Mechanical Advantage - MA

[Hunter216]

I've been trying to figure out what the total MA is for this system. I am not sure about a few things so would appreciate some help. The diagram is the Hunter 212 centerboard raising/lowering system which I think has a total MA of 18.

The area that I circled in the "blown up" area I believe has an MA of 9.
I believe the block labeled "5" is a cascade and effectively doubles the 9 to 18. (not absolutely positive about this)

Questions:
I'm not sure if the trunk sheave labeled "4" has any effect on the total MA?
I'm not sure if the cheek block labeled "3" has any effect on the total MA?

 

[jviss]

I say 18.

 

[kloudie1]

18

 

[Hunter216]

Thanks. It's been a LONG time since physics class! Please excuse me if I use the incorrect terminology.

Another question I have about the cascade section (relevant to determining the "load" rating of the line and pulley in that section) .

I believe the line to the right of the block "sees" the entire load as it passes over the trunk sheave "4". Does the line on the left that passes from the Quad sheave block "7" - through "5" and back to "8" "see" only 1/2 or should it be rated the same as the right side?

 

[Johnb]

I see the block number 7 as having only 8 cords leaving it therefore the force on it would be 8 X
"tension in the cords". This would then be doubled by the block at 5 for a total of 16.

 

[Will Gilmore]

I'm sorry, but I only count a 16:1.
Help me out.
How do you get 9:1?
All stationary blocks, regardless of the force experienced by their fasteners, are simply turning blocks and transfer the forces 1:1 along the load line to the next block. Block 3, sheave 4 and the three blocks labeled 8 appear fixed and stationary, therefore they don't reduce the load. Each sheave in block 7 should provide a 2:1 advantage to the system. I believe this would be additive. 2:1 + 2:1 + 2:1 + 2:1 = 8:1.
The cascaded block multiplies the advantage by another 2:1. This gives me 16:1.

I have never done this except in physics class, so I assume I'm missing something and, it's been a while for me too.

-Will (Dragonfly)

 

[Jackdaw]

18:1 theoretical.

The 4-sheave block moving 1 inch to the left requires 9 inches of line (the circle) being pulled out of the system from the line #1. 9:1.

The 2:1 created by block #5 doubles that.

Of course you will loose about 30% of that to mechanical friction and widening angles, in particular as the blocks get closer.

 

[Hunter216]

My method wasn’t very sophisticated I just counted the arrows!
I seem to recall something about the MA is the same as the number of ropes “ supporting” the load so if that’s accurate and you ignore the cascade and mentally rotate the system clockwise and hang a weight off the quad block the last line exiting the “right” “8” block you would pull down on maybe doesn’t count.
This is why I needed the help, confusing to me.

 

[Jackdaw]

My method wasn’t very sophisticated I just counted the arrows!
I seem to recall something about the MA is the same as the number of ropes “ supporting” the load so if that’s accurate and you ignore the cascade and mentally rotate the system clockwise and hang a weight off the quad block the last line exiting the “right” “8” block you would pull down on maybe doesn’t count.
This is why I needed the help, confusing to me.

Of course it counts. The first line '8' before the block is 1:1, no mechanical advantage. One inch effort equals one inch work. Turn the block and now we are 2:1. Two inch effort equals one inch work. etc. etc.

 

[Davidasailor26]

The 4-sheave block moving 1 inch to the left requires 9 inches of line (the circle) being pulled out of the system from the line #1. 9:1.

Sorry, it's probably just me, but I'm not seeing 9:1 there. The block has 4 sheaves, so 8 lines in/out. The first sheave reduces to 2:1, then 4:1, 6:1, 8:1. But after those 4 sheaves you're at a fixed point, so where does the 9 come from?
Looks to me like the right most block in this:

but with 4 sheaves instead of 2, therefore 8:1 instead of the picture's 4:1. Then the other 2:1 block doubles it all to 16:1.

 

[Hunter216]

Of course it counts. The first line '8' before the block is 1:1, no mechanical advantage. One inch effort equals one inch work. Turn the block and now we are 2:1. Two inch effort equals one inch work. etc. etc.

So if I can take the liberty of paraphrasing each time a continuous line passes around a sheave it increases the MA by 1 so I can see where you get 9. However wouldn’t the MA increase by one more as it passes around the cheek block “3”?

 

[Johnb]

All you have to do is figure how much force is required to balance the tension in the line.

In the case of line 1 it is connected to the centerboard a total of 9 times - once at the end and 8 times around block #8. Thus if the tension in the line was T the force generated there would be 9T

In the case of the block number 7 the total force on it is 8T because the line goes to it a total of 8 times. This creates a tension in the line that goes to the left side of block 5 of 8T. When this is connected back to the centerboard it adds 8T

Total force is therefore 17T= 9+8

 

[Hunter216]

I’m not sure if it helps this discussion; in another thread I asked @JimInPB who owns a H212 how much actual effort it took to raise the centreboard. He broke his luggage scale while it was reading about 60lbs, the boat was on trailer so almost fully up. I also read the board weighs about 150lbs, somehow the math of all of this isn’t making sense???

 

[Will Gilmore]

Of course it counts.

I don't see how that is any different than not having that first turn. A straight pull along the direction of movement would be exactly the same force as turning that pull through that first block. To get a 9:1, the last segment would have to return to an anchor point on the moving block.
Please help me see this, because I can't see it any other way.

-Will (Dragonfly)

 

[Davidasailor26]

In the case of line 1 it is connected to the centerboard a total of 9 times - once at the end and 8 times around block #8. Thus if the tension in the line was T the force generated there would be 9T

I count 8 "connections" of line 1 to the board - the 8 places it goes over Block 7. The bitter end gets pulled on, and the other end is fixed to the trunk assembly.

 

[Davidasailor26]

One key point - the lower block 8 is not providing any advantage. Both lines are just tied off onto it; the lines are not running through it.

 

[Will Gilmore]

So, Hunter216, have we been helpful? You less confused now?

-Will (Dragonfly)

 

[Hayden Watson]

Simple statics problem and the purchase is 8x2 = 16:1. Only lines that are connected to the moving blocks count. #7 has 4 sheaves = 8 lines. cascade as 2 lines.

 

[MikeHoncho]

I've taken Rope Rescue and Rescue Systems and I have and will always be confused by this topic. That's all I have to add....

 

[Hunter216]

So, Hunter216, have we been helpful? You less confused now?

-Will (Dragonfly)

All opinions helpful and welcomed. It refreshing to know my original guess was close to whatever the
“correct” answer is for total MA as the range seems to be 16-18.

What doesn’t make sense is if I take the weight of the board which I think is 150lbs as the load the system needs to handle and for the sake of argument, accounting for friction and to make the math simple etc lets say the system makes the load “feel” like 15 lbs or a perfect MA of 10 or 1/10th of 150lbs.Thats a lot less than @JimInPB measured???