Mathematic approach to anchoring scope

[MathiasW]

Originally Posted by barnakiel

This may be a good idea. I wrote my own AIS app as well as a number of non sailing Apps, but here at CF there are people who wrote anchor alarm apps - I believe this popped up in threads some time back.Dig into older anchoring App threads and send them PMs.


barnakiel

Great idea! Will do!

[MicHughV]

most GPS units have a built in anchor alarm, letting you know if you drift to far from your original location. Doesn't help much in a tidal area, where you may swing one way in the morning and the opposite in the afternoon....

I don't see a solution to the thread. There is a theoretical approach here that will, in most cases, not jive with an actual anchoring situation.

I remember a situation where a yacht had swung to the wind, and in the process, the chain on the bottom had snagged an object, reducing his scope by half.

[Pete7]

Originally Posted by MathiasW

So, with that total weight of the chain, the thinner chain is the only option, really. You are rather chain-weight limited in your configuration. If you expect more than 8 BFT in gusts, or large swell, or the effective windage area being larger, you may even want to consider a slightly thinner chain of higher quality.

Than you for this synopsis as I suspect we also fit Barnakeil's numbers.

Assuming a smaller yacht can't carry a larger amount of of either size of chain, but may need to anchor very infrequently in BF 7or 8, what happens if say another 100% (30m) of warp were to be spliced on to the chain?

Thanks

Pete

[MathiasW]

Originally Posted by Pete7

Than you for this synopsis as I suspect we also fit Barnakeil's numbers.

Assuming a smaller yacht can't carry a larger amount of of either size of chain, but may need to anchor very infrequently in BF 7or 8, what happens if say another 100% (30m) of warp were to be spliced on to the chain?

Thanks

Pete

My model does not include a mix of chain and rope yet, so please use Bjarne's calculator to see the effect in detail. (Or Alain's excel spread sheets.) But I would assume that such an approach would improve results greatly.

In fact, if one can only anchor in very shallow water, for what-ever reason, then a combination of a shortish chain and a longish rope would be best. In such a case a large scope during storm cannot be avoided, anyway, and so I might as well replace an almost horizontal chain with a rope having much better elasticity. I then accept a small pulling angle at the anchor and need not increase my swinging circle, really. Chafing needs to be taken care of, of course.

[barnakiel]

Originally Posted by rslifkin

The swell in deep vs shallow water thing makes a lot of sense. Especially if you're reaching the point where your rode is stretched pretty much tight. At the same rode angle, the change in angle from a 3 foot swell will be much less in deeper water where its relative height change of boat vs anchor is much smaller. Because of that, the rode won't be trying to pull the boat forward as far while it's rising up on the swell, which should reduce the load spikes on the system (particularly if there's enough load already that catenary and stretch can't readily smooth out all of the swell load).

Coming now backwards (never do!) to 3 ft swell.


Do you mean wind waves.


Or do you actually mean swell.


For 3ft wind waves to build over a 1 mile fetch, it takes 64 knots of wind.


https://planetcalc.com/4442/


What kind of practice is it to anchor your boat 1 mile offshore in 64 knots of wind?


Now. Swell.


If your anchorage is the one you should be in, swell should be well controlled, minimal or nil.


If swell is significant, this is not the anchorage you want to be in.


Another detail to consider:


How much 3ft of swell will lift the bow of your boat. If your boat is like mine, then by about 2 ft. But if your boat is a typical 45ft long 10t heavy cruising boat most people have - by about 1 ft maybe.


So.


What I am saying is that arriving at a good mathematical model is difficult, and comes not only from good mathematics.


b.

[rslifkin]

I absolutely agree that 3 foot waves of any kind shouldn't happen in a good anchorage. But in some places where one might anchor during the day, you can get significant boat wakes at times. I've also been known to anchor in totally unprotected waters (with mild wave action plus boat wakes) to watch sailing races and such. In my mind, it's always good to know how much of an issue movement like that really is (comfort aside) even if it's generally avoided.

In shallow water, any issues from wave action are likely to be further compounded by the waves stacking up higher in the shallows. So I guess the idea is to avoid wave action as much as possible, but if you can't, deep is better than shallow.

[barnakiel]

As much as possible, excessive rope should be avoided - especially in heavy conditions.


The huge disadvantage of plenty of rope is that now you you have too much of that bungy effect, the boat has too much freedom, and your may and will be thrown sidewise and sail about wildly. This sure adds to the shaking loads on the rode and anchor.


Someone before rejected this position, but I can only say this happened to us and I have also watched the same problem with some boats anchored nearby. Upon investigation, they all had plenty of rope rode.

b.

[rslifkin]

I think in deep water, the ideal would be a water depth of rope and the rest chain. More than a water depth would be needed in shallow water. It would give more scope for a given chain weight and keep the rope off the bottom.

[NPCampbell]

Originally Posted by Pete7

A minor point but I think you mean elastic deformation. Plastic deformation occurs once the elastic deformation is exceeded past the yield point and means the material won't return to its original dimensions. Failure is likely to occur in short order with on a small increase in force, not something we want to do with an anchor chain.

Pete

I actually meant plastic deformation as elastic deformation would be considered a form of potential energy (even though a large portion of that energy would not be in the direction of the released force).

However, you are correct, depending on the material, if you don't exceed the yield point you won't get plastic deformation (or at least not more than .2% deformation). Since chains are typically made of steel the likelihood of plastic deformation, except at the contact points, is pretty low.

[MathiasW]

Originally Posted by Dsanduril

The diagram is about what I have experienced in coral sites. Usually more buoys, but small, so that is variable depending on the boat.

The values you are proposing are the size of the buoys? How much flotation they should have? So b1 has enough buoyancy to float the chain length L1? And the last buoy is then supporting L3 + half the chain to the boat? This seems right for selecting the flotation/buoyant value for each buoy.

In essence then, the chain has almost zero weight (or a very little weight near the anchor = L0-L1). This becomes quite interesting.

One other thing from real-world conditions, when yachts are yawing, having the buoys can create a significant amount of drag through the water, reducing the magnitude of yawing. Another piece solely from empirical observation, but it does seem to make a (noticeable) difference.

So, it took me quite a while, but here it is...

Tuamotu Anchoring with floating chains:

As before, I work out the elasticity of the chain by calculating the potential energy as a line integral and then differentiate with respect to the anchor load F. In what follows I ignore the elasticity related to the final leg Lbow, between last buoy and bow, since this can be calculated independently and simply added later. So, my calculation stops at the last buoy.

As to the line integral: Starting with the catenary formula y = sqrt(L^2 + a^2) - a, one sees that the potential energy of any chain segment hanging between two points is given by

E_pot = integral dr (sqrt(r^2 + a^2) - sqrt(La^2 + a^2) + y_La)

where the integral runs from -La to +Lb. La is the length of the chain left to its lowest point, and Lb the length to the right.

This can be done analytically.

The buoys are easy to add.

Then, I need to do the derivative. It is not useful to write the result in a simple text editor, and even in LaTeX etc it looks lengthy and it is difficult to gain more understanding from looking at it. At least for now, and for me...

So, enclosed are two graphs. The first is what I had shown before, but with a few more details on notations.

The second is the elasticity of the system up to the last buoy, but excluding the elasticity of the final leg between last buoy and bow.

Plotted is chain elasticity as a function of a/F, scaled with reference to the peak when no buoy is used at all (black curve). As before, these curves scale with anchor depth Y. In all cases I have assumed L1 = 1.5 Y, and all subsequent buoys being equidistantly spaced. Three groups of curves are shown: Spacing of 0.5 Y, Y, and 1.5 Y. Of course, larger spacing means that the buoys need to be correspondingly bigger as well.

Clearly, the buoyancy of the buoys has a very positive effect on the elasticity of this system, and the more buoys are being used, the better it is. However, all these curves have their peak at rather small values of a/Y, so well before a strong storm has developed. In fact, their peak is at even smaller values of a/Y than for the normal curve without any buoys (black). Secondly, all curves stop at a certain maximum value of a/Y. After this point, the pulling angle at the anchor is not horizontal anymore and the last buoy will dip under water. Again, the more buoys, the later this effect will happen, but even with 9 buoys spaced 15 Y apart, I barely reach a value of a/Y = 10. And this requires a lot of chain, often well in excess of 100 m! The fact that the elasticity of this system eventually drops below that of a simple no-buoy approach is ok, since this graph does not include the elasticity of the last leg Lbow yet. It needs to be added.

So, this looks like a great approach to keep the chain tidy at all times and away from the corals. In a severe storm it is at a disadvantage compared to the normal way of anchoring, though, and sooner will depend on the anchor holding well even when it is being pulled at an angle.

Next step is to see whether reducing the buoyancy of the first buoy a little (or increasing L1) can improve the matter somewhat and allow to anchor at larger values of a/Y without pulling the anchor at an angle. Doing so will mean that in calm weather the first buoy (and subsequently all others) will slightly sink below the water surface and possibly this could mean one has to reduce L1 somewhat to make sure this slack is not interfering with the corals.

[MathiasW]

PS: It appears beneficial to keep the distance between the buoys as large as possible (of course, without the chain in-between touching the corals when slack), and rather have two buoys bundled together and then have twice the chain to the next pair of buoys. This moves the peak a little bit to the right, and also the maximum value for a/Y is increased somewhat.

[MathiasW]

To allow anchoring also in stronger wind, we need to modify the above model somewhat. All we have to do is to increase L1 so that there is more slack on the seabed, without compensating for this with a larger buoyancy of the first buoy. Everything else we keep unchanged. Doing so will mean that in calm weather the first buoy (and subsequently all others) will sink slightly below the water surface, and so this has to be balanced in such a way that the corals are still unharmed. So, possibly, rather than increasing L1 we may instead want to decrease the buoyancy of the first buoy. If the last buoy precisely compensates for the lack of buoyancy of the first buoy, it would still act as an indicator when the pulling angle at the anchor starts to increase - as at that moment it would start to dip below the water surface.

[MathiasW]

So, I made a few improvements to the buoyancy of the first buoy, closest to the anchor. I have placed all this on my web page for reference.

In a nutshell, the strategy appears to be as follows:

- Use as much chain for the first segment from anchor to buoy as possible, but make sure this chain segment stays out of the corals' reach in any scenario.
- Place buoys along the chain such that they balance out the weight of the chain in calm weather. The idea is that they can just support the chain floating in the water off the seabed, but not more than that. The longer this floating chain is, the better, obviously.
- It is preferable to have a wider spacing between two buoys, possibly bundling two buoys, instead of a narrow spacing with lighter buoys.
- The total chain needed is easily a factor 2 or 3 larger than for conventional anchoring at the same water depth.
- In a storm, it is inevitable that there will be a non-zero pulling angle at the anchor. Using the normal scope analysis of water depth and entire length of the chain gives a good upper limit to this angle, despite of all the buoys.
- The buoys are great when there is not a lot of wind, they keep the chain tidy and have a huge elasticity at lighter wind, but they lose their effectiveness in storm very rapidly. So, in most cases, it will be a shallow anchoring scenario, and good snubbers or bridles are needed.

[MathiasW]

So, things seem to have gone a bit quiet here...

Here is a graph I have created to assess the situation when there is some tilt / slope in the seabed. For simplicity, I am assuming the same slope all the way from the anchor to the vessel's position.

Plotted is the chain's elasticity as a function of a/Y, where a = F/(m g) is the catenary parameter and Y the anchor depth. From this one derives the scope as usual as L/Y = sqrt(1 + 2*a/Y).

The curves are all normalised to 100% at the peak of the curve at zero slope, so a flat seabed.

Clearly, when the seabed slopes such that the vessel is in deeper water than the anchor (so negative angles), it is very beneficial as far as the chain's elasticity is concerned. Of course, this comes at the expense of more chain that is needed.

On the other hand, for a positive slope of the seabed, which is good in terms of the angle at the anchor shank (in order not to pull out the anchor), and the amount of chain needed, the elasticity gets very poor very quickly.

Looking at this, if I can have my way, my preference would be to anchor at -1 to -3 degree slope of the seabed...


All updates can be found at

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

[MathiasW]

Somebody very early on in this thread said, if I include snubbers, it might start to get eventually useful...

So, I did that and the graphs for dynamical anchoring do look quite interesting. One can clearly see a strong effect of the snubber in shallow water, but it disappears in deeper water. The right-hand graph features a more powerful snubber.

It also shows that it needs to be a snubber that can really absorb some energy to have an effect. Not these toy versions one sometimes sees that are just 2-3 metres long. The snubber must be able to stretch by 1-2 metres, to really have an effect. A short snubber cannot do that.

By and large, the characteristics of dynamic anchoring and the associated advice to stay clear of too shallow water remain. The snubber can dampen the effect somewhat, but by its very nature as a reactive device, it cannot completely compensate for the poor performance of a chain in very shallow water.

As usual, more details on the web page.

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