Anchor Scope

[BruceK]

I had a look at the site he pilfered the numbers from and am not convinced of the applied mathematics around his snubber equations or that they conform to the accepted mathematics of a hyperbolic curve under tension or what he calls chain elasticity. Nonetheless he shows a reduction of impact force using a poor snubber and any grade 2 will tell you the forces behind initial acceleration is far less than momentum impact. An insufficient snubber will always result in greater impact forces than tension under an almost straight catenary

 

[MathiasW]

I had a look at the site he pilfered the numbers from and am not convinced of the applied mathematics around his snubber equations or that they conform to the accepted mathematics of a hyperbolic curve under tension or what he calls chain elasticity. Nonetheless he shows a reduction of impact force using a poor snubber and any grade 2 will tell you the forces behind initial acceleration is far less than momentum impact. An insufficient snubber will always result in greater impact forces than tension under an almost straight catenary

I did not "pilfer" anything from anywhere. No need for it, really. I suggest that you simply perform all the mathematics yourself, if you can, and then come back with a perhaps more educated response. Just for your information, I have done the maths from first principles: Deriving the catenary using a variational approach to minimise the potential energy of a chain in a uniform gravity field. That is 2nd year stuff in theoretical mechanics in physics studies and a delight to do. Beautiful mathematics. I have derived the analytical equation for the potential energy of a catenary chain and this is the base of all that follows. Snubbers are bolted on to this using continuity of forces at the joint. So, that is all a pretty established procedure and no pilfering needed at all... The biggest simplification is assuming the snubbers to follow Hook's law.

When a swell or gust hits the vessel and it starts moving backwards, the initial additional load on the chain is small. It keeps building up as the chain gets pulled tighter and tighter, reaching its maximum when the vessel has come to a standstill at a point furthest away from the anchor. I derive the shock loads from this point where the vessel is at rest for a brief moment.

My results are confirmed by the great work done by Bjarne for his online catenary calculator (http://svamanda.dk/anchor/intro). He is including even more effects than I do.

If your German is up to it, I suggest you read my long treaty on this, which you can find on my web page. Only some 38 pages or so full of math... You can step through it and verify or falsify it. Then there would be no need to make vague statements about "not convinced" or or so. The beauty of mathematics is that it can be verified, if one accepts the effort. But if this is too much work for you, I suggest you stop making unqualified comments. Thanks.

Mathias

 

[BruceK]

Fair enough, I did not know you were the author. So retract the pilfer statement. I would very much like to challenge some aspects of your argument specifically around the snubber. (Challenge not handbags at dawn) However rather than just mathematics I'd like to demonstrate with an empirical test. That way everyone can judge for themselves the truth behind your claim. Here comes the dodgy bit, I'm off for the next couple weeks on a cruise, (no it's not a late surprise but been in the planning) but when I get back in early August I'll set up the stage and video the results. Thereafter we can discuss the mathematics behind it.

Book mark this. Until then have some great days on the water ?

 

[Neeves]

I had a look at the site he pilfered the numbers from and am not convinced of the applied mathematics around his snubber equations or that they conform to the accepted mathematics of a hyperbolic curve under tension or what he calls chain elasticity. Nonetheless he shows a reduction of impact force using a poor snubber and any grade 2 will tell you the forces behind initial acceleration is far less than momentum impact. An insufficient snubber will always result in greater impact forces than tension under an almost straight catenary

Frankly I think it is in poor taste, I'm being polite, to say the you think an author pilfered data from a site - but not to add a link to the site from which the numbers are supposedly pilfered. So - show us the data, show us the link.

It seems to engender so much more support if instead of insulting someone - you actually have something that substantiates the reason that you disagree. I am very much in favour of healthy debate but I simply don't respect someone at all, who cannot justify their comments. All talk and no trousers comes to mind. Maybe you were on The Apprentice and learnt your skills there?

I have done the tests, load cell, measured wind speed - my results don't replicate Mathias results, I used a real yacht, in real wind and Mathias used 'theoretical' inputs - but my results in the feld and Mathias results don't look too far apart. I confess I don't have Mathias academic background - and resorted to simple measurements under as controlled conditions as possible - it is anchoring after all - many variables.

I cannot speak for Mathias but I don't need to justify what I do and publish - the results stack up, are reviewed by my peers across a broad spectrum of the marine press, Yachting Monthly, Multihulls, Sail, Practical Sailor, Cruising Helmsman.

Show us your results, do the work, produce the numerical data - and instead of a video (which can be easy to manipulate and might be desperately tedious, videos of a load cell monitor have even less excitement than grass growing) find a reputable individual who can monitor what you do and verify the results.

I look forward to your tests - few are prepared to invest the time so you offer a refreshing addition to the data base. If I may make one request - when you post your initial thread be so kind to post a link to the PBO and Scuttlebutt sections of the Forum - there are a few of us interested and we would welcome the education and the opportunity to comment.

Enjoy your cruise, make the most of it - Covid is not yet beaten.

Stay safe, take care

Jonathan

 

[BruceK]

Oh get back in your handbag. I already apologised to Mathias on that score. As he referenced a webpage that doesnt show the author I was unaware he had written the article on Catenary Anchor Chain Length - Die Kettenkurve - Fun Facts - SAN If you can show the author's credit I'll grovel too. In the comments it looks like Trimaran-San is the author but I dont speak German.
On another note I am pleased you are an acolyte even though your real world tests dont quite marry. Mine dont either. I used to use a rubber snubber but now just use a suitable length of nylon 3 braid. The rubber snubber used to promote snatch at the end of it's travel and caused cracks in the gelwork around the bow cleats. I found that the absence of it was far more beneficial. As such I find the applied mathematics showing a poor snubber reduces shockload in his table highly dubious and I failed to see any equations governing this in the calculation F • t = m • Δ v. nor can I understand snatch force when the chain is at or near maximum extension with the simple formula of p=mv when v is going to be as near zero as dammit. Simple schoolboy equations. Then there is the first year calculation of tension in a hyperbolic arc. The applied mathematics for I am reasonably familiar with and there is enough examples and videos on the net to show this. The calculations leading to proofs for their tension do not resemble what Mathias is arguing. However on that score I will defer to him, on the snubber question, empirical evidence would show that his application of mathematics is not absolute and therefore cannot be considered as proof. But we shall see. I am not so egotistical that I wont eat humble pie publicly.

 

[BruceK]

As for his calculation showing chain elasticity here:

I would have used the difference in tension given as the difference in the two equations for tension as tension = Mg/2 . 1/sin of theta where theta is the angle at the end of the catenary to the horizontal X axis. If the two equations deliver the same result then I'll accept his proof.

 

[Neeves]

BruceK - we will all look forward in anticipation to your data toward the middle/end of August or even September (it can take a long time to set this all up)

Mathias sadly does not define what he means by a good, indifferent and bad snubber. Or I think I know what a good snubber is but the other two might enjoy a bit of detail.

I may misinterpret but you seem to be looking at a static environment with no movement 'v' of the vessel, you are simply looking at tension developed as a result of windage and a steady wind. Your wind does not veer and there is no velocity caused by swell (I confess we try to anchor - swell free)

Don't forget to post on PBO and I'll come over here - I don't visit here very often ( cannot imagine why ).

Jonathan

I also tried a rubber snubber, sort of dog bone thing. If you set it up as instructed then it does not offer sufficient elasticity. It stretches less than needed and then any further elasticity is dictated or restricted by the 'coil' of rope round the snubber - so you enjoy elasticity and then a snatch. To be useful you would need to use a number of them in series and they are then expensive and heavy. As you point out a decent length of nylon rope, I assume you use 3ply, is better and cheaper. It depends on your yacht size - but look at dynamic climbing rope - better than 3 ply (but difficult to knot). It may not be 'big' enough for you - maximum size, normally, is 12/13mm.

 

[Jamie Dundee]

So given that the last time I looked at equations was more than 40 years ago, and e=mc^ seems to be now dodgy, can I assume that my 12m of 8mm chain and 30/40/50m of 3 strand nylon actually is the dog’s danglies?? ?

 

[MathiasW]

As for his calculation showing chain elasticity here:

I would have used the difference in tension given as the difference in the two equations for tension as tension = Mg/2 . 1/sin of theta where theta is the angle at the end of the catenary to the horizontal X axis. If the two equations deliver the same result then I'll accept his proof.

Bruce, I am afraid your equations are too simplistic to catch what is going on. The (my) graph you show is also an approximation only, as it is not precisely the area that matters (the angle at each point of the curve is neglected here). But my actual calculations are based on the exact formula for the potential energy of a catenary-shaped chain (possibly starting at an angle at the anchor). So, I simply take the difference of the two potential energies, and this needs to be equal to the energy that is introduced by swell and gusts. Energy conservation, simple. A snubber would take some (or most) of the energy of gusts and swell away, so that the chain needs to absorb less energy.

It is a simple fact that a chain that is stretched almost horizontally - as is the case in shallow water - cannot absorb a lot of more energy. This should be obvious, as the chain cannot raise much higher than it already is. And so it cannot gain much more potential energy. You can make the chain as long as you like, and it will not improve a lot.

Because of this effect the chain will not help you to absorb shock loads from gusts or swell in shallow water. It would become bare-tout in seconds as we all know, and then all bets are off. You do need very elastic snubbers to absorb these shock loads - particularly in shallow water, but they do help even in deeper water. That was the point of my table.

Jonathan has made a lot of experiments that are all in agreement with this analysis. Whether we have numerical agreement within 10% - probably not, as my model is just a model, whereas he is doing real measurements. But what his results do show is that the physics behind my model is the relevant one to capture.

And finally, my notion I used for the various snubber qualities - apologies for that. They come from my app, where they are defined, and are only meant to give you an idea where you are with your snubber. Most folks do not measure their snubbers, and so in my Basic Mode it is common language descriptors like that. The Expert Mode gives you the metrics you are after. But in any case, in each row I have listed by how much the snubber stretches, and this gives you an idea what requirements the snubber has...

So, I would be really surprised if your results deviated a lot from Jonathan's results.

Cheers

Mathias

 

[MathiasW]

Oh get back in your handbag. I already apologised to Mathias on that score. As he referenced a webpage that doesnt show the author I was unaware he had written the article on Catenary Anchor Chain Length - Die Kettenkurve - Fun Facts - SAN If you can show the author's credit I'll grovel too. In the comments it looks like Trimaran-San is the author but I dont speak German.

Well, this web page is clearly part of our web site www.trimaran-san.de and in this hierarchy you find the "About" web page: About - SAN - sailing around the world with a Neel 51 trimaran which clearly states my name. Yes, in German, but the name is universal. And before I start barking at somebody in a forum I would use DeepL or Google Translate to make sure I am not making a fool out of myself...

But ok, no hard feelings, apologies accepted. Just curious to see your results later in the year!

 

[BruceK]

It is a simple fact that a chain that is stretched almost horizontally - as is the case in shallow water - cannot absorb a lot of more energy. This should be obvious, as the chain cannot raise much higher than it already is. And so it cannot gain much more potential energy. You can make the chain as long as you like, and it will not improve a lot.

Hi Mathias, this is precisely the part I am struggling the most with. In my mind if the chain is under sufficient tension to be considered taught (which mine is in very adverse conditions) there is not much movement to be had, as stretching the catenary any straighter requires a logarithmic increase in force to infinity according to the equations. Now the force is always there. On that we agree. Where we seem to disagree is the impact forces imparted by any further momentum brought to an abrupt halt by an inadequate snubber. In my mind the less movement (stretch coming to an abrupt halt) there is the better. Of course I would concede that if there was more than sufficient stretch to allow for a graceful halt to momentum without snatch then the model works. But a poor snubber with insufficient stretch will exacerbate the impact in comparison to no stretch at all and a bow being pulled through a wave rather than riding the crest of it and snatching will impart less stress. (all with in reason of course. I'd expect that last statement to change as wave amplitude increases, at least above bow height)

 

[BruceK]

Bruce, I am afraid your equations are too simplistic to catch what is going on. The (my) graph you show is also an approximation only, as it is not precisely the area that matters (the angle at each point of the curve is neglected here). But my actual calculations are based on the exact formula for the potential energy of a catenary-shaped chain (possibly starting at an angle at the anchor). So, I simply take the difference of the two potential energies, and this needs to be equal to the energy that is introduced by swell and gusts. Energy conservation, simple. A snubber would take some (or most) of the energy of gusts and swell away, so that the chain needs to absorb less energy.

I'm not sure you can say my equations are too simplistic, they are after all the accepted proofs of a (catenary) chain under tension whether the difference in energy is applied by wind waves or steaming astern, and the difference in tension will be the energy imparted? So to the equations for momentum.
Bringinging it back to a poor snubber metaphor I can take a sledge hammer with a rubber stopper glued to the end and impart all my strength in pushing against the cleat but if I half-heartedly swung the hammer at it, rubber stopper and all, I'd stand a greater chance of knocking it off.

 

[longjohnsilver]

Looks as though the original poster lost interest 10 days ago (His last activity on YBW). I wonder why?

 

[BruceK]

Actually I am lying down in bed in a Spanish hotel. Feeling pretty chilled and in no mood to argue with the forum anchor windbag, sorry, I mean expert.

I take it you're no longer lying down?

 

[MathiasW]

Hi Mathias, this is precisely the part I am struggling the most with. In my mind if the chain is under sufficient tension to be considered taught (which mine is in very adverse conditions) there is not much movement to be had, as stretching the catenary any straighter requires a logarithmic increase in force to infinity according to the equations. Now the force is always there. On that we agree. Where we seem to disagree is the impact forces imparted by any further momentum brought to an abrupt halt by an inadequate snubber. In my mind the less movement (stretch coming to an abrupt halt) there is the better. Of course I would concede that if there was more than sufficient stretch to allow for a graceful halt to momentum without snatch then the model works. But a poor snubber with insufficient stretch will exacerbate the impact in comparison to no stretch at all and a bow being pulled through a wave rather than riding the crest of it and snatching will impart less stress. (all with in reason of course. I'd expect that last statement to change as wave amplitude increases, at least above bow height)

Hi Bruce, ok, let me see whether I can explain my view on this: The tension in the rode is only a consequence of the vessel pulling at it, it is not a given per se. Let's look at what happens when a gust or swell hits the vessel and sets it in motion. I think we can agree on the tension being largest when the vessel has come to rest and is farthest away from the anchor. This is like a pendulum - all energy has gone into the potential energy of something. In the present case it is the potential energy of the chain AND the elastic energy of the snubber that will absorb the initial kinetic energy of the vessel after getting hit by a gust or swell. Now, I do not need to calculate how tensions and loads change over time in this process, which would be complicated. I am only interested in the maximal shock load that reaches the anchor, and for this it is quite enough to study this point in time when the vessel has come to a brief rest.

Now, how the energy that needs to be absorbed is split between chain and snubber depends on both their characteristics. What is always true is that the tension at the point of the chain where it connects with the snubber is the same on both sides. Otherwise one side would be moving and even accelerating. So, that makes things easy. Once I have the swell / gust energy that needs to be taken care of (and which I estimate by looking at the maximum value for the kinetic energy after impact), I can then work out what the split is between chain and snubber. When the chain is already more or less taught, then the snubber has to take most of it, whether it can cope with it or not. Even a very poor snubber will try to take the additional load - but it may very well fail and snatch in the process of doing so.

I believe where you err is the assumption that there is less movement when the snubber is not very elastic. The movement is always there, it is the kinetic energy of the vessel after a hit by a gust or swell. Your assumption could only be true if there is really no slack left in the chain at all (nor snubber), but then the loads would go to infinity. So, this is definitely not a situation you would want to have. What I always consider is a chain with at least a little slack left, still.

Thus, to summarise, when the chain is almost bare-taught, the load is very high, and a snubber will be stretched enormously. It may very well break, if it is not designed for such a load and stretch. But if it doesn't, no matter how poor the snubber is, the tension will less than in the absence of this snubber, since a good part of the energy to absorb has gone to the snubber. Only the part of the energy that goes to the chain will increase its tension. And this is what is seen in my tables. I am showing the anchor load, not the bow load, but these two are closely related.

Cheers,

Mathias

 

[MathiasW]

I'm not sure you can say my equations are too simplistic, they are after all the accepted proofs of a (catenary) chain under tension whether the difference in energy is applied by wind waves or steaming astern, and the difference in tension will be the energy imparted? So to the equations for momentum.
Bringinging it back to a poor snubber metaphor I can take a sledge hammer with a rubber stopper glued to the end and impart all my strength in pushing against the cleat but if I half-heartedly swung the hammer at it, rubber stopper and all, I'd stand a greater chance of knocking it off.

OK, fair enough. I have not come across that formula for tension, but then again, the catenary problem is known for surprisingly simple equations in the end. It is what makes their mathematics so beautiful! For instance, the difference between anchor load and bow load is simply the weight (in water) of the same type of chain hanging vertically from the bow roller to the depth of the anchor. So, it almost looks like you can add forces linearly here and folks tend to frown. But it is just the property of the catenary.

As to your example with the sledge hammer: In one case it is kinetic energy, which needs to be absorbed, in the other case an additional force needs to be absorbed. So, very different. I view a gust or swell as an energy transfer, not the application of an additional force, as I am lazy and want to do simple maths. You can do the latter, and then integrate force over distance to get the energy. What you are saying is that there is no distance to integrate over, as it is bare taught. In reality, there is always a little difference left, and the smaller it is, the larger the forces are... In your scenario you would have to work out Zero times Infinity...

Cheers

Mathias

 

[Portofino]

Did anyone mention ^^^ , just fire up the engines and move Fwds ?