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gunther85
Sep 25, 2005, 8:11 AM
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While driving back from a good day of climbing i was talking about slacklining with my friend and we got to wondering how much tension was actually in the system. We know its a lot, but were kinda looking for a number we could calculate. We are both engineers (or going to be soon) and tried to think of some crazy equations to find out but came up empty. I was wondering if any of you guys knew a way to calculate how much tension there is in the line?
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dutyje
Sep 25, 2005, 1:42 PM
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Dude -
Basic trigonometry. I'm sure if you two are soon to be engineers, you had to take a course on statics. Go back to your book on that, and apply the math skills you learned in high school.
You've got a force being applied on a vertical axis. The line sags a certain distance, and the line is a certain amount long. You should be able to figure out the amount of tensile force from there.
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misanthropic_nihilist
Sep 25, 2005, 4:21 PM
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Those calculators work well for the simple situation of a single weight on the middle of the line (which the above site mentions). By doing some quick geometry in my head, I think the forces will always be less, for a given weight, at points closer to the ends. Someone let me know if I jumped to a conclusion to soon on this. (My reasoning was that the amount of stretch in the system, although less if the weight is towards the ends, will contribute more to increasing the line's angle from horizontal.)
If you're solely interested in making sure your setup is safe, the above calculator will work for you. If you are interested in other states of the line (like the tension of an unweighted line), you may need to use other engineering procedures. Analysis of statically indeterminate structures comes to mind.
Speaking of which, does anybody know the Young's modulus (E) of 1" tubular webbing. I tried looking it up a while ago, but was unsuccessful. If you know Young's modulus/modulus of elasticity, you should be able to find the forces on a weighted line a completely different way than using "basic geometry" and "high school math." To do so, you basically treat the webbing like a spring, and figure out the stress due to extension.
Also, does anyone know if a slackline set up can be treated as elastic (allowing you to use simple statics equations)? For the most part, the webbing returns to it's original, unloaded state, but there is some permanent elongation. The webbing also seems to stretch a greater percentage than most other materials would within their elastic region.
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slacklinejoe
Sep 25, 2005, 4:32 PM
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In reply to: Speaking of which, does anybody know the Young's modulus (E) of 1" tubular webbing. I tried looking it up a while ago, but was unsuccessful. If you know Young's modulus/modulus of elasticity, you should be able to find the forces on a weighted line a completely different way than using "basic geometry" and "high school math." To do so, you basically treat the webbing like a spring, and figure out the stress due to extension. Also, does anyone know if a slackline set up can be treated as elastic (allowing you to use simple statics equations)? For the most part, the webbing returns to it's original, unloaded state, but there is some permanent elongation. The webbing also seems to stretch a greater percentage than most other materials would within their elastic region.
Tried that, and it won't work cleanly. Webbing's elasticity varies too damn much. From batch to batch of the same color of web from the same company varies, much less once you consider different manufacturers, the effects of humidity and how it becomes less elastic with wear.
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addiroids
Sep 25, 2005, 4:43 PM
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I love how nerdy climbers can be. Such a range of people from pot smoking college dropouts (no offense to anyone) to guys with PhD's in physics or mechE all out there enjoying themselves to the fullest!!! Have fun and never stop learning.
TRADitionally yours,
Cali Dirtbag (soon to be Master's of Physical Therapy)
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misanthropic_nihilist
Sep 25, 2005, 5:28 PM
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In reply to: Tried that, and it won't work cleanly. Webbing's elasticity varies too damn much. From batch to batch of the same color of web from the same company varies, much less once you consider different manufacturers, the effects of humidity and how it becomes less elastic with wear.
Thanks. I tried working out the values with some pure nylon data I found (treating the webbing like a cable of nylon), and got data ~75% off of the "sum of the forces" results. I didn't realize the webbing properties are so variable. I guess as long as the Load Limit is correct, that's all that matters.
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superbum
Sep 25, 2005, 5:34 PM
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for all of us dropouts...dont make me do the equation! Just post the results!
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misanthropic_nihilist
Sep 25, 2005, 5:58 PM
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Just check out the calculator posted by slacklinejoe.
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iltripp
Sep 25, 2005, 6:33 PM
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Do those calculators find the force using purely trigonometric means (i.e. finding the angle at which the line sags and calculating the force using vectors)? Is that accurate without taking the elongation of the line into account?
It would be really nice to look at this from a more engineering standpoint. Do the Young's modulii vary too much to even get an estimate for this? Do webbing manufacturers provide information about the modulus of the webbing?
There are also other factors to take into consideration. Stress decay or relaxation would certainly be an issue. This would be accentuated if the line has gotten wet while under tension at any point. It would be very interesting to see an in-depth analysis of the situation.
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greenketch
Sep 25, 2005, 10:04 PM
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I believe that the stretch affects the tension a fair amount. I work with other forms of lines as well. Some of them are a near static cable. In those applications the plain trig functions calculate tensions quite accuratley. On the rare occasion that I have tried to measure tension on webbing I have consistantly been off. I have attributed that to stretch affecting the geometry. Than I walk away before I get serious and I make my brain hurt for no reason.
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iltripp
Sep 26, 2005, 12:20 AM
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I read through the whole "analysis of a slackline" page and it seems to be operating purely on trigonometric principles. I wonder if these are completely applicable to this situation.
For starters, imagine a situation with no one on the line. I know there is still considerable tension, yet the equation used would give a 0 value for the force.
To find the tension on a line with no one on it, you would have to know the original length of the line, the amount it has stretched, and the elastic modulus of the webbing. I'm not completely sure, but I think this information would also have to be taken into account to find the tension when someone is on the line.
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slacklinejoe
Sep 26, 2005, 1:06 AM
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On my calculator page I metion some of the limitations of the equation Eric posted. It only works assuming: there is some weight on the line (no pretensional measures), you are standing still, you are exactly in the middle - assuming those, it's moderatel accurate from the measurements we've heard. The reason why static calcs work under that scenario is that the line isn't stretching a the moment, the slacker isn't moving and for calculation simplicity your in the exact middle of the system.
Things that blow that calc all to hell:
Standing on 1 side means more force is on that side and less on the other
Your trying to measure pre-tension (do yourself a favor and assume pretension is irrelevant, it's usually around 300-500 lbs pull on a normal line)
Any movement on the slackers part, what I believe WILL fix that limitation is take the additional weight the slacker is imparting on the line and feed that back as the input for slacker weight, i.e. if jumping and landing back down creates an impact equal to double your weight, then input that back as the slacker weight and you'll be in the ball park. Part of the reason I can't trust that completely is under that the system isn't static and time and stretch/recoil enters the equation.
Trying to calculate loads created by falling on a highline leash.
The first person who can give me a accurate, usable equation to create a more accurate calculator for the above scenarios without making it mind boggling for inputs, something where someone can input the measurements without equipment like dynometers, make up for the variable elasticity in the webbing, and give me permission to use it for my revised calculator; I would not just buy you a beer, but buy you a case of beer and ship it to you (assuming it's less than $20 / case).
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tangen_foster
Sep 26, 2005, 1:19 AM
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In reply to: I love how nerdy climbers can be. Such a range of people from pot smoking college dropouts (no offense to anyone) to guys with PhD's in physics or mechE all out there enjoying themselves to the fullest!!! Have fun and never stop learning. TRADitionally yours, Cali Dirtbag (soon to be Master's of Physical Therapy)
serious nerdiness in this thread...incalculable nerdiness
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lewisiarediviva
Sep 26, 2005, 3:14 AM
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In reply to: Do those calculators find the force using purely trigonometric means
"find the force" It's all you need.
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poedoe
Sep 26, 2005, 4:39 AM
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In reply to: Things that blow that calc all to hell: Standing on 1 side means more force is on that side and less on the other
In reply to: Any movement on the slackers part, what I believe WILL fix that limitation is take the additional weight the slacker is imparting on the line and feed that back as the input for slacker weight, i.e. if jumping and landing back down creates an impact equal to double your weight, then input that back as the slacker weight and you'll be in the ball park. Part of the reason I can't trust that completely is under that the system isn't static and time and stretch/recoil enters the equation.
Trying to get this part right I think is super difficult. You could go with something like knowing how high the person jumps (so that is how far he will fall before touching the line) and then if you know his weight you can calculate the momentum he has when he touches the line again. However since the line stretches you would have to know where he is on the line, how long the line is, and how much the line is going to stretch. And on top of that, this is all assuming the webbing follows hooks law. Anyways if we did have all this then we could calculate the impulse of the person when he lands on the line, and thus the downward force. Then you could go back to using statics and trig to find the horizontal force on the anchors.
Gosh that was long and I hope that was right and made sense to someone. Its late and I have exams tomorrow (and the rest of the week).
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slacklinejoe
Sep 26, 2005, 4:55 AM
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In reply to: For this one couldn't you just recaluate the angle created at each point? What you should end up with is at each anchor is a different value of force in the y direction, however because the line is still in equilibrium the force in the x direction should stay the same.
In reply to: Anyways if we did have all this then we could calculate the impulse of the person when he lands on the line, and thus the downward force. Then you could go back to using statics and trig to find the horizontal force on the anchors.
Yep, that's what I was getting at; but I've yet to see it all put into work with a reasonably accurate result. However just to muck with it all even more, not all of the moves are straight down, i.e. surfing. Basically I'm working under the premise that we have to find the points of breaking it down to statics since we can't calculate the elongation of webbing reliably. Perhaps with field testing you could get numbers for new web, old web, wet web and such and suppliment the numbers where appropriate, however if the manufacturing company won't even publish elongation %'s it probably would be futile or else they would be publishing those specs too.
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areyoumydude
Sep 26, 2005, 5:02 AM
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My head hurts. :?
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veganboyjosh
Sep 26, 2005, 6:15 AM
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In reply to: In reply to: My head hurts. :? Don't worry about it man. I'd avoid the math side of things too if I could get away with it. I built that calculator doo-hikey just to avoid having to answer questions about this stuff since people kept asking.
fat lotta good that didja, huh?
interesting thread, btw.
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poedoe
Sep 26, 2005, 1:51 PM
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after thinking about this after I woke up I'm almost convinced that statics won't work. I mean you could try to find the elognation in the line and then fine out for the weight and distance how much it will stretch. However I see now that the problem witht that is: depending on how tight you strech the line, it will stretch more or less, so that throws trying to figure out a new angle based on the stretch to shit.
I guess what you could do is though is use statics to find the worst case scenario, ie find the instantanious force that the person would generate if they were instantly stoped the second the landed back on the slackline after jumping. Then you could go back to the wonderfull world of statics!
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misanthropic_nihilist
Sep 26, 2005, 2:21 PM
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In reply to: I guess what you could do is though is use statics to find the worst case scenario, ie find the instantanious force that the person would generate if they were instantly stoped the second the landed back on the slackline after jumping. Then you could go back to the wonderfull world of statics!
It seems like it would work at first...but it's never that easy, even to find the "worst case secenario." If you assumed the person instantaneously stopped, that means infinite accelerate, which means infinite forces (i.e. broken slackline, and more importantly, broken legs :D ).
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gunther85
Sep 26, 2005, 7:46 PM
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I e-mailed Blue Water to try to get some data about the elastic properties of their webbing, but i didn't get anything back from them. They said
"Do you own a load cell or dynamometer? You must determine the actual peak
load to calculate." that was all :(
Can't say i know exactly what they means, but maybe some of you guys do.
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