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What produces the most power on the same fully loaded winch :-
1. More turns but thinner rope.
or
2. Thicker rope with less turns ?
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Do you mean which gives the most grip? If so I find that self-tailing winches always grip with no slippage whereas without self-tailing the grip depends upon the tension applied to the tail of the line and this variability will mask any difference due to number of turns etc. I use three turns on self-tailers.
In a 'line tension vs applied force on handle' test, thin rope wins. Better leverage. Frictional losses within rope/drum probably self-cancel.
Edit: Only applies to the line tension. If you were going to put the line around another drum with the intention of getting power from that drum, it wouldn't make any difference. Just thought I'd clear that up before I was tripped.
The number of turns has no mechanical effect on the power as they are all on the same drum. No multiplication of effort. Perhaps there may be a difference in grip. But probably as much decided by the type of rope and friction between coils as on the drum surface.
However, it's easier to pull a thicker rope, so particularly for a non-self-tailing rope, you'll do better with a thicker one, and it's less likely to slip if you put more turns on.
There is no difference in mechanical advantage but the thicker ropoe ie easier to grip and handle when notapplying load without winch handles and just pulling.
More turns, ie: a full drum, create less wear on the rope as each turn is sliding up the drum less per rotation. Only really relevant on self tailers.
As to power, there is, as already said, no difference.
I'm afraid that I disagree. Increasing the rope diameter is also increasing the effective diameter of the drum, which decreases the mechanical advantage.
My choice would be based on what sort of sailing you're doing.
If you're cruising, go for thick and comfy.
Racing, it's thin and mandatory gloves.
On sheets, guys etc. thick wins for gloveless comfort. But even when cruising, the low friction aspect of the Dyneema type stuff makes life incredibly easy, gloves notwithstanding.