Reeving a Tackle to Advantage -- What am I Missing?

[Seaworthy Lass]

Originally Posted by Dockhead

But it cannot be. Erase the words "fixed block" and "moving block". This is irrelevant to the geometry. This can only be a question of geometry; the motion is relative.

The geometry is exactly the same in both drawings.

It is not irrelevant. It is actually the crux of the matter.

The geometry is not the same. There is extra purchase on the moving block in the second example.

Originally Posted by Dockhead

I don't know about that, but I just did empirical research. I rigged tackle in my salon according to SWL's drawings and measured the pull. Exactly 2:1 in both cases.

I would suggest trying it in real life, and measuring it.

I have just rigged it up too LOL.

The initial distance between the fixed and moving object is irrelevant, but I made it 1m in both examples. I pulled on the line 1m in both cases.

In the first example the object moved 0.5m.
In the second example the object moved 0.33m.

Dockhead, are you sure you have made one object fixed?

[Dockhead]

Here is the correct illustration of this principle, as correctly described by Nick:




Here you can clearly see that the geometry is determined by whether the line is anchored or not.

In the Sea Scouts' and in SWL's drawings there is no difference in the anchor point, and thus no difference in purchase.

I will measure it one more time, but I'm now quite sure about this. Sea Scouts just have the wrong drawing. Valid principle, but illustrated incorrectly.

[jkishel]

Exactly wrong

[Departing2017]

I feel like I just stumbled across long lost members of my tribe. I am an unrepentant rope nerd. That's right I said rope, not line. In addition to a possibly unhealthy passion for all things sailing, I teach rope rescue to firefighter and SAR types. One of my favorite pastimes is blowing minds with the magic of rope and pulley (block and tackle) mechanical advantage (MA) system physics.

As has already been pointed out, the OP drawing is a 2:1 on one end and a 3:1 on the other. The MA one realizes just depends on which end of the MA system is moving the load and which end is attached to the non-moving "anchor." Even with the 2:1 end of the system oriented toward the moving load and the 3:1 end attached to an anchor, the 3:1 end is still 3:1, the anchor point "feels" 3x the tension you are putting into the system when you haul on it, and load "feels" 2x the tension. Put another way, and this is something to think about when you construct a system with the greater MA end attached to an anchor point and the lesser end attached to the load, the anchor point will "feel" 3/2 the weight of the load, and that is because the anchor point is carrying the full weight of the object you want to move plus a portion of your weight as you haul against the anchor point. In other words your anchor point needs to be able to bear more than the force of your load.

Building on this concept, no matter the amount of MA you build, one end will always have one fraction unit more MA than the other. A set-of-fours or gang-of-fours generates 4:1 MA on one end and 5:1 on the other, and with the 5:1 end attached to an anchor and the 4:1 attached to the moving load, the anchor "feels" 5/4 of the load. Flip it around so you are hauling with the 5:1 end and the anchor will "feel" 4/5 of the load.

Someone also said, to calculate the MA you can simply count the number of strands sharing the work. BUT counting strands only works with simple MA systems, and we have only been discussing simple systems. There are also compound and complex block and tackle MA systems; these are systems with MA pulling on MA and the total advantage is multiplicative so counting strands doesn't work. A 2:1 system pulling on a 3:1 system, for example, will generate a 6:1 MA, but you will only count 5 strands in the system.

One final note to really blow your mind (assuming you're still awake). And this will probably assuage any remaining doubts anyone might have regarding my status as the worlds biggest geek. A pulley is one of the most elegant machines ever created by man. A pulley is a lever, but not just any lever, a pulley oriented to generate MA is an infinite (rolling) Class 2 lever, and as Archimedes said, "Give me a lever and a place to stand and I will move the earth."

[cal40john]

Originally Posted by Dockhead

I would suggest rigging it up and trying it in real life. I cannot get this result empirically.

Edit: Just saw your picture, apply it to below:

Then you must be doing something wrong. It might be easier to try lifting weights off the ground. This is all in the Wiki posted earlier. Attach a block to a ceiling beam, stand on the ground and lift 100 lb weight off the ground using the block attached to the beam. There is 100 lbs of tension in the line everywhere. The weight is pulling down with 100 lbs, you are pulling down with 100 lbs, so there is 200 lbs of force on the ceiling. There is no advantage, you are feeling the 100 lbs of the block. (This is a turning block on your deck.)

Now stand on the beam in the ceiling, attach the end of the line to the beam, have the block attached to the weight, run the line down through the block then back up to you. The weight applies 100 lbs to the block. The line has equal tension everywhere, since the block rolls. The 2 parts running up share the load equally, so each part carries 50 lbs of force. One part attached to the beam, the other part you are holding, so you experience 50 lbs.

Stand on the floor again. Block attached to ceiling beam, another block on the weight. (Note that the block on the beam is your turning block on your deck again.) `End of the line attached to the beam, down to the block with the weight, up to the block on the beam and down to you. The weight attached to the block applies 100 lbs to the block, there are 2 lines leading up from the block, again sharing the load, so 50 lbs on each, equal tension everywhere in the line, so the line leading to you through the block on the beam has 50 lbs of force that you have to pull. Same as the previous example. The beam experiences the 50 lbs of you pulling down, the 50 lbs from the other line on the other side of the block and 50 lbs from the end attached to the beam, so 150 lbs load total.

If you want instead of attaching the end to the beam attach it to the becket on the block on the beam.

Repeat above with more parts as needed.

[monte]

SWL, you truly are magical if you did the experiment as per your second drawing and the blocks only moved 33cm. Assuming the distance between is 1m, then the two lengths between the blocks will total 2m. There's only two lines in the drawing between the blocks. Place a Mark on the rope at the block and pull the end until the mark moves 1m from the block. How much line is left between the blocks. 2m - 1m. Divide that by the two lines and you have .5m.
But I think what you have done is placed a mark next to the line where it runs next to the fixed block. Pull 1m there and you have .3333 m. This is the extra purchase gained when pulling in line and not using the fixed movable object block as a turning block. In that case to have 3:1 purchase. If it's a turning block you have 2:1. Ie, you have more purchase when you pull in line with the blocks

[Seaworthy Lass]

Originally Posted by Dockhead

Here is the correct illustration of this principle, as correctly described by Nick:

Here you can clearly see that the geometry is determined by whether the line is anchored or not.

In the Sea Scouts' and in SWL's drawings there is no difference in the anchor point, and thus no difference in purchase.

I will measure it one more time, but I'm now quite sure about this. Sea Scouts just have the wrong drawing. Valid principle, but illustrated incorrectly.

Dockhead - in your diagrams, in the first case there is no purchase at all - pull the line a metre and the bucket will come up a metre.

In the second case you illustrated, yes, it is rove to advantage. But only @ 2:1 compared to 1:1.

I am not sure what you mean by "no difference in anchor point" for the examples the Sea Scouts and I gave . In the first example (rove to disadvantage) the line is anchored at the fixed end, and in the second example (rove to advantage) it is anchored at the moving object. The anchor point only makes a difference in the final purchase given a certain number of turns though, it does not specifically determine if the set up is rove to advantage or disadvantage.

[Dockhead]

No, I was wrong, and SWL is right.

The moving and fixed objects are relevant because that is in relation to you.

I was measuring in relation to the anchor point, in which case both cases give 2:1.

But if you measure in relation to you, then it's 3:1.

As Gilda Radnor used to say -- never mind!

Thanks all, for the education!

[Seaworthy Lass]

Originally Posted by monte

SWL, you truly are magical if you did the experiment as per your second drawing and the blocks only moved 33cm. Assuming the distance between is 1m, then the two lengths between the blocks will total 2m. There's only two lines in the drawing between the blocks. Place a Mark on the rope at the block and pull the end until the mark moves 1m from the block. How much line is left between the blocks. 2m - 1m. Divide that by the two lines and you have .5m.
But I think what you have done is placed a mark next to the line where it runs next to the fixed block. Pull 1m there and you have .3333 m. This is the extra purchase gained when pulling in line and not using the fixed movable object block as a turning block. In that case to have 3:1 purchase. If it's a turning block you have 2:1. Ie, you have more purchase when you pull in line with the blocks

Shucks, I have been called lots of things before, but never "magical" .

I will go and photograph the set up

[monte]

Magic mermaid it's ok I understand the setup. My point was that if you pull the line 1m horizontally from the block, your purchase is 2:1 and the blocks will pull together .5m
Pull 1m in line with the lower block, purchase is 3:1 and the blocks will move .33m

[Dockhead]

Here is how it evolves:



Awfully basic things. Better late than never!

[Seaworthy Lass]

Originally Posted by monte

Magic mermaid it's ok I understand the setup. My point was that if you pull the line 1m horizontally from the block, your purchase is 2:1 and the blocks will pull together .5m
Pull 1m in line with the lower block, purchase is 3:1 and the blocks will move .33m

Getting so late I am getting confused myself.
Night all, been a fun exercise .

SWL

[cal40john]

Originally Posted by Dockhead

Here is how it evolves:

Attachment 100266

Awfully basic things. Better late than never!

Your 2nd pic is 3:1, 3rd is 3:1, 4th is 5:1

2nd pic get rid of block on beam and dead end rope there and it's 2:1.

3rd pic, get rid of left block on beam and dead end rope there and it is also 2:1.

[Bill Seal]

If you guys had spent more time in High School physics class listening to the teacher instead of checking out the cheer leader in the next row, it wouldn't present so much of a problem.

[monte]

haha, I love dockheads drawings. I guess graphics wasn't a priority in lawyer school :P
Oh BTW heres the quiz, exam will be tomorrow 0900!
Block and Tackle