Mathematic approach to anchoring scope

[MathiasW]

Safer at anchorage!

It had been suggested by some in this thread that an app might be beneficial to the community...

So, here it is! AnchorChainCalculator

I have used the corona lock down time to develop an app to calculate what the minimal required anchor chain length needs to be. More precisely, the App

- Calculates the required minimal anchor chain length based on vessel characteristics and weather / sea conditions.
- Calculates the anchor load and pulling angle at anchor shaft.
- Works with snubbers & bridles.
- Deals also with this case: Chain not long enough? The Anchor Chain Calculator will tell you what effect this has.

You can find more information on its home page:

https://trimaran-san.de/anchor-chain-calculator/

For now I have created Apps for iPhone and iPad. The latter needs iOS 13 or more to make use of the screen size and not default to the screen size of an iPhone 5 (), but both Apps work all the way back to iOS 10. If there is sufficient interest, I might create an Android version as well.

The app was developed whilst anchoring here for 6 months, so I had ample time to test it...

And thanks to this community for all the feedback in this rather long thread!

Cheers

Mathias

[MathiasW]

Hi, whilst uploading my own AnchorChainCalculator to the Google Play Store (link on my web page), I came across this free Anchor Chain Simulator:

https://play.google.com/store/apps/d...in&hl=en&gl=US

It calculates the catenary for static anchoring, but does not include dynamic anchoring effects as discussed earlier in this thread. So, no account for the elasticity of the snubber / bridle, for instance. It also does not cater for imperial chains, but you can edit an existing chain, if you like. In fact, it does not have imperial units at all, and it also requires you to know the windage area of your vessel, which I had addressed using the late Robert Smith's anchor gear tables, which are based on real measurements. With that approach you only need to know the length of the vessel and make an adjustment for mono / cat / tri, etc.

So, I still prefer my own app, but I thought it is only fair to mention this one as well.

[Texasvlad]

Originally Posted by MathiasW

All, I have stumbled across this rather useful link - the late Robert Smith's Ground Tackle Loads Table:

http://www.plaisance-pratique.com/IM...0-17-Smith.pdf

These are based on real measurements of a variety of vessels and wind strengths and then interpolated for a range of wind strengths and vessel sizes.

Mathias,
Are tensions in Robert Smith Table that you have referred in N or in lb-s? What is UoM?
Regards,
Vlad

[MathiasW]

Originally Posted by Texasvlad

Mathias,
Are tensions in Robert Smith Table that you have referred in N or in lb-s? What is UoM?
Regards,
Vlad

Vlad, the Robert Smith Table is in lbs.

UoM I do not see in that table. Where did you read that? LOA is Length Over All, in feet in that table.

Cheers

Mathias

[Alan Mighty]

Originally Posted by MathiasW

I came across this free Anchor Chain Simulator:

https://play.google.com/store/apps/d...in&hl=en&gl=US

It calculates the catenary for static anchoring, but does not include dynamic anchoring effects as discussed earlier in this thread. So, no account for the elasticity of the snubber / bridle, for instance. It also does not cater for imperial chains, but you can edit an existing chain, if you like. In fact, it does not have imperial units at all, and it also requires you to know the windage area of your vessel, which I had addressed using the late Robert Smith's anchor gear tables, which are based on real measurements. With that approach you only need to know the length of the vessel and make an adjustment for mono / cat / tri, etc.

Yes, ChainSim (aka Anchor Chain Simulator) has been around for several years, although the user base is tiny.

I have used ChainSim as my primary tool for calculating scope for a year or two. I quite like its approach, forcing the user to be aware of the likely maximum wind.

I live in a metric world, so I see not the limitations of traditional units to which you refer. I use BBB chain (the old US standard of Burden's Best Best iron) and did not have a problem entering its technical specs into ChainSim.

I've not been in contact with the creator of ChainSim, but have the understanding that it is based on Alain Fraysse's mathematics.

Before I adopted ChainSim, I used look-up tables based on John Knox's anchor mathematics. Knox's approach also focused on windspeed as a major variable; Knox identified 40 knots as an inflexion point.

I've attached two screenshots I've just taken of ChainSim. The difference between the two screenshots is only the estimated max windstrength while at anchor.

The deal is that:

1. you set up the app for your boat, chain, offset between your depth gauge reading and the height of your bow roller etc;

2. at anchoring you input your depth gauge reading, estimated max wind speed while at anchor, length of snubber, and your estimate of optimum rode; and

3. the app shows your estimate of optimum rode in black & red and paints beside it (or over it) the app's calculated optimum rode in green.

The zero cost of ChainSim (Anchor Chain Simulator) is of course in its favour!

I also retain respect for the work of John Knox.

[MathiasW]

Alan,

Yes indeed, I like that approach as well, and it has also been my approach.

Out of curiosity - how did you determine the windage area of your vessel, which is a required input? I had tons of feedback that this would be a major blocking point for this kind of approach and that something simpler would be needed.

Cheers

Mathias

[Alan Mighty]

Originally Posted by MathiasW

Out of curiosity - how did you determine the windage area of your vessel, which is a required input? I had tons of feedback that this would be a major blocking point for this kind of approach and that something simpler would be needed.

Indeed.

John H. Knox took the view that a strain gauge is needed to deal with the complexity of windage and a few other factors. All calculations and other estimates are a joke. Knox marketed a strain gauge to do the job for cruisers.

Larsson & Eliasson present a beautiful study in calculating the frontal effective area of yachts. See attached Larsson Eliasson.gif.

The sad truth is that all (or almost all) boats tack to strong winds and move to waves. The usual textbooks dealing with boats (both power and sail) suggest a fudge factor 130% (i.e. increasing the frontal area by 30%).

I've read Japanese naval architecture books dealing with cargo ships that go further and suggest the fudge factor has to be 200% of frontal area (because of Covid-19, I cannot get to where I have those books stowed). Nipponese authors (translated into English in academic works) have done considerable work on the dynamics of cargo ships as they approach the point of dragging anchor in strong winds (Nippon has not a few ship anchorages that are open). Should you have the capacity to search academic journals and books, the magic terms to use in English are "figure-eight horsing" and "dragging anchor with yaw and sway".

In my case, I played with the established estimates (e.g. including those you have cited yourself such as 0.717*LOA*LOA - likely all derived from R Smith) and work such as from the Flook anchor people (see: Windage & Velocity) and then fudged frontal area until the results looked acceptable.

All because John H Knox convinced me that a strain gauge (which I don't have) is the only way of accounting for otherwise immeasurable and uncalculatable factors such as the aerodynamic roughness of sail covers and dodgers.

One job I haven't done yet is to work through Knox's formula for 40 knots, compare that to what ChainSim currently calculates for 40 knots, and then adjust the effective windage area in ChainSim until it meets Knox's formula.

[Alan Mighty]

Originally Posted by Alan Mighty

One job I haven't done yet is to work through Knox's formula for 40 knots, compare that to what ChainSim currently calculates for 40 knots, and then adjust the effective windage area in ChainSim until it meets Knox's formula.

I found my look-up tables based on John H Knox's work from nearly 20 years ago.

I made one major error when I said earlier Knox "identified 40 knots as an inflexion point." The correct version is that Knox identified 30 knots as an inflexion point.

Knox, or at least my reading of him, divided anchoring into three conditions:

a. anchoring in protected waters;

b. anchoring in less protected waters; and

c. anchoring in above 30 knots.

For >30 knots, my look-up table (based on my reading of Knox's work, which was largely published in UK magazines including Practical Boat Owner and Yachting Monthly), suggest that for my boat, Knox suggested one of two strategies: i. a scope of 10:1; or ii. a chain rode (in metres) = k * windspeed (in knots). K was a factor that for my boat ranged from 1.0 (at depth + offset of 5.3 m) to 1.6 (at depth + offset of 13.3 m). Using 40 knots as the windspeed, my Knox table recommends rode 5% longer than ChainSim recommends.

For protected waters, Knox's recommendations are exceeded by the recommendations of ChainSim.

For less protected waters and <30 knots, Knox's calculation of chain force is a good match for that of ChainSim, but Knox recommended more chain (I have to try a range of depths before I have a clear picture).

My conclusion so far is that I need to increase my windage estimate!

[MathiasW]

Alan, thanks for sharing all this information!

In fact, I had also studied some Japanese research papers on this topic (translated, fortunately ). It would appear to me they are more advanced than their European counterparts in commercial shipping.

I would also tend to say that one needs to measure the windage area, everything else is potentially dodgy. For this end I got myself a gauge for really heavy suitcases, and the idea is that I attach the boat to a free-standing pole in the water and measure the tension in a more or less horizontal rode. But Corona has so far prevented me from finding such a pole...

On the other hand, most folks will not go to that trouble and thus in my model / app I introduced the Basic Mode, where the windage area is derived from Robert Smith's table and then I apply a fudge factor as you say, to account for different vessel types - roughly at least. But one can always switch back and forth between Basic and Expert mode to see what one has done.

The one important aspect that I find missing in the ChainSim app is the lack of support for snubbers / bridles. Yes, one can configure a snubber in this app, but the author says it is not elastic at all, meaning that an important aspect of the snubber / bridle is not taken into account. Only its length is.

In particular in shallow water, when chains are getting to their limits, the elasticity of a snubber / bridle is vital for absorbing shock loads.

In fact, shock loads is something that ChainSim does not model at all. As you say, it is compatible with Alain F. approach from years back, but this is static anchoring only. Dynamic anchoring is not accounted for.

When anchoring in calm water, this will not matter, but when swell becomes important, it can easily add 10 metres or more to the required minimal chain length. And without a snubber one can even have an inversion, where MORE chain is needed when anchoring in more shallow water, rather than LESS - quite counterintuitive at first.

But in any case, in my view ChainSim is MUCH better than the conventional scope approach.

[thinwater]

Originally Posted by Alan Mighty

Indeed.

John H. Knox took the view that a strain gauge is needed to deal with the complexity of windage and a few other factors. All calculations and other estimates are a joke. Knox marketed a strain gauge to do the job for cruisers...

I've read Japanese naval architecture books dealing with cargo ships that go further and suggest the fudge factor has to be 200% of frontal area ...the magic terms to use in English are "figure-eight horsing" and "dragging anchor with yaw and sway"...


All because John H Knox convinced me that a strain gauge (which I don't have) is the only way of accounting for otherwise immeasurable and uncalculatable factors such as the aerodynamic roughness of sail covers and dodgers....

You can get a serviceable digital chain scale on Amazon for ~ $150 and get an actual feel for the effect of water depth, yawing, and rode type on your actual boat. A much more efficient use of time than pondering the imponderable. I'm an engineer and understand the calculations, but I also understand that when the inputs are crap and the theory contains too many simplifications and assumptions, it's time to measure.


In most cases, the calculators are pretty good. But is your boat typical? Maybe. Maybe not. Maybe you yaw more. Maybe the waves are at an odd angle. Measure it.

[MathiasW]

Originally Posted by thinwater

You can get a serviceable digital chain scale on Amazon for ~ $150 and get an actual feel for the effect of water depth, yawing, and rode type on your actual boat. A much more efficient use of time than pondering the imponderable. I'm an engineer and understand the calculations, but I also understand that when the inputs are crap and the theory contains too many simplifications and assumptions, it's time to measure.


In most cases, the calculators are pretty good. But is your boat typical? Maybe. Maybe not. Maybe you yaw more. Maybe the waves are at an odd angle. Measure it.

Yes, measuring the forces on the vessel is definitely the right thing to do. However, I am struggling a bit how to decompose the measured force into the wind component (aka windage area), and the force caused by swell and other effects.

Of course, one could lump it all into an effective windage area, but at least with regards to swell this approach is not preferred, since the effect of swell is dependent on water depth.

For this reason I would want to measure the force in calm sea and when the vessel is not "sailing at anchor". Then I should mainly measure the windage area.

[Bill_Giles]

Of course one can assist the anchor by using an anchor weight, called variously a kellet, chum or angel. But this throws all the calculations out of the window. But it is useful in a crowded anchorage or a tight spot as a shorter scope can be used. Knowing what it should be is still a problem. Not that I have ever used one although I have a 10kg weight on standby.

[rslifkin]

Originally Posted by Bill_Giles

Of course one can assist the anchor by using an anchor weight, called variously a kellet, chum or angel. But this throws all the calculations out of the window. But it is useful in a crowded anchorage or a tight spot as a shorter scope can be used. Knowing what it should be is still a problem. Not that I have ever used one although I have a 10kg weight on standby.

Pretty much the only use for one of those is to keep rope rode from wrapping around the keel. Other than that, they're pretty much worthless. You're far better off taking the weight you'd carry in that form and just adding it to the anchor.

[MathiasW]

Originally Posted by rslifkin

Pretty much the only use for one of those is to keep rope rode from wrapping around the keel. Other than that, they're pretty much worthless. You're far better off taking the weight you'd carry in that form and just adding it to the anchor.

Yes, anchor or chain.

If the kellet is positioned very close to the anchor, but floating, it can at best be equivalent to slightly less than its own weight in water as additional chain.

If you position it at half the anchor chain, it is more to add more dampening into the system.

But anything that you can reasonably handle whilst hanging head over at the bow roller, will not amount to much, really.

So, for perhaps 5 metres less swinging radius, you get a lot of extra hassle to work through if you have to weight the anchor in an emergency...

[MathiasW]

And some more brain gymnastics on the subject of anchoring.... 😜

What is the maximum amount of energy an anchor chain can actually absorb? To solve this, I look at the attached diagram. In the first case, the boat lies at an anchor depth of Y in absolute calm. The chain hangs vertically downwards. Then comes a gigantic gust or swell, so that the chain gets completely taut and practically forms a straight line between anchor and bow. The potential energies of these two states are easy to calculate, as it is always only the respective chain weight at half height (Y/2). The difference is then the maximum energy the chain can absorb: m g /2 Y (L - Y), where m g is the weight of the chain per running metre in the water, and L is the chain length.

So we see - once again - that in shallow water, as Y becomes smaller and the chain length L remains constant, the chain can absorb less energy than in deep water. So the chain likes depth and hates shallow water. And how deep should it be, if the chain has its way?

The maximum of m g /2 Y (L - Y) is reached for a fixed chain length at L/Y = 2, i.e. when the chain has twice the water depth and the scope is 2. Then the chain works best in this scenario.

Unfortunately, the chain has done the maths without the anchor. If the chain gets so taut that it is almost a straight line, then the load transferred to the anchor is enormous and it will break out easily.

Therefore, in practice, one will choose a much larger chain length to water depth ratio - the scope L/Y.

But as I said, the chain does not like shallow water. There, a very elastic snubber / bridle must take over and absorb all load peaks.

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