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Old 11-03-2019, 09:21   #1
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Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight Chain

We've all read, I guess, Peter Smith's article about the limits of the effect of catenary, on anchoring: Scope vs catenary (Rocna Knowledge Base)


The idea is that at some point the chain gets "bar tight" and catenary ceases to improve the angle of pull on the anchor. This idea was taken up enthusiastically by the great cruising guru Steve Dashew, who argues that since catenary will come out anyway, we might as well use lighter, higher grade chain.


This idea has always bothered me. It more or less corresponds to my experience with shallow water and light chain, but not at all to my personal experience in deep water with heavy chain. And ships don't use snubbers -- indicating that catenary must always be working, even in extreme conditions, at that scale.


As I thought about this, I realized that you can't generalize these statements for all scales in terms of depth, length of chain, and weight of chain. At some point, you can't pull all the sag out of a piece of chain, or even most of it, without exceeding the breaking force of the chain. Just like you can't even hang a piece of chain with no load on it, of unlimited length -- at a certain point it can't support its own weight.



I've been trying to calculate the sag of a 100m piece of 12mm chain, weighing 3.3kg/m or 330kg, at the chain's breaking strength, or 8480 kgf, stretched between two points 30 meters different in height, and the resulting angle of the chain at the lower point.

Is it "bar tight" at the limit of its breaking strength, or is it still sagging, and therefore creating effective catenary effect? That is the $64 question, so to speak.

Unfortunately I have not been able to find a calculator for this, and I get a little lost in the formulae. If someone with better engineering chops than me, and likewise curious about this question, would like to help me out with this, I would be most grateful.


If my hunch about this is right, there is still useful catenary -- that is, useful reduction of the angle of pull on the anchor chain, even at the limit of strength of the chain, which busts the myth that chain always gets "bar tight" at some point, and catenary ceases to play a role in anchor performance, in every case.



Besides angle of pull on the anchor, the sag in the chain influences the effective elasticity of the rode and its ability to continue to absorb energy. When there is almost no sag, then the chain behaves like bar and won't absorb energy anymore -- you need a snubber. But if there is still a certain amount of sag, then the curve of increasing force is gentler, and the rode is still absorbing force. I suspect and guess that 100 meters of 12mm chain will still be sagging enough at its breaking force, to effectively absorb energy, whereas that would not be true of shorter and/or lighter pieces of chain.


To show the idea using reductio ad absurdum (which is not a proof that I'm right) -- imagine a 1000m piece of 12mm chain. This weighs 3.3 tonnes so such a piece of chain can still support its own weight. The catenary will have huge energy absorption ability -- given enough depth for the catenary to work. Even at its breaking strength, most of the sag will be there so great decrease of the angle of pull on the angle, and great amount of energy absorbing ability. There is clearly no "bar tight" effect, with such a piece of chain. This is actually a proof, that the "bar tight effect" does not exist in every case -- that it has certain limits somewhere.


The question is, where are those limits? Where does the "bar tight effect" give way to the "1km long chain effect", for what size chain? That I can only guess at, based on observations of my own rode. I'm guessing that 100m of 12mm chain already has a lot of the "1km long chain effect" and little of the "bar tight effect", but the numbers won't lie, when we have them!
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Old 11-03-2019, 09:36   #2
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

Dockhead, another consideration about a long, heavy chain's catenary is that not only must the chains WIEGHT be overcome, but also it's INERTIA and DRAG through the water as the forces (wind gusts and waves) cycle. Both of these improve the chain's energy absorbing ability.

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Old 11-03-2019, 09:44   #3
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

This is the curve calculated by Peter Smith, for 48 meters of 12mm chain, under 2 tonnes of force (about 50 knots of wind on a certain size boat) and in only 8 meters of water:


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That's the "bar tight effect", which I think clearly exists under these conditions.



But what does this curve look like with 100 meters of chain and 30 meters of depth? The sag goes up with the square of the length of the cable, all other things being equal, so length changes a lot.
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Old 11-03-2019, 09:48   #4
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

Quote:
Originally Posted by Panope View Post
Dockhead, another consideration about a long, heavy chain's catenary is that not only must the chains WIEGHT be overcome, but also it's INERTIA and DRAG through the water as the forces (wind gusts and waves) cycle. Both of these improve the chain's energy absorbing ability.

Steve

Thank you! Brilliant comment


Unfortunately, adds a whole nother layer of complexity to the problem.


Also raises an interesting question -- whether it would make sense to interpose your Jordan Series Drogue into your anchor rode, in case you have enough room to have such a long rode, for anchoring in really extreme storms. Possibly a very good idea.
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Old 11-03-2019, 09:53   #5
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

I doubt an anchor chain can ever be pulled completely straight, just as a rope attached to the top of two poles can never be pulled tight enough to remove all slack.
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Old 11-03-2019, 09:56   #6
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

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I doubt an anchor chain can ever be pulled completely straight, just as a rope attached to the top of two poles can never be pulled tight enough to remove all slack.

That's definitely true. But lighter and shorter pieces of chain, can be pulled straight ENOUGH, that they don't significantly improve the angle on the anchor and don't absorb any significant amount of energy. At a certain point, enough of the curve has been pulled out that the chain behaves much like a bar. The question is when is a chain long and heavy enough, that this doesn't happen any more. I honestly don't know the answer to the question, and will have to either make more progress figuring out the formulae, or get some help from a proper engineer.
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Old 11-03-2019, 10:02   #7
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

It happens where the pull on the chain exceeds the weight of the chain to point of reducing the anchor pull angle to less than what anchor is designed for.

If you knew that angle you could calculate the pull for a given weight/size of chain with known length and water depth.
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Old 11-03-2019, 10:05   #8
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

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Originally Posted by sailorboy1 View Post
It happens where the pull on the chain exceeds the weight of the chain to point of reducing the anchor pull angle to less than what anchor is designed for.

If you knew that angle you could calculate the pull for a given weight/size of chain with known length and water depth.

Indeed, and that is a very complex calculation. As the chain gets longer and/or heavier, the point at which catenary no longer becomes effective, comes later. Eventually, even a force equal to the breaking strength of the chain is not enough to pull out the catenary. That is the whole point.
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Old 11-03-2019, 10:14   #9
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

a. Ships are different, because they are barely affected by gusts or chop. Primarily just the steady load.


b. Drag through the water is trivial and can be effectively neglected. I've done the math. Look at the actual speed (1-2 knots) and this is obvious. A red herring.



c. At 30 knots or so the chain lifts off the bottom, depending on scope, chain weight and water depth. In shallow water it happens early, in deep water, hardly at all. Another way to think about this is that it is not so much the scope, as the to total amount of chain out; once you reach 250+, it's a lot more weight and better leverage.


d. Then both the angle AND the amount of energy absorbed declines, gradually, until at 40-55 knots (again, depends on the depth and scope, so don't try to pin me down) the angle at the bottom is between that off 100% rope and flat, and the energy dissipation is effectively zero. Though not straight, the difference between straight and the curve you have is only inches.


The math is complex, particularly when you consider the dynamic effects. I've measured and I've dived when it was blowing. The true is in the middle and hard to nail down. But something the math will quickly show you is that with G70 chain you can fit twice as much in the locker, and that will ALWAYS hold better. I think that is unarguable.


There is a common area, with medium depth water and moderate weather, where heavy chain allows less scope and might be helpful. Thus the popularity of heavy chain; it is a good answer in 25-30 knots, in 15 feet of water, in a crowded anchorage. In 60 knots and enough room, not so much.


The breaking strength argument is off the point for three reasons:
*The rode better not operate above the WLL, or it won't last long.
*No, it does not take nearly that much force for the difference to become academic.

* Using a proper snubber you should be several times below the WLL. If not, the anchor will drag.


I suggest you take a length of chain and a come-along (chain hoist), and stretch a chain between two trees. Do you really believe it takes 4 tons to get the chain pretty straight? I don't think you believe that, but try it. You will also learn the stretching that last bit is so hard there is not shock absorption; tje stretch/stress relationship is not linear, like rope.



Seriously, stretch a chain at the boatyard. You will find it enlightening.
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Old 11-03-2019, 10:17   #10
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

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I doubt an anchor chain can ever be pulled completely straight, just as a rope attached to the top of two poles can never be pulled tight enough to remove all slack.
I have to agree. What appears to be 'bar tight from the pulpit (or snubber) down the first 'n' distance appears to be so. I suspect that if you dove on the chain leading up to the anchor is still laying on the seabed.

I dove on a nylon rode with only 30 feet of chain. The line near the waters surface felt you could tight-rope walk, while 20 of the 30 feet of chain was still laying on the seabed.
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Old 11-03-2019, 10:34   #11
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

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.............b. Drag through the water is trivial and can be effectively neglected. I've done the math. Look at the actual speed (1-2 knots) and this is obvious. A red herring.
...........
Thinwater, when I mentioned DRAG upthread, I was speaking about the chain's VERTICAL motion as the chains catenary changes.

Please clarify if your speed of "1-2 knots" is pertaining to this or something else (boat speed?).

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Old 11-03-2019, 10:38   #12
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

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Thinwater, when I mentioned DRAG upthread, I was speaking about the chain's VERTICAL motion as the chains catenary changes.

Please clarify if your speed of "1-2 knots" is pertaining to this or something else (boat speed?).

Steve

I understood you. Measure it. It's typically not fast. 2 knots is 3.4 ft/s. Yes, it is a factor, but far less than other factors unless the boat is truly unruly. that is all I meant.
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Old 11-03-2019, 11:00   #13
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

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I understood you. Measure it. It's typically not fast. 2 knots is 3.4 ft/s. Yes, it is a factor, but far less than other factors unless the boat is truly unruly. that is all I meant.
Ok. Got it.

Perhaps the slow speed is DUE (significantly) to the drag?

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Old 11-03-2019, 11:15   #14
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Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight Chain

Given that most of us have a limited amount of weight that we can carry in the bows Iím a proponent of putting the weight in that anchor and, with high test chain, carrying more than I could with heavier chain.

Catenary is effective in moderate conditions, not so much when itís really howling. And as Thinwater points out, the important factors are angle of attack and shock absorption to keep the anchor from breaking out, not the actual strength of the chain.

Big anchor, more rode, use a snubber. And not some 6í toy to protect your windlass...a proper long stretchy snubber of 30í or more.
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Old 11-03-2019, 11:46   #15
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Re: Possibly Original Thought About Chain Catenary - or - The Myth of the Bar Tight C

Quote:
I've been trying to calculate the sag of a 100m piece of 12mm chain, weighing 3.3kg/m or 330kg, at the chain's breaking strength, or 8480 kgf, stretched between two points 30 meters different in height, and the resulting angle of the chain at the lower point.
my days of solving this kind of maths analytically are over ... but it's fairly easy to produce a numerical approximation.

The catenary curve for chain of 3.3 Kg/m and 8480Kgf horizontal tension will always look the same no matter how deep the water, we just have to find on which part of the curve your scenario of 100m of chain in 30m depth sits.

I plotted the catenary every m using the formula y=(exp(ax)+exp(-ax))/2a where a=density/tension = 3.3/8480. ... Then looked for the point 100m further up the chain and checked to see where it was 30m higher ... then found the angle at the anchor at this point.

The biggest approximation is that I used a horizontal force of the chains breaking strength, not the force along the chain, but I don't think it makes much difference at this extreme pull.

If my calculation is correct (no guarantees) then the answer to your question is that the chain will be 99.995% straight and pulling at an angle of 16.3 degrees on the anchor.


so it's not pulling horizontally, and it doesn't have much snub to give.
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