Mathematic approach to anchoring scope

[barnakiel]

Originally Posted by MathiasW

Oh, I just see my mistake, water density is 1000 kg / m^3, this changes something... Sorry, was a bit too quick with this.

Then this is indeed something to be reckoned with!!!

No problem. Looking forward to hear what you find when the calculation is updated with the density figure.


barnakiel

[MathiasW]

Originally Posted by barnakiel

No problem. Looking forward to hear what you find when the calculation is updated with the density figure.


barnakiel

Thanks!

For a start, I think one needs to separate two different aspects here: There is a velocity perpendicular to the plane spanned by the anchor chain. This is where the dampening by dragging the bridle through water will mostly apply, as in this direction the bridle has the largest cross section. Then there is a velocity towards or away from the anchor, and if it is away from the anchor, it will have to be absorbed by the chain's potential energy or the elasticity of the bridle.

So, I will think about this more, but it looks like two orthogonal processes, really.

[barnakiel]

Yes.


Mind it is a bridle in one case, but another case will have chain all the way to the surface - some boats opt for 'chain only' rodes. (=99% chain 1% snubber).


I think chain may have a much higher drag factor than same diameter rope - it is a relatively irregular shape and will create quite some turbulence. The things of turbulent flow vs. laminar flow you know probably very well from fluid dynamics.



barnakiel

[MicHughV]

here's what you do....this is what I did using the dink anchor line/chain...about 6' of chain...
lay this on a table, cockpit seat or other available flat surface...use a towel to replicate the seabottom.....ie, not the shiny surface of a table top...

you can arrange the chain to lie in a long straight line or on a curve...or an S-curve....take your pick or try them all..

then pick up the dink anchor rope.....straight up...at an angle....whatever you want.....allow about 4' of rope between your hand and the chain....and pull on the rope....and see what the chain does....

let me know what you think

[MathiasW]

Originally Posted by MicHughV

here's what you do....this is what I did using the dink anchor line/chain...about 6' of chain...
lay this on a table, cockpit seat or other available flat surface...use a towel to replicate the seabottom.....ie, not the shiny surface of a table top...

you can arrange the chain to lie in a long straight line or on a curve...or an S-curve....take your pick or try them all..

then pick up the dink anchor rope.....straight up...at an angle....whatever you want.....allow about 4' of rope between your hand and the chain....and pull on the rope....and see what the chain does....

let me know what you think

I am lacking the ingredients here at anchor, like a dinghy chain, but I guess your point is to say that the curled up anchor chain will follow the pull at the chain's end like a snail moving in the sand.

I can only speculate as to what physics is behind this. Normally, static friction is higher than sliding friction. I do not know, but perhaps even when the chain starts gliding, in the direction orthogonal to its movement it is still kind of static friction. But this is pure speculation. I am not an expert on those matters.

But in any case, all this is only relevant when the forces are small. In stronger winds, the chain will be pulled straight and all this effect is gone, I am sure.

[MicHughV]

I have not delved into the sailboat anchoring theory as much as you have.....and I laud your efforts...but to my way of thinking....each link in a chain is it's own master....each connection between links will be different from the one before or behind....incrementally or otherwise...

I am a retired structural marine engineer by profession...my experience with chain is mounting massive ship fenders to a dock...many chains holding up a flat plate fender up, yet be allowed to move as well.... as well as anchoring ship buoys offshore. Many chain designs call for different weight and size links to be incorporated, as chain weight must also be accounted for..besides everything else....

I don't think I've ever seen a long chain pulled straight...the weight of a chain over a long distance is practically impossible to straighten out...

Chains don't always lie flat, ie, the chain will develop a twist, which provides yet another structural concern....etc..etc..I've often pulled up my sailboat anchor and have noted that the chain may have several twists to it...if a chain has a twist in it, it also means, the connection between links will affect chain catenary, etc...
I don't think there is a one size fits all....different link designs....different weights..different lengths...twist....etc..etc...

Nonetheless, I follow your thread with interest and may yet learn something I did not know or was aware of...so keep at it !!!

[barnakiel]

Originally Posted by MicHughV

I don't think I've ever seen a long chain pulled straight...the weight of a chain over a long distance is practically impossible to straighten out...

OK, but just when it is 'practically impossible to straighten out' it stops acting as a cushion and starts acting as if you were tied to a rock with a short piece of wire.


So whether the chain is straight or just nearly straight, we need to provide some kind of 'rubber' bumper to the last part. Or at least a kind of a fuse - something that will give before the boat fittings give.


a fine nylon snabba !!!!


;-)

b.

[MicHughV]

when is straight "straight ?...a very good question....

a chain hanging down vertically is straight...so depending on depth of anchorage, it's possible to have a "straight" anchor line....won't be doing any good...but it will be "straight".....

after that it's a simple matter of math....trig actually.....I'd have to sketch it out for you...to make sense...

but I've opined on this before....get a 100' of chain....say it weighs 1 lb per ft....100lbs....so hanging straight down....it's a 100 lbs of weight...

now, if you doubled up the chain so the links were together and have a one guy holding each end but still hanging straight down.....each leg of the chain would be 50 lbs each...easy peasy...

now, have the guys walk way from each other, still holding the chain at an angle to the horizontal......say 45 degrees to the horizon....wow....do the trig...still manageable.....yes, but no longer 50 lbs.....remember, the tension required to pull the chain " up" is now a component of " up" and "sideways" with a resultant force in line with the chain angle of 45 degrees.

but now, reduce the angle to 30 degrees....15.....5....1.....as you approach 0 degrees, you will quickly see as the angle reduces, the amount of pulling (tension) goes up substantially....ie, the tension (pulling power) required to pull a 100lb chain " up" by pulling it "sideways" becomes enormous...

don't make me break out a pencil and paper...trust that explanation will suffice..

[MathiasW]

Soooo, it has been a while...

After the encouraging feedback on app coding I started looking into that myself. I have a rough version running now on the simulator for iPhone and iPad. It can only do chain, no mix of chain and rope yet, but it can do different sizes of chain, swell energy, snubber / bridle, and a seabed that is not horizontal. Whilst the default is to calculate the amount of chain needed to have the chain pull horizontally at the anchor shank, it is also possible to specify a maximum amount of chain and then see what pulling angle this results in. For the snubber/bridle I have been poking my brain how to specify them in an intuitive way without having to know their 'spring constant' (knowing that they are non-linear, strictly speaking, which does not help, really). In the end, I decided to characterise a snubber / bridle by the amount of stretch it would see at 8 BFT for the given vessel - and in the absence of any swell. This seems to me a reasonable metrics that one can guestimate on a vessel without too much hassle.

Enclosed is a brief flyer with some screen shots from the simulator. I think I need some encouragement to finish this project and make it work on many operating systems and devices... So, please drop me a PM for that...

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

[DanielPerry]

If in deeper water you have more rode hanging (instead of resting on the bottom waiting to be picked up), that would mean you have a higher hanging center of gravity. Would therefore the remaining chain need to "sweep up" (while picking up) a greater angle than at longer scopes, requiring more energy to do so BECAUSE the hanging center of gravity in a shorter scope that has to be lifted is much much larger .. even if significantly shorter vertical distance than that of a longer scope is needed to end up with the anchor breaking out, its much much harder. Definitely exponentially to some degree, depending on the rode density.
And after spending ten minutes writing that, Ive simplified the above statement to:

The cantenary force in shorter scope in deep water is less resistive but its magnitude is much higher than that of a longer scope. With a constant load (boat blowing backwards) the shorter rode reaches sufficient "pull" from the cantenary effect much earlier in the loading of the rode.

[MathiasW]

Originally Posted by DanielPerry

If in deeper water you have more rode hanging (instead of resting on the bottom waiting to be picked up), that would mean you have a higher hanging center of gravity. Would therefore the remaining chain need to "sweep up" (while picking up) a greater angle than at longer scopes, requiring more energy to do so BECAUSE the hanging center of gravity in a shorter scope that has to be lifted is much much larger .. even if significantly shorter vertical distance than that of a longer scope is needed to end up with the anchor breaking out, its much much harder. Definitely exponentially to some degree, depending on the rode density.
And after spending ten minutes writing that, Ive simplified the above statement to:

The cantenary force in shorter scope in deep water is less resistive but its magnitude is much higher than that of a longer scope. With a constant load (boat blowing backwards) the shorter rode reaches sufficient "pull" from the cantenary effect much earlier in the loading of the rode.

Not quite sure I understand you, in particular the 'less resistive' part...

The efficiency of the catenary depends on how much difference in potential energy there is between the catenary with some slack chain still lying on the seabed before the onset of swell or gust, and the full catenary with the last chain link just coming off the seabed when the swell / gust has kicked in.

Now, in shallow water the chain resting on the seabed before the onset of a swell or a gust will be lifted off the seabed alright by the swell / gust, but it cannot be raised a lot, simply because the chain is almost horizontal already, anyway. So, only little energy can be stored.

In deeper water, however, any chain resting on the seabed in the same situation has a lot more headroom to get lifted up to. And this is the large potential energy to store the energy of the swell or gust in.

Of course, if you make the chain infinitely long, you can store any energy in it that you like, but for any chain of finite, fixed length, the above reasoning holds.

Does this make sense?

[DanielPerry]

Originally Posted by MathiasW

Not quite sure I understand you, in particular the 'less resistive' part...

The efficiency of the catenary depends on how much difference in potential energy there is between the catenary with some slack chain still lying on the seabed before the onset of swell or gust, and the full catenary with the last chain link just coming off the seabed when the swell / gust has kicked in.

Now, in shallow water the chain resting on the seabed before the onset of a swell or a gust will be lifted off the seabed alright by the swell / gust, but it cannot be raised a lot, simply because the chain is almost horizontal already, anyway. So, only little energy can be stored.

In deeper water, however, any chain resting on the seabed in the same situation has a lot more headroom to get lifted up to. And this is the large potential energy to store the energy of the swell or gust in.

Of course, if you make the chain infinitely long, you can store any energy in it that you like, but for any chain of finite, fixed length, the above reasoning holds.

Does this make sense?

My strong suit is not communications

"less resistive" was a more-than-poor wording choice. I meant the point at which the chain comes off the bottom is closer to the andchor; from a side view drawing one might say, "it has to lift less chain therefore it is less resistive to reach the point of dragging, but a simple drawing on paper does not readily show that the required force (windage/current/waves on boat) would have to be huge. Im saying this is all because the center of gravity of the hanging portion of chain in the 5:1 scope is of much much larger magnitude. Im really enjoying this but I may be way off.

[DanielPerry]

I like how you put that, makes sense. I was saying something along those lines, not exactly but I think you've got the reason for sufficient holding power right when you say there is more "head room".

I love this ****.

[MathiasW]

Originally Posted by DanielPerry

I like how you put that, makes sense. I was saying something along those lines, not exactly but I think you've got the reason for sufficient holding power right when you say there is more "head room".

I love this ****.

Good to be d'accord!

[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.

One can condense the table and extract an effective windage area as I have been using it in all my calculation as:

A_eff = 0.069 * L_m^2

where L_m is the length of the vessel in metres and A_eff is in square metres.

This is for an average monohull. If your vessel is slim and sleek, you can shave perhaps 20% off that. If your vessel is bulky, you will need to up this value.

There are no such tables for catamarans and trimarans, unfortunately, but perhaps one can get some idea by adding 50% for a cat, and 60% for a tri? And then again vary based on sleek / bulky shape.

I think this table is a good substitute, if one has not actually measured A_eff.

Please note that the values derived with this formula are substantially less than the ABYC recommendations. In my understanding, the reason for this is that the ABYC recommendations originally came about as guidances for selecting suitable anchor gear that can withstand the loads with a substantial (but unknown) safety margin, like any other deck gear. They were never meant to characterise the actual load.

Cheers

Mathias