Mathematic approach to anchoring scope

[MathiasW]

Originally Posted by 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

Yes, this is a link often quoted!

But even there the authors agree that the catenary is at least partially existent, and the more so the deeper the water is.

It seems there are two big camps - those that believe catenary is largely gone when it matters most in a severe storm, and those that find that catenary still works even then, provided you have enough chain to pay out.

There is often also a misperception about the straight chain, it MUST be a scope, because it goes straight into the water at the bow roller, without any bending seen what-so-ever - I can see it! This is misleading. For the longest part the catenary will be almost straight. Only close to the seabed will it start to turn.

I think the physics and mathematics of catenaries is undisputed. Based on this, nobody can argue that a perfect catenary will be in place if only you pay out enough chain. And if you don't, it will be a partial catenary, so strictly speaking no scope either. Anybody who argues about that should just do the basic maths. Some folks argue the chain gets too heavy when it is too long, but one can show, actually, that the catenary shape causes a smaller load at the bow roller than any scope would. So, scope is no escape from this problem...

The difference of opinions comes about whether it is realistic to pay out enough chain. Here, folks clearly have different views.

And yes, we have all seen pictures of chains being attached at an angle to the anchor shaft. If your chain is not long enough, this is for sure what will happen.

The problematic regime starts when we anchor in shallow water in a severe storm. The chain is so close to being horizontal that it is difficult for the chain to absorb additional energy in the form of potential energy. It is already pulled almost straight. (Even if it is a nice catenary.) In such a situation a swell can easily overload the chain and then indeed lead to a temporary breakdown of the fully developed catenary shape. To prevent that, snubbers and bridles have been invented.

And, btw, the authors of the link referenced above - they want to sell BIG anchors, and so naturally, they lean towards downplaying the catenary and pushing the importance of the anchor. You just tweak the parameters a bit and then make nice conclusions. Any good sales person would do that!

But as said in the very beginning, everybody should anchor in a manner they are comfortable with and are safe.

[MathiasW]

Originally Posted by barnakiel

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

I'll be most curious to learn what you will have discovered!

[CaptMDG]

Many NW sailors and fishermen anchor in 200-300 feet of water and typically use 3 to 1 scope because of the depth. I have never done this because I live in Florida. It is shallow until you drop off to 4000-5000 feet at the continental shelf. Following the NW boaters advice, I may need to get 3 miles of rode! LOL

[MathiasW]

Originally Posted by CaptMDG

Many NW sailors and fishermen anchor in 200-300 feet of water and typically use 3 to 1 scope because of the depth. I have never done this because I live in Florida. It is shallow until you drop off to 4000-5000 feet at the continental shelf. Following the NW boaters advice, I may need to get 3 miles of rode! LOL

Oh no no no. At that kind of depth, I am sure 3:1 is perfectly fine. Probably less would also be quite ok.

The very point is that the scope does not scale across the range of anchor depths you might encounter. In very deep water 3:1 or perhaps even 2:1 might be very ok and lead to a fully developed catenary, whilst in 4 m depth a scope of 7:1 might still not be enough.

[Lodesman]

Originally Posted by MathiasW

The problematic regime starts when we anchor in shallow water in a severe storm. The chain is so close to being horizontal that it is difficult for the chain to absorb additional energy in the form of potential energy.

It can absorb a fair bit of energy lifting 100' of chain off the seabed.

[rslifkin]

Originally Posted by MathiasW

Oh no no no. At that kind of depth, I am sure 3:1 is perfectly fine. Probably less would also be quite ok.

The very point is that the scope does not scale across the range of anchor depths you might encounter. In very deep water 3:1 or perhaps even 2:1 might be very ok and lead to a fully developed catenary, whilst in 4 m depth a scope of 7:1 might still not be enough.

For that last bit, if you're dealing with all chain, in deep water you eventually reach a point where you won't pull out all of the catenary, so you don't need more scope. In shallow water, you end up adding scope to limit the max angle when you inevitably do pull out all of the catenary.

[MicHughV]

I am not a proponent of all chain, as discussed in many responses above.

Over the years, I've "experimented" with a wide variety of anchor rodes, chains, different anchors, ad nauseam....

For me, personally, I have come to appreciate the value of a rode/chain combo.

Besides taking weight out of the bow, this combo has many other values.

In previous emails, I've pointed out that I have dove on my anchor in windy conditions. Out of a 75' length of chain, perhaps only a third is off the seabed....the rest is laying, in a not alway, straight line..not doing much of anything regarding the catenary load.

This is where the stretchiness of nylon rode comes in. The nylon rode can " "absorb" a lot of anchor pull, before reaching it's limit. The " absorption" of the nylon rode, in addition to the 25' part of chain catenary, is what allows half of the chain to just lay flat on the seabed.

In trying to make an analogy, I would use a car's shock absorbers to illustrate. Going over a bump, it's the shock absorbers, that take the brunt of this load. Were a car to have no shock absorbers, the chassis and frame would have to take the load. This, it can do, if it were built sufficiently strong enough, but then it would be too heavy, hence the shock absorbers.

A chain catenary, complimented by the stretchiness of the nylon rode acts as the boat's shock absorber. Off course, despite this, you can bottom out the absorbers, and the car will let you know with a load thump....I would equate this to one's anchor line being stretched straight to it's limits...

Then there is this....nylon abrades rather easily. My nylon rode goes over a rubber pulley. A night of bobbing up an down can be seen the next morning by a frayed nylon anchor line. Even that relatively short section of nylon rode from cleat to roller stretches and moves. I have addressed this by placing a 24" long piece of slit plastic tubing, which can be opened up, and placed over the rode and its held in place by a short length of string. Every time I anchor I pay out an additional 6" of rode so that there is "new" rode for the roller to eat.

In the 40 odd years of my sailing life, I've come to appreciate that every sailor has his or her own take on correct anchoring methods, rarely the same for two people.
Ironically, every time I have sold one of my previous boats, the new owners have changed out, what I considered, the perfect anchoring system. Not only changed out the entire rode system, but also the anchors.

I'm hurt

[MathiasW]

Originally Posted by MicHughV

I'm hurt

I do hope not by this thread?

As to a mix of chain and rope - that would be ideal, if it wasn't for the chafing that you mention, and the difficulty of the connection between rope and chain, which does not work well with the gypsy.

Next best thing is a really long snubber or bridle, and with that I mean at least 10 metres.

[MathiasW]

Originally Posted by Lodesman

It can absorb a fair bit of energy lifting 100' of chain off the seabed.

Not really, no it can't. You need to keep in mind that the two end points of the chain are fixed in height. One side being the anchor, the other the vessel. If the chain is already pulled hard, and then you pull it a bit harder to ride a gust or swell, then the chain will be lifted only by a few cm more, and this does not amount to a lot of energy.

I have derived the exact formula for the potential energy of a chain in catenary shape. You can see it in one of the diagrams on the web page. If you keep the length of the chain fixed, and the anchor depth a very small fraction of the chain length, then you will find that the energy DIFFERENCE between two chains, one with base load and the other with additional load, is quite tiny. It gets smaller and smaller the more shallow the water gets.

[rslifkin]

Originally Posted by MathiasW

I do hope not by this thread?

As to a mix of chain and rope - that would be ideal, if it wasn't for the chafing that you mention, and the difficulty of the connection between rope and chain, which does not work well with the gypsy.

Next best thing is a really long snubber or bridle, and with that I mean at least 10 metres.

Chafe is an issue with a mixed rode, but given a windlass that handles line and chain well plus a good splice between the 2, the transition isn't necessarily an issue. I always use chafing gear at the bow on my setup to avoid chafe against the cheeks on the roller.

With my Maxwell HRC10 and 5/8" 8 plait spliced to 5/16 G43 chain, it's completely seamless going out, you just hear the clatter of the chain stop and just the smooth humming of the windlass as the line feeds out. Coming in, you let off the up button just before the splice hits the gypsy so the windlass slows down. Usually it'll coast right over and grab the chain. If it stops short, just bump it up and it'll pull the splice through, then resume lifting. It's hit or miss whether it'll grab the chain if you try to transition at full speed (at least in deeper water with 50+ lbs of load at the transition), but if you do it slowly, I haven't had it fail to grab yet.

[MathiasW]

Originally Posted by rslifkin

With my Maxwell HRC10 and 5/8" 8 plait spliced to 5/16 G43 chain, it's completely seamless going out, you just hear the clatter of the chain stop and just the smooth humming of the windlass as the line feeds out. Coming in, you let off the up button just before the splice hits the gypsy so the windlass slows down. Usually it'll coast right over and grab the chain. If it stops short, just bump it up and it'll pull the splice through, then resume lifting. It's hit or miss whether it'll grab the chain if you try to transition at full speed (at least in deeper water with 50+ lbs of load at the transition), but if you do it slowly, I haven't had it fail to grab yet.

Aha, most interesting! I"ll look into that. Thanks for sharing this!

[Lodesman]

Originally Posted by MathiasW

Not really, no it can't. You need to keep in mind that the two end points of the chain are fixed in height. One side being the anchor, the other the vessel.

The height might be fixed at the height (depth) of the anchor, but it's not fixed at the anchor. As excess anchor chain is lifted from the seabed, the catenary grows in length - the longer the catenary, the more potential energy.

[MathiasW]

Originally Posted by Lodesman

The height might be fixed at the height (depth) of the anchor, but it's not fixed at the anchor. As excess anchor chain is lifted from the seabed, the catenary grows in length - the longer the catenary, the more potential energy.

Very true, but once it is all lifted off the seabed - and this will happen quickly in severe conditions - there is little additional energy that can be stored in the chain.

[MicHughV]

The topic of anchoring is not new. I've seen countless threads on this over the years, with just as many opinions, facts and theory, never with any common census or clear direction. Numerous published anchor holding tests, comparo's..etc...etc...etc..

There are so many variables involved.

Let's list a few...

1)Type of bottom, can be further sub-divided into rock, coral, marl, sand, mud, etc...take your pick.
2) Depth of water, this can vary from 10' to 300', and everything in between, that's a huge difference.
3) Height of anchor roller above water....single anchor setup or dual.
4) Type of boat, can be further sub-divided into sloop, ketch, high freeboard, low freeboard, windage of superstructure, etc. A boat that swings...a boat that lays steady to an anchor and more.
5) Type of rode, can be further divided into nylon, chain, nylon/chain, type of chain, type of rode, etc..
6) The big one...anchor selection.....ho boy, take your pick here.
7) Scope of line
8) Anchor bridles.
9) Anchor snubbers...
10) Material of rode/chain.....foreign..local...
11) Windlass. More diversity here....and let's not forget nylon/chain connection. Also, don't forget many anchors are brought aboard by hand.
12) Anchoring in current.
13) Fouled anchor.
14) Diving on an anchor.
15) Retrieving a fouled anchor
16 ) Dinghy anchor.
17) Skill of the captain in setting the anchor.
18) Dragging anchor....in day...and night...
19) Dual anchor setups..
20) Catenary.

There's likely more....

Yep, sort thru' that...

[MathiasW]

Originally Posted by MicHughV

The topic of anchoring is not new. I've seen countless threads on this over the years, with just as many opinions, facts and theory, never with any common census or clear direction. Numerous published anchor holding tests, comparo's..etc...etc...etc..

There are so many variables involved.

Let's list a few...

1)Type of bottom, can be further sub-divided into rock, coral, marl, sand, mud, etc...take your pick.
2) Depth of water, this can vary from 10' to 300', and everything in between, that's a huge difference.
3) Height of anchor roller above water....single anchor setup or dual.
4) Type of boat, can be further sub-divided into sloop, ketch, high freeboard, low freeboard, windage of superstructure, etc. A boat that swings...a boat that lays steady to an anchor and more.
5) Type of rode, can be further divided into nylon, chain, nylon/chain, type of chain, type of rode, etc..
6) The big one...anchor selection.....ho boy, take your pick here.
7) Scope of line
8) Anchor bridles.
9) Anchor snubbers...
10) Material of rode/chain.....foreign..local...
11) Windlass. More diversity here....and let's not forget nylon/chain connection. Also, don't forget many anchors are brought aboard by hand.
12) Anchoring in current.
13) Fouled anchor.
14) Diving on an anchor.
15) Retrieving a fouled anchor
16 ) Dinghy anchor.
17) Skill of the captain in setting the anchor.
18) Dragging anchor....in day...and night...
19) Dual anchor setups..
20) Catenary.

There's likely more....

Yep, sort thru' that...

Yes, surely, all valid points to look at, but fortunately one can group them into clusters and deal with those clusters one by one, having minimal interaction between them. For instance, the holding power of the anchor as a function of seabed is something that does not affect the catenary calculations as long as a critical load is not exceeded. If it is exceeded, the anchor will start dragging. So, all I need to do is to stay 'below that F_max line' in all the graphs. In my digests I have plotted various F_max curves that would reflect different grades of seabed. Without claiming to know the precise values... It is an assumed input.