Mathematic approach to anchoring scope

[barnakiel]

Quite possibly a cell can be wired onto an Arduino.


This would make reading and logging easy.


b.

[conachair]

Originally Posted by barnakiel

Quite possibly a cell can be wired onto an Arduino.


This would make reading and logging easy.


b.

See post 234. Or a few moments on google.

Using an ESP32 is a much better idea as it can send the data over wifi. It's also far faster and has far more memory than an arduino. You also need an amplifier board, costs next to nothing.

https://www.youtube.com/watch?v=iywsJB-T-mU

[barnakiel]

Yes. Looks excellent solution.



b.

[MathiasW]

So, thanks to a discussion with Bjarne I have updated all documents on my web page to include now also the energy when the vessel moves in the wind. This does not affect the calculations on elasticity, or static anchoring, but it does have an effect on what I had labelled dynamic anchoring. It makes matters worse in shallow water.

Secondly, the brief customised digests now also include diagrams showing the effect of snubbers / bridles. If you did download a version pertinent to your vessel, I recommend downloading the update.

I have compared sample points in each digest with the results Bjarne's online calculator gives, and I found good agreement...

For reference, here is the link to the epic story again:

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

[MathiasW]

Originally Posted by conachair

Oh I feel for you!!! Get 2 of everything when you can

Thanks! I have now managed to order an electronic hanging scale here in Panama, and when my wind sensor is working again (also ordered), I might be able to make some progress at last...

[RaymondR]

Resistance strain gauges are cheap and instrument amplifiers chips cheap and readily available. Also AD converters and the software to do the logging on a computer. The strain gauges can be glued onto a metal rod or bar to form a load cell. Calibration tends to be the difficult part.

[Rothblum]

Thanks to all for this thread. I have been trying with difficulty to follow it. I'm not a very experienced sailor, nor am I much of a mathematician. I can only make one minor comment -- in calculating the energy of a boat moving in response to a surge, the mass to be considered is not just the displacement of the boat, but there is an additional apparent mass that is caused by the induced movement of the water surrounding the boat. A rule-of-thumb approximation of this effect is to add a mass that would be the equivalent of a sphere of water whose projected area is equal to the projected area of the submerged portion of the boat perpendicular to the longitudinal axis (assuming that is the direction of the surge).

[RaymondR]

MathiasW,

Your model must be getting very sophisticated if you are taking water displacement, and consequent damping, into consideration.

Reminds me of an argument I had with a collage professor about friction pressure losses around a pipe being inserted into a fluid filled hole. His model had a "clinging factor" included which I disagreed with. After trying to politely hint as to why I thought his model was wrong to no effect I got exasperated and declared that he was trying to apply a steady state equation to a dynamic situation and that blood Newton would agree with me. His response was that I might be right but was going to get poor marks anyway, right or wrong, because he now disliked me.

[Rothblum]

Well, if you are going to consider the energy of the moving boat, it is actually a significant factor. It is not damping -- system is overdamped, unless you consider swinging -- but rather the frictionless inertia of the water that has been set in motion by the motion of the boat. I'm not sure what the underwater frontal area of my boat (LOA 40 ft) is, but I think you have an estimate of the above water frontal area of a similar boat. I just arbitrarily picked 50sqft. That's a circle of radius 4ft. That results in a rule-of-thumb virtual or added mass of 16,000 lb-mass, c.f. my boat's displacement of 20,000 lb. Of course, a lot of other things, already mentioned by you, such as the angle the boat might have to the wind, are not accounted for, understandably.

So, if you are in the mood, and have time on your hands, one of the very first things that came to my mind in looking at your model, is how does the virtual elasticity of the chain catenary compare to the conventional elasticity of, for example, nylon rope? If you already made this comparison and I missed it, I apologize. The reason for asking is that if the virtual elasticity of the chain is much less than that of the elasticity of a reasonable length of nylon rope (and maybe a rubber dog bone), then perhaps the rationale for choosing the scope to maximize chain catenary elasticity could be replaced with some other criterion, leaving the job of absorbing energy to the bridle. An example would be to deploy only enough chain to ensure that the angle of the chain to the bottom at the anchor is zero. It might also affect a decision whether to anchor in deeper water, which is maybe a tad counterintuitive.

[RaymondR]

Decades ago I carried out a mathematical modelling exercise for a drill rig I was working on with my sons TI94 computer. I found that mist if the chain loads in that instance were caused by the vessels pitching and not by the horizontal translations.

The exercise confirmed what the Offshore Drilling Company had found with there turret moored drill ships. On these vessels eight anchor winches were mounted on a rotating turret in the middle of the ship with the anchor lines carried down vertically through the cylindrical turret with fairleads around the bottom circumference. The ship was rotated around the stationary turret to provide minimum anchor wire loads.

[MathiasW]

Originally Posted by Rothblum

Thanks to all for this thread. I have been trying with difficulty to follow it. I'm not a very experienced sailor, nor am I much of a mathematician. I can only make one minor comment -- in calculating the energy of a boat moving in response to a surge, the mass to be considered is not just the displacement of the boat, but there is an additional apparent mass that is caused by the induced movement of the water surrounding the boat. A rule-of-thumb approximation of this effect is to add a mass that would be the equivalent of a sphere of water whose projected area is equal to the projected area of the submerged portion of the boat perpendicular to the longitudinal axis (assuming that is the direction of the surge).

Well, yes, I had thought about that and it is relevant, I believe. It is like the exciton in solid state physics, which acquires a different mass because it drags other stuff with it. But I have no sense, really, what to assume for this in practice. Will give this some more thoughts...

[MathiasW]

Originally Posted by Rothblum

So, if you are in the mood, and have time on your hands, one of the very first things that came to my mind in looking at your model, is how does the virtual elasticity of the chain catenary compare to the conventional elasticity of, for example, nylon rope? If you already made this comparison and I missed it, I apologize. The reason for asking is that if the virtual elasticity of the chain is much less than that of the elasticity of a reasonable length of nylon rope (and maybe a rubber dog bone), then perhaps the rationale for choosing the scope to maximize chain catenary elasticity could be replaced with some other criterion, leaving the job of absorbing energy to the bridle. An example would be to deploy only enough chain to ensure that the angle of the chain to the bottom at the anchor is zero. It might also affect a decision whether to anchor in deeper water, which is maybe a tad counterintuitive.

In the latest digests for vessels of various windage areas I include now also the effect of bridles / snubbers, which I have simply 'bolted onto' my equations by imposing that the force at the bow is the force that will elongate the bridle. It took me a while to find a measure for this which is sufficiently easy and intuitive and does not require to actually measure the spring constant of the bridle / snubber.

I have now settled for the following: In a steady-state 8 BFT, the bridle / snubber will be elongated by x cm. So, in the absence of swell or anything. This is something one can hopefully grasp with a practical meaning. I have chosen two different snubbers/bridles: One with x = 10 cm, another one with x = 25 cm. This does not appear much, perhaps, but in a swell, the snubber/bridle may have to hold much more than 8 BFT steady wind, and so these 10 respectively 25 cm can easily become 3 times of that or more.

With this, one finds indeed that the divergence of chain length (and anchor load) for small anchoring depths does not exist anymore. The snubber/bridle is taking care of this. But one still sees the anchor load to increase quite a bit in shallow water, and one might want to avoid that and still relocate to deeper water.

But funnily, the stronger the wind blows, the better the bridle/snubber works, and the less difference is seen between shallow and deeper water.

But it all hinges on having a very good snubber / bridle.

I had said earlier in this thread the elongation of the snubber/bridle needs to be a couple of metres, but there was an error in conversion of units , it is not quite as much needed...

So, yes, you are right, it is possible to do an approach as you suggest it.

[MicHughV]

yes, as a retired marine engineer, I agree with the above posts.
A simple explanation would be, trying to push a man standing in a swimming pool backwards. The man will have a given weight or displacement if you wish, that requires a certain force to move backwards.
Were the man standing on land, one would only need to contend with the mass of the man, but in the pool, the water surrounding the man also provides support for the man, which must also be overcome in addition to the weight/displacement of the man.

[MathiasW]

Originally Posted by MicHughV

yes, as a retired marine engineer, I agree with the above posts.
A simple explanation would be, trying to push a man standing in a swimming pool backwards. The man will have a given weight or displacement if you wish, that requires a certain force to move backwards.
Were the man standing on land, one would only need to contend with the mass of the man, but in the pool, the water surrounding the man also provides support for the man, which must also be overcome in addition to the weight/displacement of the man.

ok, makes sense. This is for the acceleration phase when a swell is coming in. What about the deceleration phase?

[MicHughV]

well, a body in water, has water on all sides, front, back and sides, no matter which direction you push the body, there will be water resistance.

go to the beach, and stand in the surf...wait for a big wave to hit you, it will likely push you over without any trouble....we think of water as being " soft" but not so....
ever belly flopped into a pool from a high diving board ? ouch !!

then there is the frictional side of it. Many formula's around to estimate water flow in open pipes, ditches, etc, etc...manning's "n" number is assigned to all sorts of surfaces, which will affect the frictional losses.

besides the frictional losses, there is "shape" losses, also well documented.

I think I've told you, computer modeling can show shape and frictional losses quite well visually.

try to pull a long rope that is just floating on water, you will be surprised at the effort it takes. Pulling a long rope that is submerged even more so.

it's a complicates science and trying to arrive at some or other conclusion must take into account a variety of variables.