# Friction Saver Friction -- some measurements



## moray (Mar 19, 2008)

Anyone who has climbed DRT with a friction saver knows it reduces friction dramatically compared to tree bark. A pulley likewise is dramatically better than a friction saver. A couple of days ago I decided to actually measure the friction of a few devices.

Partly I was motivated by the diagram below, from Petzl, part of a large amount of info they supply if you buy one of their pulleys. The pulley in this case is a so-called rescue pulley, a model with ball bearings and low friction.







From the diagram it appears that 1.1 lbs are needed to lift 1 lb of load, which is an efficiency of about 91%. It is interesting that they show the efficiency of a carabiner in the same setup to be only 50%.

I used the same setup for my measurements. The load was a 20-lb dumbbell, the rope was a 1/2 in climbing rope, and I was standing on a pretty good bathroom scale to take the measurements. To get more bang per setup, I did the Petzl-style measurement while pulling down on the rope, but then took another measurement while slowly lowering the weight. It was the _difference_ between these two measurements, in lbs., that I recorded; later I combined them mathematically to get the efficiency.

The measurements turned out to be more reproducible than I expected: for a given device I could take measurements 4 or 5 times and record the same difference every time within a pound or less for high-efficiency devices, and within 2 or 3 pounds for the low-efficiency devices; the averages in the table should be a bit better than that. 

The results are shown in the table below.






The results surprised me. The first surprise was the poor performance of the micro pulley, which I had climbed under a number of times. The other pulleys waste 1/3 as much energy. Second, the aluminum rings, at under 50% efficiency, were much worse than I imagined. This would mean that footlocking or hip-thrusting under the rings would cost you 4 feet of work for every 3 feet of actual height gained. No wonder SRT feels so clean and efficient.


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## Adkpk (Mar 19, 2008)

I have climbed on the rescue pulley and I went immediately back to the friction saver. I was footlocking and with every upward advance there was close to equal descent. The friction saver did some of the work as to hold a little to allow me to advance my hitch without slipping back down. Of course I have learned a few tricks by now and should try again using a different hitch and maybe a slack tender. With the spring coming it time to dust off the climbing sack and get up some tree. Can't wait.


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## Mikecutstrees (Mar 19, 2008)

thats cool, I have noticed myself the huge difference a smaller smooth TIP makes compared to a larger rougher TIP.... Thanks for the experement and results....


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## D Mc (Mar 19, 2008)

Moray, thanks for posting the numbers. Interesting information. I have been climbing with a pulley as my tie-in point a little over a year now and absolutely love it. I am reminded just how well it works when I can't use it and have to use the friction or rope saver. 

I think it is the wave of the future.

D Mc


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## ATH (Mar 19, 2008)

Wow...makes the pully look pretty attractive!

It'd be interesting to try the same measurement with the rope over a few different species and diameters of limbs (and even some crotches that the rope ends up in). Obviously harder to have the scale on a good solid/level surface when the rope is in a tree...

So, if the assumption (unmeasured at this point??) is that a friction saver reduces the friction by 50%, that means if you use nothing, you are lifting 40 lbs to move 20lbs, right?

Even if the friction saver saved no work, I still think they are better than climbing on the bark alone (cambium saving, and reduced wear/tear on the rope for those who aren't interested in the tree's bark...)


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## moray (Mar 20, 2008)

ATH said:


> ...It'd be interesting to try the same measurement ...
> 
> So, if the assumption (unmeasured at this point??) is that a friction saver reduces the friction by 50%, that means if you use nothing, you are lifting 40 lbs to move 20lbs, right?



I hope I am understanding your question correctly... The measured friction of the aluminum rings is such that it takes 40 lbs to lift 20 lbs. The rough bark of a tree limb will be much worse--maybe it would take 80 lbs to lift 20. I do intend to measure that, and do some experiments with a Port-a-Wrap as well. Stay tuned...


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## ATH (Mar 20, 2008)

Yeah...poor wording on my part. I'll look forward to seeing more!


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## tomtrees58 (Mar 20, 2008)

yes works good but every tree is different tom treesopcorn:


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## pdqdl (Mar 20, 2008)

*Rethink your analysis !*



moray said:


> Anyone who has climbed DRT with a friction saver knows it reduces friction dramatically compared to tree bark. A pulley likewise is dramatically better than a friction saver. A couple of days ago I decided to actually measure the friction of a few devices.
> 
> [parts deleted for brevity]
> 
> ...



There is a bit of an error here, unless I have misunderstood your test measurement method. When using DRT (Double Rope Technique?), the forces are not applied as shown in the diagram you provided. SINGLE rope technique offers 1:1 lifting "mechanical advantage", but using a pulley (of any efficiency rating) gives a 2:1 theoretical advantage, because the load (the 20 lb dumbell) is not being lifted by an outside source (you, on the scale).

A single pulley arrangement always puts a 2:1 mechanical advantage (theoretical) on a system. As shown in your diagram (using a frictionless pulley), you would be applying 40 lbs of downforce on the pulley anchor point, with matching loads on the lines. Keep that in mind, if you ever have ground men pull on your "down" line to help you up the tree: it MORE than doubles your weight as the force on the tie in, due to your weight, the friction, and their downward pull.

In DRT, as you pull DOWN on the rope with say, 100lbs force, you are reducing your own weight load by the amount you are pulling down with. Using a 100% efficient (frictionless) system means that a 200lb man can climb the tree using only arms strong enough to pull down with +100lbs of force. 

A consideration: Since the tree bark adds friction to the DRT, it often enables a fellow to hold the rope with only one hand, while the other hand moves the friction knot (or ascender) up the line to hold position for the next pull. Without that extra friction (Ex: using a pulley), many of us couldn't pull ourselves up the tree.

I use an ascender, because by growing middle is outgrowing my arms, and the force applied lifting the friction knot overcomes my "holding" arm. After I go up farther than I wish to fall from the ascender, I use two hands to slide the friction knot up the line while I hang from the ascender. No footlocking required! Maybe not a good technique for some of you strong guys, but it works for me.

For a better measure of how a pulley saves effort over a friction saver or just the tree bark, rig yourself from some height, and use a spring scale rigged to your pulling line, and re-do the whole test.


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## ATH (Mar 20, 2008)

pdqdl said:


> .......using a pulley (of any efficiency rating) gives a 2:1 theoretical advantage, because the load (the 20 lb dumbell) is not being lifted by an outside source (you, on the scale).
> 
> A single pulley arrangement always puts a 2:1 mechanical advantage (theoretical) on a system.........


A fixed pully changes direction only, it offers no mechanical advantage. To get MA from a single pully, the pully needs to move.


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## moray (Mar 21, 2008)

pdqdl said:


> There is a bit of an error here, unless I have misunderstood your test measurement method. When using DRT (Double Rope Technique?), the forces are not applied as shown in the diagram you provided. SINGLE rope technique offers 1:1 lifting "mechanical advantage", but using a pulley (of any efficiency rating) gives a 2:1 theoretical advantage, because the load (the 20 lb dumbell) is not being lifted by an outside source (you, on the scale)...
> 
> 
> In DRT, as you pull DOWN on the rope with say, 100lbs force, you are reducing your own weight load by the amount you are pulling down with. Using a 100% efficient (frictionless) system means that a 200lb man can climb the tree using only arms strong enough to pull down with +100lbs of force...





There are two separate ideas here--one is the friction of various devices, and the other is the practical effect of using them in a standard DRT setup. The only thing I measured--indirectly--was friction. The actual specific friction of a device in a particular setup is probably of no interest to anyone, so I calculated efficiency instead. This is the useful parameter to know for understanding all sorts of setups.

How does all this work out in the standard DRT setup? ATH is exactly right to point out there is no mechanical advantage inherent in a pulley: it merely changes the direction of a force. The advantage of a single pulley comes when the load is attached to the pulley and the pulley moves. The reason is that the rope (and the applied force) move twice as far as the load. That's where the "2" in "2:1" comes from. And that's why DRT gives you the 2:1 advantage you describe--it is just a special case of the moving pulley, even if the "pulley" is a tree limb. The "pulley" may not move, but the rope still moves twice as far as the load. 

What about a DRT setup if the "pulley" is a friction saver with 2 aluminum rings with an efficiency of 50%? As your 200 lb. climber steadily pulls himself up hand over hand, we know, because the rings are only 50% efficient, that the force on the climber's arms is twice the force on the other leg of the rope, just as my experiments (and the Petzl diagram) show. The weight of the climber is exactly equal to the sum of the tensions in the two legs, so 2/3 of the climber's weight is supported by his arms. If the climber goes up 3 feet, the rope has moved 6 feet. The arms, doing all the work, have raised 2/3 of the weight 6 feet, or, equivalently, all the weight 4 feet. There you have it. Four feet of work for 3 feet of gain. One-quarter of the energy has been wasted.


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## moray (Mar 28, 2008)

*More Data*

I now have some friction measurements of rope on wood. Since there are still 2 feet of snow on the ground outside, getting the measurements outside was going to be way too hard. Instead I chose to use stove wood rigged up with a couple of sturdy hooks. The rope is the same one used in the earlier set of measurements of rope-on-metal friction, and the method used was the same.






In this set of measurements there was no attempt to be extremely precise. The measurements were not as steady and repeatable as they were with metal, and in any event I just wanted a rough idea of how wood compared to metal. The data clearly show, for the wood I had ready at hand, that the friction is only slightly greater than for a friction saver with 2 aluminum rings.






This surprised me. Even though the data don't lie, I don't think they are a good fit to a real-world DRT situation. Two major reservations occur to me. 

The first can be illustrated with the measurements on the paper birch, which had the lowest friction in the 5 tests. I have 2 birch trees in my back yard. Even though the bark is nice and smooth, there is no place on either tree where I could rig a DRT rope over a smooth horizontal limb. The rope has to go in a crotch, and crotches are invariably very rough. They are rough and hard to the point of grabbing at the rope, producing "friction" that obviously greatly exceeds that of 2 aluminum rings. My simple tests involved a configuration that is probably rare as a DRT setup.

This leads to the second reservation. With a climber's full weight on a DRT rope, the rope flattens and deforms where it goes over the support. If the support is smooth metal, this should have little effect compared to the light loads in my testing, except to increase the friction in proportion to the force. In the case of tree bark, where surface irregularities are typically much larger than the diameter of a rope fiber, the rope may skate over these irregularities in light testing, but under heavier loads fibers will begin snagging and breaking, and the bark promontories will begin abrading away. All of this is extra "friction" that prevents my light-load results from scaling up properly.

Tomorrow I will try to post results of another experiment that investigates the effect of large-scale irregularities.


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## pdqdl (Mar 28, 2008)

You are one dedicated researcher. Keep it up !  

I am looking forward to seing your results.


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## 046 (Mar 28, 2008)

moray... nice work!!! thanks for sharing


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## reachtreeservi (Mar 29, 2008)

Morey, I just go to the saw shop when it snows. But You....

I enjoy reading your posts , keep it up !


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## moray (Mar 29, 2008)

Thanks for the kind comments, everyone!

This last experiment is in some ways the most interesting to me. Even if it doesn't definitively answer any particular question, it has a strong bearing on the question of how friction of a rope around a limb actually works--is the friction related to the amount of contact surface, or to the size of the limb, or to the number of wraps? What is the "contact surface", anyway?

One of my stove logs in the previous experiment was a piece of locust with deeply furrowed bark. I expected a lot of friction from it because of this, but it differed only slightly from much smoother logs. It had been under the snow all winter, and the bark seemed a little soft to me. Perhaps the softer bark produced less friction. There were just too many variables floating around: hardness of bark, species of wood, amount of resin in the bark, presence and size of furrows, etc. To control all this, I decided to make my own "bark".

It was easy to strip the bark off the birch log that had been used earlier. A router was used to cut 6 parallel longitudinal grooves to simulate bark grooves, but a control section was left ungrooved. To remove any sharp edges, a chisel was used to chamfer both edges of each groove. The entire debarked area was then hand sanded with 80 grit paper. Finally, the groove edges were sanded to give them a soft rounded profile that would not interfere with rope movement in any way. The photo shows the log ready for testing.






The standard friction test was peformed on both the grooved and ungrooved sections. Both sections were subjected to 6 or 8 pulls to get the readings to stabilize (The friction declined slightly during this preliminary as the wood took on a slight polish.) The chart shows the results.






After the test I measured the width of all the grooves where the rope had crossed them. The sum of the gaps was 2.6 in; half the circumference of the entire log was exactly 6 in. Just over 43% of the contact surface had been removed to form the grooves, yet the friction, compared to the ungrooved control, was virtually identical. Clearly, the contact area, when everything else is held constant, has little or no relation to friction.


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## Nailsbeats (Mar 29, 2008)

Word. I think that is an interesting experiment with and interesting outcome. I am gonna go out on a limb here, lol, and say that the rope surface has the most effect on friction. The kind of rope you use (I mean style like braid and material, not diameter), not the kind of tree your in, in most cases. Granted your line is over a horizontal limb and not a crotch, or bound up in pine sap. It seems we use a lot of natural crotches and different style ropes "run" differently. They seem to cut a groove and go. Just a bullsh*t guess.


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## pdqdl (Mar 31, 2008)

moray said:


> ...yet the friction, compared to the ungrooved control, was virtually identical. Clearly, the contact area, when everything else is held constant, has little or no relation to friction.



That's a pretty remarkable conclusion, given that it flies in the face of how most people think friction works. 

When I took physics (many years ago), formulas using coefficients of friction, mass, force, etc were used to demonstrate exactly the the same point that you have found by experimentation. Over the years, I have tried at different times to explain that principle to others less educated, and I think they usually concluded I was off my rocker. My hat is off to you.  

But...it might have been easier for you to read a book on physics. I have never tried, but I'll bet some ambitious researcher like yourself has developed a table of some sort for the coefficient of friction for braided rope on different types of bark. It would take some really deep research to find it though, so I think I'll pass.


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## moray (Mar 31, 2008)

Nailsbeats said:


> ...I am gonna go out on a limb here, lol, and say that the rope surface has the most effect on friction. The kind of rope you use (I mean style like braid and material, not diameter), not the kind of tree...



I think you are exactly right. More than that, if you only consider climbing ropes and bull ropes, you can probably simplify even further and say rope on wood friction is roughly the same in all situations.


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## lumberjack333 (Mar 31, 2008)

Very interesting moray, personally wouldn't have guessed that contact area has almost no effect on friction... gives me something to think about next time I'm picking up climbing line! Nice work!


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## moray (Mar 31, 2008)

pdqdl said:


> ...My hat is off to you.
> 
> But...it might have been easier for you to read a book on physics...



Don't give me too much credit, pdqdl; my little experiment certainly is not breaking any new ground! And as you may have guessed, I have read a book or two on physics. The exponential formula that describes friction of a rope around a post is very cool, and, as you say, flies in the face of how most people think about it. It was partly to test out the formula for myself that I did the experiment with the grooves. One of the great things about doing experiments, besides making you think hard about what you are doing, is that quite often they serve up a reminder that you don't know as much as you think you do. That was the case here. 

Even though I vaguely expected the grooves would not reduce the friction, I assumed, without thinking much about it, that the remaining wood would make up the difference. That is, the lands between the grooves would now be supplying more friction than before the grooves were installed. But I was wrong!! That isn't what happens. More to come...


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## moray (Mar 31, 2008)

lumberjack333 said:


> Very interesting moray, personally wouldn't have guessed that contact area has almost no effect on friction...



Lumberjack, I need to be careful how I say things. Contact area has everything to do with friction. But when everything else is held constant, VARYING the contact area doesn't cause any change in friction. There. That's clearer.


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## pdqdl (Mar 31, 2008)

Formula for friction of rope around a post ?

Now that's one they never told us about ! I know for a certainty that it is not in my old physics book. If you stumble across that one, please send it to me. If you do, I will actually study that a bit and learn some about that.

I'm getting pretty rusty on all that stuff, anyway.

Wouldn't it be cool if some of the makers of the friction devices would publish some useful tables that would let a treeman know how many wraps are needed for however much weight we were going to cut off ?


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## lumberjack333 (Mar 31, 2008)

So your saying that the friction on a set diameter (birch log) with the same rope and weight is equal between the grooved area and the untouched area, but if diameter increased and the contact area increased friction would then be greater? Thats what I was assuming before, should have worded my response better as well I supposed :yoyo: , none the less interesting that removing contact area while keeping everything else constant doesn't affect friction. Thanks for clarifying!


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## moray (Mar 31, 2008)

lumberjack333 said:


> So your saying that the friction on a set diameter (birch log) with the same rope and weight is equal between the grooved area and the untouched area...



Yes. This is what I measured.



lumberjack333 said:


> ...but if diameter increased and the contact area increased friction would then be greater?...



No. This is why I love this problem! This will not increase the friction.


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## lumberjack333 (Mar 31, 2008)

lol, well you've caught my interest now too moray, so increasing the contact area does nothing... just surface type/texture and rope design/material affect friction?


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## moray (Mar 31, 2008)

And number of wraps. This is key.


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## moray (Mar 31, 2008)

*the equation*

OK, here is the equation. Now a peculiar expression will come over a lot of people's faces when they see an equation--what I call the "equation look". It is precisely the same expression you'll see when they discover fresh wet dog sh*t stuck to their boot. Fortunately this equation, at least, can be explained pretty well in plain English.







In MathSpeak: The two T's are the tensions on the two legs of the line. The constant _e_ is the base of the natural logarithms (2.71828...), A is the angle of wrap in radians, and C is the coefficient of friction between the rope and the post.

In English: This is just a growth equation, exactly like the equation that describes the growth of a savings deposit where the interest is compounded continuously. This is smooth type of growth such that any particular time interval always produces the same percentage of growth. If the savings grow 1% every 10 days, for example, then you can pick any arbitrary date, X, look at the value of the savings on that date, and know that 10 days later the value will have increased 1%. Obviously a bigger account will grow faster in absolute terms than a smaller one, but in percentage terms they both grow at the same rate.

In the case of the rope around the post, as you move around the post, let's say from the low- to the high-tension side, the tension increases by the same percentage each time you move one degree. The tension in the rope is smoothly growing, just as the savings did, by a constant percentage amount per degree of wrap. The percentage is governed by the coefficient of friction, and it is the accumulated friction around the post that causes the tension in the two legs to be different.

In summary: in the bank case we have an interest rate defined by the bank and growth occurring over intervals of time. In the rope case, we have a friction "rate" defined by nature, and growth in tension occurring over intervals of degrees.


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## pdqdl (Mar 31, 2008)

Well ! That was a much simpler formula than I expected. 

I presume that the units of tension are generic? Do the "T" variables represent static or kinetic loads, or does it matter (after all, the coefficient of friction would change when the load starts moving) ?

For the record: I always hated working with radians and natural logs,  and I am not likely to work too long on bringing this into a useable table for a guy with a log, rope, and a chainsaw. However...I might figure out how much each wrap adds to the change in T1/T2. THAT would be really practical to know !


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## moray (Mar 31, 2008)

pdqdl said:


> ...Wouldn't it be cool if some of the makers of the friction devices would publish some useful tables that would let a treeman know how many wraps are needed for however much weight we were going to cut off ?



I think you can come pretty close and still be on the safe side. If the ground guy is lowering a piece and the rope is wrapped around a limb, you could assume, as I discovered in my primitive experiments, that a half wrap has an efficiency of about .5. That means the groundie has a 2:1 advantage in controlling the load. Add another full wrap, and the advantage goes up to 8:1. Another full wrap and it's 32:1. Even a 1000 lb load would be easy to handle with 2 1/2 wraps. I'll bet 2 1/2 wraps is actually closer to 50:1 for most rope/wood combos.

Last fall I was the groundie on the lowering rope when we lowered a 2000 lb tree and laid it flat in a driveway. At one point the truck was pulling the butt, which was off the ground, while I controlled the top with the lowering rope, and the whole affair was suspended in midair. It was a 3/4 in nylon bull rope with 2 1/4 wraps around a maple tree right next to me, at waist height. At one point I added another 1/4 wrap and noticed a significant drop in tension.

In the case of metal devices like the Port-a-Wrap, I'll bet an efficiency of .5 for a half wrap is very close. I want to measure that one of these days, but it won't be as easy to set up as a chunk of wood.


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## moray (Mar 31, 2008)

Wow, pdqdl, we seem to be on exactly the same page! Yeah, I'm not taking my slide rule into the woods either, but a rough rule of so much advantage per half wrap would seem pretty useful.


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## moray (Mar 31, 2008)

*Warning, math inside...*

I have made a diagram that dissects my experiment with the grooves, ties everything together, and shows how close I came to walking away from this whole problem thinking I understood it when I really didn't. But first, here are a few preliminary ideas that seem necessary to understanding the problem. Some of these probably deserve discussion in their own right, but I will just toss them out there for now. Throughout all of this we are assuming that we are operating in a region where the "laws" of friction hold--the rope is not smoking, fibers are not snagging, bark is not being ripped from limbs, etc. Assume we are talking about sliding friction, and assume that the coefficient of friction between rope and wood is constant over the range of loads we apply. Static friction will be similar, but the numbers would be a bit larger.

1. Friction between two objects in contact is equal to the force holding them together multiplied by the mutual coefficient of friction between them. This is the standard law of friction. There is no mention of the area of contact!

2. A rope under tension is straight. To bend a rope under tension a force must be applied perpendicular to the rope.

3. Conversely, if a rope under tension is bent, it must have a perpendicular force acting on it.

5. For small amounts of bend (on the order of a degree or so) the force needed to bend a rope is proportional to the amount of bend multiplied by the tension. The force needed to bend a tensioned rope 1/2 degree is 1/2 the force needed to bend it a full degree. For a rope under 1000 lbs tension, the force needed to bend it 1 degree is twice what it would be if the tension was 500 lbs.

6. From (5) we can directly derive this: the perpendicular force per unit length of rope around a bend is reciprocally related to the radius of bend. This is a key relationship. 
Imagine a horizontal log 360 inches in circumference deflecting a vertical tensioned rope 1 degree. Then one inch of the log circumference will be in contact with the rope. Let's say it takes 10 lbs. to cause this deflection. 
Now halve the size of the log. Again push the log into the rope till there is a one degree deflection. From (5) we know this still takes 10 lbs. But, obviously, now there is only 1/2 inch of rope length in contact with the log. In the first case we have a total force of 10 lbs spread over one inch of circumference, but in the second case the 10 lbs is spread over 1/2 inch. We can loosely think of this as "pressure", and say the pressure of a tensioned rope against a surface is inversely proportional to the radius of curvature at the point of contact. A sharp bend means a lot more pressure than a gentle bend.

7. Finally we can get at the friction. Remember from (1) that friction is the product of force times coefficient of friction. Remember also that the coefficient of friction for a particular combination of rope and wood is more or less a constant. Then the 10 lbs of force in (6) produces the same amount of friction between rope and wood in both the big log and the half-size log. The quantity that is the same in both cases (and the source of the 10 lbs) is the one-degree bend of the rope. The size of the log is not a factor. Conclusion: over any small-angle section of tensioned rope around a post, the friction generated by that section is the product of tension X angle X coefficient of friction. We're done. 

This is all the background for my diagram, which I'll try to post tomorrow. All the hard ideas are here, so tomorrow will be a breeze...


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## pdqdl (Mar 31, 2008)

*Damn the complexities !*

There may be another stumble in the path to our plan to calculate the number of wraps needed for any load: almost always (in the real world of tree work) the rope will be feeding off the axis of rotation at a variable angle from perpendicular, as in wraps taken around a vertical tree trunk to control an overhead load. 

Do you suppose that influences the holding force of x(radians) rotation ? I haven't thought about it enough yet, and it was a LONG time ago that I studied any physics.


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## rahtreelimbs (Mar 31, 2008)

All interesting stuff!!!

I go by what my hands and body tell me. A 2 ring friction saver is nice because it lowers friction and is consistant fro tree to tree. A rope guide setup with a pulley is a whole differant animal. With the pulley setup you have zero friction to hold you while hip thrusting and also you hitch has to be tailored for it. So far I wil stick with the 2 ring setup.........although the jury is still out on the pulley deal!!!


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## moray (Apr 1, 2008)

pdqdl said:


> There may be another stumble in the path to our plan to calculate the number of wraps needed for any load: almost always (in the real world of tree work) the rope will be feeding off the axis of rotation at a variable angle from perpendicular, as in wraps taken around a vertical tree trunk to control an overhead load.
> 
> Do you suppose that influences the holding force of x(radians) rotation ? I haven't thought about it enough yet, and it was a LONG time ago that I studied any physics.



I think this is an excellent question. And I am almost positive the answer will be: it makes no difference. A nice tight circular wrap around a trunk should behave the same as the spiral wrap you describe as long as they both involve the same number of degrees (or loathesome radians).


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## moray (Apr 1, 2008)

TreeCo said:


> The spiral wrapped rope will have more surface contact with the tree per radian so I would expect there to be some difference. As the rope pulls tight and the circular wraps go spiral due to the overhead loading angle there might be some beneficial shock load dissipation.



True enough, there will be more contact per radian. But the curvature of the rope is less in the spiral case, since it takes a longer piece of rope to make one circuit of the tree, so there is less pressure at each point of contact. A wash.

The second idea is an interesting one. How does the rope decide whether to create a long spiral or a compact one? Does increasing the load cause the spiral to elongate? One of you experienced riggers no doubt has the answer to this.


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## moray (Apr 1, 2008)

*diagram one*

This diagram shows a section view of the rope on the surface of the log crossing a groove. The curved dashed line at the top represents the contours of the rope on the ungrooved original surface. The meaning of the various labels is as follows:

C is the center of the log. Moving clockwise around the log, starting at far left, we have:
X is any arbitrary point on the ungrooved log surface.
A represents the last point on the original surface before the groove begins. Beyond A the wood smoothly drops away towards the bottom of the groove.
B represents the last point of wood-rope contact before the rope begins crossing empty groove space.
Line RC divides the groove, and the rope span, in half.
P is the mirror of B. It is the first point where the rope regains contact with the wood after crossing the groove.






When a tensioned rope is draped over the log, grooved or not, the wood obviously is supporting the full load. In my experiment, the load was 20 lbs on one leg and my pull (about 40 lbs) on the other. It seemed pretty obvious that this 60-lb load had to be supported by the lands between the grooves once the grooves had been cut. This would mean that an arbitrary point like X, situated in one of the lands, would now be under more pressure than before. Not only would this extra pressure, distributed over all the remaining surface, be enough to support the 60 lbs, but the extra pressure would mean extra friction, thus supplying the friction previously supplied by the missing groove wood. This seemed pretty obvious. But it is completely wrong!!

Imagine we have a researcher ant who will inspect the rope for us with 2 instruments. The ant can measure the rope tension at any point and the rope curvature at any point. Assume there is a 40-lb load on the left leg, 20 lbs on the right, and the rope is slowly moving downward on the left. We send the ant crawling up the left leg. Her instructions are to record frequent readings as she hikes the rope.

In the ungrooved case, the ant's bendometer shows a perfectly steady reading all the way across the top of the log. The tensionometer shows a maximum at the beginning, but declines in a steady fashion from the initial 40 lbs to 20 lbs when she reaches the free-hanging right leg.

Now we move the rope to the grooved section, and send the ant up again. Contrary to expectations, when she reaches point X, the bend reading and the tension reading are exactly the same as in the ungrooved case! Things start to change at A, though. The bend reading jumps by a factor of about 6! Moreover, the tension starts plummeting. After a few more steps, the ant reaches point B. Her bendometer suddenly drops to zero, and the tension becomes constant. Both stay perfectly steady all the way across the groove until she reaches P. There the tensionometer resumes dropping very rapidly and the bendometer jumps again to a high value. A few more steps and she reaches the undisturbed section of log, whereupon the tension resumes dropping at a steady, much slower rate, and the bendometer reading becomes perfectly steady.

When the ant analyses the data later, she realizes that all the missing friction and missing support previously supplied by the missing groove wood are now supplied by the _edges_ of the groove! The little section between A and B now does all the work previously done by the surface from A to R.

But it gets better. See next post...


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## moray (Apr 1, 2008)

*diagram two*

As the ant discovered in traversing the rope across the groove, nothing is happening there. No friction, no bend, no change in tension, no rope-wood contact. _This section plays no role at all in the experiment!_ So let's remove it...







Here the section has been removed. Note points P and B, previously at the extreme edges of the groove, now coincide. Every atom of wood in the previous diagram that was in contact with wood is still there. Every tiny section of curved rope is still present. Only the groove is gone. All the tension and friction and bent sections of rope are still there. But where there was a groove, now there is a ridge. For a rope wrapped around a post, _a groove and a ridge are the same thing!_ How cool is that?


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## pdqdl (Apr 1, 2008)

moray said:


> ... How does the rope decide whether to create a long spiral or a compact one? Does increasing the load cause the spiral to elongate? One of you experienced riggers no doubt has the answer to this.



If you are holding a load overhead by wrapping the holding line around a nearby tree, it has a huge tendency to form a spiral wrap. It is not uncommon sometimes to do a spiral wrap on the trunk of the tree being removed. For large limb lowering, a good understanding of the holding power of spiral wraps might be helpful.

Having done spiral wraps a few times myself, I am not sure. Sometimes it worked better than I wanted, and other occasions, the load had a tendency to pull harder than expected. Since every load is different, I suspect that the angle of the rope was not as significant as the judgement of the holder of the rope. Certainly, it is physically harder to hold the rope against a spiral direction than it is perpendicular to the tree, unless it happens to be an overhead pull.


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## pdqdl (Apr 1, 2008)

moray said:


> As the ant discovered ... How cool is that?



Pretty cool indeed. My analysis would have been different, however. Since the surface area of the rope contact with the log had been reduced by the groove, the pressure applied per unit of area would have been correspondingly greater. With no theoretical difference in the coefficient of friction, and the radians of rotation being the same, I would expect the same amount of resistance.

Your analysis is much more fun, however, and probably makes more sense to the typical non-mathematical thinker. I gotta give you some points for that.

I do have a sneaking feeling that somewhere we are missing a practical application for our theoretical analysis. Somewhere there MUST be a consideration for the radius of the object being wrapped. I suspect that the coefficient of friction must vary acording to the radius that the rope is bending over, because we all know that a rope wrapped around a square bar has much more resistance than a round bar. (it's a lot more destructive to the rope, too!) The only difference between the two objects is the miniscule radius for each of the 4 corners and the deformation of the rope as it passes over those tiny arcs.


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## moray (Apr 2, 2008)

pdqdl said:


> ...*the pressure applied per unit of area would have been correspondingly greater*...
> Somewhere there MUST be a consideration for the *radius of the object being wrapped*. I suspect that the coefficient of friction must vary acording to the radius that the rope is bending over, because we all know that a rope wrapped around a square bar has much more resistance than a round bar. (*it's a lot more destructive to the rope, too!*) The only difference between the two objects is the miniscule radius for each of the 4 corners and the deformation of the rope as it passes over those tiny arcs.



You've nailed it--we didn't miss it. The practical effect of smaller radius is greater pressure per unit area. The smaller radius is harder on the rope. It's also harder on the tree. In two otherwise identical heavy-load setups, one with big limb and the other with a small limb, you could have a safe and normal operation with the big limb, but the small limb would get stripped of its bark and the rope surface would start melting.

My buddy Jack with 35 years in the business likes to tell me about a huge (1 1/2 in?) nylon bull rope he used to have. It was used rarely, mostly on highway projects where heavy equipment was available to pull a whole tree out of the way. On one such job the rope passed over a small crotch. The load was far smaller than the rope capacity, but Jack was shocked to find later that the rope had undergone some serious melting where it had passed over the crotch. The intense friction around the tight radius meant intense local heating, like holding a torch to the surface of the rope as it passed by. A much bigger radius would have lowered the intensity and given the rope time to absorb the heat, more like heating it with an electric blanket. Nowadays Jack always uses blocks and steel capstans to deal with big loads.

This is one of those cases where things don't scale together as one might expect. That big rope would have been almost 10 times as strong as a little 1/2 in rope, and able to do a lot more work per minute than the little rope. But it couldn't absorb heat through a square inch of surface at 10 times the rate of the little rope. Maximum heat absorption rate doesn't scale up at all, and this led to an early grave for the huge bull rope.


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## pdqdl (Apr 2, 2008)

I still believe that the coeffecient will actually change according to the radius of the curvature, especially (as you pointed out) relative to the diameter of the rope. Granted, we understand the contact surface area is not a theoretical variable in calculating the friction. It is also well known that the coefficient of friction often changes according to the forces applied. 

A good example might be steel on concrete. At a high enough pressure, the steel is no longer "rubbing" against the concrete, it begins to deform it's shape into the molecular crevasses of the concrete, and the coefficient changes. 

I suspect that there may be similar changes for the coefficient of friction for a rope around an axis of varying radius. Unfortunately, I have not been able to find ANY information on "coefficient of friction" relative to ropes and wood.

I think I'll e-mail a couple of rope manufacturers. I'll bet their engineers have all this figured out already.


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## pdqdl (Apr 2, 2008)

*rope melting is NOT a determined by just the force applied.*



moray said:


> ..
> My buddy Jack with 35 years in the business likes to tell me about a huge (1 1/2 in?) nylon bull rope he used to have. It was used rarely, mostly on highway projects where heavy equipment was available to pull a whole tree out of the way. On one such job the rope passed over a small crotch. The load was far smaller than the rope capacity, but Jack was shocked to find later that the rope had undergone some serious melting where it had passed over the crotch. The intense friction around the tight radius meant intense local heating, like holding a torch to the surface of the rope as it passed by. A much bigger radius would have lowered the intensity and given the rope time to absorb the heat, more like heating it with an electric blanket. Nowadays Jack always uses blocks and steel capstans to deal with big loads.
> 
> This is one of those cases where things don't scale together as one might expect. That big rope would have been almost 10 times as strong as a little 1/2 in rope, and able to do a lot more work per minute than the little rope. But it couldn't absorb heat through a square inch of surface at 10 times the rate of the little rope. Maximum heat absorption rate doesn't scale up at all, and this led to an early grave for the huge bull rope.



Rope only melts because it is exposed to more energy at a given point than it can dissipate. So far, our equations have not been used to relate the energy applied to any situation, only forces. Energy + friction= heat 

Static friction can be infinite, the force applied to overcome it can be almost infinite. Until something moves, there is no heat generated. This is why injection molding and aluminum extrusion work so well.

If the same situation described had been pulled at a slow enough rate, the rope would never have melted. The applied forces would have been exactly the same, but the velocity would have been different. Increase velocity, keep the forces the same, and the energy applied to the rope increases. 

The rope melted because they pulled too hard, too fast. It probably didn't help that they smoked it going over a small crotch.


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## moray (Apr 3, 2008)

pdqdl said:


> ...A good example might be steel on concrete. At a high enough pressure, the steel is no longer "rubbing" against the concrete, it begins to deform it's shape into the molecular crevasses of the concrete, and the coefficient changes.
> 
> I suspect that there may be similar changes for the coefficient of friction for a rope around an axis of varying radius...



I am sure this is true; the question is when does the ideal equation start to break down and how badly does it break down? 

The rope is non-ideal from the get-go. The internal fibers move and slide with respect to each other every time the rope goes around a bend or is crushed against a surface. The sharper the bend, the more severe the effect. This internal friction shows up in the tension difference between the two legs of the rope, but it is not accounted for by the ideal equation. Is it a big deal? For light loads and gentle bends certainly not. I don't know at what point internal rope friction becomes a significant part of the total, if ever.

Your comment about surface deformation identifies the issue that seems most significant to me, but again, it is just guesswork on my part, as I have no evidence. I could (and would) measure this myself if I had two things: a convenient way to apply large known loads, say 1000 lbs, to a rope; and a reasonably accurate way to measure pulling force, up to say 3000 lbs, in the other leg of the rope. This would be fun!


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## pdqdl (Apr 3, 2008)

This could turn into a huge time-killer for me. I'm thinking about loading up some logs of varying sizes & types of wood for rope wrapping points, getting a standardized weight of say 500-1000 lbs, and seeing how many wraps (in radians!) that it takes to get a 50lb draw force (spring scale, I have one) to hold in a slow descent. Then we could do the math, and establish an experimental coefficient of friction for OUR application, and establish an experimental (not theoretical) ratio of wraps to load reduction.  

I have a small crane, I c_ould_ do that. Unfortunately, it is the spring rush, and I don't have time for that.  
Perhaps in the summer doldrums ?


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## moray (Apr 3, 2008)

Hmmm... I have some time... Wouldn't wanna loan a feller yer crane, would ya?:lifter:


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## pdqdl (Apr 4, 2008)

Maine ? ......!!!

You could probably BUY my old beat-up chipper truck with crane for the fuel expense just to get it there & back. About 5-6 mpg: gas. Only goes about 50 MPH.

Pretty cool old RR service truck, it has a 12,000lb knuckle boom crane (35' height) behind the "man-cab", and a dump body behind the crane. We built a removeable top for the dump bed: we can go to a job, chip the brush, remove the 1000 lb "lid", load the logs, and drive away with the whole job done. Ugly as all get out, we never have painted it.

It's the best toy I own for fixing broken stuff. Pick up dead equipment, pulls engines, and it is the absolute thing to have when something metal gets bent.

Not bad for a truck I bought for $7500 in early 2001. Been working fine, all this time, except for what we have broken by abuse or normal wear. Kills us on gas, though.


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## moray (Apr 4, 2008)

I like it!


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## pdqdl (Apr 5, 2008)

Don't unsubscribe from this thread yet. When I get some more data, I will post it. Right now, I'm trying to find some relevant coefficients, I just haven't found any yet.

I'm avoiding the experimental route.


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## moray (May 6, 2008)

pdqdl said:


> ...The saw on the winch is a Shindaiwa 488. Pretty good little saw, but I don't even know the cc on it. Just guessing.



Pretty damn good guess. 47.9 cc, 3.5 HP (2600 W)



pdqdl said:


> ...I think the 3/8th amsteel will work much better, but I will be very watchful for meltdowns.
> 
> By the way, the capstan is aluminum, about 2 1/4" diameter, with a drum width of 2.75". Four wraps fits well for the 9/16" stable braid, 5 wraps is overlapping a bit, but really pulls then.



I didn't have any Amsteel Blue when I did my friction experiments, so I just now measured the efficiency of AmB over 2 aluminum rings: 0.6. This is definitely less friction than the same setup with polyester. Since this represents 1/2 wrap, one can calculate that 4 full wraps would give a load-to-control ratio of 60:1. For 5 full wraps, the ratio is 165:1. With your winch setup, using 5 wraps of AmB, you should be able to pull 1000 lbs with just 6 lbs of pull force on the tail. 

What is really cool about this powered capstan, which is just a special case of friction around a post, is it can act as a force multiplier. If I had a bigger version of your winch, say one that could pull 10,000 lbs, and I knew that 6 wraps of my winch rope would give me a force ratio of, say, 500:1, I could easily do measured break tests of ropes and splices and knots with reasonable accuracy. Just hook up everything for a destructive pull test, run the control tail over a small pulley and hang a bucket from it. Start the motor and start filling the bucket with water. When the test item finally fails, The weight of bucket plus water, multiplied by the force ratio, derated by the pulley efficiency, gives the force that caused failure.


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## pdqdl (May 6, 2008)

165:1 ! That will be cool to use, but I'll bet it's not that good. We were doing 5 wraps with the 9/16 stable braid, and we were pulling WAY harder than that on a load.

When the amsteel comes in, I'll do a test pull. I'll weigh something heavy (at least 500 lbs, and I will rig the amsteel over the pully on my crane. Then I will hook up my tension scale and see how much feed force is required to move the load on however many wraps. THEN we will have a definative measure of the lifting capacity of the winch and the feed force required to move the load.

Then we can do cool things like weigh heavy loads with the feed force scale and we can confirm the coefficients involved. I might even do a scale test on the same heavy load rigged to my Nickle coated port-a-wrap.

You have been pretty enthusiastic about this physics stuff, I can do a little bit of work as well.


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## moray (May 7, 2008)

*Excellent!*

I had forgotten about your crane--you're all set to do the stuff I can only dream about.

Trying to get a good value of the friction coefficient with just half a wrap and a bathroom scale is like trying to measure the speed of a car whizzing by if you only have 1 millisecond to make the measurement. If you can get a good measurement with 3 or 4 wraps, the calculated coefficient would be many times more accurate than what I can do. If you repeat the experiment several times with 3 wraps, and several more times with 4 wraps, we could combine all your data to nail it down closer than anyone could possibly need.

Good work! I look forward to your results.


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## moray (Jun 7, 2008)

*I was wrong!*



TreeCo said:


> The spiral wrapped rope will have more surface contact with the tree per radian so I would expect there to be some difference. As the rope pulls tight and the circular wraps go spiral due to the overhead loading angle there might be some beneficial shock load dissipation.





moray said:


> True enough, there will be more contact per radian. But the curvature of the rope is less in the spiral case, since it takes a longer piece of rope to make one circuit of the tree, so there is less pressure at each point of contact. *A wash.*



It is not a wash; I was wrong.

While working on another problem I again came across the issue of a rope under tension wrapped in spiral fashion around a pole, and this time I engaged the brain before engaging the mouth. There are a number of ways of working out the math, but they all give the same answer: a spirally-wrapped rope produces less force against the pole, and less friction, than a straight wrap. The effect is negligible for a tight spiral, but becomes significant for a very long spiral.

We can quickly run through this without any difficult math. First, remember that a rope under tension applies force to the post only because it is curved where it contacts the post. A straight rope cannot apply a sideways force to anything. What's more, the total force applied to the post is proportional to the amount of curvature in the rope. Every degree of curvature is like every other degree of curvature--each one applies the same amount of force.

Now imagine a really extreme case. Assume a tensioned rope is spirally wrapped around a vertical pole and the angle of inclination of the rope is 89 degrees, just one degree off true vertical. Allow the rope to wrap around 180 degrees to the other side of the pole. My error in the shoot-from-the-hip "wash" comment was to imagine this also meant the rope had curved 180 degrees. How much has it actually bent? About 2 degrees! After all, it is inclined 1 degree from vertical at the bottom, and after travelling halfway around the pole, it is now inclined 1 degree the other way.

The exact result, when you work out the formal math, is that the degrees of pole curvature times the cosine of the angle of inclination gives the degrees of rope curvature. A practical example: you start out with two tight wraps around a tree. As the load starts moving, the spiral stretches out to give a 45-degree inclination. You have effectively just lost about 30% of your wraps.


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## Adkpk (Jun 8, 2008)

Speaking of friction savers I went to retrieve mine today out my giant white pine. Left it up there last climb of year, last year. I knew it was going to be a while till I got back up there. Anyhow, after a few tosses with the slick line I noticed a little stickiness on my fingers. I could see sap glissening on the branches. I decided to wait till I don't have to worry about getting my ropes full of sap. I'm sure the fiction saver will be ok. It's on the north side of the tree back in the woods and the tree is monitored for squirrels.


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## pdqdl (Jun 9, 2008)

*I kinda thought so, but I didn't say anything...*

I have often observed that the rope wrapped in a spiral up the tree failed to hold as well as I had hoped. 

It just took your thoughtful effort and insight into the math of the situation to point out why.


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## moray (Jun 10, 2008)

Adrpk said:


> Speaking of friction savers I went to retrieve mine today out my giant white pine. Left it up there last climb of year, last year. I knew it was going to be a while till I got back up there. Anyhow, after a few tosses with the slick line...I'm sure the fiction saver will be ok. It's on the north side of the tree back in the woods and the tree is monitored for squirrels.



Nice to hear from you again, Adrpk. Unless I misunderstand your post, you left your FS up there without a clothesline through it? Did it get stuck up there unintentionally?

I just retrieved mine out of my big pine a week ago. It had been there since last September and was still in perfect shape when I climbed up to it. I have now installed a much better system for this particular tree--a clothesline that goes over a sort of saddle at 62 feet where the tree had been topped about 50 years ago. Now I can pull up my SRT line up on short notice and zip up the clear side of the tree, something I couldn't do before.

As far as pitch goes, summer seems to be the bad season. Here in Maine, in the winter, the flow of pitch seems to virtually stop. I do all my trimming then, and give it up come Spring.


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## moray (Jun 10, 2008)

pdqdl said:


> I have often observed that the rope wrapped in a spiral up the tree failed to hold as well as I had hoped.
> 
> It just took your thoughtful effort and insight into the math of the situation to point out why.



Very kind of you. It is nice that your practical experience bears out the calculations. 

Have you had a chance to use your Amsteel Blue, yet?


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## Adkpk (Jun 10, 2008)

moray said:


> Nice to hear from you again, Adrpk. Unless I misunderstand your post, you left your FS up there without a clothesline through it? Did it get stuck up there unintentionally?
> 
> I just retrieved mine out of my big pine a week ago. It had been there since last September and was still in perfect shape when I climbed up to it. I have now installed a much better system for this particular tree--a clothesline that goes over a sort of saddle at 62 feet where the tree had been topped about 50 years ago. Now I can pull up my SRT line up on short notice and zip up the clear side of the tree, something I couldn't do before.
> 
> As far as pitch goes, summer seems to be the bad season. Here in Maine, in the winter, the flow of pitch seems to virtually stop. I do all my trimming then, and give it up come Spring.



Yes, quite unintentionally. I think it was something like wanting to leave it up there with a slick line through it for a future climb but as I untied it from the climbing line I didn't realize the other end had tangled into a ball and when I let go it pulled the end of the slick line out of my reach. I have a spare.


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## moray (Jun 10, 2008)

*me too*

Yes, on at least 2 occasions I started pulling my rope down, and just as the other end rose out of reach, realized I didn't have a line attached. It's not the end of the world when you have to climb back up there to retrieve your false crotch, but it's nice when no one is around to see how stupid you are.


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## pdqdl (Jun 12, 2008)

moray said:


> Very kind of you. It is nice that your practical experience bears out the calculations.
> 
> Have you had a chance to use your Amsteel Blue, yet?



We used it on the capstan winch just yesterday. It worked fine, but I don't like it for that application. The rope winch relies on friction, and the amsteel is slick as glass. With the small diameter of this rope, we can put on enough wraps to compensate, but you still need to pull on the rope with your hands. Difficult to pull hard with hands on the amsteel.

I admit, the rope winch states that it works best with a 3/8th twist rope. I am saving the amsteel for long reaches into a muddy area for retrieving stuck vehicles or logs. It's strong enough for that, and I do like the weight.


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