Study: Webbing Elongation and its Relationship to Load and Sag

This is a quick study I wrote for a slacklining website, but I figured some of you may find some of this information useful, so I copied it over onto MP. I know there is no abstract. There is no abstract because the owner of the site I wrote it for does not want one.

Introduction

Some slackliners believe that, for a given in-use tension, the amount of sag subjected to a slackline from a slackliner will remain the same regardless of the type of webbing used. An argument in favor of this theory would state that trigonometry equations dictate sag and not webbing elongation. Others believe that the webbing does play a major role in determining how much sag a slackliner will subject to a line. Supporting arguments include the notion that increased elongation translates to increased length, which translates to increased sag. As I continue, it will become apparent that the true product of slackline sag is, in part, a function of both of these theories.

Theory

I need to start by defining two terms: in-use tension and standing tension. In-use tension refers to the tension on the anchor when a slackliner is standing on the line. Standing tension refers to the tension on the anchor presented by the tensioning of the pulley system when the slackliner is not standing on the line.

The in-use tension subjected to a slackline anchor is a function of three main parameters: the slackliner’s weight, the amount of sag subjected by the slackliner at a given point and the length of the line. Three constants exist with regard to these parameters: an increase in the weight of the slackliner yields an increased anchor load, decreased sag yields an increased anchor load and increasing the line length for a given sag yields an increased anchor load. This rule model forms the backbone structure that the first theory explained in the introduction is based off. You can follow the parameters of this model using the calculator posted following.

slack.e30tuner.com/articles…

However, although the above is accurate, one critical parameter that slackliners need to understand is that the mathematical model used to calculate the tension on the line is only relative to the in-use tension. Because we are measuring the anchor load after the webbing has already elongated, anchor load is not a function of webbing elongation following this theory. Nonetheless, webbing with higher elongation will sag more for a given tension than lower elongation webbing will. Consider a slackliner who steps up on a chain fence and imagine that, clearly, the chain will not stretch. Next, consider the slackliner swaps the chain for an untensioned bungee cord. Clearly, the slackliner would fall to the ground, and the ground would support the majority of the slackliner’s weight. These examples form the basis for the second theory expressed in the introduction.

So, how can both theories be right? They can both be right because they are referencing two different phenomena. The mathematical model references the condition of the line after a slackliner steps on it, and the other theory references the condition of the line before a slackliner steps on it.

Test Methods

The methods applied in this study is quite simple. I started the test by stretching a 103’ milspec line across two trees. I tensioned the line and walked the line a few times to stabilize the line. I then fine-tuned the standing tension to 838 lbf. After, I sat in the middle of the line, I measured the deflection and I measured the average in-use tension. Last, I swapped the sample out for the next sample and repeated the test.

I used five webbing types in my study, in order from highest to lowest elongation: milspec tubular (nylon-6 tubular), type-18 (nylon flat), Mantra MKII (polyester flat), Green Magic (polyester flat) and Kevlar (para-aramid flat).



Tree-to-tree slackline length: 103’ (+/- 1 ft)
Standing tension: 838 lbf (+/- 2 lbf)
Load weight: 153 lbs (+/- 1 lb)
Load position: Within 1.5 ft of middle
Height measurement accuracy: +/- 2 in
Load acquisition and averaging accuracy: +/- 5 lbf., +/- 10 lbf. for Kevlar sample.

Results

The first graph shows the load experience by the anchors when subjected to the testing criteria listed above. It is worth nothing that high-elongation lines are well able to absorb small load fluctuations caused by wind or other influences whereas low-elongation lines are not. The graph displays this observation clearly.



The next graph displays the total sag of the line in relation to the load subjected to the anchors.



The final graph illustrates the anchor height requirement for a particular webbing type as well as the difference between the standing tension and the in-use tension. Interestingly enough, the in-use tension difference for the milspec tubular line is less than my weight (153 lbs load, 120 lbf increase), but the Kevlar-line increase is 383% of my weight. This information sheds light on why it is ultra-critical to use exceptionally strong components when highlining on polyester or high-tech webbing types.



It is worth further noting that this study was conducted on a 103' line. Duly, a slackliner walking a 412' line would need to multiply the anchor heights listed above by a multitude of four! A milspec tubular line that long would need an anchor height of 18', whereas a Kevlar line that long would require an anchor height of 12.5'.

Conclusion

Low-elongation webbings will produce less sag than high-elongation webbings for a given standing tension; however, at the price of increased in-use tension. Overall equal, slackliners can expect to utilize lower-spaced anchors with lower-elongation webbing types.

Overall, I like the approach taken. Grabbing empirical data is always a good idea.

I like the argumentation presented. I would work a little bit more on the grammar & verb tense, but overall that's a solid way to approach the merits of this study.

Nice write up, Sayar.

Btw, before I put much more thought into it, any interest in discussing this further? I agree with your data, methodology and conclusions, but think you're off on the reasoning. Short version is that it can be modeled as a spring quite simply and the results are fairly obvious given Hooke's Law (which IIRC is taught in high school physics, so nothing too complex or scary). I'd have to flesh it out a bit to make sure that approach is valid, and frankly it would be interesting to test theoretical v practical if you have elongation values for those lines.

Buff Johnson wrote:Overall, I like the approach taken. Grabbing empirical data is always a good idea. I like the argumentation presented. I would work a little bit more on the grammar & verb tense, but overall that's a solid way to approach the merits of this study.

Sure, thanks. I looked over the article and I did not find any grammar or tense issues, but then again it is likely I missed something. Can you point out some examples? Thanks.

Aric Datesman wrote:Nice write up, Sayar. Btw, before I put much more thought into it, any interest in discussing this further? I agree with your data, methodology and conclusions, but think you're off on the reasoning. Short version is that it can be modeled as a spring quite simply and the results are fairly obvious given Hooke's Law (which IIRC is taught in high school physics, so nothing too complex or scary). I'd have to flesh it out a bit to make sure that approach is valid, and frankly it would be interesting to test theoretical v practical if you have elongation values for those lines.

Sure, what do you want to discuss? You are correct that the webbing is basically a really long coil spring. However, I dont see how that invalidates my explanations in the theory section. Can you provide additional details?

As far as the elongation goes, that is a complex issue. I spent a month writing a study about webbing elongation last year. What I found is that the true elongation of a piece of webbing always changes. I could test three brand new samples and get three different values (although they were close). In addition, I could repeat the same test five times in a row and observe a subsequently different value for every test.

My favorite factor regarding webbing elongation is a phenomenon that occurs after a continuous high load. If you stand on a slackline for a while and then jump off, the load on the anchor will be lower than when you first jumped on the line. However, the webbing will actually fight to regain its original tension, and overtime the load on the anchor will actually increase. This phenomenon is visible on the first graph. If you look carefully, you will notice that as soon as I jumped off the line, the tension started to increase although nothing was touching the line. I have a couple of ideas as to why this occurs, but I have not been able to find any definitive fact-proven answers.

The phenomenon of elastic recovery and time dependent recovery of nylon is well known, there was an unfortunate accident many years ago concerning a couple of French cavers whose abseil rope had shrunk back out of reach.

20 kN wrote: Sure, what do you want to discuss? .

Well, I guess first thing I'd float for discussion is that this bit of the Introduction is decidedly incorrect:

20 kN wrote:Some slackliners believe that, for a given tension, the amount of sag subjected to a slackline from a slackliner will remain the same regardless of the type of webbing used. An argument in favor of this theory would state that trigonometry equations dictate sag and not webbing elongation.

Yet seems to be accepted as correct in later discussion, by way of your stating:

20 kN wrote:As I continue, it will become apparent that the true product of slackline sag is, in part, a function of both of these theories.

As I mentioned, this can be modeled as a simple Hooke's Law problem and there really isn't any room for interpretation. It's a fairly simple spring problem with differing spring constants, and there isn't much more to it than that unless you delve into the nuance of the behavior of woven textiles, which is beyond the scope of your study. Fortunately the data support your argument, but that doesn't mean it's actually correct. I'd suggest taking some elongation measurements on those samples, backing into a spring constant and then looking at the problem from that direction. While the results will undoubtedly be the same (less elongation = higher tension and less sag), the reasons for it will be different than you proposed.

-aric.

"Some slackliners believe that, for a given tension, the amount of sag subjected to a slackline from a slackliner will remain the same regardless of the type of webbing used. An argument in favor of this theory would state that trigonometry equations dictate sag and not webbing elongation."

As Aric says, this is clearly wrong. An infinitely inextensible line will never sag no matter the weight and and infinitely extensible one will sag an infinite amount with any weight. Trigonometry covers the load on the anchors, not sag.

Yup. Sag is a function of the spring constant/elasticity/elongation, and tension is a function of sag. Therefore tension is a function of the spring constant and low stretch lines will *by definition* sag less and increase anchor force.

I'm curious your thoughts on this, Sayar, as it directly contradicts one of your supporting arguments. An interesting test you could do to prove this to yourself is rig two identical-length lines, one from standard webbing and one from a tech fiber. First rig the normal one and measure sag, then rig the tech fiber one ignoring the free tension and instead match it for the same amount of sag. You should end up with the same loaded tension on both lines (same amount of sag), and when unloaded the tech fiber one will have (significantly) less tension and proves it's a simple Hooke's Law problem.

-a.

Btw, I mean all this constructively and my only interest is correcting possibly bad information. :-)

Guess you're not up for discussing this, Sayar? Bummer. That looks like it took a fair amount of work, and it's a shame for the reasoning to remain incorrect.

Aric Datesman wrote:Guess you're not up for discussing this, Sayar? Bummer. That looks like it took a fair amount of work, and it's a shame for the reasoning to remain incorrect.

Sorry, I have been training for my summer-long climbing trip so I have been ultra-busy.

Yup. Sag is a function of the spring constant/elasticity/elongation, and tension is a function of sag. Therefore tension is a function of the spring constant and low stretch lines will *by definition* sag less and increase anchor force.

I'm curious your thoughts on this, Sayar, as it directly contradicts one of your supporting arguments

Not my supporting arguments, “the” supporting arguments. I was simply reciting the two most common beliefs amongst slackliners. :) Anyway, we need to remember that they are supposed to contradict each other. I specifically said they would. I also said they appear to contradict each other because they are referencing two different phenomena, and therefore can appear to contradict each other because they are not actually referencing the same thing. One references in-use tension and the other references standing tension. As you said, if I rig two different lines so the sag is the exact same, the anchor load will be the same. That consequence supports the argument that math can dictate anchor load if we know the sag distance. However, as my study shows, if we match standing tensions amongst samples, webbing elongation does play a role in determining anchor load. Remember, we are talking about two different phenomena here, and two completely separate events.

I will give you two examples using my own quotes.

Some slackliners believe that, for a given tension, the amount of sag subjected to a slackline from a slackliner will remain the same regardless of the type of webbing used.

I rig two different lines, one polyester and one nylon. I then fine-tune the tension using a dynometer so that when I step in the middle of the line the load on the anchor will be the same for both lines. Upon doing so I will find that the sag for both lines will be exactly the same. That is because sag distance = anchor load, irrelative to webbing elongation. However, I will also observe that upon stepping off the line the standing tensions will be different for each line because the nylon line will require more standing tension to match the sag with the polyester line.

Others believe that the webbing does play a major role in determining how much sag a slackliner will subject to a line.

If I match the standing tension for a nylon and polyester line, I will find that upon stepping on the lines the nylon line will sag more than the polyester line will and therefore the nylon line will see a lower load at the anchor. Thus, webbing elongation + load weight + standing tension = sag distance = in-use tension anchor load.

Does that answer your questions?

I'll edit and critique just because I'm bored..... take it or leave it:

20 kN wrote:Some slackliners believe that, for a given tension, the amount of sag subjected to a slackline from a slackliner will remain the same regardless of the type of webbing used.

You're starting off confusing people immediately. "For a given tension"... is that your "in-use" tension, or your "standing" tension? Rewrite.

20 kN wrote:... An argument in favor of this theory would state that trigonometry equations dictate sag and not webbing elongation.

My response to someone who said that would be: Trigonometry equations can DESCRIBE the sag, or the force, but they don't DICTATE the sag. Problem is, anyone interested in this is probably MEASURING the sag, cuz that's the easiest thing to measure! And so you don't need equations to describe the sag. More likely I want equation to describe the FORCE on the anchor. Rewrite.

20 kN wrote:Supporting arguments include the notion that increased elongation translates to increased length, which translates to increased sag.

If something gets longer (increased elongation), then it gets longer (increased length). It's not a "notion".... blue is blue. Rewrite.

20 kN wrote:Three constants exist with regard to these parameters

Not "constants". You mean variables. Variables. If it can change, it's a VARIABLE. (In fact you say it in the next sentence.... "An INCREASE in the weight of the....") Rewrite

20 kN wrote:Nonetheless, webbing with higher elongation will sag more for a given tension than lower elongation webbing will.

Sure, but what good is that? After all, what doesn't change is my weight, and the distance between the trees. I can change the starting tension on the line, and the type of line. If my weight stays the same and the length of line stays the same, the tension can't stay the same at different sags, right? In this sentence you're trying to hold tension constant and change sag, which requires a change in load on the line. Stay in the real world, not in text book fantasy land, and..... Rewrite. :)

20 kN wrote:So, how can both theories be right? They can both be right because they are referencing two different phenomena.

I'm struggling with you calling them "theories". Usually a theory is based around (1) something that is not well understood, (2) a phenomena that yet needs to be explained, or (3) a new twist on something everybody thought was previously and adequately explained, but you think it's not. You don't have any of those here. You're hashing over material that's been hashed over in every mechanics of materials class since 1962. I guess it's a good exercise in technical writing and thinking....but.... rewrite. :)

20 kN wrote:It is worth nothing that high-elongation lines are well able to absorb small load fluctuations caused by wind or other influences whereas low-elongation lines are not.

^^^ Interesting you say that.... also interesting Aric suggests that you STUDY SPRINGS. DOh! Another thought experiment to help you answer this one.... a leader takes 2 falls, everything the same except rope elongation. Which anchor experiences the higher load? Why? And how does this relate to slightly bouncing on different slacklines with different material properties?

20 kN wrote: My favorite factor regarding webbing elongation is a phenomenon that occurs after a continuous high load. If you stand on a slackline for a while and then jump off, the load on the anchor will be lower than when you first jumped on the line. However, the webbing will actually fight to regain its original tension, and overtime the load on the anchor will actually increase. This phenomenon is visible on the first graph. If you look carefully, you will notice that as soon as I jumped off the line, the tension started to increase although nothing was touching the line. I have a couple of ideas as to why this occurs, but I have not been able to find any definitive fact-proven answers.

http://bit.ly/YEpe3H

Some interesting thoughts above. But, sorry. No new discoveries.

One variable: the material used
two constants: the weight put on the line and the initial tension on the line.
Two results: the sag, as you call it giving an angle on the anchors
And the load on the anchors

A trigonometric equation will describe this behavior quite well. But you are trying to chicken, egg these reactions. They are all related.

The equitation describing tension includes the tangent function. The tangent function tends toward infinity as the angle approaches 90°. 90° equates to zero sag in this formula.

Therefore, any material with less elasticity will result in less sag... Will result in higher loads on the anchors. Slight differences in sag will result in significantly higher loads especially as the sag.as you call it tends toward zero.

Try it with a steel cable.

A bit hard to follow your response, Sayar, due to the quoting having gone screwy. Regardless, I actually didn't have a question so much as a concern that some of your reasoning is incorrect. I suppose that leads to the question of whether or not you'll be fixing it...

Anyway, not much more I have to say on the subject that hasn't been touched on by others above. If it were me (or me the one paying for it), I'd scrap it and start over with an explanation of how Hooke's Law plays into this and then deriving the formula that will determine both sag and tension for a given length, load and elongation. It would be much shorter and clearer this way, and more importantly, correct.

Greg D wrote: One variable: the material used two constants: the weight put on the line and the initial tension on the line.

Those three are variables, dude. Constants are like e, pi, gravitational constant, spring constant, etc...

Eric Krantz wrote: Those three are variables, dude. Constants are like e, pi, gravitational constant, spring constant, etc...

Thanks. But in the op's tests his body weight Will remain constant. His pre tension should remain constant for all materials.

Greg D wrote: Thanks. But in the op's tests his body weight Will remain constant. His pre tension should remain constant for all materials.

What if he poops then goes back on the line?

This: Variables, mathematically speaking, don't HAVE to vary. We say, "we're going to hold this variable constant" - that doesn't imply that the variable IS a constant, just that we're holding it constant. They're still variables. His weight is an extensive property, therefore a mathematical variable. All extensive quantities are variables.

As (un)interesting as this debate about variables is, it's likely not helping with the bigger issue of convincing Sayar to rework his article.

:-(

Eric Krantz wrote: What if he poops then goes back on the line? This: Variables, mathematically speaking, don't HAVE to vary. We say, "we're going to hold this variable constant" - that doesn't imply that the variable IS a constant, just that we're holding it constant. They're still variables. His weight is an extensive property, therefore a mathematical variable. All extensive quantities are variables.

Although your words are variable, you constantly provide little results. Care to add any value to the discussion?

Oh, and looks like we lost Sayar again. Bummer, as I really like what he did here and would like his reasoning to be correct. :(

^^ I agree. Sorry for being the constant ass. Cool comparison of how different webbings vary, though.

Greg's right in that it appears you're trying to chicken/egg the system. It's all tied together, not really cause/effect relationships, but each a piece of the whole pie.

I'd suggest: Instead of saying "some people believe this and that, and so there are these two theories", just lay out the math... none of this is "theory". That's like proposing the theory that c^2 is equal to a^2 + b^2 in a right triangle. If it can be proven mathematically, there's no need to call it a theory. Tension, sag, angle, load etc etc are all related. Draw a FBD and sum your forces, and therein lines the proof. Then show your cool charts, talk a bit about elasticity maybe....

Charts... please change X axis to "seconds" instead of "ms * 100". As most people, I think in seconds, not ms * 100. Einstein and a hundred other people said "make it as simple as possible, but not simpler". Also, if you use both left and right Y axis, have the same number of divisions on each side so labels on both sides will line up with the grid marks.