Mathematic approach to anchoring scope

[Bill_Giles]

I can understand that however, if one is expecting gusty, windy weather then one likes to ‘set’ the anchor by reversing up until it is set into the sand or mud. If the angle of the pull is more in deeper water then is the set poorer?

[MathiasW]

Originally Posted by Bill_Giles

I can understand that however, if one is expecting gusty, windy weather then one likes to ‘set’ the anchor by reversing up until it is set into the sand or mud. If the angle of the pull is more in deeper water then is the set poorer?

Yes, definitely, you would want to set the anchor with proper reversing. I am not suggesting to set the anchor at a scope of 2. You would want to set the anchor at a larger scope, if possible (i.e. enough chain available). Pulling angle at anchor shaft should be as small as possible for good results. Only if you do not have enough chain, you would have to set the anchor at that smallish scope.

Some folks in this thread have successfully anchored at 40 m depth with 100 m chain, in a storm. That is a scope of 2.5 and they were doing fine, they said.

[MathiasW]

In the table attached I have calculated the anchor loads for three different anchor depths of 3, 5, and 9 metres, and for no snubber at all and various degrees of better and better performing snubbers (for definitions of those snubbers see https://trimaran-san.de/anchor-chain-calculator/).

All other parameters were the same, so wind strength, (very strong) swell, etc. The chain was limited to a maximum of 50 metres.

The top left case, 3 metres anchor depth and no snubber at all has no solution. This is because the chain alone cannot absorb the swell energy. See my previous post discussing the extreme cases for a chain.

At 5 metres anchor depth the chain can cope, if barely, with a huge anchor load of 1322 daN.

But even a very poor snubber / bridle will bring down this anchor load substantially, which proves the point that they are an essential component of your anchor gear in shallow water.

The columns for 5 and 9 metres anchor depth show that the same amount of swell is less dangerous in deeper water, as it leads to a smaller maximal anchor load. This supports my earlier statement that in very strong swell it may be beneficial to relocate to deeper water - provided that the swell is not worse there - without necessarily requiring more chain.

The long story can be found here:

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

[Lodesman]

Originally Posted by MathiasW

The top left case, 3 metres anchor depth and no snubber at all has no solution. This is because the chain alone cannot absorb the swell energy. See my previous post discussing the extreme cases for a chain.

At 5 metres anchor depth the chain can cope, if barely, with a huge anchor load of 1322 daN.

But even a very poor snubber / bridle will bring down this anchor load substantially, which proves the point that they are an essential component of your anchor gear in shallow water.

I'm trying to wrap my head around how the snubber reduces the load at the anchor? If I apply a load of X daN to the boat-end of the snubber, the snubber stretches, but at the other end of the snubber where it attaches to the chain, the load is still X daN, is it not?

[thinwater]

Originally Posted by Lodesman

I'm trying to wrap my head around how the snubber reduces the load at the anchor? If I apply a load of X daN to the boat-end of the snubber, the snubber stretches, but at the other end of the snubber where it attaches to the chain, the load is still X daN, is it not?

Obviously.


If you hit your head on a wall with or without a helmet it feels different. If you drive a car with no springs and solid tires it feels different. No shocks it feels different. A car with both is better.



It's about spreading energy over a distance, not a static force balance. If there are no waves and the chain catenary never deminishs significantly, there is very little difference. In fact, that is what many sailors know, since they only anchor in moderate depth water with good protection. In the open and in in relatively shallow water is different.

[MathiasW]

Originally Posted by Lodesman

I'm trying to wrap my head around how the snubber reduces the load at the anchor? If I apply a load of X daN to the boat-end of the snubber, the snubber stretches, but at the other end of the snubber where it attaches to the chain, the load is still X daN, is it not?

Yes, correct, the force on either side of the chain is the same, if the chain is perfectly balanced, like at the extreme point when the vessel has come to rest. Then the forces are the same on either end of the chain. But at any other moment they may not, necessarily.

But as Thinwater was saying. It is not about static forces, but how well the maximum load of the anchor can be reduced by adding elasticity to the system and absorb some of the shock load elsewhere.

The energy that needs to be absorbed is always the same. In a simple picture, think of it as energy = force times distance. If I can increase the distance (by adding elasticity), I can reduce the force. That is essentially what is happening...

[dfelsent]

What was the wave height used for these calculations?

[MathiasW]

Originally Posted by dfelsent

What was the wave height used for these calculations?

It is difficult to use the wave heights for such a calculation - at least for me...

So, my approach is to look at the impact these waves are having on the vessel. The impact is simply that the vessel starts moving. As far as the load on the anchor is concerned, the only relevant movement is that away from the anchor.

Consequently, when I read the maximal speed over ground AWAY from the anchor, like on the chart plotter, I have a measure for the impact the waves are having on the vessel. (Of course, a gust can do the same thing, but this does not matter for the current discussion.)

When I have the maximal vessel velocity v, and the vessel's mass M, I can calculate its kinetic energy as 1/2 M v^2.

This energy needs to be absorbed by the anchor gear. So chain and snubber / bridle. When it has been fully absorbed, the load on the anchor will be highest.

In a way, you can compare this with a pendulum. When it is at the bottom, it has some kinetic energy, and when it has reached its point of return, all its kinetic energy will have been converted to potential energy.

In the calculations above I assumed 0.6 kn of maximal vessel speed and a mass of 12 metric tonnes.

[dfelsent]

Thank you. I ask, because some time ago I came across a nice paper (since lost) that had some theoretical/empirical formulae for wave height as a function of fetch, depth, and channel width. It was a us government publication from some time ago I think.
When I looked at your model results I was wondering whether the model incorporated assumptions about the lower wave heights in shallow water.
I enjoy your work, just poking at it in a spirit of curiosity.
And in a spirit of thinking about optimal snubber size and construction for differing conditions.
Assuming all nylon there are three I see for snubbers.
Three strand, double braid, or brait aka 8 strand.
Within that there are material and processing and constructional differences, for example Yale Brait vs Yale Oceanographer’s Brait. These two both have energy absorption data published by the manufacturer
All really interesting for me.
Do I use 1/2” where the strength is marginal but the stretch is greater? 5/8 with less stretch but strength comparable to the chain? Double braid where the heat issues are worse? Three strand where twist becomes an issue at higher loads? Brait where the chafe is more of an issue but the energy absorption is better?
No right answers of course
Btw I am about 18 metric tonnes. And while anchored in shallow water (3 meters) and 50 knot squalls it’s been more oscillating yawing than jerks back and forth. Wave heights are severely limited in shallow water.

[MathiasW]

Originally Posted by dfelsent

Thank you. I ask, because some time ago I came across a nice paper (since lost) that had some theoretical/empirical formulae for wave height as a function of fetch, depth, and channel width. It was a us government publication from some time ago I think.
When I looked at your model results I was wondering whether the model incorporated assumptions about the lower wave heights in shallow water.
I enjoy your work, just poking at it in a spirit of curiosity.

<snip>

Btw I am about 18 metric tonnes. And while anchored in shallow water (3 meters) and 50 knot squalls it’s been more oscillating yawing than jerks back and forth. Wave heights are severely limited in shallow water.

Hmm, indeed, I have a vague memory of somebody in the past having made a reference to that paper relating wave height, fetch, etc. When my internet is better, I might do a search.

In my model I just consider the impact swell has on the vessel in terms of setting it in motion. So, if swell is less effective doing this in shallow water, it would automatically be accounted for. And incidentally, with this approach I could also deal with gusts, instead of simply using their max value as mean wind...

[MathiasW]

Originally Posted by dfelsent

And in a spirit of thinking about optimal snubber size and construction for differing conditions.
Assuming all nylon there are three I see for snubbers.
Three strand, double braid, or brait aka 8 strand.
Within that there are material and processing and constructional differences, for example Yale Brait vs Yale Oceanographer’s Brait. These two both have energy absorption data published by the manufacturer
All really interesting for me.
Do I use 1/2” where the strength is marginal but the stretch is greater? 5/8 with less stretch but strength comparable to the chain? Double braid where the heat issues are worse? Three strand where twist becomes an issue at higher loads? Brait where the chafe is more of an issue but the energy absorption is better?
No right answers of course

Great to hear hear that some manufacturers provide all this information!

For my app I settled for a "simple" measurement of the snubber / bridle: All I need to know is by how much it stretches in 8 Beaufort of wind (and no swell). The beauty of this approach is that it is automatically 'calibrated' for the vessel at hand.

If one has a luggage scale or something like that, one can measure this without having to experience 8 Beaufort at anchor. From the app one reads off the wind force / anchor load (in the absence of swell). Next one pulls the snubber / bridle on the deck until it matches that force and then one measures the stretch. One may have to settle for less than 8 Beaufort, if the scale cannot cope with such a high load. Since the wind force goes quadratically with the wind speed, it is easy to do the scaling arithmetic.

[MathiasW]

Sometimes I hear folks saying it is the chain lying on the seabed that is holding the vessel, not the anchor. If that were true, we would not need an anchor in the first place.

So, how much does a chain actually contribute to the holding power and in doing so provides some relieve to the anchor.

According to Taylor and Valent (https://www.orcina.com/webhelp/OrcaF...ictiondata.htm) the friction coefficient of a chain in mud is as high as 0.9.

So, a 10 mm chain weighing 2 kp/metres in water has a frictional force of 1.8 kp per metre of chain lying on the seabed. If 10 metres chain are on the seabed, it is 18 kp or 17.7 daN. This is not nothing, but only a fraction of what a modern anchor holds. Again, this would depend on the seabed, but a 28 kg anchor can hold 200 - 1000 kp.

So, I rather trust my anchor!

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

[delphys44]

Thank you Bruce K for the quote from from Big Bob
on chain in the boat. Add a period. End of discussion.

[MathiasW]

Originally Posted by delphys44

Thank you Bruce K for the quote from from Big Bob on chain in the boat. Add a period. End of discussion.

Well, despite all of your perhaps 100 metres of chain deployed and not being in the locker, you may still end up on the beach with this approach...

The entire discussion is about how to use the chain efficiently, and to know when you need to help the chain when it fails - in shallow water - by deploying effective snubbers or bridles.

And there may be situations when it is crowded and you want to know with how little chain you can get away with and still be safe at anchor. With your all-chain-out approach you will not be very popular in a crowded anchorage, for sure!

[MathiasW]

In my AnchorChainCalculator app I have so far modelled the snubber / bridle in a linear fashion: The snubber stretch x as a function of applied force f is x = c*f with a 'spring constant' c.

This is not quite realistic, though, as is easily seen when applying very large forces. At some point the snubber will stretch only very little more, and eventually it will break.

In an attempt to make a somewhat more realistic modelling I have now set my eyes on this nonlinear function: x = b*ln(1+c*f), when b,c>0. This function has some nice properties: It is monotonically increasing, it increases slower and slower as the force increases, and I can integrate it analytically to calculate the energy stored in the snubber, invert it, whatever...

The two parameters b, c are then determined by specifying the stretches at 6 Beaufort and 8 Beaufort.

Still not matching reality 100%, but I think it is getting closer...

Comments most welcome! I am coding as we speak...

Cheers, Mathias

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