Mathematic approach to anchoring scope

[MathiasW]

And if I may, for convenience the link to my web page again, as posted in the very first post of this thread:

https://trimaran-san.de/die-kettenku...atiker-ankert/

[Dockhead]

Originally Posted by Lodesman

You've misstated my position on the topic. That is proper ground tackle includes enough chain that at full-scope the catenary would not disappear before the chain parts in normal anchoring conditions. That's not to say that under extreme anchoring conditions like very deep anchorages, or where one is otherwise constrained to short scope, it is not possible to pull the chain into a straight line.

I would think that someone standing on their bow looking at the 14m of chain they have out, angled 15º below the horizontal, making a beeline to the anchor, and doesn't have the good sense to put out more chain - should probably give up boating.

I apologize if I misunderstood or mistated your position.

So anyway, whether it's what you actually meant or not, I would still say it's important to realize that catenary is not a panacea. The problem with it is that it disappears just when you need it most, unless you are in a configuration with a lot of reserve weight of chain out, and water deep enough to use it.

To go back to 8mm chain in 4m of water -- a very typical anchoring case for average sized boats --

Even 32m of chain out -- 8:1 scope -- the critical tension is only 164daN. You are within 2 degrees of the basic geometry of the scope, that is, at 5 degrees of angulation, at only 541daN.

You can keep improving this by putting out more and more chain -- but do you always have room for 10:1 scope, or even 8:1? I sure don't.

Catenary is not a big help in strong weather with average or small size chain, and shallow water. Maybe somewhat more if you have a huge amount of chain on board and room to put out a ridiculous amount of scope.

Catenary becomes much more effective with heavy chain and deep water. I'm surprised that Dashew, Peter Smith et al didn't think about that, when they recommended going with lighter chain. The idea being that the weight is more effective in the anchor than it is in the chain.

[MathiasW]

Originally Posted by Dockhead

Catenary becomes much more effective with heavy chain and deep water. I'm surprised that Dashew, Peter Smith et al didn't think about that, when they recommended going with lighter chain. The idea being that the weight is more effective in the anchor than it is in the chain.

I think the general catenary theory can explain that: If you do have a fully developed catenary, and then look how to get the most out of a given amount of weight that you can carry as chain, then you find that it is better to spend this weight on a thin, long chain, rather a thick, short chain. The total weight of the chain is the same, it is just distributed differently.

Of course, this has a very negative effect on the swinging circle, and one needs to keep an eye on the working load of the chain.

[Dockhead]

Originally Posted by MathiasW

I think the general catenary theory can explain that: If you do have a fully developed catenary, and then look how to get the most out of a given amount of weight that you can carry as chain, then you find that it is better to spend this weight on a thin, long chain, rather a thick, short chain. The total weight of the chain is the same, it is just distributed differently.

Of course, this has a very negative effect on the swinging circle, and one needs to keep an eye on the working load of the chain.

Well, but they were not recommending longer chains. Area of the swinging circle -- whom am I telling -- goes up by a factor of pi*r^2 where "r" is chain length. It becomes quickly unfeasible, which is why few people carry more than 100m of chain. They were recommending larger anchors. They specifically said -- catenary goes away when you need it most; focus on the anchor.


And of course there is a lot of truth in that-- if you upsize the anchor to get double the holding power, then you've got roughly the same holding power at 20 degrees angulation as the smaller anchor will have at 0.


Bigger anchor gives you tolerance of angulation, which might come either from really storm force winds which take all the effective catenary out, or from short scope.



I still however like to have catenary working, which is why I never downsized my 12mm chain, 330kg of it.

[MathiasW]

Originally Posted by Dockhead

Well, but they were not recommending longer chains. Area of the swinging circle -- whom am I telling -- goes up by a factor of pi*r^2 where "r" is chain length. It becomes quickly unfeasible, which is why few people carry more than 100m of chain. They were recommending larger anchors. They specifically said -- catenary goes away when you need it most; focus on the anchor.


And of course there is a lot of truth in that-- if you upsize the anchor to get double the holding power, then you've got roughly the same holding power at 20 degrees angulation as the smaller anchor will have at 0.


Bigger anchor gives you tolerance of angulation, which might come either from really storm force winds which take all the effective catenary out, or from short scope.



I still however like to have catenary working, which is why I never downsized my 12mm chain, 330kg of it.

Yes, sure, I agree with all of that! If you can carry a heavier chain and 100 m of it, then that's definitely the solution to go for. But for multihulls like us, we need to be a bit more concerned with too much weight on the nose. The standard for our tri as speced by the ship yard is 60 m of 12 mm. 60 m is not enough for blue water sailing and as I cannot increase the total weight a lot, I opted to turn this into 102 m of a 10 mm chain of higher quality.

And we swapped in a larger anchor...

[Dockhead]

Originally Posted by MathiasW

Yes, sure, I agree with all of that! If you can carry a heavier chain and 100 m of it, then that's definitely the solution to go for. But for multihulls like us, we need to be a bit more concerned with too much weight on the nose. The standard for our tri as speced by the ship yard is 60 m of 12 mm. 60 m is not enough for blue water sailing and as I cannot increase the total weight a lot, I opted to turn this into 102 m of a 10 mm chain of higher quality.

And we swapped in a larger anchor...

Well, I hear you.

It's not a simple choice for us, either. We are starting a 1000 mile ocean race in less than 2 weeks and I've got to figure out what to do with that 330kg of chain. can't leave it in the bow.


If I were in a multihull I believe I would consider a mixed rode, too.

[Dockhead]

Playing with these numbers . . .

If you have 100m of 12mm chain out in 15m of water -- not unusual for us in this boat, then the critical tension is 957daN, corresonding to 32 knots per ABYC. At 5 degrees of angulation (compare to 17 degrees at the limit for that scope), the force per ABYC is 2276, corresponding to about 50 knots.

No wonder I have little need of a snubber in such an anchorage.


In 10m of water the figures go up to 1454 and 11 276 respectively. The latter is beyond the breaking strength of the chain.

[StuM]

Originally Posted by MathiasW

Yes, sure, I agree with all of that! If you can carry a heavier chain and 100 m of it, then that's definitely the solution to go for. But for multihulls like us, we need to be a bit more concerned with too much weight on the nose. The standard for our tri as speced by the ship yard is 60 m of 12 mm. 60 m is not enough for blue water sailing and as I cannot increase the total weight a lot, I opted to turn this into 102 m of a 10 mm chain of higher quality.

Mixed rode? How often do you need more than 60 m near the bottom?



Another 50 m of rope wouldn't add that much weight.

[MathiasW]

Originally Posted by Dockhead

It's not a simple choice for us, either. We are starting a 1000 mile ocean race in less than 2 weeks and I've got to figure out what to do with that 330kg of chain. can't leave it in the bow.

The Neel 47 that won the ARC+ 2019 race and beat us by quite a margin had their anchor and chain temporarily stored deep in the central hull to get the weight balanced better. That is a painful work, but they were close to professionals.

Originally Posted by Dockhead

If I were in a multihull I believe I would consider a mixed rode, too.

Yes, I know, but the connection between the two does not glide well over the gypsy, if at all, and fiddling around with that in a storm is not what I dream of.

Instead, I am prepared to swap in an even bigger (not heavier) anchor made of aluminium, which holds better in sand.

Plus, I have 70 m of rope and another 20 m of the same chain for a 2nd anchor. So, if I really need to dig in somewhere and I have time to prepare for it, I would swap in the larger anchor as main, and use the normal main anchor with the rope and chain as a 2nd anchor. I would then still have a 3rd anchor (of the size the ship yard had specified it), but no rope for that..

[MathiasW]

Originally Posted by StuM

Mixed rode? How often do you need more than 60 m near the bottom?



Another 50 m of rope wouldn't add that much weight.

I do not have any experience with the 12 mm chain, as we never had it on board, but there had been one occasion in the Caribbean where in a rather shallow place of 6 m or so I only felt save after having paid out 80 m of the 10 mm chain. (And bridle, of course). That would still amount to less than 60 m of a 12 mm chain, agreed.

Most of the time I have at least 45 m out, even when there is little wind. Now we have 55 m out, in 5 - 10 metres of water (strong tides). And this has been so for the last 10 weeks...

But the 102 m/10 mm chain will come handy when I am required to anchor in 25+ metres. The 60 m/12 mm chain will not be enough.

[MathiasW]

Originally Posted by StuM

Mixed rode? How often do you need more than 60 m near the bottom?



Another 50 m of rope wouldn't add that much weight.

PS: In the absence of swell (not realistic, I know, but it is just to show the trend), 100 metres of 10 mm chain allow me to anchor at 25 m and 7 BFT.

Now, 100 m of 10 mm chain correspond to 71 m of 12 mm chain, weight-wise. With that amount of chain I can only anchor at 25 m up to 6 BFT. Or 7 BFT at 18 m water depth.

[MicHughV]

the " science" is understanding the "dynamics" of how a catenary works...

this can be a very complicated and in-depth discussion requiring the use of a blackboard to illustrate or a computer screen....plus a lot of mathematical mumbo jumbo and data....

to list one's personal anchoring technique's does little to explain this " science" as each sailor will have his or her's own take on the matter.....and with each anchoring depth providing a different set of catenary circumstance.

as a retired structural marine engineer I could expound on this for a long time, but y'all would get bored and fall asleep before I was halfway thru'...

[MathiasW]

Originally Posted by StuM

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

So, in response to this very valid point, I have just added a section towards the end of the web page where I discuss the effect of a snubber / bridle. I have not updated the graphs in the digests, as this would require an entire new parameter to be explored... :sigh:

But I think just by looking at the energy a spring like a snubber can store, and then looking at the energy of a swell and the fact that an almost horizontal chain finds it hard to absorb more potential energy, it becomes clear that snubbers / bridles are most important in shallow water to compensate for the shortcomings of the chain there...

And this seems to be a general experimental consensus in this thread... Theory supporting and explaining reality, this is how it should be

[MathiasW]

Originally Posted by MicHughV

the " science" is understanding the "dynamics" of how a catenary works...

this can be a very complicated and in-depth discussion requiring the use of a blackboard to illustrate or a computer screen....plus a lot of mathematical mumbo jumbo and data....

to list one's personal anchoring technique's does little to explain this " science" as each sailor will have his or her's own take on the matter.....and with each anchoring depth providing a different set of catenary circumstance.

as a retired structural marine engineer I could expound on this for a long time, but y'all would get bored and fall asleep before I was halfway thru'...

Why not give it a try, anyway?

[MicHughV]

try this simple experiment....

have two of the strongest guys you know pull a rope....say 10-15' long...I mean really pull...lean back, grab a door frame...anything for extra support...pull that rope bar tout. This is easiest to do with a small diameter line.

then stand in the middle of the rope, and using only a single finger, pull on the rope. you will be able to pull that rope with ease, pulling the two strong guys towards you and continue until the angle of the catenary becomes such that it becomes too large for your finger to exert further pressure..

Were the two guys pulling on a heavy chain.....they would not be able to pull hard enuff to straighten the chain out, the weight of the chain being much the same as my finger on the rope...

do I need to go on ??