Mainsheet system: advantage
Why use mainsheet systems described as 5:1, 7:1, or 9:1 rather than 4:1, 6:1 or 8:1?
These systems are quite common (see attached picture as example).
However, since it is only the blocks on the object which is moved (i.e. the boom) which contributes to increasing the mechanical advantage, these systems are actually 4:1, 6:1 and 8:1, respectively.
All systems which terminate the fixed end of the sheet line on the boom necessitates an extra length of rope and a block, without increasing the mechanical advantage. Hence, even if the sheet line must be pulled 5 inches for each inch movement of the boom (5:1), the mechanical advantage is 4:1.
Please correct if I am wrong!
I assume that the boom must be considered the moved object and the block on the traveller the fixed point (I know the theory of relativity, however in the moderate speeds obtained in sailing, I assume Newtonian mechanics and empirical measurements may be trusted).
Stein
I'm afraid you are incorrect. Each fall of line contributes to the overall mechanical advantage of the system regardless of whether it terminates on the
fixed
or the
moving
end (in fact, the two are moving relative to one another, so they are both moving). But regardless, a simple test: flip your blocks upside-down. You will find that you get exactly the same purcahse with the blocks in either orientation.
sm
Those blocks listed as 8:1 are 8:1. Do a load diagram...if you pull 8 inches and get 1 inch of movement than it is absolutely 8:1 - no way around it.
In hindsight, I put these block load arrows pointing the wrong way for a static diagram - but I think you get the point.
Just wait until you try to sort out a cascading system.
You must both be right; your explantions seem highly plausible. It must be correct that advantage depends on ratio of (rope length pulled):(distance moving of boom).
My simple living-room experiment must be inaccuarate. And the general rule that only blocks on the object moved contribute to advantage, must be incorrect.
Thank you!
Stein
PS: I stick with my 10:1 setup for my Taipan 5.7, though.
Yeah - I think you are getting conturbulated thinking that the kinetic system (moving) is different than the static. All loads must be equal. To quicly determine the purchase of a (non-cascading) system, you can count the running lines between the two stationary points. 2 lines is 2:1, 3 lines is 3:1, 4....and so on.
If you have a cascading system, you separate the two systems and multiply them against each other. A lower block setup with 4 runs at 4:1 that attaches to a cascading system with 2 runs at 2:1 is a total of 8:1 purchase.
I think is was Rolf that posted this as a Tornado setup. Why, you ask? Small diameter lines through the blocks, I'd guess. No taper needed. Maybe less total weight by using small blocks? Hidden mechanisms keeps the rookies staring? Easy to hide an illegal 10 or 12 setup? <img src=
alt=
/>
But this one has another line contributing to total boom movement...the black line on the extreme left. So won't is be 8:1 + 1:1 = 9:1?
It looks like the black is a cascade doubler and the red on the left is 4:1.
The red-right is ineffective, turning only.
I've been wanting to setup this exact system on my T...but I have not zero'd in on a double-block that is slim enough to fit into the Marstrom boom section. Plus, I have an outhaul system running inside already (that I quite like & use), so it would need to be removed/replaced with some other setup.
Right now I run a traditional 57mm harken carbomatic triple lower unit up to two carbo doubles (one with becket) hanging off the boom with spectra. I also put a 40mm single on the lower unit & run the tail back to the upper double's becket. Gives 9:1. Works pretty good.
The advantages are:
1. much lighter overall (blocks & 3mm vectran line)
2. Excellent easing (cascades are generally lower friction)
3. Lower cost can be achieved since blocks are small & cheap compared to 57 mm Harken Quads etc. (though I've seen several version of this running custom made blocks with carbon side plates...$$$)
Some disadvantages are:
1. can be a headache to work out
2. Can jam up inside boom if not setup right
3. Maintainance more difficult
Lots of top T guys run this setup, but it is not required to get to the top of fleet...Charlie Ogletree & Johonny Lovell run standard harken quads <img src=
alt=
/>



For anyone who doubts: 1 lb of tension on the sheet (black line) leads to 2lbs of tension on the red lines, which is obviously 9lbs of tension between the boom and main traveller, or 9:1.
Yes, and there are 4 red lines in the moving part of the system. (up and down from the boom to the back beam (well the wire to the back beam)
8:1
You have a 2:1 on the Black line system, the black line system is then pulling on a 4:1; 2:1:4:1 = 8:1

I've had another look at this and think thus
Red system is a 4:1.
The black system is a 3:1 as the both blocks (2 and 3) on the boom are (in effect) moving in relation to the back beam.
As you pull the mainsheet in, the first block on the boom(2) is also moving down, as is the big block inside the boom(3), so the black system is a 3:1, making the total system a 12:1.
I cannot see how it can be a 9:1 as the internal cascade is 4:1 and so any multiplier must result in an even number unless there is just a
routing
block, which there are none as all the
big/black
blocks are moving except the back beam block.
Okay, let me explain how it works.
But first lets derive the tension in each line because we'll need that later.
Black line is held in hand and so all the black lines are under 1 unit tension; the pull of the skipper.
The red line is attached to the black line by an 1:2 purchase system so the tension in the red line is 2 units.
It is impossible for any line to have different tensions at different points. Think about this.
When a line makes a full 180 wrap around a block then it pulls 2 times the line tension downward, that is obvious. If a line makes a 90 wrap then the block is pulled down by 1 times the line tension. A termination point equal 1 times the line tension downward. All still pretty straight forward.
Now lets count the loads when looking only at the boom blocks, the others are unimportant.
Black line : about 1 partial wrap so roughly 1 unit down pull and nothing else
red line : 1 full wrap, 1 partial wrap and a termination point ; total = 4 times the line tension of 2 units = 8 units of downward pull
Add them all up and you get (by approximation) 9 units of downward pull for each single unit of pull by the skipper, ergo it is a 1:9 system.
And this is one of the few ways to do it right.
Wouter
Wouter,
You can't keep writing purchases a 1:x unless you are talking about an inverse purchase system. The standard nomenclature has the advantage shown FIRST.
8:1, 4:1, 6:1, 12:1 etc.
by writing 1:9 you are in effect saying that for every 1lb of effort applied at the load you need to apply 9lbs - usually bloody hard work!!!
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