to sit down and remember my trig and figure what ac and bc were and there I was. Looking at the forces acting is what finally convinced me that hitchcraft and BB351 were right - only one vertical force acting - occupant weight + hammock weight.

Shiny!

At our house dinner time conversation is usually steered by my better half towards literature, religion, politics, and current events.

(while I'm thinking about whatever technical problem I happen to be working on that day. )

Grizz

[TeeDee]

I finally measured the angles on my hammock with the two ridge lines. My "eyeball" estimates were off by a factor of at least 2.

angle beta for the long ridge line: 29.8 deg (less sag)
angle beta for the short ridge line: 38.3 deg (lots and lots of sag)

angle alpha for both: 20.6 deg

That gives me the following tension force on the ridge line:

long ridgeline: 78 lbf - 156 lbf total (cord rated at 563 lbf)

short ridge line: 119 lbf - 238 lbf total (cord rated at 1,000 lbf)

The ridge line cords I've used are way over what is necessary. That puts me well within any safety factor the engineers would want.

I could have used the Mountain Laurel Designs guy line cord for the long ridgeline and the BPL cord for the short ridgeline.

[btourer]

I ordered the Mini RopeTie's on the evening of 6/6 and got them on 6/9. Very fast service.
Set up on my Expedition Hennessy was real quick using the instructions. The 1/4 inch spectra is at the top of the Mini's range so it was tight going in but that also keeps it from going down into the grooves very far, which should be beneficial to the spectra over time.
Hitchcraft said he was comfortable using the Mini's with his 180# so I stuck my 180# in the hammock. So far, so good. Once I laid there for a bit and got my confidence up I started flopping around a bit, then harder, then even harder and they were good to go.
Normally when I lash the hammock I have to sit on it to take the slop out and then tighten it again. Then as the night passes the sag still increases. With the HitchCraft, I set it and it stayed right there all night.
After years of lashing these things are great. Fast, easy, light and cheap.
Final analysis: I'll have to keep an eye on them over time and see how they do in the long haul and do some winter tests. But for right now I believe these little jewels come in somewhere just below pizza and beer.

[hitchman]

...
Normally when I lash the hammock I have to sit on it to take the slop out and then tighten it again. Then as the night passes the sag still increases. With the HitchCraft, I set it and it stayed right there all night.
After years of lashing these things are great. Fast, easy, light and cheap.
Final analysis: I'll have to keep an eye on them over time and see how they do in the long haul and do some winter tests. But for right now I believe these little jewels come in somewhere just below pizza and beer.

I take it that's an endorsement. Thanks for trying my product. The key is not to overtension the hammock (under 30 deg loaded) since it will drive the load beyond the safe working load. I would be interested in getting wear data over time.

[Just Jeff]

Holy crap, you guys are smart.

Mathematicians look for "truth"...this time I'll settle for "true enough that I don't fall on my butt." In the search for "true enough," as you might have heard in the other threads I haven't read yet, I handed out a few pair of these Hitchcrafts at the Hot Springs SEHHA this weekend, courtesy of Hitchcraft. The testers will report their conclusions back to this site...when they're ready I'll consolidate them so it's easy to find.

Thanks, Hitchcraft!

[Coffee]

hitchman, if you come up with a product that will do straps instead of rope I would be interested in a set.