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Old 04-28-2013
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Re: Forces on a dockline while docking....

1. This is more about energy absorption than strength. While you could plan on easing the line and do this with steel cable, I think you want to build a passive system. I'm betting he slipped some line, though.

2. What is the maximum load you want on the cleats and line? I don't know your boat.

3. The length of the rope matters. Ropes will absorb X energy/ft.

4. Speed. Convert to feet/second.

4. The energy of the boat is about 1/2(M/32)V^2. Pounds and ft/s. At 5 ft/s this is about 12,000 ft-pounds. at 5 knots this is more like 35,000 ft-pounds.

5. The below is the maximum for GOOD nylon rope to survive a dozen times (empirical testing). You'll need larger. The risk of too large is that the forces go up fast. Knots and sharp turns reduce strength.

7/16"---300ft-pounds/ft. Peak load about 2000 pounds.
1/2"---400. Peak load about 2700 pounds.
3/4"---900. Peak load about 6000 pounds.

Assuming 30 feet of rope, 1/2" line will do it at 5ft-sec, but 3/4" rope will be needed at 5 knots. A conservative sizing would be 1" inch and peak loads would be over 8000 pounds! A big range of answers. If anything breaks someone gets hurt. I wouldn't dare this above 3 knots, and you shouldn't need to. In that case, ordinary dock lines are about right, if they are in new condition.

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Unless fusion or fission are involved, that is E=1/2 MV^2.
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