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

[Seaworthy Lass]

Originally Posted by Lodesman

Your second example is 2:1 also. See diagram in post above

OK, we are getting somewhere.
You have illustrated example 1 in the OP's first post ie 'tackle rove disadvantaged'.
We both agree this is 2:1 .

Now what happens if you draw example 2 the same way? (= same as my example 2 = tackle rove advantaged).

By the way, this is your image rotated to match example 1 in post#1:

[conachair]

Originally Posted by monte

Correct. Nice drawing btw! So in that example the load moved 1m and you hauled in 2m of line. 2:1

And badly drawn with the rope at the load.. As you said, the load moves as well..

[CHAZ]

Originally Posted by Seaworthy Lass

Martin, we are regressing here . Even Lodesman agrees the first example in post #78 illustrates a 2:1 purchase.

Lodesman, can you explain why the first example is 2:1 please while I think of how to explain to you that the second example is 3:1? Although my magic seems to increase with a glass of wine my explaining abilities seem to deteriorate

SWL

SWL, (nicer than SL)
be careful with it could hurt
From my side everything today is a progress after a saturday party with enough wine to deteriorate all abilities

Fair winds and this hand-width of water under your keel.

Martin

[Seaworthy Lass]

Lodesman, my best bottle of scotch will be cracked open tonight when the situation becomes clear for you .

SWL

[Seaworthy Lass]

I have been shackled by my apron strings to the galley , but settling down again after dinner, here is my contribution of a diagram for "tackle rove to advantage" to match the second example in post #1.

I hope this illustrates that to move the object, the line needs to shorten three times the amount of movement (less if the tail is pulled at an angle, following the proportion of the cos of the angle of deviation of the tail section as explained earlier). The purchase is therefore 3:1.

In example 1 the purchase was only 2:1. The "advantage" in example 2 is real, not just a figure of speech.

Lodesman, will you let us all know if the penny drops?

[goboatingnow]

Originally Posted by Lodesman

The third drawing is only 2:1

It's correct at 3:1. Do a division of tension it's rigged to advantage.


Sent from my iPad using Cruisers Sailing Forum

[StuM]

Originally Posted by 2Hulls

Actually, it is the way it's drawn, but it does make a difference.

Very simply, the mechanical advantage can be determined by counting the number of lines to and from the movable block. In this example, when reeved to advantage, it's three total lines, hence 3:1. It has nothing to do with any "angles" of pull. All this assumes, from high school physics, a massless rope and frictionless pulleys.....

Dave

Thank you!

[carstenb]

: peace:
ok after landing my boat in force 9-10 in the dark in a harbour I've never been in before (at midnight after sailing for 16 hours in 6 degree C weather), I give in and surrender.

I've had two g&ts and a bottle of red wine and right now I don't give a damn (thank you - rhett butler)- Tomorrow I'll try to make sense of all this

Until then - yes it does make a difference where the line is attached. I will dig out some proof tomorrow (when I'm sober and rested). Gads - 4 hours straight into the wind force 8-9-10, waves washing right over the deck and not able to make more than 2 knots due to the wind/waves

I'm burned right out (and now drunk)

[StuM]

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).

1.414 to be exact (i.e.square root of 2 )

[StuM]

Originally Posted by Lodesman

The force is applied in drawing the two blocks together - the angle at which the hauling part leaves the block plays no part in it at all the line pull remains the same.

If the line is pulled at 90 degrees, only half of the force from the last fall on the last pulley is moving the object forward. The other half is trying to pull it sideways.

Edit: to clarify

[Dockhead]

Originally Posted by Seaworthy Lass

Lodesman, my best bottle of scotch will be cracked open tonight when the situation becomes clear for you .

SWL

Lodesman, if it helps --

You might have been led astray by the idea of relative motion, as I was.

The difference is that it's not just motion of the two objects relative to each other, but relative to you. That's what makes the difference between the fixed and moving objects, which doesn't make any sense without this.

I learned a lot in this thread -- and in fact, I learned something of absolutely practical value as I am designing various tackle on my boat right now.

[Seaworthy Lass]

Originally Posted by 2Hulls

Very simply, the mechanical advantage can be determined by counting the number of lines to and from the movable block. In this example, when reeved to advantage, it's three total lines, hence 3:1. It has nothing to do with any "angles" of pull. All this assumes, from high school physics, a massless rope and frictionless pulleys.....

Dave

Dave, if a tackle is "rove to disadvantage", the angle the tail is pulled makes no difference. However, if it is "rove to advantage" it certainly does. As do the angles of the rest of the lines that act directly on the moveable object.

--------

Thinking about this, does anyone know how the purchase is actually defined? Is it the mechanical advantage along the direction of movement of the object or compared to the action of a single line at any specific angle? To me it would make sense to define it along the direction of movement of the object, otherwise how do work out the purchase of systems with blocks in several different locations?

I need to sleep on that one to mull it over, but in the meantime does anyone know the official definition?

[Lodesman]

Originally Posted by conachair

That works for a 2:1 as drawn, now turn the ropes upside down so the hauling part exits at the load, now you have the same 4m of travel plus the 2m the load has traveled, you need to pull 6m to move the load 2m - 3:1.

Flip it around, you still pull out 2m of rope to move the object 1 m.

[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).

Originally Posted by StuM

1.414 to be exact (i.e.square root of 2 )

Stu, my mind may be going to mush as it often does when it is getting late (I am a morning person ), but what does the square root of 2 have to do with it?

If the tail is coming off a block on the moveable object at 45 degrees to the direction of movement of the object and and there is just one other line coming off the moveable object along the direction of movement of the object, then the purchase is no longer (1+1):1, it is instead (1 + cos45):1 ie 1.7071:1

Why are you using the square root of two?

[Seaworthy Lass]

Originally Posted by Lodesman

Flip it around, you still pull out 2m of rope to move the object 1 m.

Bingo!!!
I see where you are going wrong.
This diagram below where you have tried to illustrate "tackle rove to advantage" is incorrect.
In the middle portion you have labelled the green line as moving 1m. Trace it. To reach there it had moved about 1.62 m .

You are also complicating the calculation of purchase as your tail is coming off the moveable object at an angle and not along the direction of movement of the object.