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Old 01-06-2020, 17:19   #1
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Mathematic approach to anchoring scope

Great an anchoring thread - but this time with a difference.

A German mathematician(with way too much time on his hands) has turned his eye on trying to mathematically predict the best length of you rode when anchoring. Amongst other conclusions is that in deeper water, you need less rode than in shallow water and vice versa of course.

Now, I'm not a mathematician, but I can usually follow even complicated math arguments. I admit he's lost me.

So, calling all mathematicians - trying looking at his arguments and telling the rest of us if you agree or disagree or is he a guru over all gurus or does he live on another planet.

here's the link to his webpage (it is in english)

https://trimaran-san.de/die-kettenku...UCeN1GLuBsVN-U
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Old 01-06-2020, 17:42   #2
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Re: Mathematic approach to anchoring scope

I think you/we have to investigate the basic hypothesis more than the math that follows.

The hypothesis is that a)you need to maintain a horizontal pulling angle at the anchor shank, and b) that catenary absorbs dynamic loading.

If I understand the maths correctly I couldn't anchor in 2m of water with 80 knot winds at pretty much any scope - there is no room for catenary to develop. And yet I have done just that, on more than one occasion. But I also don't rely solely on catenary to absorb dynamic loads - I use a bridle with elastic stretch to help absorb such loads.

The fact that some/many vessels successfully deploy anchoring systems with little or no chain and rope rodes that are very close to neutral density or may even float also shows that catenary is not the only game in town.

The notes actually cover these items, but without the math:

Quote:
Finally, using a long thick anchor chain bridle which can absorb a good part of the energy — best assisted by additional good rubber springs — will go a long way to help keep the effects of dynamic anchoring in check. Good bridles of more than 10 metres can easily absorb 1000 J and more, allowing one to anchor in somewhat more shallow water again. Also for monohulls one should use as long as possible elastic snubber lines for the chain and add rubber springs or the like.
If we could add the math for all of that then we might have something to discuss. There is a link at the bottom of the page to Bjarne's calculator (SV Amanda) that does more work around other elastic components and calculates that point at which catenary disappears (and also how surprisingly much elasticity there is the chain itself).
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Old 01-06-2020, 17:47   #3
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Re: Mathematic approach to anchoring scope

He certainly is a nerd.
Shooting from the hip, though, I have found that I need less [I]scope[I] in deep water; the ratio of chain to depth is less than I need for shallow water. Still works out to more chain in deeper water, but scope is less. I've also noted that in a busy harbor with lots of wakes, being out in six fathoms is more comfortable than being anchored in two. The boat rides better when there's more weight of chain pulling down before it curves. I've often thought that the hook holds better if the water's deeper, which is what this guy seems to be saying.
As far as checking his math, I'm simply not mathy enough.
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Old 01-06-2020, 18:35   #4
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Re: Mathematic approach to anchoring scope

IMNSHO, he's on another planet. There's nothing wrong with the math, it's the iniital assumptions that are dubious.

He's spend an inordinate amount of time supposedly validating what experienced sailors know empirically
"The guidance of using a fixed scope like use 3 times or 5 times the water depth as length of chain, etc., is not adequate"
Any sailor with a bit of experience is well aware of that.

For a given vessel, required chain scope is dependent on two primary factors water depth and wind strength and every scope recommendation I've ever seen makes that clear.

He then proceeds with an invalid assumption that a horizontal pull at the anchor is a necessary requirement and spends waaay too much time deriving figures for all sorts of different situations based on that assumption.

As an aside, he also bases his calculations on "all chain with no snubber".

I especially liked the implication that a cruiser who anchors in different situations should carry multiple different chain rodes.

"If the swinging circle around the anchor is not an issue, it is better to use a thinner but longer chain, perhaps of higher quality. It allows to anchor in deeper water when comparing chains of same total weight. But in crowded anchorages with small tides and not too deep water a thicker and shorter chain may be more appropriate in order to have a reduced swinging circle."
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Old 01-06-2020, 18:47   #5
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Re: Mathematic approach to anchoring scope

Hi Dsanduril,

And here is the math nerd... Hi from lockdown in Panama!

Quote:
Originally Posted by Dsanduril View Post
I think you/we have to investigate the basic hypothesis more than the math that follows.

The hypothesis is that a)you need to maintain a horizontal pulling angle at the anchor shank, and b) that catenary absorbs dynamic loading.

If I understand the maths correctly I couldn't anchor in 2m of water with 80 knot winds at pretty much any scope - there is no room for catenary to develop. And yet I have done just that, on more than one occasion. But I also don't rely solely on catenary to absorb dynamic loads - I use a bridle with elastic stretch to help absorb such loads.
Yes, the two basic assumptions are correctly noted. Of course, a small angle when pulling at the anchor can be tolerated, but I prefer to keep this as my safety margin.

And yes, anchoring in very shallow water at 80 kn will be hard to achieve, if you have only a chain. But you had a bridle, and that makes all the difference in the world in this situation.

If it were pure chain, then this is what happens: The kinetic energy of the boat needs to get absorbed as additional potential energy of the chain. Now, how can the chain do that? It needs to get raised higher than it was before. But when you are anchoring at 2 metres, the chain is almost horizontal already, with both ends more or less fixed as far as their height over ground is concerned. So, really not much room for the chain to get lifted any higher. Consequently, it cannot absorb the kinetic energy of the boat, goes complete stiff and jerks the boat. Even a very long chain will not change this a lot.

One should always use snubbers or bridles, but in such a situation you'd be lost without them. So, it was the snubber/bridle that saved you.
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Old 01-06-2020, 18:51   #6
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Re: Mathematic approach to anchoring scope

Hi,

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Originally Posted by carstenb View Post
Amongst other conclusions is that in deeper water, you need less rode than in shallow water and vice versa of course.
I don't think I quite said that! I never disputed that you need more rope in deeper water than in shallow water... That would be ridiculous...

My point was, among other things, that the scope formula is over predicting or under predicting, depending whether you are in deep water or in shallow water.

And yes, it is known that one should modify the scope approach along this line, but it is nice to know by how much, is it not?
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Old 01-06-2020, 19:15   #7
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Re: Mathematic approach to anchoring scope

Hi StuM,

Quote:
Originally Posted by StuM View Post
IMNSHO, he's on another planet.
That's what we have short wave radio for, isn't it?

Quote:
Originally Posted by StuM View Post
He's spend an inordinate amount of time supposedly validating what experienced sailors know empirically
"The guidance of using a fixed scope like use 3 times or 5 times the water depth as length of chain, etc., is not adequate"
Any sailor with a bit of experience is well aware of that.
Believe it or not, but when sitting the test for the German Sailing Association, there is one question on anchoring, where the correct answer is: Scope 3:1. Period. So, it does seem not everybody has woken up to this yet. And fact is also that I see way too many problems at anchorage that really should not happen...

Quote:
Originally Posted by StuM View Post
He then proceeds with an invalid assumption that a horizontal pull at the anchor is a necessary requirement and spends waaay too much time deriving figures for all sorts of different situations based on that assumption.
This is what a scientific approach is all about. Make clear assumptions and check what the results are. Even when they do not include everything. A horizontal pull at the anchor is a well defined situation, and therefore I picked that one. One could have also picked a 5 degree angle, or whatever. I prefer to know what the situation is like for a horizontal pull, knowing that I then still have some reserve left before the anchor does get pulled out.

Nobody requires you to follow this approach in detail, or at all, but I find it nice to know what happens under certain circumstances and given certain assumptions. And then, confronted with a given situation, I can make my decisions.

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Originally Posted by StuM View Post
As an aside, he also bases his calculations on "all chain with no snubber".
Same as above. I just want to know what the extreme situation is. And we do use long bridles with two rubber dog bones each leg. In the next step, one could add this to my work, but then I found out that Bjarne had already done that.

And incidentally, commercial vessels cannot use snubbers or bridles...

Quote:
Originally Posted by StuM View Post
I especially liked the implication that a cruiser who anchors in different situations should carry multiple different chain rodes.
That was not quite my point...

Anyway, I knew this could get rather heated, and everybody is free to believe and follow whatever they have found is working for them. I just happen to like an approach where I understand why things are happening as they do. And yes, I am aware that not all has been included in the analysis yet, but hey, you have to start somewhere, don't you...

Wishing all to stay healthy and safe at anchor in a manor they please
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Old 01-06-2020, 19:19   #8
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Re: Mathematic approach to anchoring scope

Hi Benz,

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I've often thought that the hook holds better if the water's deeper, which is what this guy seems to be saying.
Thanks for sharing this experience. That was exactly my point regarding a situation with serious swell.
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Old 01-06-2020, 19:29   #9
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Re: Mathematic approach to anchoring scope

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Originally Posted by MathiasW View Post
And yes, I am aware that not all has been included in the analysis yet, but hey, you have to start somewhere, don't you...

Absolutely! Always remember:

"Essentially, all models are wrong, but some are useful."
--- Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 424, Wiley. ISBN 0471810339.

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Old 01-06-2020, 19:36   #10
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Re: Mathematic approach to anchoring scope

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Absolutely! Always remember:

"Essentially, all models are wrong, but some are useful."
--- Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 424, Wiley. ISBN 0471810339.

Thanks. I do like that quote!!!!
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Old 01-06-2020, 19:50   #11
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Re: Mathematic approach to anchoring scope

I always remember a quote from an old Tasmanian Crayfisherman, from St Helens known as "Big Bob" (His son who is actually bigger was "Little Bob", they are HUGE. Shaking hands with Big Bob was unnerving as your han just dissapeared into this huge thing.) "Chain is no ****ing good to you in the boat"
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Old 02-06-2020, 05:33   #12
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Re: Mathematic approach to anchoring scope

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Originally Posted by StuM View Post
Absolutely! Always remember:

"Essentially, all models are wrong, but some are useful."
--- Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 424, Wiley. ISBN 0471810339.



Yep, and the combination of models and experience acquired judgement can be a powerful tool.
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Old 02-06-2020, 06:33   #13
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Re: Mathematic approach to anchoring scope

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Originally Posted by MathiasW View Post
Hi,
I don't think I quite said that! I never disputed that you need more rope in deeper water than in shallow water... That would be ridiculous...

My point was, among other things, that the scope formula is over predicting or under predicting, depending whether you are in deep water or in shallow water.

And yes, it is known that one should modify the scope approach along this line, but it is nice to know by how much, is it not?

It's very interesting and perhaps explains why catenary seems to work better in deep water.


But at the limits, when the chain is pulled out straight, it won't make any difference, right? At that point, the angle of pull on the angle is a simple function of scope.


Note Alain Fraisse's work on this. He also has some tables showing what effect angulation on the anchor has on holding power.


I don't think it's enough to assume that you can't have ANY angulation; that is too conservative and may lead you astray in some borderline situations (like when you have to anchor in very deep water and you don't have room to create much scope -- like what happened to me in Greenland). I've successfully been through a storm in a little more than 2:1 scope. The anchor was big enough and well enough set that the reduction in holding power was not fatal.
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Old 02-06-2020, 09:11   #14
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Re: Mathematic approach to anchoring scope

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But at the limits, when the chain is pulled out straight, it won't make any difference, right? At that point, the angle of pull on the angle is a simple function of scope.
That is true. If the pull is too hard, it would be more or less a straight line. One should not forget the length scales here, though. Things can be deceiving. If you anchor at 10 metres and have 100 meters of chain out, the difference between a catenary and a scope is barely visible. My point was that in deep water often the catenary is already reached when the scope formula suggests even more chain to be paid out. If that is the case, the catenary is actually not conservative, but the scope formula is.


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But at the limits, when the chain is pulled out Note Alain Fraisse's work on this. He also has some tables showing what effect angulation on the anchor has on holding power.
Yes indeed. You will find a link to his web page at the end of my web page. To keep things simple, I wanted to ignore any effects at the anchor by keeping the angle horizontal. But for sure, this is another parameter to play around with. For now, I am content knowing that it gives me a little safety margin.

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I don't think it's enough to assume that you can't have ANY angulation; that is too conservative and may lead you astray in some borderline situations (like when you have to anchor in very deep water and you don't have room to create much scope -- like what happened to me in Greenland). I've successfully been through a storm in a little more than 2:1 scope. The anchor was big enough and well enough set that the reduction in holding power was not fatal.
Yes, of course, that can happen, but when it does, at least I know I need to be on extra alert. How deep was it there? If you look at the catenary curve L = square_root(Y*(Y+2*a)) for very, very deep water where Y is larger than the parameter a, you find that L is only slightly larger than Y.

I guess in your case, if it was a severe storm, the parameter a was still considerably larger than Y, but eventually, the catenary will even beat a scope 2:1, if only it is deep enough. This cross-over will happen at a=1.5*Y (in the absence of swell).

In any case, if push comes to shove, you need to pay out as much chain as you have, use snubber or bridle, try to reduce the windage area, and ride the storm. What else can one do...
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Old 02-06-2020, 09:41   #15
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Re: Mathematic approach to anchoring scope

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Thanks. I do like that quote!!!!
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