MathiasW
Well-Known Member
It is a very conservative rule, but independent of wind strength...
Effectiveness of anchor chain weight versus, length!
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pawl
Well-Known Member
I'm quite prepared to accept that I'm as thick as a brick, but I cant see how this formula would work using "feet". Further, I don't think that the RYA would issue guidance only suitable for deep water when their whole purpose is to promote leisure sailing. If you used feet then anchoring in 6 metres of water you would only put out about 16m of chain? Using metres I would put out about 30m which to my mind is about right. In any case this is what I was taught when I learned to sail, of course this is only a guide and it is up to the skipper to adjust it to suit the circumstances in each case. I think the important point is that if you are using rope then you need a lot more of it.Yes, I am (trying to, given Corona) sail around the worldSo that is for me real life...
This British Admiralty rule is, in fact, a conservative approximation to the standard catenary result that jdc was also referring to. It holds for deep water and really is VERY conservative for most cases. It will get at its limits in shallow water with a lot of swell and wind.
And beware! Your factor 12 is only correct when you use feet! It is a different, smaller factor when you use metres. The British Admiralty rule states L = 1.5 √Y, where Y is measured in metres and chain length L in shackles (90 ft).
TernVI
Well-Known Member
I'm fairly sure that back when I did YM theory, which was a long time ago, the RYA guidance was 3x the depth for chain and 5x for rope. Maybe we didn't expect miracles from small anchors in gales in those days?
In sensible conditions you can imagine extending the curve of your chain upwards at the angle it meets the bow. Maybe closer to vertical than 45 degrees?
So some kind of 1pointsomething x depth plus n metres formula is justifiable.
I have kedged in very deep water using less than 2x rope plus a little bit of chain.
People who fish around wrecks often use quite short rodes in deep water.
In sensible conditions you can imagine extending the curve of your chain upwards at the angle it meets the bow. Maybe closer to vertical than 45 degrees?
So some kind of 1pointsomething x depth plus n metres formula is justifiable.
I have kedged in very deep water using less than 2x rope plus a little bit of chain.
People who fish around wrecks often use quite short rodes in deep water.
scruff
Well-Known Member
I've just graphed the 14 x the square root of the depth of water.
As someone who has always used 5:1 the end results look fairly reasonable of the above graph. Note the minor grid lines relate to M of chain and not the ratio.
Makes sense that you can lower the ratio as you lay out more chain.
MathiasW
Well-Known Member
Sorry, as corrected in a later post, my memory had not served me well in this point.
The square root approximation to the catenary equation - and hence the guidance by RYA - is for shallow water and / or strong wind. And of course it works for feet as well as metres, or any other metrics you choose. You just need to adjust the factor in front of the square root.
If you have for units of metres
L_m = A_m * square_root(Y_m)
where L_m is the chain length in metres, Y_M the anchor depth in metres, and A_m the coefficient,
then you have for units of feet (with L_f, Y_f, A_f)
L_f = A_m/0.305 * square_root(Y_f*0.305) = A_m/square_root(0.305) * square_root(Y_f) = A_f * square_root(Y_f)
and thus A_f = A_m/square_root(0.305)
And yes, of course, rope requires much more length than chain does.
MathiasW
Well-Known Member
The 3 x depth rule for chain is also taught in Germany, but isn't it odd that it does not account for wind strength, nor windage area of the vessel, nor any other parameter other than water depth for that matter? This rule is either too conservative, or it is true just for one singular case.
Analysis shows it is not too conservative! The British Admiralty rule with the square root normally is too conservative for all but the most extreme situations, but any scope approach, be it 3:1 or 5:1 or 7:1 can be either too conservative in a given situation, or still not enough. You just do not know and you try to work around that by adjusting this scope rule to circumstances as your experience or gut feeling sees fit.
That was my starting point for the entire analysis, actually. I am not happy when I do not know what margins I still have in my anchor setup. And I may be in a situation where I cannot pay out as much chain as I like, and then I would want to know whether it is still acceptable or I need to find another place.
The model and theory is all laid out here, Catenary Anchor Chain Length - Die Kettenkurve - Fun Facts - SAN, but it has become quite a long essay by now and may be too much to read.
What helped my understanding a lot was the study of the elasticity of the chain. With that I mean how much additional potential energy E_pot can I absorb in the chain when pulling a bit harder at the bow in horizontal direction (and thereby lifting the chain a little more), whilst still maintaining that the chain pulls horizontally at the anchor. So, it is something like d E_pot / d F, where F is the horizontal force. See the plot below, which is the elasticity as a function of scope, so the ratio of chain length to water depth.
It turns out this elasticity is a universal function of the scope, with its absolute value scaling with the anchor depth Y. For convenience, I have normalised everything to 100% of the peak, where the chain works best.
What you can see from this is that there is an optimal scope for each anchor depth, at about 1.4:1, where the chain's elasticity is highest. Of course, this does not mean that I should pay out only 1.4 of the water depth and be good, no matter what. In this plot there is always the implicit assumption that the chain pulls horizontally at the chain. Such a small scope of 1.4:1 can only be achieved in very, very deep water, where for the longest part the catenary curve just rises steeply towards the water surface.
Now, at any given water depth, I need to pay out a certain scope to satisfy the condition of a horizontal pull at the anchor. Say, this gives me a scope of 6:1. With this I go into the graph above and it tells me that the chain's elasticity is only about 30% of what it could have been at optimal usage. Optimal usage would mean going to deeper water and using more chain, which may not be realistic, but still, this graph tells me when the chain can work well to absorb shock loads, and when it cannot.
If you are in very shallow water, you need to have a very large scope, as others have already noticed here, to maintain a horizontal pull at the anchor. So then you are essentially always on the 'storm' side in this graph, whether you like it or not. Chain is not working well at all in this case, and this is why snubbers are needed. Why is the chain not working well in shallow water? Well, it has almost no headroom anymore to get further lifted and thus store more potential energy, since both ends are fixed at almost the same height - at the anchor and at the bow.
This graph also explains why the fisher men are doing ok in deep water in storm. They have a lot of chain / rope and thus can anchor in rather deep water, which gets them closer to the optimum in this graph. I know of others who have anchored in Greenland in a severe storm in rather deep water with a scope of 2.5:1 only. So, the deep water approach is a valid one to ride a storm.
Again, all this is built into my app
: Anchor Chain Calculator - SANCheers, Mathias
pawl
Well-Known Member
Unless I misunderstood your previous post you were suggesting that the formula of 12 times the square root of the depth of water would only work using "feet" as the measurement. This seems to me to be wrong, the formula works perfectly well in metres.Sorry, as corrected in a later post, my memory had not served me well in this point.
And of course it works for feet as well as metres, or any other metrics you choose. You just need to adjust the factor in front of the square root.
If you have for units of metres
L_m = A_m * square_root(Y_m)
where L_m is the chain length in metres, Y_M the anchor depth in metres, and A_m the coefficient,
then you have for units of feet (with L_f, Y_f, A_f)
L_f = A_m/0.305 * square_root(Y_f*0.305) = A_m/square_root(0.305) * square_root(Y_f) = A_f * square_root(Y_f)
and thus A_f = A_m/square_root(0.305)
And yes, of course, rope requires much more length than chain does.
MathiasW
Well-Known Member
Sorry, based on the reference to RYA and your location I had assumed you were using feet, but that was obviously wrong...
I did not redo the maths and had taken the factor 12 for face value... Sorry about that
ip485
Well-Known Member
Anchor Buddy | Kiwi Anchor Rider
Genuinely useful in some circumstances and also cuts out a lot of the snatch whether or not you are using anything else to prevent snatch.
Genuinely useful in some circumstances and also cuts out a lot of the snatch whether or not you are using anything else to prevent snatch.
GHA
Well-Known Member
As long as the wind doesn't really get up, high forces on the chain with dynamic loads on top then , like catinary, it does very little to reduce the peak loads. The maths will be on a site somewhere.
Big long snubber is much more effective for that.
thinwater
Well-Known Member
a. What is the design wind strength? Here, a 60-knot summer squall is not uncommon. Achoring for 35 knots in the thunderstorm season is shortsighted.
b. Which anchor? Some can withstand considerable up lift once set, some cannot.
c. Is it well set? Many anchors will not set deeply at short scope. They will set, but at 3:1 scope will hold less than 50%.
d. Can it reset, under load, at very short scope? With chain, probably, but not to anything near full capacity.
e. What is the bottom? This affects up lift capacity? How long has the anchor been in place? This too affects uplift.
----
Simple rules are just that. Just anchored over a very soft bottom, thunder in the distance, and shallow water, I want a LOT of scope. It will take at least 12:1 to keep the chain on the bottom, and I need that, since holding capacity is crap. Firm sand, settled weather overnight, and a light power set, I'm happy with short scope. I've anchored with as little as 30 feet out, more than three times less than the first example in the same depth. The required holding capacity is 16 times less and the bottom is 6-8 times better, resulting in 100 times the safety factor. Apples to hand grenades. Not a worthwhile comparison.
b. Which anchor? Some can withstand considerable up lift once set, some cannot.
c. Is it well set? Many anchors will not set deeply at short scope. They will set, but at 3:1 scope will hold less than 50%.
d. Can it reset, under load, at very short scope? With chain, probably, but not to anything near full capacity.
e. What is the bottom? This affects up lift capacity? How long has the anchor been in place? This too affects uplift.
----
Simple rules are just that. Just anchored over a very soft bottom, thunder in the distance, and shallow water, I want a LOT of scope. It will take at least 12:1 to keep the chain on the bottom, and I need that, since holding capacity is crap. Firm sand, settled weather overnight, and a light power set, I'm happy with short scope. I've anchored with as little as 30 feet out, more than three times less than the first example in the same depth. The required holding capacity is 16 times less and the bottom is 6-8 times better, resulting in 100 times the safety factor. Apples to hand grenades. Not a worthwhile comparison.
thinwater
Well-Known Member
As for kellets, if you are using chain it is much easier and just as effective to deploy another 10-15 feet of chain. Do the math.
For rope they have legitimate uses (controlling swing and keel wraps). But I find using a loop of chain as a kellet much easier to handle.
For rope they have legitimate uses (controlling swing and keel wraps). But I find using a loop of chain as a kellet much easier to handle.
GHA
Well-Known Member
If looking just at the force to lift the last link off the sea bed then metres 14 x sqr(depth) seems pretty much bang on for 10mm chain with a 200Kgf horizontal load on the chain. At any depth.
Equal force scope
MathiasW
Well-Known Member
Indeed. A kellet can at most be equivalent to an amount of chain that has the same weight as the kellet. For this the kellet needs to be located close to the anchor, but off the seabed. So, for any kellet that you can reasonably handle weight-wise, it does not add much. It only saves a few metres of chain but introduces a substantial amount of additional hassle if you need to get going quickly.
A snubber, in particular in shallow water, if large enough - and Jonathan has written a lot about this - will be MUCH more effective, and easier to handle as well...
MathiasW
Well-Known Member
Bang on with what? I do not see the usage of the catenary equation in your plot. That would be the reference. If you compare it with the British Admiralty rule, then of course it is bang on for all depths, as both are square root functions...
GHA
Well-Known Member
The catinary equation and your equation are on top of each other., there are 3 plots on the graph. Zoom in you'll see them all.
MathiasW
Well-Known Member
Hmm, I see three curves, but none of them is the catenary equation, if I look at the equations to the left-hand side. The catenary equation would go something like
L = sqrt(Y*(Y+2*a))
where 'a' is a parameter that depends on chain weight, windage area, and wind force.
So, for Y << 2*a, you arrive at the square root dependency of the British Admiralty. But the general catenary curve is more complicated than that.
ip485
Well-Known Member
Yep, practically have to say used mine in a good surge and it was incredibly effective, but maybe risked the chain. I do have substantial tackle including a Rocna 55 Kg.
I do find a long snubber slightly easier to use however.
TernVI
Well-Known Member
The snubber can be 80% the length of the rode. I.e. use a bit of chain and the rest nylon.
Catenary is just a small part of it. In reality, the rode moves up and down and sideways in the water, moving a rope or chain through a viscous medium like water, it will not be straight and energy will be absorbed. Your maths and graphs are simplistic and mostly irrelevant.
MathiasW
Well-Known Member
TernVI, you are a busy man, aren't you - 1564 posts in just under 3 months...
Very well. It is in the nature of modelling that not all effects are accounted for. One aims for including relevant effects and ignores the rest. Another strategy is to look at the effect each component has, and then put it all together. That is simply the well accepted approach in science and engineering...
In any case, I should like to put forward that my model and maths is ever so slightly more accurate and less simplistic than the maths you were referring to:
And yes, my model is for all chain plus snubber, so clearly, the scenario you describe is not in its scope yet.
And yes, there are effects of additional means for absorbing energy as you describe. Those I welcome as an additional safety margin for my results, but I prefer to know the worst case, really. I can always take it from there and adjust.
As long as you do not get dragged into me at anchorage, we can still be good friends, can't we...
Cheers
Mathias
Very well. It is in the nature of modelling that not all effects are accounted for. One aims for including relevant effects and ignores the rest. Another strategy is to look at the effect each component has, and then put it all together. That is simply the well accepted approach in science and engineering...
In any case, I should like to put forward that my model and maths is ever so slightly more accurate and less simplistic than the maths you were referring to:
????? Hä, really ?????
And yes, my model is for all chain plus snubber, so clearly, the scenario you describe is not in its scope yet.
And yes, there are effects of additional means for absorbing energy as you describe. Those I welcome as an additional safety margin for my results, but I prefer to know the worst case, really. I can always take it from there and adjust.
As long as you do not get dragged into me at anchorage, we can still be good friends, can't we...
Cheers
Mathias
