I re-read your post #12, which by the way comes to a different answer than your post #5. I do not understand why you are adding, rather than multiplying the forces.
Mechanical Advantage - MA
- Thread starter Hunter216
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Thank you @jviss , I had forgotten about odd numbers due to the becket, or attaching the end of the line to the moving block as in your cited diagram. The whole reason for the invention of the becket was for this added one advantage.Not so. You can reeve to advantage, have the fixed line attached to the moving block, and get an odd number for mechanical advantage.
That said, I'm thinking my original assertion of 18 might be incorrect; but I have to draw a diagram.
Speaking only for myself the reason I “like” any post is to acknowledge that I clearly understood or identify with what the author said.
I hope I’ve made it clear that I’m far from qualified to assert that any of the answers provided were “correct”.
I find the amount of feedback accessed through the kind of knowledge crowd sourcing available through this forum is incredible. Personally I don’t have to “get it” all to consider it valuable.
I have a new answer, and here's my analysis.
There are four 2:1 advantage tackles cascaded (in parallel). (See the small arrows pulling down, from left to right.) These are added. They are in series with a 2:1. They are multiplied.
2x(2+2+2+2) = 16. The MA is 16.
There are four 2:1 advantage tackles cascaded (in parallel). (See the small arrows pulling down, from left to right.) These are added. They are in series with a 2:1. They are multiplied.
2x(2+2+2+2) = 16. The MA is 16.
My post number 5 was erroneous. I mis read the question and thought it was to calculate the force in the line at the point marked 4. (Which by the way is 16 times the tension in the line at 1)
As far as adding - if a line goes to a fixed point or around a sheave on a block (perhaps with a becket for the end of the line) the total force exerted on the block will be the tension of the line multiplied by the number of times the line goes to the block.
The line from point 1 goes to block #8 9 times. Whether you add the tension (say T) together 9 times or multiply it byu 9 the result is the same 9T.
The line from point 1 goes to block #7 8 times. This means the total force exerted on block #7 is 8T. This means that the tension in the line that goes from block #7 to block number 5 is 8T.
The force in the line that goes from block #7 to block #8 is also 8T.
Therefore the total force exerted on block #8 is 9T from the original line and 8T from the line that goes around block #5. Together these add up to 17T.
The above is achieved by drawing a line through all the lines connected to block #8. This could be double checked by drawing a line through the lines between block #3 and #8 and block #5. This would cut 3 lines, 1 which would have a tension of T and two which would each have tensions of 8T. 8+8+1=17 - so it works.
You could triple check it by drawing a line through the original line and the line that goes to point 4. Since the line to point 4 has a force of 16T and the original line has a force of 1T and 16+1=17 this also works.
By virtue of the power given to me by getting this tight I hereby declare:
1 Mantus is the best anchor
2 Fords and better than Chevies
I have the same picture but i count the tied off line on the left and dont count the line leading to the right (free end) as that is a redirection.I have a new answer, and here's my analysis.
There are four 2:1 advantage tackles cascaded (in parallel). (See the small arrows pulling down, from left to right.) These are added. They are in series with a 2:1. They are multiplied.
2x(2+2+2+2) = 16. The MA is 16.
16 minus friction?
I have a new answer, and here's my analysis.
There are four 2:1 advantage tackles cascaded (in parallel). (See the small arrows pulling down, from left to right.) These are added. They are in series with a 2:1. They are multiplied.
2x(2+2+2+2) = 16. The MA is 16.
Not if the line from 2 goes back to the centerboard as it appears from the drawing.
Tackle in parallel are added, in series are multiplied. So 17 can't be right.
Due to the angle of the line after #3, #3 isn't a mechanical advantage, its a change in direction. It can give some advantage but isn't considered one in the rope rescue world
Sorry that should be the line from 5
If the centerboard is at 8 then it is 17
If the centerboard is at 4 then it is 16
Here's another means of analysis, and why I'm sure my analysis in post #44, above, is correct.
A fundamental principle of a block and tackle is that the mechanical advantage is exactly equal to the ratio of the amount of rope you pull out of the tackle to the distance the load moves. This is conservation or work (energy), i.e., a force applied across a distance.
For example, for a simple, single overhead pulley, you pull down 1' and load is lifted 1'; no mechanical advantage. If you add a pulley to the load, and run the rope up through the overhead pulley, down through the load pulley, and back up to a becktet on the over head block, or to the ceiling, you now pull 2' of rope to raise the load 1'. Your mechanical advantage is 2:1, or 2. You do the same work, you just use 1/2 the force over twice the distance.
If we continue adding blocks to the load and ceiling, and reeve our rope as one would intuitively do, we continue to add mechanical advantage. Four pulleys, you pull out 4' of line to raise the load 1', MA = 4. The second 2:1 added to the first 2:1.
In our case they've kept going, and didn't stop 'til they got to eight pulleys. You pull out 8' of rope to raise the frame of the bottom blocks 1' , 8:1. Now, the twist is they've added a 2:1 mechanical advantage between our load and the bottom block. This halves the distance the load is raised for a given pull on the rope, so it multiplies the MA: it's now 2 x 8 = 16.
A fundamental principle of a block and tackle is that the mechanical advantage is exactly equal to the ratio of the amount of rope you pull out of the tackle to the distance the load moves. This is conservation or work (energy), i.e., a force applied across a distance.
For example, for a simple, single overhead pulley, you pull down 1' and load is lifted 1'; no mechanical advantage. If you add a pulley to the load, and run the rope up through the overhead pulley, down through the load pulley, and back up to a becktet on the over head block, or to the ceiling, you now pull 2' of rope to raise the load 1'. Your mechanical advantage is 2:1, or 2. You do the same work, you just use 1/2 the force over twice the distance.
If we continue adding blocks to the load and ceiling, and reeve our rope as one would intuitively do, we continue to add mechanical advantage. Four pulleys, you pull out 4' of line to raise the load 1', MA = 4. The second 2:1 added to the first 2:1.
In our case they've kept going, and didn't stop 'til they got to eight pulleys. You pull out 8' of rope to raise the frame of the bottom blocks 1' , 8:1. Now, the twist is they've added a 2:1 mechanical advantage between our load and the bottom block. This halves the distance the load is raised for a given pull on the rope, so it multiplies the MA: it's now 2 x 8 = 16.
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That’s one of the components that I’ve been wondering about, Thanks
Do you know what the “amount” of rotation ( I guess that’s degrees) the line would have to make around the sheave to be considered a MA? The diagram shows 90deg, would it have to be full 180 to count?
Correct. If the line entering the block and the line leaving it were parallel and vertical, the advantage would be the use of your weight as a hauler which in this case is irrelevant.
I’m not sure about all the terminology that you and @jviss have used (need to soak on all of this input!) but I visualize the line entering and exiting block 3 as vertical. The majority of the other lines in the system being horizontal other than the one passing over the sheave connected to the centreboard. The sailor would position themselves above block 3 and either pull or ease the line. That’s what drove me to the idea that maybe it added to the MA.
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John, your logic is superb, but I believe either you or I is suffering from ignoratio elenchi.
One of us is proving the wrong arguement. Why don't you think the point is to find the mechanical advantage to the force on line 1? Block 8 is fixed and not in question. Or am I reading your posts completely wrong?
-Will (Dragonfly)
One of us is proving the wrong arguement. Why don't you think the point is to find the mechanical advantage to the force on line 1? Block 8 is fixed and not in question. Or am I reading your posts completely wrong?
-Will (Dragonfly)
@Johnb, I like posts that show thought, analysis, measurements, and quests for further understanding. I also like posts that have spunk - particularly in the face of insurmountable odds.
I really like posts that say MA= 16 a lot, because it is correct. But, I like posts that are in that range that show the qualities above. I like the fact that the origination post included a tension measurement which totally knocks the MA analysis on its ear. Nobody's life is in danger over this discussion, and the analyses are getting better by the minute. Even sketches! This is great.