Mechanical Advantage Pulley Quiz

Phased1 · 29th December 2008, 10:15 AM

Re. types of ratcheting pulleys.

I use the Petzl protraction.
For pulleys I use the Petzl Twins and Tandems.
I also use some "rescue" style prussik minding pulleys.
Petzl Work and Rescue - Pulleys
I also have a Petzl I'D that I'll haven't been using much in this type of work but probably could, have to check wll (working load limits).
Petzl Work and Rescue - Self-braking descenders I'D®
BTW when I've set up mechanical advantage haul systems it's been with kermantle rope even if it's then attached to a rigging (stable braid etc) rope.

Phased1

PTC · 5th January 2009, 06:57 PM

If you had 4 pulleys, you could get a 9:1 mech advantage.

Phased1 · 6th January 2009, 03:30 AM

Quote:

Originally Posted by PTC

If you had 4 pulleys, you could get a 9:1 mech advantage.

Are you suggesting piggy backing (attaching) a 3:1 on to another 3:1........

Ekka · 6th January 2009, 07:03 AM

Why, one more and you could double it again to 12:1

Phased1 · 6th January 2009, 02:04 PM

So it looks like the most advantage you could get with 4 pulleys is 16:1
I don't know how to do those nice diagrams like Ekka

JayD · 6th January 2009, 02:07 PM

Quote:

Originally Posted by Phased1

So it looks like the most advantage you could get with 4 pulleys is 16:1
I don't know how to do those nice diagrams like Ekka

Yeah but how far do you go before you get no advantage at all because all your doing is busting ropes..

...Just a thought!

Phased1 · 6th January 2009, 03:30 PM

Quote:

Originally Posted by JayD

Yeah but how far do you go before you get no advantage at all because all your doing is busting ropes..

...Just a thought!

I think if you know the forces involved you're less likely to break ropes than the guy who just hooks a rope to his truck to pull something, been there done that.

One person could pull, say about 100kg, so even at 16:1 that's 1600kgs of force on the load or about 30% of the strength of a 13mm rope......... lots ya, but at least you know the amount.

The weak link would probably the type of rope grab used, prusiks would slip or break and mechanical rope grabs (ascenders) might damage the rope.

BTW the GRCS has a dead lift rating of 3000lbs (1365kgs) so if you used that with an anchor above the load you'd have a 2:1 force on the anchor (6000lbs, 2730lbs.) Many 5\8" tenex loopie slings chokered around a tree have a WLL OF 2560LBS..... far less than the 6000lbs it is possible to achieve (safely) with the GRCS.
Ahhh...... but I ramble too much.

Ekka · 6th January 2009, 05:47 PM

Nice diagram, what are you on about.

Yeah, surprising how much MA you can get.

moray · 23rd January 2009, 12:49 AM

Quote:

Originally Posted by Ekka

Just a lil quiz.

This is a true scenario ...

True, but not quite complete. I recently pulled down a leaner that was threatening a house using a 5:1 setup. Even though we had very poor footing (an ice-covered pond) I was still surprised at how hard it was to pull the tree over. Later I calibrated my pulley setup using known weights. The 5:1 turned out to be 3.4:1 (one pulley was there just to change direction). The inefficiencies came from the pulleys and from the rope. After accounting for pulley efficiencies from the manufacturer's specs, there was still a significant loss left over. This amounted to just over 4% loss per pulley, presumably coming from internal work done by the rope in bending around the pulley.

Applying all this to Ekka's nice diagram, assuming a very decent 90% efficiency per pulley and 4% rope loss per pulley, we get a mere 86% efficiency per pulley. Here is the revised diagram:

For 2 or 3 pulleys, one can pretty much ignore the inefficiencies. By the time you are using 5 or 6 pulleys, the true MA is going to be way less than theoretical.

Ekka · 23rd January 2009, 08:21 AM

Of course, good point, friction and rope stretch influence the MA.

Phased1 · 23rd January 2009, 02:06 PM

Quote:

Originally Posted by moray

True, but not quite complete. I recently pulled down a leaner that was threatening a house using a 5:1 setup. Even though we had very poor footing (an ice-covered pond) I was still surprised at how hard it was to pull the tree over. Later I calibrated my pulley setup using known weights. The 5:1 turned out to be 3.4:1 (one pulley was there just to change direction). The inefficiencies came from the pulleys and from the rope. After accounting for pulley efficiencies from the manufacturer's specs, there was still a significant loss left over. This amounted to just over 4% loss per pulley, presumably coming from internal work done by the rope in bending around the pulley.

Applying all this to Ekka's nice diagram, assuming a very decent 90% efficiency per pulley and 4% rope loss per pulley, we get a mere 86% efficiency per pulley. Here is the revised diagram:

For 2 or 3 pulleys, one can pretty much ignore the inefficiencies. By the time you are using 5 or 6 pulleys, the true MA is going to be way less than theoretical.

These are good points,

It's good to know the difference between the theoretical and the real world situations.
I see you got the 4% reduction from the manufacturers but how did you get the 90%?
I wish I had access to a dyno so I could set this example up and see for real what force one person could exert on the tree (number 1 in the drawing).
Anyone care to try this? Hint, hint.....
I'm also curious if the diameter of the rope has any real effect, say a static 10mm Vs a static 12mm...........?

moray · 23rd January 2009, 11:14 PM

The 90% came directly from the manufacturer, CMI, who lists efficiencies of many of their pulleys. I have read in various places that 90% is considered pretty good efficiency for a small pulley. The cheaper pulleys with bushings will tend to have poorer efficiency but will be more rugged.

How do the manufacturers test their pulleys without using a rope, or, what is the same thing, how do they separate pulley losses from rope losses? I don't know.

Your question about the rope is well taken: I bet the type of rope makes a big difference but I don't have any evidence myself.

moray · 30th January 2009, 06:27 AM

A friend pointed out an error in my analysis so I want to post the correction here.

While any pulley system will require us to do work against the pulley friction and in stretching and deforming the rope, only the pulley friction affects the mechanical advantage. So the revised Ekka diagram I showed earlier would be correct for 86% efficient pulleys, and this would be true no matter what kind of rope you used. A very stretchy rope would force you to do a lot more work to move a load because you have to pull farther for each meter the load moves. The actual force you need to apply remains the same.

Use good pulleys to maximize MA; use static rope to minimize work.

A bonus to having my anaysis shot down, besides keeping me humble, is that now I have a pretty good idea why the measured efficiency of my pulleys was only about 86% instead of the 90% specified by the manufacturer. I did my calibration in my unheated garage at a temperature of minus 8 degrees C (it is winter up here in the North). The specifications probably apply at room temperature, and the friction in the bearings is probably a lot less when the bearings and bearing grease are warm.

Ekka · 30th January 2009, 06:44 PM

LOL, up here then the pulleys run around 99% efficient due to the heat and sweat I drip on them!

Ekka · 9th February 2009, 07:47 PM

Just found a great document that they tested out these theories.

In fact nothing was lost due to rope or pulleys ... there was a gain and the final test involved a vector pull in addition to the 4:1 ... that means

Quote:

A prussik was then
attached to the middle of the span and loaded traversely to create a so-called ‘vector pull’.

Another observation.

Quote:

Observation: On average a person is able to apply ~60% of their body weight to a line when free-standing. If a stance braced against/behind a stationary object is adopted, then the average loading rises to ~75% % of their body weight.

So this debunks the myth that you lose MA due to friction, you gain for a reason that becomes apparent if you have ever been in the field and "felt the heat".

moray · 10th February 2009, 01:21 AM

Quote:

Originally Posted by Ekka

...So this debunks the myth that you lose MA due to friction...

First, I am glad you are keeping this subject alive! Regretfully, I must tell you that you have jumped to an unjustified conclusion. It is not a myth, and it has emphatically not been debunked!

Second, there is one very interesting result from the Norwegian experiment: a normal person can pull with about 60% of their body weight. That's a very useful fact to file away.

Here's a quote from the Norwegians:

Observation: The above ‘Case 1’ experiment was repeated with a single pulley introduced into the system, to facilitate a change of loading direction but no modification in mechnanical advantage. This gave almost identical results, showing that the additional pulley has negligable effect (friction) on the system.

They are wrong! Or, more precisely, they cannot draw such a conclusion from their experiments. The reason is simple: they were dealing throughout with a system in which nothing is moving. Why that makes a difference is not so simple.

Here's a totally simple experiment anyone can do. Hang a pulley in your shop or garage, and hang 20 kg from a rope going over the pulley. Stand on a bathroom scale and pull down on the other end of the rope. When the weight is rising at uniform speed, read the scale. How hard did you need to pull? Probably 22 or more kg. It will ALWAYS be greater than the weight you are lifting. The ratio of the weight to your pull is the efficiency of the pulley. I have done this dozens of times; the efficiencies vary from about 80% to something above 90%.

The drawing shows a scenario with two fixed pulleys that may illuminate the situation. Let's say each pulley is 90% efficient. The person pulling at A with 100 kg force can just move a resisting force of 81 kg at B. But the diagram is perfectly symmetrical. Does this mean a person at B pulling with 81 kg can just move a resisting force of 100 kg at A? Of course not! However, and this is what the Norwegians were observing, 81 kg at B can just RESIST 100 kg at A (or 81.00001, if you want to niggle about it). There is a very large difference between what it takes to move something and what it takes to stop something.

It is hard to know what to make of the Norwegian experiments for the simple reason that static measurements involving pulleys are inherently ambiguous. Referring to my diagram, the Norsemen could measure 100 kg at A but the force at B could vary all over the map from a minimum of 81 kg to a maximum near 120 kg. Friction in the pulleys can lock in that much of a difference. If they actually measure the force at B to be 100 kg, as they imply, that certainly does not mean, as they also imply, that pulley friction is negligible!!!

In a nutshell, if you have a pulley system and you want to stop something from moving, i.e., hold a load, then use the worst pulleys you can find. Throw sand in the bearings. On the other hand, if you want to move something, then use the finest pulleys you can find, and make sure the bearing grease is warm.

Ekka · 10th February 2009, 07:48 AM

I believe the details of the experiment perform accurately for exactly the purpose of what we do.

We dont set up pulleys vertically and lift weights for starters, in these tests the pulleys are horizontal.

Secondly we use the same input method and force, a person.

In reality if a person pulling on a line varies as you suggest in "B" then that variation is a consistent fact in the field we work in every day. In saying that then these experiments show how that inconsistency can be used to an advantage in certain configurations.

Looking at JG Braced Results here's the output forces of the MA's.

Case 1, 1:1 ratio 70kg
Case 2, 3:1 ratio 230kg
Case 5, 4:1 ratio 280kg

Now that is the same guy pulling the same way. What is interesting is that in Case 2 the 3:1 is more than 3 x 70kg.

And in Case 5 the 4:1 achieved exactly 4x the MA.

Now do note, as per the way I set my rig up even more could be achieved by having a lock off device (I had a prussik). In Case 6 here they used a lock off and harnessed JG to the pull line and achieve 320kg of pull.

So in fact it proves that there's no loss for the purpose of say pulling spars over.

If, and what you are suggesting, a person can (through a 3:1 system) apply more than 70kg (of a 1:1 system) of force due to the configuration then that is a benefit of the system.

So the argument holds true.

3:1 used for this purpose in the manner illustrated offers greater than 3:1 MA and when lock off devices and vector pulls are applied even higher MA's can be achieved.

moray · 10th February 2009, 08:13 AM

Ekka, I would love to reply to this, but I'm headed to a warm, 3rd-world country for a week. If I find an Internet cafe, I will post.

Just a quick note: in arborist applications, you DO want the load to move, and that changes everything.

Ekka · 10th February 2009, 08:47 AM

Dont know what you mean by load moving.

In spar/tree felling applications I take it the load is the spar/tree, so we want that moving after the back cut.

If you are referring to the person pulling then again movement is OK provided it's in the right direction.

moray · 21st February 2009, 05:51 AM

Quote:

Originally Posted by Ekka

...We dont set up pulleys vertically and lift weights for starters, in these tests the pulleys are horizontal.

We are talking pure physics here. A force is a force. Pulleys, pulley friction, and applied forces will work exactly the same regardless of the orientation of the system.

Quote:

...
Case 1, 1:1 ratio 70kg
Case 2, 3:1 ratio 230kg

Now that is the same guy pulling the same way. What is interesting is that in Case 2 the 3:1 is more than 3 x 70kg.

Indeed!! This should be a giant red flag accompanied by deafening alarm bells. Like pouring a liter of water into an empty vessel and ending up with 1.2 liters. There is no way a pulley system will ever exceed (or even equal) its theoretical maximum. I don't dispute for a second that the Norwegians measured 230kg, just their explanation.

Quote:

...So in fact it proves that there's no loss for the purpose of say pulling spars over...So the argument holds true.

Before I try to take this on again and argue how pulley friction has led the Norsemen astray, I refer everyone to the following interesting link: Sailing Smacks Tackles; Their types, use and power statistics

The linked page shows a bunch of interesting pulley setups, and it discusses some of the properties of pulleys, including friction. At the very end is a nice table showing how friction eats a serious hole in mechanical advantage in multi-pulley configurations. Since the page cites no references or experiments, and makes no arguments, it does not bolster my argument in any way, even though it fully agrees with my position. In the next post I will try to lay out an improved version of my earlier argument.

Ekka · 21st February 2009, 06:43 AM

They sort of explained that having to pull more rope means you get a better grip/ergonomics of pulling.

He could apply more force, a spin off. You could argue that the force I exert on the end of a 12" wrench is always the same, however by changing the direction, grip, handle style etc I could get a higher output ... it's that factor which gave the increased outcome.

moray · 21st February 2009, 01:35 PM

OK, here's a first pass at the friction problem. This first example is not about pulleys at all, but illustrates the issue everyone seems to be missing.

There is an old beater car parked on a deserted paved airstrip with its brakes locked. You happen to know it weighs exactly 1000kg, and you also know that the coefficient of friction between the rubber tires and the asphalt is 0.3. This means it will take a 300kg horizontal force to slide the car across the pavement. Anything less than that and the car won't move. One day you drive by and notice a large bull pushing against the motionless car. Quick, how hard is the bull pushing? Even a rocket scientist can't tell you. The force applied by the bull could be anything between zero and 299.999... kg. ANY number in that range is a plausible answer.

A day later you drive by again and notice an even larger bull pushing the car at a slow but steady rate. Quick, how hard is the bull pushing? Easy, 300kg.

The difference between these two cases, obviously, is that in the first one nothing is moving--friction is preventing motion. You could measure the force applied by the bull, of course, but it could turn out to be any number less than 300kg. In the second case the steady motion against friction instantly tells you the unique solution: 300kg.

Here's another example before we get to pulleys. A little further down the road is tree with a nice horizontal limb 30cm in diameter. You happen to know from your rigging experience that the friction between that limb and your favorite bull rope is such that if you drape your rope over the limb you can lower a 30kg weight at a steady rate while only applying a resisting force of 15kg. The friction is doing half the work for you.

One day as you drive by you notice someone actually has the very same rope draped over the limb and is holding a 30kg weight suspended motionless by pulling down on the other leg of the rope. Quick, how hard is she pulling? Those same rocket scientists are helpless to tell you. The range of possible answers includes every number between 15kg and 60kg! Less than 15kg and the weight will start descending; more than 60kg and the weight will start rising. Everything in between, the weight stays put.

The next day you drive by again, marvelling at all the interesting physics on display by the side of the road, and, sure enough, the lady is at it again, this time lowering the 30kg weight at a uniform speed. Quick, how hard is she pulling on the other leg? Easy, 15kg. Once again we get an exact answer when there is uniform motion against friction. When there is no motion, the possible answers fall in a wide range.

The next day when you drive by, the lady is using a pulley attached to the limb. You recognize the pulley as your favorite, Model X, which has an efficiency of 90%. This means that to lift a 90kg weight you must pull down with a force of 100kg. The lady is still using the 30kg weight and she is holding it motionless by pulling down on the free leg of the rope. Quick, how hard is she pulling? By now we know not to call the rocket scientists; the possible answers fall in the range from 27kg to 33.33kg. If the 30kg weight is descending at a steady rate, we know she is applying exactly 27kg pulling force.

Tomorrow I'll go after the Norwegians.

Ekka · 21st February 2009, 04:39 PM

Quote:

Originally Posted by moray

Tomorrow I'll go after the Norwegians.

No bull.

moray · 22nd February 2009, 05:24 AM

OK, no bull, and no lady, either; the next time you drive by there is a crowd of Norwegians by the tree so you stop to watch.

A rope with a tension gage on it is tied to the tree at waist height, and a big guy is pulling on it as hard as he can. Someone reads off 70kg.

Next they tie a pulley at waist height to the neigboring tree and run the rope through it. You note with interest the pulley is your very own Model X! Arne leans hard into the rope and strains for a couple seconds while Olaf reads off 77kg. Whoa! How can this be? By now we should know the answer. When Arne leaned hard into the rope, temporarily he signifcantly exceeded his steady pull strength of 70kg. When he then relaxes his pull down to his steady max of 70kg, the pulley friction between him and the gage permits a force differential of about 10% to exist between the two sides of the pulley. More than that and the pulley will begin to turn. If Arne relaxes his pull down to 50kg, the gage won't show 50kg, it will show 55kg.

But the Norwegians aren't through. They replace the Model X pulley with a tiny cheap micro-pulley, Model M. This one, like one I own and have measured, has an efficiency of only 73%! Arne steps up to the plate and, as before, leans hard into the rope. Olaf reads off the force: 96kg!! Wow! Arne, tired by now, relaxes his pull down to 50kg, and the gage drops down to 68kg. Olaf watches the gage as Arne, getting a second wind, increases his pull back up to his steady max of 70 kg. The gage never even trembles, but remains rock-steady at 68kg.

Finally the Norwegians realize the error of their earlier hasty conclusion. The fact that Arne's pull force was measured at 70kg both with and without a pulley involved tells you nothing about the quality of the pulley. When the pulley is involved there is one thing you do know for sure: when the gage reaches its maximum value during the pulling event, Arne is actually pulling harder still, as he has to overcome the extra burden of the opposing pulley friction. But when the Norwegians actually get around to recording the gage reading at 70kg, we can no longer know how hard Arne is pulling. With the Model X pulley it could be 10% more or 10% less than 70kg. With the really bad Model M pulley Arne's actual pull could be anything between 51kg and 96kg!

Postscript: The Norwegians publish a gracious retraction of their exhuberant but erroneous conclusion. They advise others interested in the mechanical advantage of pulley systems to take measurements when the pulleys are in motion, because only then can you know exactly the relationship between forces on the two sides of each pulley.

Ekka · 22nd February 2009, 09:38 AM

Quote:

Originally Posted by moray

Postscript: The Norwegians publish a gracious retraction of their exhuberant but erroneous conclusion. They advise others interested in the mechanical advantage of pulley systems to take measurements when the pulleys are in motion, because only then can you know exactly the relationship between forces on the two sides of each pulley.

Did they or are you just toying?

moray · 22nd February 2009, 01:44 PM

Quote:

Originally Posted by Ekka

Did they or are you just toying?

Ah, you saw right through that.

Fairfield · 24th April 2010, 11:38 AM

I know I am going to have people scratching there heads or saying I am way off, but I'm going to throw this out there.

In the pic from ekka ( original), you see what is being thought as a piggy backed 3:1 making a 6:1. I was saying the same thing till I put some thought into what I was looking at with where all the forces were going to. To have what you are calling a 3:1 be a true 3:1 the second pulley would have had to been anchored directly to the tree. This is why: If you just have the line tied to the tree go through the first pulley and that is it you get a 1:1 ma. To make that be a 2:1 the tie off would be on the anchor and the pulley on the tree ( the pulley needs to travel to have a 2:1 ratio).

So what you are really looking at in the pic is a 4:1 ma, you have a 2:1 piggy backed by another 2:1. To test my thought make up what is in the pic when you pull the line hold the first part of the line from moving ( the #2 spot). This will have no effect on the ma due to the pulling force is being applied to the line it's self above. If the second pulley was on the tree then your hand when holding the #2 section would be pulled into the first pulley. So again, truely what you have is a 4:1 MA.

Therrin · 24th April 2010, 10:55 PM

*Therrin scratches his head, then watches as Bill hooks the rope which is tied to the tree, to his pickup truck's bumper and slams on the gas*

Ekka · 24th April 2010, 11:02 PM

Quote:

Originally Posted by Fairfield

I know I am going to have people scratching there heads or saying I am way off, but I'm going to throw this out there.

In the pic from ekka ( original), you see what is being thought as a piggy backed 3:1 making a 6:1. I was saying the same thing till I put some thought into what I was looking at with where all the forces were going to. To have what you are calling a 3:1 be a true 3:1 the second pulley would have had to been anchored directly to the tree. This is why: If you just have the line tied to the tree go through the first pulley and that is it you get a 1:1 ma. To make that be a 2:1 the tie off would be on the anchor and the pulley on the tree ( the pulley needs to travel to have a 2:1 ratio).

So what you are really looking at in the pic is a 4:1 ma, you have a 2:1 piggy backed by another 2:1. To test my thought make up what is in the pic when you pull the line hold the first part of the line from moving ( the #2 spot). This will have no effect on the ma due to the pulling force is being applied to the line it's self above. If the second pulley was on the tree then your hand when holding the #2 section would be pulled into the first pulley. So again, truely what you have is a 4:1 MA.

I have broken down the picture to show what is going on and where you might be getting confused.

Does this make sense?

Fairfield · 24th April 2010, 11:55 PM

Looking at thas e pic you just put up, that would be a 2:1. If the tree was a 100 lbs weight with that setup it would only take 50 lbs of force to move it (2:1). If the set up was reversed it would be a 1:1. Granted I know there is elongation in the rope and friction loss at the pulleys that dont make it a true 2:1 or 3:1 or whatever you make, I am not going with all that just the rounded off version. Here is a link that backs up what I am saying using a newton scale.
YouTube - Mechanical Advantage - Pulleys

Ekka, I like the idea of having your mini problems to chew on you should put some more up.

29th December 2008, 10:15 AM	#31
Phased1 Sappling Join Date: Sep 2007 Location: Alberta, Canada Posts: 25	Re: Mechanical Advantage Pulley Quiz Re. types of ratcheting pulleys. I use the Petzl protraction. For pulleys I use the Petzl Twins and Tandems. I also use some "rescue" style prussik minding pulleys. Petzl Work and Rescue - Pulleys I also have a Petzl I'D that I'll haven't been using much in this type of work but probably could, have to check wll (working load limits). Petzl Work and Rescue - Self-braking descenders I'D® BTW when I've set up mechanical advantage haul systems it's been with kermantle rope even if it's then attached to a rigging (stable braid etc) rope. Phased1

5th January 2009, 06:57 PM	#32
PTC Sappling Join Date: Oct 2007 Location: Sydney Posts: 45	Re: Mechanical Advantage Pulley Quiz If you had 4 pulleys, you could get a 9:1 mech advantage.

6th January 2009, 07:03 AM	#34
Ekka Admin - Dip Arb & Hort & Seldom Wrong Join Date: Jan 2007 Location: Brisbane Posts: 10,587	Re: Mechanical Advantage Pulley Quiz Why, one more and you could double it again to 12:1 Attached Thumbnails __________________ TAS Training & Assessment Services\| Arb and Hort Training available here Free Online Tree Value Calculator by TreeWorld Free Online TPZ and SRZ AS4970-2009 Calculator by TreeWorld Free Online Tree Surface Area and Tree Volume Calculator by TreeWorld Free Tree and Green Industry Deep Link Directory ... Yes, I also SEO (Optimize) and build websites that fly high in Google Qualified Brisbane Tree Lopping \| Stump Grinding Brisbane Brisbane - Gold Coast Consulting Arborist, Tree and Arborist Reports \| Project Arborist

6th January 2009, 02:04 PM	#35
Phased1 Sappling Join Date: Sep 2007 Location: Alberta, Canada Posts: 25	Re: Mechanical Advantage Pulley Quiz So it looks like the most advantage you could get with 4 pulleys is 16:1 I don't know how to do those nice diagrams like Ekka Attached Thumbnails

6th January 2009, 05:47 PM	#38
Ekka Admin - Dip Arb & Hort & Seldom Wrong Join Date: Jan 2007 Location: Brisbane Posts: 10,587	Re: Mechanical Advantage Pulley Quiz Nice diagram, what are you on about. Yeah, surprising how much MA you can get. __________________ TAS Training & Assessment Services\| Arb and Hort Training available here Free Online Tree Value Calculator by TreeWorld Free Online TPZ and SRZ AS4970-2009 Calculator by TreeWorld Free Online Tree Surface Area and Tree Volume Calculator by TreeWorld Free Tree and Green Industry Deep Link Directory ... Yes, I also SEO (Optimize) and build websites that fly high in Google Qualified Brisbane Tree Lopping \| Stump Grinding Brisbane Brisbane - Gold Coast Consulting Arborist, Tree and Arborist Reports \| Project Arborist

23rd January 2009, 08:21 AM	#40
Ekka Admin - Dip Arb & Hort & Seldom Wrong Join Date: Jan 2007 Location: Brisbane Posts: 10,587	Re: Mechanical Advantage Pulley Quiz Of course, good point, friction and rope stretch influence the MA. __________________ TAS Training & Assessment Services\| Arb and Hort Training available here Free Online Tree Value Calculator by TreeWorld Free Online TPZ and SRZ AS4970-2009 Calculator by TreeWorld Free Online Tree Surface Area and Tree Volume Calculator by TreeWorld Free Tree and Green Industry Deep Link Directory ... Yes, I also SEO (Optimize) and build websites that fly high in Google Qualified Brisbane Tree Lopping \| Stump Grinding Brisbane Brisbane - Gold Coast Consulting Arborist, Tree and Arborist Reports \| Project Arborist

23rd January 2009, 11:14 PM	#42
moray Sappling Join Date: Jan 2009 Location: Maine, USA Posts: 28	Re: Mechanical Advantage Pulley Quiz The 90% came directly from the manufacturer, CMI, who lists efficiencies of many of their pulleys. I have read in various places that 90% is considered pretty good efficiency for a small pulley. The cheaper pulleys with bushings will tend to have poorer efficiency but will be more rugged. How do the manufacturers test their pulleys without using a rope, or, what is the same thing, how do they separate pulley losses from rope losses? I don't know. Your question about the rope is well taken: I bet the type of rope makes a big difference but I don't have any evidence myself.

30th January 2009, 06:27 AM	#43
moray Sappling Join Date: Jan 2009 Location: Maine, USA Posts: 28	Correction, my bad A friend pointed out an error in my analysis so I want to post the correction here. While any pulley system will require us to do work against the pulley friction and in stretching and deforming the rope, only the pulley friction affects the mechanical advantage. So the revised Ekka diagram I showed earlier would be correct for 86% efficient pulleys, and this would be true no matter what kind of rope you used. A very stretchy rope would force you to do a lot more work to move a load because you have to pull farther for each meter the load moves. The actual force you need to apply remains the same. Use good pulleys to maximize MA; use static rope to minimize work. A bonus to having my anaysis shot down, besides keeping me humble, is that now I have a pretty good idea why the measured efficiency of my pulleys was only about 86% instead of the 90% specified by the manufacturer. I did my calibration in my unheated garage at a temperature of minus 8 degrees C (it is winter up here in the North). The specifications probably apply at room temperature, and the friction in the bearings is probably a lot less when the bearings and bearing grease are warm.

30th January 2009, 06:44 PM	#44
Ekka Admin - Dip Arb & Hort & Seldom Wrong Join Date: Jan 2007 Location: Brisbane Posts: 10,587	Re: Mechanical Advantage Pulley Quiz LOL, up here then the pulleys run around 99% efficient due to the heat and sweat I drip on them! __________________ TAS Training & Assessment Services\| Arb and Hort Training available here Free Online Tree Value Calculator by TreeWorld Free Online TPZ and SRZ AS4970-2009 Calculator by TreeWorld Free Online Tree Surface Area and Tree Volume Calculator by TreeWorld Free Tree and Green Industry Deep Link Directory ... Yes, I also SEO (Optimize) and build websites that fly high in Google Qualified Brisbane Tree Lopping \| Stump Grinding Brisbane Brisbane - Gold Coast Consulting Arborist, Tree and Arborist Reports \| Project Arborist

10th February 2009, 07:48 AM	#47
Ekka Admin - Dip Arb & Hort & Seldom Wrong Join Date: Jan 2007 Location: Brisbane Posts: 10,587	Re: Mechanical Advantage Pulley Quiz I believe the details of the experiment perform accurately for exactly the purpose of what we do. We dont set up pulleys vertically and lift weights for starters, in these tests the pulleys are horizontal. Secondly we use the same input method and force, a person. In reality if a person pulling on a line varies as you suggest in "B" then that variation is a consistent fact in the field we work in every day. In saying that then these experiments show how that inconsistency can be used to an advantage in certain configurations. Looking at JG Braced Results here's the output forces of the MA's. Case 1, 1:1 ratio 70kg Case 2, 3:1 ratio 230kg Case 5, 4:1 ratio 280kg Now that is the same guy pulling the same way. What is interesting is that in Case 2 the 3:1 is more than 3 x 70kg. And in Case 5 the 4:1 achieved exactly 4x the MA. Now do note, as per the way I set my rig up even more could be achieved by having a lock off device (I had a prussik). In Case 6 here they used a lock off and harnessed JG to the pull line and achieve 320kg of pull. So in fact it proves that there's no loss for the purpose of say pulling spars over. If, and what you are suggesting, a person can (through a 3:1 system) apply more than 70kg (of a 1:1 system) of force due to the configuration then that is a benefit of the system. So the argument holds true. 3:1 used for this purpose in the manner illustrated offers greater than 3:1 MA and when lock off devices and vector pulls are applied even higher MA's can be achieved. __________________ TAS Training & Assessment Services\| Arb and Hort Training available here Free Online Tree Value Calculator by TreeWorld Free Online TPZ and SRZ AS4970-2009 Calculator by TreeWorld Free Online Tree Surface Area and Tree Volume Calculator by TreeWorld Free Tree and Green Industry Deep Link Directory ... Yes, I also SEO (Optimize) and build websites that fly high in Google Qualified Brisbane Tree Lopping \| Stump Grinding Brisbane Brisbane - Gold Coast Consulting Arborist, Tree and Arborist Reports \| Project Arborist

10th February 2009, 08:13 AM	#48
moray Sappling Join Date: Jan 2009 Location: Maine, USA Posts: 28	Re: Mechanical Advantage Pulley Quiz Ekka, I would love to reply to this, but I'm headed to a warm, 3rd-world country for a week. If I find an Internet cafe, I will post. Just a quick note: in arborist applications, you DO want the load to move, and that changes everything.

10th February 2009, 08:47 AM	#49
Ekka Admin - Dip Arb & Hort & Seldom Wrong Join Date: Jan 2007 Location: Brisbane Posts: 10,587	Re: Mechanical Advantage Pulley Quiz Dont know what you mean by load moving. In spar/tree felling applications I take it the load is the spar/tree, so we want that moving after the back cut. If you are referring to the person pulling then again movement is OK provided it's in the right direction. __________________ TAS Training & Assessment Services\| Arb and Hort Training available here Free Online Tree Value Calculator by TreeWorld Free Online TPZ and SRZ AS4970-2009 Calculator by TreeWorld Free Online Tree Surface Area and Tree Volume Calculator by TreeWorld Free Tree and Green Industry Deep Link Directory ... Yes, I also SEO (Optimize) and build websites that fly high in Google Qualified Brisbane Tree Lopping \| Stump Grinding Brisbane Brisbane - Gold Coast Consulting Arborist, Tree and Arborist Reports \| Project Arborist

21st February 2009, 06:43 AM	#51
Ekka Admin - Dip Arb & Hort & Seldom Wrong Join Date: Jan 2007 Location: Brisbane Posts: 10,587	Re: Mechanical Advantage Pulley Quiz They sort of explained that having to pull more rope means you get a better grip/ergonomics of pulling. He could apply more force, a spin off. You could argue that the force I exert on the end of a 12" wrench is always the same, however by changing the direction, grip, handle style etc I could get a higher output ... it's that factor which gave the increased outcome. __________________ TAS Training & Assessment Services\| Arb and Hort Training available here Free Online Tree Value Calculator by TreeWorld Free Online TPZ and SRZ AS4970-2009 Calculator by TreeWorld Free Online Tree Surface Area and Tree Volume Calculator by TreeWorld Free Tree and Green Industry Deep Link Directory ... Yes, I also SEO (Optimize) and build websites that fly high in Google Qualified Brisbane Tree Lopping \| Stump Grinding Brisbane Brisbane - Gold Coast Consulting Arborist, Tree and Arborist Reports \| Project Arborist

21st February 2009, 01:35 PM	#52
moray Sappling Join Date: Jan 2009 Location: Maine, USA Posts: 28	friction physics OK, here's a first pass at the friction problem. This first example is not about pulleys at all, but illustrates the issue everyone seems to be missing. There is an old beater car parked on a deserted paved airstrip with its brakes locked. You happen to know it weighs exactly 1000kg, and you also know that the coefficient of friction between the rubber tires and the asphalt is 0.3. This means it will take a 300kg horizontal force to slide the car across the pavement. Anything less than that and the car won't move. One day you drive by and notice a large bull pushing against the motionless car. Quick, how hard is the bull pushing? Even a rocket scientist can't tell you. The force applied by the bull could be anything between zero and 299.999... kg. ANY number in that range is a plausible answer. A day later you drive by again and notice an even larger bull pushing the car at a slow but steady rate. Quick, how hard is the bull pushing? Easy, 300kg. The difference between these two cases, obviously, is that in the first one nothing is moving--friction is preventing motion. You could measure the force applied by the bull, of course, but it could turn out to be any number less than 300kg. In the second case the steady motion against friction instantly tells you the unique solution: 300kg. Here's another example before we get to pulleys. A little further down the road is tree with a nice horizontal limb 30cm in diameter. You happen to know from your rigging experience that the friction between that limb and your favorite bull rope is such that if you drape your rope over the limb you can lower a 30kg weight at a steady rate while only applying a resisting force of 15kg. The friction is doing half the work for you. One day as you drive by you notice someone actually has the very same rope draped over the limb and is holding a 30kg weight suspended motionless by pulling down on the other leg of the rope. Quick, how hard is she pulling? Those same rocket scientists are helpless to tell you. The range of possible answers includes every number between 15kg and 60kg! Less than 15kg and the weight will start descending; more than 60kg and the weight will start rising. Everything in between, the weight stays put. The next day you drive by again, marvelling at all the interesting physics on display by the side of the road, and, sure enough, the lady is at it again, this time lowering the 30kg weight at a uniform speed. Quick, how hard is she pulling on the other leg? Easy, 15kg. Once again we get an exact answer when there is uniform motion against friction. When there is no motion, the possible answers fall in a wide range. The next day when you drive by, the lady is using a pulley attached to the limb. You recognize the pulley as your favorite, Model X, which has an efficiency of 90%. This means that to lift a 90kg weight you must pull down with a force of 100kg. The lady is still using the 30kg weight and she is holding it motionless by pulling down on the free leg of the rope. Quick, how hard is she pulling? By now we know not to call the rocket scientists; the possible answers fall in the range from 27kg to 33.33kg. If the 30kg weight is descending at a steady rate, we know she is applying exactly 27kg pulling force. Tomorrow I'll go after the Norwegians.

22nd February 2009, 05:24 AM	#54
moray Sappling Join Date: Jan 2009 Location: Maine, USA Posts: 28	those Norwegians again... OK, no bull, and no lady, either; the next time you drive by there is a crowd of Norwegians by the tree so you stop to watch. A rope with a tension gage on it is tied to the tree at waist height, and a big guy is pulling on it as hard as he can. Someone reads off 70kg. Next they tie a pulley at waist height to the neigboring tree and run the rope through it. You note with interest the pulley is your very own Model X! Arne leans hard into the rope and strains for a couple seconds while Olaf reads off 77kg. Whoa! How can this be? By now we should know the answer. When Arne leaned hard into the rope, temporarily he signifcantly exceeded his steady pull strength of 70kg. When he then relaxes his pull down to his steady max of 70kg, the pulley friction between him and the gage permits a force differential of about 10% to exist between the two sides of the pulley. More than that and the pulley will begin to turn. If Arne relaxes his pull down to 50kg, the gage won't show 50kg, it will show 55kg. But the Norwegians aren't through. They replace the Model X pulley with a tiny cheap micro-pulley, Model M. This one, like one I own and have measured, has an efficiency of only 73%! Arne steps up to the plate and, as before, leans hard into the rope. Olaf reads off the force: 96kg!! Wow! Arne, tired by now, relaxes his pull down to 50kg, and the gage drops down to 68kg. Olaf watches the gage as Arne, getting a second wind, increases his pull back up to his steady max of 70 kg. The gage never even trembles, but remains rock-steady at 68kg. Finally the Norwegians realize the error of their earlier hasty conclusion. The fact that Arne's pull force was measured at 70kg both with and without a pulley involved tells you nothing about the quality of the pulley. When the pulley is involved there is one thing you do know for sure: when the gage reaches its maximum value during the pulling event, Arne is actually pulling harder still, as he has to overcome the extra burden of the opposing pulley friction. But when the Norwegians actually get around to recording the gage reading at 70kg, we can no longer know how hard Arne is pulling. With the Model X pulley it could be 10% more or 10% less than 70kg. With the really bad Model M pulley Arne's actual pull could be anything between 51kg and 96kg! Postscript: The Norwegians publish a gracious retraction of their exhuberant but erroneous conclusion. They advise others interested in the mechanical advantage of pulley systems to take measurements when the pulleys are in motion, because only then can you know exactly the relationship between forces on the two sides of each pulley.

24th April 2010, 11:38 AM	#57
Fairfield Semi-mature vigorous tree Join Date: Mar 2007 Location: Bucks county Pa USA Posts: 136	Re: Mechanical Advantage Pulley Quiz I know I am going to have people scratching there heads or saying I am way off, but I'm going to throw this out there. In the pic from ekka ( original), you see what is being thought as a piggy backed 3:1 making a 6:1. I was saying the same thing till I put some thought into what I was looking at with where all the forces were going to. To have what you are calling a 3:1 be a true 3:1 the second pulley would have had to been anchored directly to the tree. This is why: If you just have the line tied to the tree go through the first pulley and that is it you get a 1:1 ma. To make that be a 2:1 the tie off would be on the anchor and the pulley on the tree ( the pulley needs to travel to have a 2:1 ratio). So what you are really looking at in the pic is a 4:1 ma, you have a 2:1 piggy backed by another 2:1. To test my thought make up what is in the pic when you pull the line hold the first part of the line from moving ( the #2 spot). This will have no effect on the ma due to the pulling force is being applied to the line it's self above. If the second pulley was on the tree then your hand when holding the #2 section would be pulled into the first pulley. So again, truely what you have is a 4:1 MA. __________________ Hi yes you know me I am B.A.M.F nice to meet you

24th April 2010, 10:55 PM	#58
Therrin Tree World Ninja Monkey Join Date: Oct 2007 Location: Bakersfield, Ca Posts: 2,705	Re: Mechanical Advantage Pulley Quiz Therrin scratches his head, then watches as Bill hooks the rope which is tied to the tree, to his pickup truck's bumper and slams on the gas __________________ Stihls: 200T, 011, 028, 260p, 361, 660 Give a man a match and he'll be warm for a moment, but light him on fire and he'll be warm the rest of his life.

24th April 2010, 11:55 PM	#60
Fairfield Semi-mature vigorous tree Join Date: Mar 2007 Location: Bucks county Pa USA Posts: 136	Re: Mechanical Advantage Pulley Quiz Looking at thas e pic you just put up, that would be a 2:1. If the tree was a 100 lbs weight with that setup it would only take 50 lbs of force to move it (2:1). If the set up was reversed it would be a 1:1. Granted I know there is elongation in the rope and friction loss at the pulleys that dont make it a true 2:1 or 3:1 or whatever you make, I am not going with all that just the rounded off version. Here is a link that backs up what I am saying using a newton scale. YouTube - Mechanical Advantage - Pulleys Ekka, I like the idea of having your mini problems to chew on you should put some more up. __________________ Hi yes you know me I am B.A.M.F nice to meet you Last edited by JayD; 25th April 2010 at 08:26 AM.

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