Mathematic approach to anchoring scope

[MicHughV]

ok, then try this...

Have the same two strong guys pull on the rope again, but have one guy standing on a ladder. This changes the curve of the catenary, as the weight of the rope or chain now comes into play as well......when the two guys where both standing on the floor, the catenary is parabolic...ie, the same on both sides of the center.

but with one guy standing on the ladder, the dynamics change...

[CarlF]

Left out of this discussion is anchor type. I believe that most of the "accepted" scope recommendations have come to us from the Danforth and the CQR.

The Danforth needs a horizontal pull to set but once buried will hold just as well with a slight angle to the chain. The CQR in my experience requires close to horizontal for both setting and maximum holding. The very idea of a farm "plow" is to not go too deep. I used a CQR for 15 years and became very familiar with its need for lots of scope.

But today the need for low angles or arguments about the catenary effect may not be as important. Most modern anchors do not need such low angles. And once well buried they will continue to dig deeper even if the chain is not horizontal. This varies by anchor based on how the designer has set various angles of shank and blade. Over the last few boats I have used a Manson Supreme, Spade, and Ultra and found that they all held much better with less scope than my old CQR.

That's not to suggest that you should anchor with 3:1 scope but I think picking heavier chain to get an extra degree or two from catenary effect isn't necessary if you use a modern anchor.

What is MUCH more important is to back down firmly to set the anchor deep. A lot of scope won't help if the anchor is lying mostly on its side.

[MathiasW]

Originally Posted by 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 ??

Yes, sure, I know all that. I knew that already when I was a small kid balancing on a slack line. But I am afraid I do not get your point...

[MathiasW]

Originally Posted by MicHughV

ok, then try this...

Have the same two strong guys pull on the rope again, but have one guy standing on a ladder. This changes the curve of the catenary, as the weight of the rope or chain now comes into play as well......when the two guys where both standing on the floor, the catenary is parabolic...ie, the same on both sides of the center.

but with one guy standing on the ladder, the dynamics change...

Well, I think some guys in 1600 something already established that the curve is NOT a parabola, but in fact a hyperbolic cosine function...

[MathiasW]

Originally Posted by CarlF

Left out of this discussion is anchor type. I believe that most of the "accepted" scope recommendations have come to us from the Danforth and the CQR.

The Danforth needs a horizontal pull to set but once buried will hold just as well with a slight angle to the chain. The CQR in my experience requires close to horizontal for both setting and maximum holding. The very idea of a farm "plow" is to not go too deep. I used a CQR for 15 years and became very familiar with its need for lots of scope.

But today the need for low angles or arguments about the catenary effect may not be as important. Most modern anchors do not need such low angles. And once well buried they will continue to dig deeper even if the chain is not horizontal. This varies by anchor based on how the designer has set various angles of shank and blade. Over the last few boats I have used a Manson Supreme, Spade, and Ultra and found that they all held much better with less scope than my old CQR.

That's not to suggest that you should anchor with 3:1 scope but I think picking heavier chain to get an extra degree or two from catenary effect isn't necessary if you use a modern anchor.

Yes, I agree with all that. Modern anchors are not that picky any more. But my preference is still to work out what the chain length is assuming a horizontal pull, and then having this extra angle as a reserve if push comes to shove.

And if you really want to include the angle, then that can be done. On my web page there is a path outlined how to do it, and Bjarne with his online calculator allows that as well. As does Alain's spreadsheet.

The main point of my work was to study how the energy burst of a swell can be included in the catenary framework. It is not done by simply increasing the windage area, which would be the same independent of anchor depth. Swell, it turns out, is most problematic when we are in shallow water. Simply because the chain cannot easily absorb more energy in the form of potential energy when it gets pulled flatter and flatter.

Well, we all knew that, didn't we, but it is good to have a model agreeing with experimental evidence...

[barnakiel]

I think the point they are making is that it takes an immense power to get rid of all catenary as any weight (and chain is a way weighty item) along the line (chain, in our case) creates force (considerable) making up this catenary.


This is in fact 100% correct.


I looked at our chain in very very windy situation - the chain was off the ground but there was still huge amt of catenary, perhaps as much as 5%.



And I am surprised few people make experiments like this. Do dive on your chains at times. I encourage you!



Perhaps this is because cruisers are like doctors - a narrow specialization, little former experience in real life stuff like climbing , Camel Trophy Rallies, highline ballet, etc.


And yes the shallower the anchorage, the harder the exercise. It is only easy to get rid of all catenary if you are in very deep water (e.g. water=chain length).



;-)


b.

[MathiasW]

Originally Posted by barnakiel

I think the point they are making is that it takes an immense power to get rid of all catenary as any weight (and chain is a way weighty item) along the line (chain, in our case) creates force (considerable) making up this catenary.


This is in fact 100% correct.


I looked at our chain in very very windy situation - the chain was off the ground but there was still huge amt of catenary, perhaps as much as 5%.



And I am surprised few people make experiments like this. Do dive on your chains at times. I encourage you!



Perhaps this is because cruisers are like doctors - a narrow specialization, little former experience in real life stuff like climbing , Camel Trophy Rallies, highline ballet, etc.


And yes the shallower the anchorage, the harder the exercise. It is only easy to get rid of all catenary if you are in very deep water (e.g. water=chain length).



;-)


b.

OK, THAT I understand! And I am in full support of that view.

I lean towards catenary and not towards scope, in case somebody failed to notice that...

[barnakiel]

BTW the mathematics does not seem overly complex to me. Perhaps in pen and paper approach it was more work, but back then the species had better brains too.


Now with excel or a couple of lines of Python code you can get the results and visualise them in miliseconds.


Level: easy/medium.


Off course, if we want to add the pumping effect of swell, it stops being very simple. Also because modelling of dynamic situations is not 100% reliable. Unless we use pretty broad margins to allow for those far out of average inputs (which statistically must happen if our experience / experiment lasts long enough).



b.

[MathiasW]

Originally Posted by barnakiel

BTW the mathematics does not seem overly complex to me. Perhaps in pen and paper approach it was more work, but back then the species had better brains too.

Correct!

Originally Posted by barnakiel

Now with excel or a couple of lines of Python code you can get the results and visualise them in miliseconds.

Correct!

Originally Posted by barnakiel

Level: easy/medium.

Correct!

Originally Posted by barnakiel

Off course, if we want to add the pumping effect of swell, it stops being very simple. Also because modelling of dynamic situations is not 100% reliable. Unless we use pretty broad margins to allow for those far out of average inputs (which statistically must happen if our experience / experiment lasts long enough).

In principle, of course, you are right. The dynamics is most complex. But if one simplifies it by only looking at energy balances and not trying to understand how the vessel got into that position in the first place, it gets easier.

And this is what I tried to do when working out the potential energy differences between the situation of a vessel just having fully absorbed a swell, and the same vessel without that swell.

It turns out you can still use a catenary then, but its effective force (or windage area, if you will) will be depend on the anchor depth. And for this reason I do not like to simply increase the windage area in a static way, independent of water depth - which is what these ABYC rules seem to imply, if I understand them correctly. It is too much of a simplification.

Of course, when the chain gets pulled tighter or when it slackens, it may not have a perfect catenary shape in those transition periods. But in the extreme case of at maximum tightening, just before it slackens again, it will be quasi static for a split second, and in some sense that is the situation I am looking at: Maximum energy transfer.

[StuartWeibel]

I am no mathematician and confess my most deeply rooted arguments about ground tackle arise from my own experiences (300 days on the hook in the Pacific Northwest).

But when I unpack theoretical arguments I always return to this article:

https://www.petersmith.net.nz/boat-anchors/catenary.php

The gist of it is that catenary is a straw man -- the dislodging of an anchor occurs almost exclusively when there IS NO CATENARY -- in wind and wave conditions make your rode a straight pipe with elastic properties ranging from near zero (an un-snubbed chain), to rubber-bandish (nylon that stretches somewhere between 5 and 15 percent.

Your mileage may vary. Stay safe

[barnakiel]

Originally Posted by MathiasW

(...)





But in the extreme case of at maximum tightening, just before it slackens again, it will be quasi static for a split second, and in some sense that is the situation I am looking at: Maximum energy transfer.

OK. Thank you for pushing me this way. I will study maximum energy transfer now. I knew it was somehow related to car crash tests that I helped modelling (back about 1996 I think). But I was on the outskirts of the thing and not directly involved in the study (I was in the outsorced part of the algorithm / coding team).


We learn new things daily. That's awesome.


barnakiel

[MicHughV]

true...the curve is not a true parabola....just trying the keep my explanation simple..which is why I made the guy on the ladder explanation to demonstrate the curve difference that would be noted.

like others here, I have dove on my anchor in very windy conditions, also with wave action...and it was interesting to note the action of the chain/rope combo on the ocean floor..my chain is 75' long, coupled to usually another 75' of nylon rode, typical Bahama depth.. and I've never seen an instance where more than about one third of the chain was off the ocean floor..the swells would cause the bow to raise, hence lifting some chain of the bottom..but never more than about one third...and no, I did not measure this, simply my eyeball estimate, as the catenary of the chain being clearly visible.
Ironically, in the same dive, I would also inspect how deep the anchor had buried and to my surprise, not very deep at all...lending credence to the fact that catenary does most of the work...

It would take some kind of wind to straighten that catenary out, by which time, I'd be blown ashore..

[MicHughV]

yep, once that catenary straightens out to a straight line, you're gonna be in trouble !

[rslifkin]

Originally Posted by MicHughV

yep, once that catenary straightens out to a straight line, you're gonna be in trouble !

Not necessarily. As long as you've got enough line somewhere in the system to provide stretch and enough scope to limit the maximum angle of pull on the anchor to something it can handle while still providing good holding, you'll be fine. In heavy weather, that's typically what'll happen. Depending on depth, chain size, etc. the catenary may not be totally gone (so it may still be reducing angle slightly) but it'll be close and not really absorbing much energy anymore.

[MathiasW]

Originally Posted by MicHughV

true...the curve is not a true parabola....just trying the keep my explanation simple..which is why I made the guy on the ladder explanation to demonstrate the curve difference that would be noted.

like others here, I have dove on my anchor in very windy conditions, also with wave action...and it was interesting to note the action of the chain/rope combo on the ocean floor..my chain is 75' long, coupled to usually another 75' of nylon rode, typical Bahama depth.. and I've never seen an instance where more than about one third of the chain was off the ocean floor..the swells would cause the bow to raise, hence lifting some chain of the bottom..but never more than about one third...and no, I did not measure this, simply my eyeball estimate, as the catenary of the chain being clearly visible.
Ironically, in the same dive, I would also inspect how deep the anchor had buried and to my surprise, not very deep at all...lending credence to the fact that catenary does most of the work...

It would take some kind of wind to straighten that catenary out, by which time, I'd be blown ashore..

We are in complete d'accord then!