The Trucker's Hitch

[TS]

I have a problem with the often-repeated claim that the Trucker's hitch gives a leverage advantage of THREE-to-one.

I believe this is incorrect, and that the advantage is just a factor of TWO.  The loop in this hitch acts identically to the {upper} pulley in the simplest block-and-tackle arrangement.  The WEIGHT is being 'lifted' by the bight at the bottom, (in most illustrations), and this bight thus carries ALL of the weight, on two ropes!  All that the loop, or pulley, really does is to REVERSE the direction of the final pull, so it adds no advantage.

I recall from high-school physics that the rule is: 'Count the amount of rope-lengths hanging down, then subtract one, to find the advantage.'  This can be checked very simply: pull DOWN on the end rope by a certain distance, say 12 inches.  If you are TRULY getting a 3-to-1 advantage, then the loop should rise just FOUR inches.

Yet, it goes up SIX inches, in the Trucker's hitch, when you pull 12.  Thus, your advantage must be 2-to-1.  If you test this, under load, you'll see that I'm right.  All the books seem to be giving incorrect information about this hitch, {in my opinion}.

Am I missing something about how this hitch is used?  I know that it is NOT used as a pulley for lifting, generally, (though it COULD be used in this way), but more for tying down bulky loads, on top of an open truck, to achieve a tight lashing.  Still, I don't see any way of using it, even for this purpose, that would yield a 3-to-1 advantage.

It's always bad news when someone believes they've tightened something securely, only to have physics prove them wrong.

I'd appreciate any feedback.  Are the books wrong, or am I?

[[Inkanyezi] gone]

The books aren't wrong, you pull the end, and for every three inches you pull it down, the knot is pulled one inch, because there are three parts pulling; the one that is fixed to the knot, the one that comes back from below, and the one you are pulling. You pull three inches, two come out from where the working end leaves the loop, the knot itself comes down one.

Of course friction works to your disadvantage, so the power gain is not 3x. Then when you belay, it's easy to understand that the three parts of rope that are tied down take the entire load, each one a third of the load that the lashing is tied down with. And of course, you won't want the houdinghy _{(tribute to Brion Toss)} to escape too easy, so you add frapping turns between the lashings to increase tension.

Of course it also depends on what "fixed" point you choose to compare with. If you for example grab the part that rises up to the loop from the hook/ring, and see your endeavors as relative to a point on that part, you have six times advantage. But generally, we regard the wagon as the fixed object, and there's where we have a three times advantage on the standing part of the rope.

[Dan_Lehman]

[ THIS SHOULD BE POSTED UNDER >>> PRACTICAL KNOTS <<< , NOT CHIT-CHAT. ]

Yes, the books are VERY wrong, re actual mechanical advantage.
You are wrong about what moves (typically):  it is not what is attached
to the hanging bight but the (typically shown) upper knot acting qua
sheave; and then by your thinking you see it is 3 lines bearing load
when hauling.

But the books are utter rubbish on the actual advantage that such
in-rope pulley systems deliver -- it is WAY less than theoretical MA.
You can (should) test this for yourself, to gain insight.

More discussion on this very point (re VersaTackle) can be found
here igkt.net/sm/index.php?topic=384.0 .  I have done
some tests using barbell weights and checking for movement or not;
there is much "not" where the books would have you be performing
heroic feats!   

--dl*
====

[Gleipnir]

TS -

You are correct.  The advantage is 2:1 not 3:1.  People are getting confused by the third piece of rope that they are holding in their hand.  It is not load bearing it is redirecting the force down of a 50% load.

see: http://www.instructables.com/id/Truckers_Hitch_THE_most_awesome_knot_on_the_plan/
see: http://upload.wikimedia.org/wikipedia/commons/8/86/Pulley1a.svg
see: http://en.wikipedia.org/wiki/Pulley
For an explanation of pulleys. 

The truckers hitch just creates an inefficient pulley system.  There is no magic.  The same rules of physics apply.

This 3:1 stuff wouldn't pass high school physics.

[knudeNoggin]

TS - You are correct.  The advantage is 2:1 not 3:1.
People are getting confused by the third piece of rope that they are holding in their hand.
 It is not load bearing it is redirecting the force down of a 50% load.

see: http://www.instructables.com/id/Truckers_Hitch_THE_most_awesome_knot_on_the_plan/
...
This 3:1 stuff wouldn't pass high school physics.

As was explained carefully above, the Trucker's Hitch has a theoretical  advantage of 3:1 .
Perhaps this was not understood?  The reply here indicates that, loudly.  This is also discussed
by the same protagonist elsewhere, so I can repeat the explanation here.   It is the in-line-formed
impromptu sheave that moves (increasing tension to the single line going away, over the truck's
load to the other side of the bed, e.g.), and tensioning this puts load on
 (1) the haul line (end)
 +(2) the continuation of this end running from the impromptu sheave down to this side's anchorage
 + (3) the continuation running back up into the knot-sheave.
THREE parts bearing tension against the one part run over the truck's load.

Or, to put in terms of distance of respective movements, the hand grabbing the haul-end AT the impromptu
knot-sheave will move the full span of rope (twice times the span X between sheave & anchor) to pull it all
through the knot-sheave (to close the span) AND will have started span-X distance above the anchorage.
That's X + 2X of rope = 3X pull distance for 1X closing of span -- 3:1.

What is stated above by Gleipnir is that as the haul line pulls in one direction the load will move
in the opposite direction, to move towards the sheave and not vice versa.  G.'s reasoning is correct
for this pulley system, but this system is not that called "Trucker's Hitch", which is as has been
stated now several times, with movement in the direction hauled.

This should be perspicuous, now.

*knudeNoggin*

[[Inkanyezi] gone]

Of course sometimes it is convenient to disregard friction, while at other times it has to be considered as an important part of the outset. In the Trucker's, friction works against the theoretical mechanical advantage, but then again when we belay, it is an asset, as it helps us hold what we have gained. Of course, if we belay to the rope itself, the resulting hitch will have only two parts bearing, but as a system, when we pull downwards, there are three parts pulling on one. When we try it in practice, we will often find that it is possible to tighten harder than with one part only, hence there is a mechanical advantage, although not as large as three times the power. Sometimes you might see a second trucker's added to the working end of the first one, raising the theoretical advantage to 3²=9. This second one of course is added after tensioning as much as possible with the first one.

[Dan_Lehman]

There is another concern in such pulley systems, when sheaves are of unequal
quality vis-a-vis friction:  one should put the best sheave at the point where
the haul line runs (where most rope movement comes).

The inefficiency of pseudo-pulley sheaves (even 'biners) can be readily seen
by the slackening of parts that in theory are bearing equal load.  And the
Versatackle works because of such (great) differences, the hauled end being
buried against the sheave during tensioning, and then being locked against
it upon release.

I hope that by now all can see that the pulley model put up by Gleipnir is NOT
representative of the Trucker's Hitch; it shows a different part moving.

--dl*
====

[TS]

It's taken me awhile, (11 years), but I finally understand why the Trucker's Hitch does, in fact, give a 3 to 1 advantage, (ignoring friction).

Since all the "pull" is towards the fixed end of the rope, then flipping the typical model upside-down, (as though lifting a weight with the rope arrangement), makes the true advantage of 3-1 the only possible conclusion! (see drawing).

If you picture the situation as "lifting a weight from above", it becomes clear that ALL THREE LINES are contributing to the support of the load. Hence, each line is supporting a third of the weight.  In the particular way the Trucker's Hitch is normally used, (to tie down a load), no "weight" is being raised, which was what led me astray, initially.  In other words, I was WRONG to think that the third line needed to be subtracted, since it holds fully 1/3rd of the weight at all times.

Thanks to [Inkanyezi] gone, Dan Lehman, and all the other members who replied to my original post.

 

[KC]

To me a 1x, 2x and  3x positions (potentials) by count of legs of pull to them.
General use for trucker would be as compression jig from  input:1x to output 3x thru pivot 2x.
>> pull down on load stack for transport.
.
Could seize 3x point  to make it stationary pivot of machine
And input to 1x to output 2x on lift.
>> up to bodyweight as input unless other factor.
.
Can invert  to give 2x compression or 3x lift from 1x input
>> that now can be up to leg strength input unless other factor
.
Can also look as gearbox, for as compressing 3x for output is 3x slower reciprocally.
>> the 3x compression output force is friction buffered/reduced
>> but not the speed difference.
>> can even reverse to input at 3x, pivot of 2x and get a 3x faster (and thus 3x weaker ) output at 1x position.
.

In Conserving Pulley Forces for More Output i make wild claim that in 3xCompression position for Trucker tightening down tarp over top of stack of pallets etc.
>> can get 4xEffort at either 2x or 3x position compress or lift.
+ 3xBodyweigh compression / 2x Bodyweight lift.
Not choice of either effort or bodyweight, but using both, and the equal and opposite of effort collectively as inputs.

Geometry gives position potentials, friction buffers forces in and out of pivot.
>> degrading efforts input position thru pivot to output position 'purchasing rope' against load
>> but then helping to hold against statically hold against load or to controlled relieve rope to load pull/lowering etc.
So friction only degrades movement against load, to less efficiency than outer benchmark potential
>> might take from 3x potential to 1.65 actual gain i think was mentioned, as friction leveraged against potential
>> but leverages for other 2 cases,  friction compounds potential to maybe 5/1
IF 1x tie off outside of system as hold, leaves only 2x on anchor pulled same direction
>> note tie off 1x around self the load on 2x anchor increases to half again as much.

[mcjtom]

Wikipedia seems to explain it quite well - https://en.wikipedia.org/wiki/Trucker%27s_hitch

[KC]

Really just usable end points in geometry of build,
>>potentials are ratio of chosen input to output as defining benchmark framework
>>actual force then reduced from potential per frictions
In end a trade of distance for power to same sum, less loss(friction co$t)
>>reciprocal distance is mostly noted as speed differential here tho....
>>so is like gearbox of achievable ratios between wall crawl/granny gear and highest speed/least power to same sum
BUT, the speed differential is more on the reciprocal of the potential than actual
>>frictions does fight effort, but so does load
>>but the speed differential will be full 3xFaster input than output in main Trucker's (tarp covering)compression down to truck bed.
>>even if power output is only 1.65x etc. (in 0 elasticity model)..
.
Really could say this is a 1,2,3(count of unique end or arc position can make input, output or pivot in mechanical equation)
>>as geometry build and define input/output positions for various ratios
Common is to input on single leg in gravity direction
>>and take 'purchase' as output from the 3x position
Such as compressing a tarp over a load on a truck.
.
Pull backwards from 3x on this to re-extend for next time
>>now less power and 3x speed seen at 1x position that usually pull to use Trucker's Hitch
>>this is just rolling levers version, rather than rigid levers to trade distance/speed for power.
Nothing free, trading distance for power to same volume>>less  friction as conversion co$t/tax.
>>instead of counting ratio of distances from pivot for rigid lever power ratio potential (less pivot frictions) and what is input/direction
>>count legs of  pull to pivot , define input/output ratio and direction/position of input as potential (less pivot frictions)
Can have some rope rubbing frictions too in tight system
>>linear partial frictions of usual rope rubbing most different than full power arc frictions partial force than the arcs frictions
>>arc frictions are at full force and compound by degrees
>>linear frictions only at sine force on pretty linear run, and compounded  by distance/not degree.

[agent_smith]

Dear KC,
Your content posted at reply #10 is incoherent and abstract.
I am a native English speaker and I also have a solid understanding of practical M.A. systems... and yet, I struggle to comprehend your narrative.

Note: This is NOT intended as an insult.
I am simply pointing out that even for me, it is difficult to extract a coherent meaning from your post.

I noted that you retaliated in the treebuzz forum when it was pointed out that you engaged in copyright infringement... and I hope that you will not interpret my post as a personal attack and also suddenly delete your posts?

There are easier ways to explain M.A. (mechanical advantage) in relation to improvised systems such as the 'truckers hitch'...

[agent_smith]

Per 'Brocky"

Perhaps a little more patience and effort is needed?  Saying twice it is not an insult leads one to think it is.

Thank you 'Brocky'.
A very interesting post that was neither required or appropriate.
There is an underlying motive behind your post - but I wont explore it in detail with you because it will need to nothing of value.
Unlike other discussion forums on the internet, the moderators are quick react and ensure that discussions stay focused and relevant - with a minimum of personal distractions.
So you can cease and desist with any further posts of this nature.

Relevant content:

1. The truckers hitch - is an improvised M.A. system (it is built from available rope material, using no manufactured pulleys or progress capture devices - PCD's).
2. It is a 'simple' M.A. system.
3. The theoretical yield (ignoring frictional losses and system stretch) is 3:1
4. Actual yield will be less than 3:1
5. Once the desired level of tension has been reached, the system needs to be secured - so it doesn't release and slip.
6. There are a few different ways of constructing the system - local/regional variations - but all draw on the same fundamental principals.

If I find time, I'll post some photos with notes to illustrate concepts - which will contribute to this topic.

[KC]

But, i very purposefully am trying to be abstract to draw to bigger, truer picture of more depth and fabric than usually seen.
And then what i see as key concepts within this, beyond normal scope of view from that vantage point.
Our knot island is small speck deep inside over-ruling domain of rope mechanics small ocean inside the world of general mechanics.
>>many things can be seen from different facets, magnifying views, depth of usage/persistence, counter-intuitive twists etc.
>>while not myopically on knot island, perhaps easier or from more understandable reference to understand/some of what is per person.
Seeking a fabric of linked persisting logic to more tangibly grasp, instead of handfull of isolated points.
Diffused radial vs focused linear directional and conversion losses are basic to all mechanics as keystones to note,
>>and if linear directional, the loaded axis and input direction on that axis as a persisting quantity all it's own.
.
If i may,
i can easily describe Mechanical Advantage as i have taught myself:
>>as a volume of force spread wide in base of aquarium with low side glass pressure
>>or stacked high , to high side glass pressure in less wide aquarium
>>but always the same total volume of force  >> spread to higher pressure or longer distance reciprocals(meaning 1 recedes as the other grows).
>>no magic input of force, nor loss, but an accounting of balance, of all you get, you paid for somehow, and always loss of conversion.
Mechanical Advantage is like frozen lemonade concentrate
>> can have high pucker power thawed out of freezer or dilute to less pucker per gulp over diluted longer distance
>>but always the same amount of pucker power total
Mechanical Advantage is as like trading Amps for reciprocal Volts to the same total Wattage.
Mechanical Advantage is like funneling same amount of distance x force into a smaller distance (or diluting it out)
>>just like air pressure, same volume of air compressed into smaller container gives greater pressure but not for as long a continuous delivery
So, distance x force POTENTIALS must always be reciprocals to same total volume sum
>>every drop of force is paid for, from some previous conversion (w/loss), nothing free
>>try to leverage control over as endpoint with capitalizing on efficiency co$ts , or pass thru as w/efficiency co$t minimized as handle like precious w/o spilling a drop of force volume if can.
.
But, always expect co$t of conversion, which for us is friction(as for many other disciplines), for nothing is 100% efficient conversion
>>some of the lemonade always gets stuck to side like switching containers if convert/ conversion loss rule
>>specifically, in Hitches and Bends point of Linear(direction-ful) imposed into controlling arcs radial(direction-les) control
>>at friction lo$$ from conversion, not seen in radial 'glow' force of swell even around to again arc control of Round Binding
In Round Binding no conversion; radial force is handed of to then likewise be radial controlled,
>> then no conversion loss from linear to radial, so just mirroring force equal back, w/o degrading frictions (no capstan effect)
>>nor directional effect of linear (no compounding force/pulley effect) residual from the directional force of linear input
i really don't see how these concepts and their shear breadth can be seen in context from inside Gordian ville on knot island
>>for even as look so close at Gordian, Knot it grows tighter; let alone touch it.
Truer, wider perspective is sometimes needed.
The utility of the Trucker's GEOMETRY can be like transmission of gaining power or speed
>>the lever classes and pivot positions etc. align with rigid lever classes exactly(link)

.
But, i never really got  it until could explain 10speed bike gears (why large in front yet small in back to go fastest) and Chinese Windlass/differential.  They really beat me for awhile.
After really grasping them, that put the rest deep in my powerband of understanding, not at the tattered fringe; things clicked
>>so humbly try to offer same.
i am trying to bring beyond that to actual usage tho, and flexibility of that usage to more utilities extrudable in machine or knot of rope mechanics.
Knot necessarily an in the box mentality, but then doesn't try to be.
.
Once again the outer benchmark constraints are in the geometry of structure.
>>Can replace bend friction points in Trucker's with pulleys, to have same geometry, therefore same potential
>>just more realized of that power potential with frictions dialed down to compound more force at arc apexes
>>than compounding tension reduction thru the pipeline of the rope itself
>>2 reciprocal effects of all rope arcs with LINEAR direction-full imposed force volume, not radially imposed force volume
>>thus force input type matters(focused direction-full linear or dispersed direction-less radial),
>>and then the focused directional axis matters if linear to blur this even less..
A lower friction system is better for taking 'purchase' but in trade a higher friction system is more helpful in holding and controlled payout of the purchase; as the 'friction buffer' works to favor one way and not other fairly for you to choose what to  capitalize on.
>>but this is jsut for the force output differential to the input, the speed differential between both is always the FULL POTENTIAL of the position
.

.
There are 12 not 1 types of usage for Trucker's geometry,
>>and 2 choices of different directions of pull to those 12 builds on any loaded axis affecting input source choice (weight or effort limit of single input).
>> 1x,2x,3x per geometry of legs of pull per position is more descriptive to this wider view.
>>if can't see properties in this larger open view, probably less likely to witness same in tight closed knot, but still there in either case.

i was simply trying to say and show that Trucker's 3xCompression is tip of iceburg usage range to this view
>>also just looking at getting more power, sometimes want less/lighter touch to next position
>>or sometimes faster or slower speed is target.
So here then again, Trucker's offers more utility than just 3xPower output
>>and all the other functions follow same rules, even around counter-intuitive turns
>>and persist openly here and hidden in knots


Have never seen speed differential is per POTENTIAL ratio stated, not ACTUAL stated, but is what i find.
>>load and inefficiencies drag against effort, but input/out ratio speed i find the same
>>inefficiencencies reduce ACTUAL force part of return below POTENTIAL tho, to lower force ratio as conversion loss.





Out of all my many vices; i am only really here for the rope ones.
i hope i have completely answered all your questions.

[agent_smith]

Hello KC,

I have had a close look at the images in your post at reply #13.
Are you aware that none of these images actually closely resemble a real in-the-field truckers hitch improvised just from rope?

To Brocky - Stop.
This is not an insult.
Think of this post as a statement of fact.

To KC. Your passion is appreciated.
I am not insulting you.
I am giving you some feedback in good faith.

Sit down, have a cup of coffee, and take a nice deep and slow breath.
Its all good, you're not being insulted or attacked

Now, it would be helpful to put your content into an actual context that resembles a real-world truckers hitch (with no manufactured pulleys, the SPart disappearing over the opposite side of the load that is being tied down and secured, etc. And to finish with a simple 'tie-off' so the truckers hitch doesn't slip.

In particular, it would be instructive to show the rope-on-rope contact point where a lot of localised friction is being generated. Is it possible to cause localised heat glazing and/or abrasion damage at this conjuncture point?
Where is most of the efficiency being lost in a truckers hitch (ie at which points or localised point)?