Swinging circle

[PhilipStapleton]

Any mathematicians out there?

When at anchor, how much does the radius of the swinging circle change as the tide falls/rises?

I went cross-channel to Alderney a week or so ago but it was absolutely full when I got there - all the moorings taken and boats everywhere. It was high water springs and it was hard to find anywhere to drop the hook to avoid the resident's moorings that now extend all the way across to the east of the harbour. I gave up when even 60m of chain failed to take on the rock/kelp combo. If I had succeeded, what would have happened to my swinging circle as the water fell from 13m to 3.4m?

Fortunately the timing was right for a pleasant night-motor to Jersey, and we got there just after the gate had opened ready for a nice long sleep!

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[duncan]

all depends on the winda and current - if neither significant you could have remained static over an increasingly high pile of chain!
In a similar vein it is common to go one way with the wind/current as you lay the anchor but only a short way back as you are held on the chain! Especially on a rocky bottom.

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[Paul_H]

Assuming your chain is impossibly straight then simple pythagorarse gives a rough answer. Horizontal radius from anchor point equals square root of ((chain length squared) + (depth squared)). This not surprisingly gives a worst case radius at zero depth equal to the chain length but by then your more worried about the crockery. Anyhow, with 4-5x scope and 3x change in depth there is very little difference in radius to warrant the calculation. True the catenary will reduce the radius a little but safer to look at worst case.

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[Paul_H]

oops should be Horizontal radius from anchor point equals square root of ((chain length squared) - (depth squared))

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[Roberto]

have you thought about that all night ?!

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[Paul_H]

couldnt sleep for the shame of it.

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[Spacewaist]

Very Interesting

This is a very interesting result. A yacht needs materially the same swinging room at high water as it does at low water.

Even in a more extreme example of a yacht lying to a 60 metre rode, with a high water depth of 13 metres and a range of 10 metres, on this basis there is less than 1.5 metres difference in the 58 metre swing radius between high and low water.

Hmmmmm... not an answer I would have guessed at; (neither is the 58!).



<hr width=100% size=1>A pontification from the Panjandrum of orotund bloviation AD2003

 

[PhilipStapleton]

Re: Very Interesting

I can confirm Paul-H's formula - I found it on the web so it must be right
However, it really doesn't seem logical (or fit with experience) that the linear distance from bow to anchor with a rode of 15m in 5m of water is 14.14 (a mere .8m shorter than the rode) and 14.69m at 3m of tide - an increase in swinging distance of only half a metre.

I definitely fall back from the anchor and get then nearer to other boats as the tide goes down!

I'll take a tape measure with me next time I'm in Newtown Creek!

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[Mirelle]

There are two other factors here...

The formula (and I was surprised, too, but I don't doubt it) must be right.

However, a yacht lying to chain will tend to lie to the pile of chain and a more or less vertical line from fairlead to chain, thereby shortening her swinging circle unless tide and wind are strong enough to stretch it out, and in 3 metres most of the chain will have laid itself out in a line (of unknown, but possibly interesting shape!) on the bottom.

Much more significant, if any of the boats in the vicinity are lying to moorings of the usual type with a ground chain between two anchors and a riser not much longer than the depth at HWS, the swinging circle of the moored boat is tiny at HW and significantly larger at LW.

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[vyv_cox]

For a moment I thought that Monty the Mountie had reappeared. His posts on "Swinging Circles" had little to do with anchoring and it didn't take a mathematician to work out what he had in mind!

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[peterb]

Re: Very Interesting

The formula assumes that there is so much load on the cable that it is virtually straight, an extreme condition. However, a much more likely situation is either a pile of chain as Mirelle suggests, or a line mostly along the bottom with a short, almost vertical, riser. As the tide rises or falls the riser length changes, and the difference is taken up by the bottom length. The result will be a swinging circle that changes with the tide; each extra metre of tide will give a metre less on the swinging circle.

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[Paul_H]

Re: Very Interesting

As you rightly say, the radius will vary metre for metre according to the depth in gentle wind/tide condtions cos it hangs down from the bow and then runs flat on the bottom (radius = chain length - depth). However in worst case conditions the radius will be approx the chain length especially if youve extended the scope to 5x depth. The point was to determine the safe separation in crowded anchorage and its easy to assume radius = chain length to be on the safe side. The main problem is determining what the other b****rs are doing. You lay 3x and hes laid 5x, youve got a long keel he's lifted his the winds shifting and the tides turned.....

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