Online tutorial tool for calculating anchor loads and required minimal chain lengths

[MathiasW]

Anchoring is a very controversial topic, I know! Still, I would like to put forward a free tutorial tool my son and I have created that allows one to estimate the maximal anchor load and the minimally required chain length after providing input parameters for the vessel as well as sea and weather conditions (i.e. swell and wind / gusts). It works with various physical units, like daN (deka Newton), kp (kilo pond, which is roughly a daN), or imperial units of pound and feet - the button on the top far right. Depending on which country you are coming from, the tool will try to make an intelligent guess to set the default correctly. The tool can be used in Basic Mode and Expert Mode. Advise is to start in Basic Mode and take it from there.

Have a look at the enclosed table, which shows the results for various anchoring scenarios. Wind and (large) swell is always the same and the maximally available chain is fixed at 50 metres. I chose three different anchor depths (measured from the bow, of course): 3, 5, and 9 metres. Finally, I varied the quality of the snubber / bridle - I define the quality by the snubber stretch at a given wind strength. First, if you look at 3 metres and no snubber, the tool gives an error, meaning that within my model the chain alone cannot cope with the (large) swell energy. Then, comparing 5 and 9 metres of anchor depth, one finds that, naturally, the pulling angle at the anchor shaft will slightly increase as the chain length is fixed, but at the same time the anchor load will go down from 1322 daN to 480 daN, which is less than half! This massive reduction of the anchor load more than compensates for the slight reduction in maximal holding power caused by the increased pulling angle. Finally, when you use an "excellent snubber", the anchor load gets further reduced to a mere 156 daN. This is less than 1/8 of the anchor load at 5 metres anchor depth and no snubber. What a difference! These results clearly show the importance of using excellent snubbers in shallow water in particular. Using more chain would not make much of a difference, as the chain is not effective in shallow water.

Of course, I did assume here the swell to be the same at all anchor depths (and rather large), which may not be true. But if it is, then it is definitely safer to anchor in deeper water with that amount of swell. (In my model, vessel velocity at anchor defines the swell.)

So, contrary to popular belief, it is not always better to seek the most shallow place to anchor. Experienced sailors will know this, but at least for me I did not know this when I started sailing - in my sailing classes there was no mentioning of this and the simple rule was: Use a scope of 3:1 in calm weather and more when it gets windy...

Here is the link to the online tool: https://anchorchaincalculator.com

If you do not like to read the tutorial or watch the short tutorial video, here are some comments on the required inputs: Vessel type refers to whether it is a monohull, a cat, or a tri, and how its built is: slim, medium, or bulky. This information is required to estimate the Windage area of your vessel. Anchor depth is divided into two fields, which you can use as, e.g., freeboard and water depth, but any other split is fine as well. Vessel velocity at anchor is the maximally observed speed over ground in reverse direction away from the anchor, whilst at anchor. It is difficult to get this one precise, as plotters are not very precise, but often it is something in the range of 0.1 to 0.7 kn. This entry, together with Vessel weight determines the swell energy. As to Snubber quality - in Basic Mode I define it qualitatively in plain English words. Not scientific, I know, but the names do have a meaning - a good snubber is a good snubber, and a lousy one is a lousy one... If you want to dig deeper here, use the Expert Mode. For instance, an "Excellent snubber" has a stretch of 1.6 metres at 8 Beaufort wind strength, or 40.2 kn (in the absence of swell, which would come on top as a load). If you do happen to have the data sheet of your snubber line, you can use the Rule of Three to work out the input that the tool requires. If you use the qualitative descriptions of the snubber and find that the snubber stretch the tool calculates is very different from what you actually observe, you need to adjust the snubber quality rating you have given your snubber. My observation is that many people overrate their snubber initially - certainly I did when I started this... Obviously, a snubber of only 2 metres length cannot stretch by yet another 1.6 metres!

And when I say swell, I mean all kinds of waves hitting the vessel.

This tool is not meant to be used every time you anchor, but rather as a tool to play around and see how different scenarios pan out. For instance, it may allow you to make a first quick assessment of the quality of the snubber you are using. I hope it will help you to make better choices for anchoring more safely.

Feedback most welcome!

Cheers, Mathias

PS: If you want to understand the physics and model in more detail, in a nutshell, it is catenary plus a spring (the snubber) bolted onto it with matching loads. For yet more information, please visit: https://trimaran-san.de/die-kettenku...atiker-ankert/

[dfelsent]

Mathias I truly appreciate the effort you put into this. I have learned quite a bit from you.
But I do think that your assumption that the swell is the same at all anchor depths can lead to false conclusions about ideal anchoring locations.
I understand that modeling sea state with fetch and depth and width is yet one more complication. But I think it may be worthwhile incorporating a pre-existing model into your swell input. In 50 knots of breeze the wave height in 10 meters of water is wildly different from the wave height in 3 meters.

But yes, lots of chain and appropriate snubber length helps in both cases. [emoji1]

[HankOnthewater]

Thank you Mathias
Have you ever used a load cell to check if the calculated data matches the actual forces?
I have used formulas in an Excel sheet to calculate the forces, and have not been able to make it as simple as you did. Well done.
what else would be do on a cold and rainy night playing with figures. Even if the figures are out, then at least we get a much better understanding of the forces at play.

[MathiasW]

Originally Posted by dfelsent

Mathias I truly appreciate the effort you put into this. I have learned quite a bit from you.
But I do think that your assumption that the swell is the same at all anchor depths can lead to false conclusions about ideal anchoring locations.
I understand that modeling sea state with fetch and depth and width is yet one more complication. But I think it may be worthwhile incorporating a pre-existing model into your swell input. In 50 knots of breeze the wave height in 10 meters of water is wildly different from the wave height in 3 meters.

But yes, lots of chain and appropriate snubber length helps in both cases. [emoji1]

Hi defelsent, thanks for this!

Perhaps I should clarify my statement a bit more. I am not making the assumption per se that the swell in shallow water is always the same as in deep water. What I am saying is that IF it is the same, then it is easier to absorb in deeper water. But folks will have to judge each time, whether this is the case for them. For me, as a scientist, it is preferable to compare situations where as few as possible parameters are different, so that I can understand the effect of the changing parameter. So, assuming the swell to be the same is just one such exercise. It is a bit formal, admittedly, but if helps to understand what is going on.

If you happen to have a pointer to a pre-existing model for wave heights etc, I'd appreciate if you could provide it. Thanks

At 50 kn of wind, the waves in 10 m anchor depth will most likely be more tolerable than in 3 m. For one thing, one might already be in the surf in the latter case. And in a wave bottom one might scratch the sea ground.

Again, thanks for this very positive feedback!

Cheers, Mathias

[MathiasW]

Originally Posted by HankOnthewater

Thank you Mathias
Have you ever used a load cell to check if the calculated data matches the actual forces?
I have used formulas in an Excel sheet to calculate the forces, and have not been able to make it as simple as you did. Well done.
what else would be do on a cold and rainy night playing with figures. Even if the figures are out, then at least we get a much better understanding of the forces at play.

Hello HankOnthewater, thanks also to you for this kind feedback!

I have calibrated my bridles with crane load cells before using them. So stretching them with a winch and comparing this with the wind load, and calibrating it this way. But I have not measured it whilst in use at 8 Beaufort. Others have done, like Thinwater, and he reported back that his measurements are within 10-15% of my calculations. That is more than enough for me in terms of accuracy. I am rather confident that the numbers are reasonably close as the Basic Mode is based on real measurements done by the late Robert Smith. His work was on normal sized monohulls, and it showed very beautifully the dependency on vessel length and wind speed. I then only added fudge factors for slim and bulky vessels, for cats and tris.

But even if the numbers were less precise, the trend is very obvious and the main conclusions will stay. In fact, this is my biggest take-away and I use that when judging a new anchorage.

Most of this was done whilst being in a lockdown anchoring close to Panama City. I needed something to keep me sane - or at least make my state of mind not worse...

Cheers, Mathias

[Stu Jackson]

Originally Posted by MathiasW

Anchoring is a very controversial topic, I know! ............
..........
...............

Actually, it is not.



What is controversial are the anchors themselves.


Interesting effort, enjoy your anchorage in Panama.

[MathiasW]

Originally Posted by Stu Jackson

Actually, it is not.



What is controversial are the anchors themselves.


Interesting effort, enjoy your anchorage in Panama.

Thanks! Actually, I am about to enter Sea of Cortez now - Mazatlan...

[rondelais]

Mathias - Great work. I installed the app on my phone and it works great. As a note - I also did some anchor rode modeling, and have been using the result for a few years. My model was not as sophisticated as yours, with some simplifying assumptions. Despite that, the results match quite closely for all the cases I have tried so far. One thing I did include in my model was the yawing behavior, but I did it based on experience with my boat - I really don’t know how to work that out in a generic model, since hull geometry and above-deck windage will be so different from boat to boat. I appreciate the way you have tried to educate all on the fact that shallow water is not always your friend, and that one needs a lot more “scope” in shallow water. With chain, deep water (up to a point) is much more comfortable, and easier on your gear. For my boat, I created a simple nomograph for depth, wind, and wave to recommend scope. Of course, I am too lazy to refer to it every time, although I do if any weather is expected. What is your next math project?

[dfelsent]

MathiasW
I have spent a few minutes looking for limited fetch and depth wave height prediction models.
I found a few interesting papers, and a handbook written by the US Army Corp of Engineers.
In the US the Corp is charged with (among other things) navigation,flood and storm damage protection, and aquatic wetlands restoration. Canals, bridges, dikes etc.
ACE wrote a Shoreline Protection Manual that has some empirically derived models. It is sometimes referred to as SPM ‘84

https://usace.contentdm.oclc.org/dig...coll11/id/1933

Volume 1 has the wave model.

I found an interesting survey of the state of the art from 2020.

https://www.mdpi.com/2077-1312/8/4/260/htm


And a few other references

https://www.jstor.org/stable/4298844

https://www.nature.com/articles/srep40654

https://static-content.springer.com/...ESM234_ESM.pdf

I hope these are of some use.

David

[MathiasW]

Originally Posted by rondelais

Mathias - Great work. I installed the app on my phone and it works great. As a note - I also did some anchor rode modeling, and have been using the result for a few years. My model was not as sophisticated as yours, with some simplifying assumptions. Despite that, the results match quite closely for all the cases I have tried so far. One thing I did include in my model was the yawing behavior, but I did it based on experience with my boat - I really don’t know how to work that out in a generic model, since hull geometry and above-deck windage will be so different from boat to boat. I appreciate the way you have tried to educate all on the fact that shallow water is not always your friend, and that one needs a lot more “scope” in shallow water. With chain, deep water (up to a point) is much more comfortable, and easier on your gear. For my boat, I created a simple nomograph for depth, wind, and wave to recommend scope. Of course, I am too lazy to refer to it every time, although I do if any weather is expected. What is your next math project?

Thank you! Your feedback is really much appreciated! I am not sure on my next project, but perhaps it is pointed at in the next response already?

One thing I guess I need to do is to add a mix of chain and rope to the calculator. I know how to do the maths, but getting the interface intuitive and keep it simple is quite a challenge...

When working on this project I realised that it is very hard to cater for everybody's taste. Some want to be able to characterise non-linear snubbers and more, whilst others want it to be even simpler than the Basic Mode. For some it is easy to get the data sheet of their snubber line, whilst for others it would be a tricky task.

In short, I need to give this some more thoughts...

Cheers, Mathias

[MathiasW]

Originally Posted by dfelsent

MathiasW
I have spent a few minutes looking for limited fetch and depth wave height prediction models.
I found a few interesting papers, and a handbook written by the US Army Corp of Engineers.
In the US the Corp is charged with (among other things) navigation,flood and storm damage protection, and aquatic wetlands restoration. Canals, bridges, dikes etc.
ACE wrote a Shoreline Protection Manual that has some empirically derived models. It is sometimes referred to as SPM ‘84

https://usace.contentdm.oclc.org/dig...coll11/id/1933

Volume 1 has the wave model.

I found an interesting survey of the state of the art from 2020.

https://www.mdpi.com/2077-1312/8/4/260/htm


And a few other references

https://www.jstor.org/stable/4298844

https://www.nature.com/articles/srep40654

https://static-content.springer.com/...ESM234_ESM.pdf

I hope these are of some use.

David

Hi David, thanks so much for all this input! It'll keep me busy for a while!

Cheers, Mathias

[MathiasW]

All, just to update on this thread... I have now uploaded version 2.0.0 to the Apple and Google store, which can now also deal with a mix of rope and chain. The online web tool has not been updated yet - I need my son's help for that...

In a nutshell, I have made quite some fuzz in the past that anchoring in shallow water can lead to dangerous anchor loads when there is no decent snubber / bridle to absorb the shock loads. Chain likes depth was my mantra there.

Now, when using a mix of chain and rope, the story is entirely different. With a chain shorter than the rope, the chain does not absorb energy at all anymore and its main function is to provide the initial turn upwards, away from the seabed. It is the rope which is storing all the energy. With this in mind, it is obvious that unlike a chain, a rope will work equally well in all kinds of water depths, and it is the fact that deeper water means a poorer pulling angle at the anchor shaft, which is to be kept in mind. Consequently, when using a mix of rope and chain, the advice is to stay in shallow water.

Have a look at the table enclosed.

Cheers, Mathias

[Manateeman]

You did a lot of work to construct this calculator. Thank you. I like your blog. The calculator might be useful to folks with similar vessels or that like apps they can plug numbers into. Probably will get them to sleep better at night.
I honestly think the subject is so complex, no computer will give a solution.
Anchor war threads are just the tip of the iceberg.
Vessel design, bottoms, wave action...there are just so many variables.
For example, I have posted many times on the Kodiak anchoring system. It’s not possible to use your calculator with this system. The US Navy Hammerlock, two anchor system will not work either. There are just too many “ systems” .
Anyway, I appreciate all posts even those with whom I disagree so thank you for your work...it gets people thinking.
Kindest regards,
Captain Mark and his manatee crew.

[MathiasW]

Originally Posted by Manateeman

You did a lot of work to construct this calculator. Thank you. I like your blog. The calculator might be useful to folks with similar vessels or that like apps they can plug numbers into. Probably will get them to sleep better at night.
I honestly think the subject is so complex, no computer will give a solution.
Anchor war threads are just the tip of the iceberg.
Vessel design, bottoms, wave action...there are just so many variables.
For example, I have posted many times on the Kodiak anchoring system. It’s not possible to use your calculator with this system. The US Navy Hammerlock, two anchor system will not work either. There are just too many “ systems” .
Anyway, I appreciate all posts even those with whom I disagree so thank you for your work...it gets people thinking.
Kindest regards,
Captain Mark and his manatee crew.

Thank you very much for this kind feedback. And yes, I agree, there are many variables and many approaches to anchoring. But I still believe my approach will catch 80% or so, at least for the 'normal' non-professional sailing community, which is a start.

I do believe, though, that it would be possible to create a computer program that could calculate it all. But it would require a lot of precise input data to give precise results, and nobody will be able to provide those on a 'normal' vessel. Hence, there is no point in creating such a super powerful tool and one is better off trying to focus on the most important variables - as few as possible - to get it right to perhaps 80% for the average user.

And yes, the most important thing is to think about the anchoring and weigh the different pros and cons when making an anchoring decision, not the precise numbers. My work will hopefully help others as one of a couple of inputs for their thoughts. I use the app myself only very occasionally nowadays. It helped me to understand the matter better and with that additional insight, I now make my decisions where and how to anchor - and it is quite different to what it was 3 years ago. It is my crew who uses the app sometimes to double-check my decisions...

So, this insight is what I like to pass on to others. Like chain performance in shallow water, or lack thereof, importance of very elastic snubbers, etc.

Thanks again for the feedback! Much appreciated!

Cheers, Mathias

[carlosproa]

Originally Posted by MathiasW

All, just to update on this thread... I have now uploaded version 2.0.0 to the Apple and Google store, which can now also deal with a mix of rope and chain. The online web tool has not been updated yet - I need my son's help for that...



In a nutshell, I have made quite some fuzz in the past that anchoring in shallow water can lead to dangerous anchor loads when there is no decent snubber / bridle to absorb the shock loads. Chain
Cheers, Mathias

I did not understand the table, but you are saying for shallow depths better to have a combination on chain and rope? When I was a kid back in late 60’s in Venezuela’s Morrocoy keys, we had a stilt house back then and my Dad did used that combination for up to 5 meters depth and changed to all chain for deeper anchoring. He just used what the local fisherman did back then