I do thinks that's the point. Thats the line being pulled down, rightmost, in my diagram. Pulley 3 doesn't enter into it, doesn't contribute to MA.
Thank you!
jv
Mechanical Advantage - MA
- Thread starter Hunter216
- Start date
jv
Oops, sorry. My spell check changed Johnb to John and I didn't catch it.
-Will (Dragonfly)
So I’m going to attempt a Huck Finn and try to get someone who’s brighter than I am to answer this question:
Assume the centreboard is all the way down, how much line would need to be pulled out of the “system” at diagram point 1 to move the tie off point of block 5 to the left 1 foot?
Assume the centreboard is all the way down, how much line would need to be pulled out of the “system” at diagram point 1 to move the tie off point of block 5 to the left 1 foot?
To move block 5 to the left one foot, block 7 needs to move two feet.
To move block 7 two feet, the 8:1 pull on line 1 needs to be sixteen feet. Every time a foot is pulled out of line 1, each of the 8 segments going around the sheaves of block 7 gives up an equal portion of that foot or 1/4 foot per sheave. That means, the last or lowest sheaves gives up 1/4 of a foot that passes through, at the same time, the other three sheaves. The next sheave also gives up 1/4 of a foot, so 1/2 of a foot passes through it. It's own 1/4 foot plus the 1/4 foot pulled from the lowest sheave. In turn, the next sheave would see 3/4 of a foot pass through while the last, top sheave gives up the whole foot. This would only move the block 1/8th of a foot and block 5 1/16th of a foot. So 16 feet need to be pulled out of the system to move block 5 one foot.
-Will (Dragonfly)
16 feet, but that's true regardless of where the board is. The block arrangement in the diagram will always provide that 16:1 advantage.
Yes there was some difference between pulling the board up & holding it in place, due to friction. The difference was probably about 15#.
You can look up mechanical advantage of a block & tackle in a large number of places, including wikipedia, so I'm not going to give a lecture on that subject.
In the case of a pivoting centerboard, as the board rises, the angle of force relative to the angle of resistance (gravity) changes as the board moves, and some lever arm lengths change too, so the force required on the centerboard line will change with board position. Therefore a vector equation will need to be added into the calculations if you want an accurate number. I just finished up lobster mini-season & I'm a little beat right now, so I'm really not in the mood to post all the inane details of that trivial calculation at this time. Sorry about that. Maybe someone else can exercise there google-foo & come up with those details.
I'm not going to go out to the 212 to double check the rigging right now, but the diagram that was posted earlier looks about right.
Bottom line is still that if you can't lift 65#, you're not going to have much luck pulling up the board on my 212, unless you employ a trick or two.
That is an awesome detailed description of how the line moves through the system!
This was a lame attempt at teasing - humour on my part that has me looking like a total DA. Sorry!
I mentioned above that I was thinking of MacGivering a replacement for the Sailtec hydraulic ram used on the Hunter 216 as it is only a matter of time before it fails. Min $800 to send away to rebuild or $2000 to buy a new one. I think I will pay a visit to our local marine store to pick up some blocks to tinker with. I’m pretty sure I would spend less and assuming I can work out any kinks I would end up with a system that I can maintain myself. The board on the 216 is about 500lbs and there are no winches so it will be interesting to see if will work out.
The CB raising and lowering system on my Mariner is quite a bit simpler that yours, never the less, I've been thinking about replacing it with a worm screw crank. No cable dragging in the water, easily adjustable to any angle and depth, locking so it doesn't collapse in a knock down.
-Will (Dragonfly)
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.
Reading through all this has been both interesting and entertaining. As a retired Mechanical Engineer I think I can add a little insight. Jviss, your conclusion is correct for your diagram, however your diagram is upside-down. It should look more like the following:
It may be counter-intuitive but jimb is correct. MA = 17:1
But your picture doesn't match the original diagram. In your picture the input tension is pulling against W. In the original diagram the input tension goes through block 8 to change its direction (with no mechanical advantage), before going on the first leg to block 7. That difference is giving you an extra T that doesn't exist in the original.
That's a good point. I think that the confusion comes in in determining which is the moving part, #4, or #6. It's not clear from the original drawing. If #4 is the moving part than Jviss is correct. If #6 is the moving part than jimb is correct.
Agree. The way I read the diagram #4 is where the output line goes to the board, and everything to the left of that is attached to the hull.