Mathematic approach to anchoring scope

[MathiasW]

So, here are some new thoughts on how to account for the effect of currents in the water one the anchor load:

Let me start with an engine of, say, HP horse power and I am using it in calm sea, no tide or current in the water, without wind, or even better wind from the aft so that the apparent wind is zero. In this scenario I achieve a certain maximum speed V. I also assume that this speed is below the hull speed, as beyond that the physics will be different.

Then the work done per second is HP = F * V, where F is the friction force acting on the hull. Or, in other words, we have F = HP/V. (This assumes that 100% of the horse power is actually being used. In reality, it may be less than that.)

Now, how to map this to a current pushing the vessel in a certain direction? Let the current run at a velocity v. Frictional force will be quadratic in velocity, and so I would say the additional anchor load due to current will be

f = (v/V)^2 * F = v^2/V^3 * HP.

Does this make sense? (Of course, this force would need to be added to the anchor load given by wind and waves using a force parallelogram)

[Bill_Giles]

I am an aircraft engineer and am ok with maths. But I’d never sit at my chart table with my slide rule in hand and work out how much chain to lay out. My view is that 5 it is times in shallower water and three times in deeper with a long snubber.

Then after ensuring that the anchor is set observe the chain angle, if it comes anywhere near tight with no catenary then let out a bit more. Then set the anchor alarm and don’t drink.

Always have an escape plan if it kicks up in the night and you cannot get the anchor to hold.

[MathiasW]

Sure, I am just curious and like to understand things...

My latest attempt got triggered by the photo I made earlier today here in La Cruz, Mexico...

Clearly, wind and current have different thoughts where to pull the vessel.

[MathiasW]

So, after a long silence, a small update:

The other day, harbour police forced me to relocate into a crowed anchorage field, where I could not deploy as much chain as I would like. And as a storm was heading towards us -- the very reason the harbour police forced me to leave the previous anchorage, which I consider very safe with the anchor gear I have -- I was a bit uneasy and started to think how to get more elasticity into my anchor gear without increasing my swinging radius. I had more than enough chain in the locker, but I could not make any use of it...

The solution I found was to massively increase the length of the slack chain segment between bow and chain hook. In the past, I had always kept this segment short enough so that it would limit the maximal stretch of the (long and elastic) snubber / bridle that I deploy. The idea had been that this approach will prevent the snubber / bridle from being overloaded in very severe gusts.

Well, but if overload is not the issue, then one can figure out what happens when increasing the length of this segment.

After some mathematical analysis, I found that the potential energy stored in this slack chain segment is quadratic in its length, and this can be tapped into when the snubber / bridle starts to stretch (and thereby stretch and lift the slack chain segment). Because of the quadratic dependency, it pays off to make this slack chain segment as long as possible, then the gain is the largest. One should not expect a miracle here, though, and it will only work if the snubber / bridle is very elastic to begin with, but it does help the snubber and the rest of the chain to buffer strong gusts.

In some sense, this approach is similar to deploying a kellet closer to the bow - yet without the hassle the latter brings in its deployment.

One does need to pay attention to the nature of the seabed, though. If it is all sand like here, there is no risk of this very long slack chain segment getting caught somewhere and thereby killing the entire setup. In other cases, one has to make sure it will never touch the seabed.

A bit more detail can be found here, including an update to the long LaTeX document:

https://trimaran-san.de/en/die-kette...atiker-ankert/ (in English, despite the German in this link... )

My anchor chain calculator at

Anchor Chain Calculator

does not include this effect yet, but it may be useful to test out other setups.

And yes, no problems with the storm that has just passed us.

Cheers, Mathias

[wrwakefield]

Originally Posted by MathiasW

So, after a long silence, a small update:

The other day, harbour police forced me to relocate into a crowed anchorage field, where I could not deploy as much chain as I would like. And as a storm was heading towards us -- the very reason the harbour police forced me to leave the previous anchorage, which I consider very safe with the anchor gear I have -- I was a bit uneasy and started to think how to get more elasticity into my anchor gear without increasing my swinging radius. I had more than enough chain in the locker, but I could not make any use of it...

The solution I found was to massively increase the length of the slack chain segment between bow and chain hook. In the past, I had always kept this segment short enough so that it would limit the maximal stretch of the (long and elastic) snubber / bridle that I deploy. The idea had been that this approach will prevent the snubber / bridle from being overloaded in very severe gusts.

Well, but if overload is not the issue, then one can figure out what happens when increasing the length of this segment.

After some mathematical analysis, I found that the potential energy stored in this slack chain segment is quadratic in its length, and this can be tapped into when the snubber / bridle starts to stretch (and thereby stretch and lift the slack chain segment). Because of the quadratic dependency, it pays off to make this slack chain segment as long as possible, then the gain is the largest. One should not expect a miracle here, though, and it will only work if the snubber / bridle is very elastic to begin with, but it does help the snubber and the rest of the chain to buffer strong gusts.

In some sense, this approach is similar to deploying a kellet closer to the bow - yet without the hassle the latter brings in its deployment.

One does need to pay attention to the nature of the seabed, though. If it is all sand like here, there is no risk of this very long slack chain segment getting caught somewhere and thereby killing the entire setup. In other cases, one has to make sure it will never touch the seabed.

A bit more detail can be found here, including an update to the long LaTeX document:

https://trimaran-san.de/en/die-kette...atiker-ankert/ (in English, despite the German in this link... )

My anchor chain calculator at

Anchor Chain Calculator

does not include this effect yet, but it may be useful to test out other setups.

And yes, no problems with the storm that has just passed us.

Cheers, Mathias

Mathias,

I have always followed your work with interest, use your anchoring app to sanity check my own conclusions, and appreciate the effort that goes into maintaining an anchor app that isn’t just a scope ratio calculator.

Your comment highlighted above caught my attention as it describes one of my inclement weather precautions when at anchor [typically in ‘deeper’ water; 60-90+ ft; all chain rode].

From a page of ideas and notes I maintain regarding anchor bridle considerations for our boat:

If inclement weather is anticipated, I will pre-install a second, independent bridle, with a loop of chain in the water representing the new desired rode length in case it is needed. [e.g., perhaps another 60-100ft of chain to improve holding (increase scope) in a blow- but not touching the bottom.]

The 2nd bridle is fully installed and can be either flaked on deck [with a sacrificial twine belaying the chain at the bridle attachment point] or deployed as a lazy back-up.


Back-up bridle rigged awaiting pre-deployment with additional chain in loop.

If this additional rode [with it's own bridle] is needed, I can cast off the original bridle [i.e., no need to retrieve enough chain in inclement conditions to remove it first...] and let it dangle underwater until retrieved in the future.

This 2nd bridle also serves as a hot backup in case the first bridle is compromised. [e.g., breaks, chafes, etc.]

Rinse. Repeat. If the secondary bridle is deployed in a storm, I will set up a new back-up bridle in case the secondary bridle fails or more scope is needed.

Having realized decades ago that kellets contribute little to my longish [360ft on main bower] all chain rodes in deeper anchorages, I have wondered at the effect of the 60-100lb loop of chain I pre-deploy with my back-up storm bridle.

I look forward to following your findings.

Thank you for sharing your efforts.

Cheers, Bill

[MathiasW]

Originally Posted by wrwakefield

Mathias,

I have always followed your work with interest, use your anchoring app to sanity check my own conclusions, and appreciate the effort that goes into maintaining an anchor app that isn’t just a scope ratio calculator.

Your comment highlighted above caught my attention as it describes one of my inclement weather precautions when at anchor [typically in ‘deeper’ water; 60-90+ ft; all chain rode].

From a page of ideas and notes I maintain regarding anchor bridle considerations for our boat:



Having realized decades ago that kellets contribute little to my longish [360ft on main bower] all chain rodes in deeper anchorages, I have wondered at the effect of the 60-100lb loop of chain I pre-deploy with my back-up storm bridle.

I look forward to following your findings.

Thank you for sharing your efforts.

Cheers, Bill

Bill,

Thanks for this feedback, and I am glad you appreciate my app. It has indeed been (and still is) a lot of work for me, but enjoyable...

I love your setup for storm preparations, as I also have a 2nd bridle laid out in case I need it when a really hefty blow is forecasted.

360 ft is quite a stretch of chain! I have 335 ft and rarely have enough swinging room available to deploy it all.

As to kellets, I could not agree more. If placed at the optimal place, so as close as possible to the anchor, but such that it is not touching the seabed, it will be roughly equivalent to extending one's chain by a stretch of chain having the same weight as the kellet. So, in your example, for 360 ft of chain, if you want to virtually increase this chain by 10%, so by 36 ft, and if I assume for the sake of argument it is a 3/8 inch chain, then you would need a kellet that weighs 48 US pounds in water. This is not a piece of cake to man-handle anymore.. And it just gives only 10%..

Cheers, Mathias

[malbert73]

Hi Mathias
Just downloaded the app. It looks like a great tool.
One question- in the basic version once you calculate chain length, it then enters that length into the "Fix" field near the top. But that needs to be cleared every time you increase or decrease wind strength.
Why is that the case? Seems the app would be most usable if one could just toggle the wind up and/or down (representing real world conditions) as things change, and let out chain.

Most likely, I (as a below average tech user) haven't figured out the fix to this.

[MathiasW]

Originally Posted by malbert73

Hi Mathias
Just downloaded the app. It looks like a great tool.
One question- in the basic version once you calculate chain length, it then enters that length into the "Fix" field near the top. But that needs to be cleared every time you increase or decrease wind strength.
Why is that the case? Seems the app would be most usable if one could just toggle the wind up and/or down (representing real world conditions) as things change, and let out chain.

Most likely, I (as a below average tech user) haven't figured out the fix to this.

Hi, thanks for this feedback!

The Fix field (which indicates a fixed length of chain paid out) stays clear unless one of two things happen:

- you fill this field yourself with a value
- you use the +/- 5 kn buttons to increase or decrease the wind strength.

The reasoning behind the 2nd possibility is the following way of how I use the app:

I first start with wind conditions as I see fit. The Fix field may be left empty or not. I usually leave it empty for a while and play with the wind strength to see how quickly the chain length increases to accommodate for a vanishing pulling angle, even if I do not have that much chain or cannot deploy it for one reason or another. Then, in a 2nd step, I want to know how much more wind can be coped with WITHOUT changing the chain length. That's what the +- 5 kn buttons are for. So, what they do is they will set the current value of the chain as the FIX length, whether you have specified it earlier or not, and step up or down the wind in steps of 5 kn. What will change is the anchor load and the angle of pull there. In particular, I monitor this angle of pull - if it stays less than 5 degrees and the seabed is sand, I say it is still OK for my anchor (other anchors may behave differently). This is my short-cut to see quickly how well the currently used setup (i.e. chain and rope length, type of snubber, if it is chain only) can cope with more wind, without actually changing the setup.

If you just want to see how much chain is needed ideally to make sure the angle of pull at the anchor is zero, you have to leave the FIX field empty and key in a new wind strength by hand, I am afraid. The +- 5 kn buttons would mess this up. They only come in at the 2nd stage.

I designed it with this preference, as this is how I use the app. But I can see that others may have different preferences. Let me think what I can do.

Cheers, Mathias

[malbert73]

Originally Posted by MathiasW

Hi, thanks for this feedback!

The Fix field (which indicates a fixed length of chain paid out) stays clear unless one of two things happen:

- you fill this field yourself with a value
- you use the +/- 5 kn buttons to increase or decrease the wind strength.

The reasoning behind the 2nd possibility is the following way of how I use the app:

I first start with wind conditions as I see fit. The Fix field may be left empty or not. I usually leave it empty for a while and play with the wind strength to see how quickly the chain length increases to accommodate for a vanishing pulling angle, even if I do not have that much chain or cannot deploy it for one reason or another. Then, in a 2nd step, I want to know how much more wind can be coped with WITHOUT changing the chain length. That's what the +- 5 kn buttons are for. So, what they do is they will set the current value of the chain as the FIX length, whether you have specified it earlier or not, and step up or down the wind in steps of 5 kn. What will change is the anchor load and the angle of pull there. In particular, I monitor this angle of pull - if it stays less than 5 degrees and the seabed is sand, I say it is still OK for my anchor (other anchors may behave differently). This is my short-cut to see quickly how well the currently used setup (i.e. chain and rope length, type of snubber, if it is chain only) can cope with more wind, without actually changing the setup.

If you just want to see how much chain is needed ideally to make sure the angle of pull at the anchor is zero, you have to leave the FIX field empty and key in a new wind strength by hand, I am afraid. The +- 5 kn buttons would mess this up. They only come in at the 2nd stage.

I designed it with this preference, as this is how I use the app. But I can see that others may have different preferences. Let me think what I can do.

Cheers, Mathias

Thanks, that's a helpful explanation. It would be nice if you could select whether to "fix" the length of chain or not by pressing a button- that way you could fix your chain length for your use case, and others could vary wind speed many times to see how much chain to adjust without having to manually clear the "fix" field.

[MathiasW]

Originally Posted by malbert73

Thanks, that's a helpful explanation. It would be nice if you could select whether to "fix" the length of chain or not by pressing a button- that way you could fix your chain length for your use case, and others could vary wind speed many times to see how much chain to adjust without having to manually clear the "fix" field.

okido, thanks for this feedback! I will give this some thoughts how best to go about it without making the interface even more busy...

Cheers, Mathias

[wrwakefield]

Originally Posted by MathiasW

okido, thanks for this feedback! I will give this some thoughts how best to go about it without making the interface even more busy...

Cheers, Mathias

Mathias,

To me your current logic makes sense because it answers the question: How much more wind can I safely tolerate with the current length of rode (and snubber/bridle)?

If I decide a longer rode might be appropriate, I can then remove the fixed rode value and let the calculator estimate what it deems an appropriate length for the new conditions entered.

I suspect this was your intended workflow.

If you changed the UI, I don’t see a way myself to reduce the number of ‘clicks’ a user would have to perform in this specific what-if scenario; only the workflow would change.

Just another perspective.

Carry on! We trust your judgment…

Cheers, Bill

[davefromoregon]

So, I downloaded the app. I must be doing something wrong since it suggests putting out about half my chain and all of my rope in a given scenario.

I’m also a bit surprised that it doesn’t ask for the weight of the anchor.

What am I doing wrong?

35’ boat
13500lbs
20kg Bruce anchor
Monohull sailboat
130’ of 5/16s”
140’ of rope

[TeddyDiver]

Shallow water catenary (or the lack of it) was discussed earlier in this thread. One point I'd like to make is the reduced size and length of waves in shallow water (the math here https://en.wikipedia.org/wiki/Dispersion_(water_waves) ). Anyways which makes it less prone depth for high wave induced shock loads..

[sv_pelagia]

Originally Posted by davefromoregon

So, I downloaded the app. I must be doing something wrong since it suggests putting out about half my chain and all of my rope in a given scenario.

I’m also a bit surprised that it doesn’t ask for the weight of the anchor.

What am I doing wrong?

35’ boat
13500lbs
20kg Bruce anchor
Monohull sailboat
130’ of 5/16s”
140’ of rope

Depth?!

Wind?

[davefromoregon]

Originally Posted by sv_pelagia

Depth?!

Wind?

Almost any depth or wind. The point is that at least in my experience, the chain is attached to the anchor and the rope is attached to the chain. Until 130’ of chain has been deployed, no rope will be deployed. Under no circumstance will I put out rope until the chain is fully deployed. The app shows 50’ of chain and 20’ of rope being used( more or less). If I’m going to put out 70’, it will all be chain.

however, I assumed 50’ of depth and 20 knots.

I assume I’m making a mistake on the app.