Trucker's hitch myths

[Tex]

I started to make this post, deleted it because I didn't like it and now inspired by the knot myths thread, I brought it back.  I'm still making it a separate thread to avoid having a possible discussion interfere with the myth thread too much.

Wikipedia actually has this covered pretty well.  Since Wikipedia evolves I will quote it:

There is sometimes confusion about how much theoretical mechanical advantage is provided by the trucker's hitch. If the trucker's hitch were to be used as in the pulley diagram at right, to lift a weight off the floor, the theoretical mechanical advantage would be only 2:1. However in the common use of the trucker's hitch, a static hook, ring, or rail, serves as the lower pulley, and the rope across the top of the load is the portion being tensioned. Thus, the standing part of the rope is represented by the top anchor point in the diagram, and the theoretical ratio is indeed 3:1 when the working end is tensioned. That is, in a frictionless system, every unit of force exerted on the working end would produce 3 units in the standing part of the rope over the load. In the typical use of the trucker's hitch, where it is used to tighten a rope over a load, when the end is secured to the loop of the Truckers hitch and let go, the tension in the two segments of rope around the ring will rise 50%, unless the rope slackens when it is being tied off, in which case the tension may drop to any value or even zero if enough slack is allowed. But when the trucker's hitch is used as in the diagram, after tying off, the load on the attachment point above the top pulley will drop to 400 lb and the tension in the two lines going to the lower pulley will not change.

The image is here (until I figure out how to attach it inline)
http://en.wikipedia.org/wiki/Trucker%27s_hitch#/media/File:PolispastoLbs.jpg

First I hate the word theoretical here because it implies that theory and thus the theorists know nothing about friction, which is false.  "Theoretical" in such contexts just means using the simplest theory that describes the fundamental properties of interest.

The point though is you get 3:1 "ideal" advantage on the end you are pulling away from, BUT I have often seen it claimed that you get a 3:1 advantage for lifting the weight on the end you are pulling towards (a scenario I've even seen extolled as a brilliant use for this knot with its 3:1 lifting power), and this is just false. Then you get an ideal advantage of 2:1.  So when people say this hitch is 2:1 and you feel tempted to correct them, think about qualifying the correction a little.

If you are really moving something, like really pulling a line in against frictional force, then these advantages (minus the frictional losses in the knot) help you greatly to do work.  Wikipedia correctly points out that if you are just tying something off to hold tension on it, you have more considerations. Obviously once you tie off the knot must be equally tight either direction so some equilibration occurs.  The lifting scenario includes a constant source of force and so that will be the total force after tie-off. 

As the article says, realistic use often involves tying two rails or such together to maintain tension between them.  The only constant source of force is the elasticity in all of the elements involved, the rope in the knot, the rope beyond the knot if it attaches far away, and the elasticity in the objects to which you've attached.  These elastic forces depend on length and length of stretch (the latter being proportional to the former for a give tension).   I think it's a little more complicated even than that article makes it out.  If the knot is long so that  the ends are attached closely to rigid objects, then it can depend on exactly where and probably to which lines you make an ideal tie off (weld, then release tension) but it also should depend on the relative elasticities of all elements involved, the rope, and the things you tied to. 

For instance if there are long ropes on each end of the knot, then the equilibrium of stretch achieved in the short knot ropes matters very little but the equilibrium of stretch between the two extending ropes becomes the main factor in determining the final tension, and they will balance somewhere between the 2x and 3x spring forces to which they were initially loaded.  In fact in this particular ideal case, if they are the same length and same rope types, they will equilibrate at 2.5x.  It's true that the way the trucker's usually tie it, the 3x end is long and and flexed and the 2x end is short and rigid, and in this case you can expect to equilibrate fully at 3x (2.999 or so), so yes, the two 2x ropes will increase 50%, stretching to match this tension level. If instead the 3x end is secured to a rigid object and the 2x end to a long rope (spring), then you will get the 2x result again.  All the more it is becoming important to use the term "ideal" instead of "theoretical".  To achieve 3x after tie off (and tying off is part of the knot) even for a frictionless scenario, you really need to use the knot precisely as it was intended to be used, including orientation and having a rigid object on the 2x end of the system and a long springy one (rope) on the 3x end.


Trucker's hitch myth 2

Once in awhile the idea comes up to use a truckers hitch as a binding hitch, after all it gets a 3:1 advantage right? Well that's the myth.  So tie it AROUND something like a sleeping bag and you can get it squished pretty tight.  I'm usually not certain what people mean when they talk about this but the simplest picture that comes to mind is tying a loop "mid-line" (end really), passing the other end around your sleeping bag or whatever, through the loop and pulling back away from the end-loop before tying off.  This does produce a pretty tight binding, but then people like to say they are getting a 3:1 trucker's hitch ideal advantage, which they are not.  In fact in the "ideal" frictionless situation this hitch gives you NO advantage of any kind over any other wrap of rope around a sleeping bag that you can possibly make.  Without friction the loop must stay centered in the direction of pull and every one inch you pull out is one inch less circumference, the worst you can possibly do.

It turns out you do get some advantages of various kinds in reality.

First you get to use two hands (and maybe a foot) to pull, secure, and tie off the hitch and this actually matters quite a bit.
But the ironic thing is that friction around the object absorbs tension along the rope allowing one end to develop more tension than the other (it's almost like creating an anchor point somewhere on the back side of the sleeping bag).  With that friction you now can pull to the side away from the end-loop and then you are gaining up to an ideal advantage of 2:1 (I'd guess 1.1 to 1 is more realistic) against the end loop, and it does pull around some as you do it (a requirement for any mechanical advantage is that you pull farther which this effects).  This advantage has only a little to do with the trucker's hitch though and nothing to do with the 3:1 ideal, since as we've seen, in the ideal situation you get nothing, 1:1, and unlike for the normal trucker's hitch, here friction actually is a required element in generating the advantage instead of reducing it. Finally the high level of friction passing through the loop at 180 helps greatly to secure the gains while tying off.   You can use a foot and two hands to pull, yet hold off the gains with one hand while you tie with the other.  This is a big deal compared to trying to find a third finger hold down a square knot (poorly).

You can get a real trucker's hitch advantage in binding a sleeping bag, but to do it you need to tie one end loop, wrap the rope maybe 3/4 of the way around the bag, tie a midline loop, and then continue around the bag, through your end loop, back through the midline loop , and out (zig zag zig), tying the trucker's hitch not around the bag, but as a closure between the two ends of the ring.  There is another way to get advantage around the bag though, just wrap around twice.  You have twice as many ropes holding the same linear pressure so they need only half the tension (and twice the pulling distance).  The number of turns that actually work for this are limited by friction, but anyway, it's not clear that the double-loop trucker's hitch closure is a much more efficient use of rope than just going around the bag twice and then, sure, using the single loop to get you that friction assisted gain at the end.

--edited for some clarification about the tie off scenarios--

[Tex]

I just had to add that this stuff is really more practical than knot. 

[Tex]

So I covered a couple of tie-off scenarios but want to add one.

If you tie the hitch directly between two rigid objects  then all the energy and force is created by the stretch of the 3 rope legs in the pulley system.  In this case an ideal tie-off of an idealized hitch without friction maintains the full 3:1 advantage IF you tie off to both of the other taut lines as low as possible, before releasing the tension.  This is effectively the same as tying off to the truck rail (or hook) directly, except to actually do that you'd have to go around the rail again, and then we'd be talking about an idealized 4:1 hitch and then this never ends. Instead we can just think of the upper limit on how well you can do tying off to the other two ropes and that limit is still 3:1.  The caveats about direction of pull during the shortening stage, and/or having a long stretched rope attached to the 2:1 side still hold.

If though you tie off perfectly but just to the second line as low as possible,  Then the first line stretches (4/3 as much as it was stretched) to balance the combined last two (each 2/3 as much as they were stretched), and assuming ropes are ideal springs, you only get a 2 2/3  (8/3) advantage when it's all done.

So, The animated knot tie-off that goes around both ropes, is in fact the best, if all else is equal about the tie-off methods.

This is not just theoretical.  I'd be willing to wager that in realistic scenarios, tying off one way vs the other can make a difference of easily 1% in tightness and I suspect for a smooth rail and a long knot, closer to 5%, maybe more.  This does assume your knot can hold as well tied to two ropes as to one.

[Dan_Lehman]

Wow, I'll guess that few are going to read through all of that,
and of those, some will come away eye-glazed!   

It would help to give the URLink to the Wikipedia article you cite.
http://en.wikipedia.org/wiki/Trucker%27s_hitch#Mechanical_advantage_and_friction
I found it, and I corrected it (we'll see if that sticks)
vis-a-vis the bogus assertion about frictionally reduced force:
"down to less than 1 to 1 in many cases."
It cannot be <1:1 by just system friction --one would at least
have direct, i.e., 1:1 force if the pulleys/knots were glued!

There is much misinformation about mechanical advantage
in such rope-pulley systems (e.g., Brion Toss's much acclaimed
Rigger's Apprentice conceded only "slightly less than ..."
which is not right : it is well less than ... !  If more people
would do some simple, rope-&-weights testing of these things,
these illusions would be challenged and (hope-hope) disappear.

But, to the reduction of actual mechanical advantage should
be presented the benefit of friction in holding surges of force,
which is something one might practically impart, and how
that makes the system seem better (well, makes it better,
but w/misattribution to why so).

As for "theoretical" vs. "ideal" : the former is in common parlance,
and I think is pretty well understood only to mean what you want
via the latter, and not taken further to impugn theoreticians!
(But I've felt your pain re this, myself, and had a grumble or two.)


--dl*
====

[Tex]

You're right.  It's better to have the link (although I think the article was pretty clearly referenced being that it's the article titled "Trucker's Hitch" on wikipedia)

You're also right about it being too long for most,  which I why I put most of the takeaway's in bold, but I'll summarize  here:

1) Yes we know friction losses reduce the ideal advantage, but a higher ideal advantage makes a higher real advantage.
2) You get a 3:1 pulling/lifting advantage if you're pulling in the direction of motion.
3) You only get a 2:1 pulling/lifting advantage if you're pulling the other way, as in the case of using it as a hoist (object moves up, you pull down)
4) The actual ideal tension after an ideal tie-off depends on some factors but
   a) a long rope attaching to the side of the knot toward you leaves you with 2:1 ideal
   b) a long rope on the side you are pulling away from leaves you with 3:1 ideal
   c) a and b are mostly true regardless of d (I never explained why)
   d) If tied between two rigid objects or with short leader ropes, you get the best results by tying off   
       around both pulley lines, as low as possible. (you can ask me how short is short)
5) A trucker's hitch tied AROUND something has no ideal frictionless advantage compared to any other binding.   The configuration can help you get things tight, but the reasons are more complicated to understand.

I did not see the quip about it being less than 1:1.  That's pretty funny.

As for theoretical vs ideal, yes it's common parlance.  Misconceptions about the distinctions between theory and reality are also common.
   

[Tex]

P.S. there have been many more words bantered here over MUCH smaller effects. I will concede though, that a trucker's hitch, is not really a knot.

[Tex]

Actually.. less than 1:1 IS possible on the 2 rope side of the hitch (zero is possible with infinite friction)!  However the statement as written, reducing from 3:1 down to less than 1:1, still did not make sense.

[xarax]

   The mechanical advantage of the static knot is calculated in the most simple way there can be, by just counting the number of the tensioned straight segments of the immobilized line.
   Lets say that this line makes one Z, a Zig-Zag-Zig ( three straight segments ). The mechanical advantage is 3. Lets say it makes a Zig-Zag-Zig-Zag ( four straight segments ). The mechanical advantage is 3. Lets say it makes two Zs, the one merged with the next, a Zig-Zag-Zig-Zag-Zig ( five straight segments ). The mechanical advantage is 5. There is no simpler thing in the world than counting ! 
  Now, when we start pulling the very end of the Tail end ( the end of the line of the mechanism ), we enter into another system, where things change. If the segment of the end of the line after the last point of contact ( were it a Zig or a Zag ) is aligned with the last segment of the Zig-Zag-..., the number of the straight segments remains the same as it was before the pulling. The mechanical advantage remains the same. If it is not, the mechanical advantage increases, just because we add one more Zig or Zag. If the end of the Tail end, the end of the line, is parallel to the last segment of the previous Zig-Zag..., but it is pointing to the opposite direction ( I say "previous", because then the "new" Zig-Zag... became more convoluted than the previous one ), it should added to the number of the already existing Zig Zags, and so the mechanical advantage increases by 1.
  No mention of friction in this explanation whatsoever. Just counting the number of parallel Zig Zag segments, suffices to calculate the mechanical advantage.

P.S. Of course, I am talking about the ideal, platonic mechanical advantage here !    I real life, things change, also because of the distance of the moon from the Earth ! "Friction", in particular, diminishes the mechanical advantage at each and every tip of the Zig Zag...   
 

[xarax]

a) a long rope attaching to the side of the knot toward you leaves you with 2:1 ideal
b) a long rope on the side you are pulling away from leaves you with 3:1 ideal

   Myth ! 
   The length of the rope does not matter ; a tension applied to the one end, will reach to the other end, unaltered, sooner or later ( I mean, after the short time the previous length of the presumably elastic rope will need to become elongated, according to Hook s law ).
   The rigger gets this false impression that he has lost some portion of the mechanical advantage, because of the more noticeable elongation of the rope during the pulling of a long segment of it, and because of the time latency the second end responds, after the first end has been acted upon.

[Tex]

xarax you are correct but you are misunderstanding what I am saying, or maybe more to the point, the reason for what I am saying.

For a long rope, for it to be at a certain tension (3x pulling force) it MUST have stretched a certain amount.  The longer the rope is the more that stretch must have been and the less relevant a small change in stretch becomes. Thus, if the rope re-adjusts a little in a relatively short knot,  while that small change in length greatly readjusts and balances the tensions within the knot,  the overall resulting change in length of the knot will not significantly change the tension of the long attached rope.  So, regardless of the exact details of what happens in the knot, the rope will maintain the same force on the knot and will determine the final tension on the knot.  The long rope acts as a constant source of tension just as a fixed weight in the hoisting case (see below). I could prove this all far more mathematically and rigorously if you really insist.

To back up a little, when you tie off this hitch a rebalancing of forces MUST occur.  Before being tied off the 3:1 side has 1T (your pulling force) more force on it than the 2:1 side, a difference supported by you. After tying off and you let go, the sides must, by Newton's 3rd law, have the same force.  There is a rebalancing of forces due to ropes stretching or contracting, and equilibrium is obtained.  In the case of the hoist, this equilibrium is simple: some ropes do contract, meaning the weight does rise very slightly, and some energy does change forms (from spring potential in the ropes to gravitational potential), but when it's all said and done, the knot is still supporting the weight, and so the total force is the same as it was on the 2x end before tying off, ie equal to the weight.  So you tie off with the 2x advantage and the force on the top of the knot is now also 2x, as is the total tension across the knot.

When the weight is not there, something else determines the equilibrium.  There could be many things involved including dissipative forces (but we exclude those in ideal examples, right?  well unless we're trying to drag something), but if tied eventually to fixed rigid objects by way of long or short ropes, then the only thing that plays in is the balancing of tensions in the ropes themselves, which are directly related to their lengths and to their changes in lengths. 

As you know, long stretched ropes contain deadly amounts of energy, which is another way of saying why a long rope will dominate the equilibration process.

[xarax]

   long rope acts as a constant source of tension
   long stretched ropes contain deadly amounts of energy, which is another way of saying why a long rope will dominate the equilibration process.

Correct.
Long ropes are long elastic mediums, and behave accordingly. They accumulate tensile forces, and they can change the way a dynamic rope-made mechanism works, how it responds to changes coming from outside or from within the knot, etc.
It would be nice if one could actually show this effect...

[Tex]

What do you mean by show?  This is extremely basic and is quite easy to "show".   I think I'm just not understanding what you're wanting.
 

[Tex]

xarax I missed this before:

The mechanical advantage of the static knot is calculated in the most simple way there can be, by just counting the number of the tensioned straight segments of the immobilized line.
   Lets say that this line makes one Z, a Zig-Zag-Zig ( three straight segments ). The mechanical advantage is 3. Lets say it makes a Zig-Zag-Zig-Zag ( four straight segments ). The mechanical advantage is 3. Lets say it makes two Zs, the one merged with the next, a Zig-Zag-Zig-Zag-Zig ( five straight segments ). The mechanical advantage is 5. There is no simpler thing in the world than counting ! 
 Now, when we start pulling the very end of the Tail end..

(my bolds)

There is no mechanical advantage to a static knot.  Mechanical advantage requires an input and and output.  I suppose you could say a static knot ties two things together, but with only two things, and a knot, the tension on one is the same as the other, so there's no point talking about mechanical advantage or inputs or outputs. There is no simple machine.   It's completely meaningless in the usual physics/engineering sense of mechanical advantage.  You can talk about the tension in the parts of the knot, and sure, more parallel segments means less tension per segment.  However, it's the part of the chain with the the fewest segments that matters if you're talking about rope failure.  This though is like calling a thicker rope a "mechanical advantage" because it has less tension per thread.  That's simply not what the term means.

Now, when we start pulling the very end of the Tail end..

Then we can start talking about mechanical advantage.

Now I bent the rules a little because I talked about "advantage after tie off".  I think it was clear what I meant then.  Then I'm talking about what level of tension is retained on various after tying off, relative to the input force before tying off, but we still had to have an input force in the first place.

Counting mechanical advantage is easy, you're right, but you have to be careful.  There are 3 zig's in a TH that are part of a continuous segment and thus ideally have equal tension, so to see the force on any part you just add up the tension.  On the weight part of the hoist there are only two lines connecting to it, so that's 2 units of tension pulling on the bottom end.  On the top part there are 3 lines, so that 3 units of tension pulling on the top end of the "knot", and on you there is 1 line so you're holding/pulling 1.  It's not enough to just say, 3 zigs so 3:1.  It depends how many zigs attach to the place where you want to know the force.  You could zig 20 zigs through all kinds of different hardware not all of which is necessarily even attached together.  Of course if zigs are at angles you have to do vector sums.

[xarax]

What do you mean by show?

3: to present as a public spectacle :  perform
In other words : YouTube it ! 

[xarax]

You can talk about the tension in the parts of the knot, and sure, more parallel segments means less tension per segment.

   That is what I am talking about ! Now, when, instead of the last tip of a Zig Zag ( be it a Zig or a Zag... )  inside the mechanism, we have the knot tyers hand, you see that your hand is feeling what a segment of rope is feeling - even if it does not move.
   The mechanical advantage is the advantage we gain, if we pull a less tensioned segment of rope instead of a more tensioned one.

1. It depends how many zigs attach to the place where you want to know the force.  You could zig 20 zigs through all kinds of different hardware not all of which is necessarily even attached together. 
2. Of course if zigs are at angles you have to do vector sums.

 

1. Of course 
2. Of course - that is why I was explicitly talking about "parallel" segments of Zig Zags.

   So, now I believe you understand what I was talking about - your statement : "there is no mechanical advantage to a static knot", or mechanism, can be misunderstood more than mine : "the mechanical advantage of a static knot...", or mechanism. I did nt want to complicate things, because, with motion, we have acceleration, inertia, "dynamic" loadings, etc.