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

[Seaworthy Lass]

Looking at this in the clear light of day (and after some sleep ), a couple of general rules stand out that simplify all this:

1. To rig a pulley to have maximum advantage given a certain amount of line (ie to achieve "tacke rove to advantage"), simply make sure the final pull is in the direction you want the object to move.

2. If all the lines are being pulled parallel to each other and one side is fixed, to calculate the purchase compared to one line pulled along the same direction, just count the total number of lines acting directly on the moveable object, including the attachment if it occurs there.
ie 2 lines, means 2:1, 3 lines means 3:1 (if no pulley is acting directly on the moveable object and there is just an attachment, it is 1:1). This simple rules works beautifully.

If any of these lines veer off at an angle compared to using a single line (eg due to size of the pulleys, placement of pulleys, final angle of pull etc), then it complicates things a little - the size of the vector in the original direction needs to be calculated (it just equals cos of the angle off parallel to the single line) and added in for each bit of line individually.

All other lines and fixed pulleys are irrelevant.

Hope that helps .

SWL

[Seaworthy Lass]

Diagram below shows example of a 4:1 purchase with the dotted lines showing the rest of the line could be doing all sorts of things without affecting the purchase.

If you apply this principle to examples given in this thread, the purchase is easy to calculate:

Post#1 (and Post#15)
Diag 1 tackle rove to disadvantage: purchase = 2:1 (2 lines acting directly on object need to be shortened when the line is pulled)
Diag 2 Tackle rove to advantage: purchase = 3:1 (3 lines acting directly on object need to be shortened when the line is pulled)

Post#32
Diag 1: purchase = 1:1 (1 line acting directly on object needs to be shortened)
Diag 2: purchase = 2:1 (2 lines acting directly on object need to be shortened)

Post#41
Diag 1: purchase = 1:1 (1 line acting directly on object needs to be shortened)
Diag 2: purchase = 3:1 (3 lines acting directly on object need to be shortened)
Diag 3: purchase = 3:1 (3 lines acting directly on object need to be shortened)
Diag 4: purchase = 5:1 (5 lines acting directly on object need to be shortened)
(as cal40john specified)

[charliehows]

and - I did try it in real life, my sheet got inexplicably much harder to sheet in for a gybe, I just never realised why til now. Like Dockhead, I assumed that theres no difference in the way the blocks are arranged - same no. of turns=same advantage. But - in practice, there is a loss of power if the blocks are reeved to disadvantage. I like the simple explanation - the most number of lines should be on the moving part for advantage.

[carstenb]

Originally Posted by 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.

Well, actually studying her was a physics problem. My buddy and I were trying to determine the total volume of two soft containers - without the help of being able to measure them with our hands(we most certainly wanted to, but she had a boyfriend . sigh)

[Lodesman]

I am amazed that this is so thoroughly misunderstood.

If you look at the physics definition of work, it is force X distance. If I lift a 1 Kg bucket to height of 1 metre, I've done 1 joule of work.

If I hoist that same bucket 1m with an overhead pulley, I still have only expended 1J.

If I add a pulley to the bucket, there will be 2m of rope that needs to be pulled in to lift the bucket 1m - the line between the fixed point and the first pulley, and the line between the two pulleys. The running end is irrelevant; it can be 30cm or 300m long, and it does not change the end effect - the work expended (1J) is the same, but I will have pulled 2m of rope to do it, so I have a 2:1 MA. If I add a third pulley, I add another 1m of rope between the second and last pulleys; I need to pull in 3m of rope to raise the bucket 1m - 3:1 MA, but still 1J of work.

You are being confused with semantics. When they say "rove to advantage", you should not take that as equating to mechanical advantage, but in the more classical sense that advantage = advance; the running line acts in the same direction that the objective is being pulled. "Disadvantage" in this case means the opposite of "advantage".


In the OP's picture, there is no difference in the work expended, or the MA.

[Seaworthy Lass]

Originally Posted by Lodesman

I am amazed that this is so thoroughly misunderstood.

If you look at the physics definition of work, it is force X distance. If I lift a 1 Kg bucket to height of 1 metre, I've done 1 joule of work.

If I hoist that same bucket 1m with an overhead pulley, I still have only expended 1J.

If I add a pulley to the bucket, there will be 2m of rope that needs to be pulled in to lift the bucket 1m - the line between the fixed point and the first pulley, and the line between the two pulleys. The running end is irrelevant; it can be 30cm or 300m long, and it does not change the end effect - the work expended (1J) is the same, but I will have pulled 2m of rope to do it, so I have a 2:1 MA. If I add a third pulley, I add another 1m of rope between the second and last pulleys; I need to pull in 3m of rope to raise the bucket 1m - 3:1 MA, but still 1J of work.

You are being confused with semantics. When they say "rove to advantage", you should not take that as equating to mechanical advantage, but in the more classical sense that advantage = advance; the running line acts in the same direction that the objective is being pulled. "Disadvantage" in this case means the opposite of "advantage".

In the OP's picture, there is no difference in the work expended, or the MA.

Lodesman, sorry, you are incorrect.

In example 1 in post #1 (tackle rove to disadvantage) the purchase is 2:1
In example 2 in post #1 (tackle rove to advantage) the purchase is 3:1

Yes, it is amazing that this is so misunderstood

SWL

[Lodesman]

Originally Posted by Seaworthy Lass

Lodesman, sorry, you are incorrect.

In example 1 in post #1 (tackle rove to disadvantage) the purchase is 2:1
In example 2 in post #1 (tackle rove to advantage) the purchase is 3:1

Yes, it is amazing that this is so misunderstood

SWL

Sorry, but I believe it is you who is incorrect. The picture in the OP shows the exact same tackle, flipped over - there is no difference in the purchase.

I dug this out of AMS:

d.

Reeving a Tackle to Advantage and Disadvantage. The number of parts at the

moving block, and therefore the mechanical advantage, is always greater when the

hauling part comes away from the moving block, and such a tackle is said to be

rove to

advantage

. Conversely, a tackle in which the hauling part comes away from the

standing block is said to be

rove to disadvantage (see Fig 3-158). Where practicable,

therefore, it is beneficial to rig a tackle so that the hauling part leads from the moving

block, and the block with the greater number of sheaves is the moving block.

In both pictures, the 'hauling part' comes away from the 'standing block', that is the one to which the standing end of the rope is attached. So both images show it 'rove to disadvantage'. If there was another sheave on the moving block, and the rope rove through it, then it would be 'rove to advantage' and the MA would be 3:1.

[Dockhead]

Originally Posted by Lodesman

I am amazed that this is so thoroughly misunderstood.

If you look at the physics definition of work, it is force X distance. If I lift a 1 Kg bucket to height of 1 metre, I've done 1 joule of work.

If I hoist that same bucket 1m with an overhead pulley, I still have only expended 1J.

If I add a pulley to the bucket, there will be 2m of rope that needs to be pulled in to lift the bucket 1m - the line between the fixed point and the first pulley, and the line between the two pulleys. The running end is irrelevant; it can be 30cm or 300m long, and it does not change the end effect - the work expended (1J) is the same, but I will have pulled 2m of rope to do it, so I have a 2:1 MA. If I add a third pulley, I add another 1m of rope between the second and last pulleys; I need to pull in 3m of rope to raise the bucket 1m - 3:1 MA, but still 1J of work.

You are being confused with semantics. When they say "rove to advantage", you should not take that as equating to mechanical advantage, but in the more classical sense that advantage = advance; the running line acts in the same direction that the objective is being pulled. "Disadvantage" in this case means the opposite of "advantage".


In the OP's picture, there is no difference in the work expended, or the MA.

That was precisely my analysis!

As it turns out, wrong!

I've worked with blocks and tackle since childhood. I have been profoundly humbled just now to discover how little I understood about how they work.

[Seaworthy Lass]

Originally Posted by Lodesman

Sorry, but I believe it is you who is incorrect. The picture in the OP shows the exact same tackle, flipped over - there is no difference in the purchase.

I dug this out of AMS:

In both pictures, the 'hauling part' comes away from the 'standing block', that is the one to which the standing end of the rope is attached. So both images show it 'rove to disadvantage'. If there was another sheave on the moving block, and the rope rove through it, then it would be 'rove to advantage' and the MA would be 3:1.

The simple way of looking at it it that if you pull on the line in example 1 in post #1 (tackle rove to disadvantage) two lines are shortened to pull the object in.

In example 2 (tackle rove to advantage) three lines are shortened when you pull.

The purchase is definitely different in the two examples.

Lodesman, why not set it up and see .

SWL

[goboatingnow]

The wiki article makes it all very clear. I'm surprised at the confusion. Where gravity is involved ergonomics they'd to mean we rig to disadvantage however


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[Seaworthy Lass]

Originally Posted by goboatingnow

The wiki article makes it all very clear. I'm surprised at the confusion. Where gravity is involved ergonomics they'd to mean we rig to disadvantage however

Particularly if you indulge in lots of Easter eggs and Easter sweet yeast loaves .

SWL x

[conachair]

Originally Posted by Lodesman

Sorry, but I believe it is you who is incorrect. The picture in the OP shows the exact same tackle, flipped over - there is no difference in the purchase.

There is a difference. The rope is pulling, it's in tension. Lets assume the tension is the same in both examples in the picture.

The top one there are 2 bits of rope pulling away from the piece you want to move,
The bottom one there are 3 bits of rope pulling the piece. Top you have 2 x the tension, bottom 3 times.

[Departing2017]

Originally Posted by Seaworthy Lass

Looking at this in the clear light of day (and after some sleep ), a couple of general rules stand out that simplify all this:

If any of these lines veer off at an angle compared to using a single line (eg due to size of the pulleys, placement of pulleys, final angle of pull etc), then it complicates things a little - the size of the vector in the original direction needs to be calculated (it just equals cos of the angle off parallel to the single line) and added in for each bit of line individually.
SWL

Lass,
Could you show a sample of this calculation? I would love to be able to add this into my lectures. Currently, i just use some sample values that I memorized, e.g. when the line enters/exits the pulley at a 45 degree angle (rather than parallel) the MA of the pulley is reduced from 2:1 to around 1.4:1 (which may or may not actually be correct).

[Seaworthy Lass]

Originally Posted by Departing2017

Lass,
Could you show a sample of this calculation? I would love to be able to add this into my lectures. Currently, i just use some sample values that I memorized, e.g. when the line enters/exits the pulley at a 45 degree angle (rather than parallel) the MA of the pulley is reduced from 2:1 to around 1.4:1 (which may or may not actually be correct).

Sure.
I will draw up some pictures.

[Lodesman]

Both images have two parts at the moving block; both only have 2 lines being shortened; both have the same line pull at the hauling part. See image, and tell me where the third line is being shortened?