Anchors, cables and catenarys.... or not?

Great calcs, jfm, but lets go back to the original point which was this. Some of us have observed that often the anchor doesn't dig into the seabed and yet the boat is still securely anchored and my suggestion was that under these circumstances, the chain is doing most of 'work'. If you consider your example of the boat anchored in 6m of water with 40m of 10mm chain, lets assume there is a 25kg anchor fitted and lets make a very big assumption that the static coefficient of friction of that anchor lying on the seabed is the same as the chain. Quite obviously because the weight of chain lying on the seabed is heavier than the anchor itself and making this big assumption about the coefficient of friction, can we say that when the weight of chain lying on the seabed is greater than the anchor weight, then the chain is providing more frictional holding force than the anchor? In this case, the anchor is providing 25 x 0.98 = 25kgf of holding force compared to 55kgf provided by the chain.
Then as you have pointed out, the chain also provides a catenary holding force which in the case of the 40m chain with 30m on the seabed is 1.85 x 10x10/12 = 15kgf. Yes I agree that the catenary force cannot be developed unless there is sufficient frictional holding force from the anchor + chain to resist it so this is certainly a good reason for putting out more chain, as you suggest. So in this case the chain is providing 55 + 15 = 70kgf of holding force compared to 25kgf from the anchor. So yes, in this case, the chain is providing more holding force in total than the anchor as I and others have suggested.
Obviously, once the anchor digs into the seabed, then potentially it can develop a much higher holding force than the chain and I don't think anyone is arguing with that, at least not me anyway and I guess thats why we all carry anchors on our boat rather than a concrete block!
 
Yes Deleted User i think we're violently agreeing. As I wrote above, "the BICHes are correct in light winds (or <1knot tide), but once you get above (say) 15kts of wind, or >1knot tide, or in a lower coeff ground (the lowest being 0.56) the anchor starts to contribute and in say 25kts wind or 3 knots of tide is doing most of the work and the BICHes are wrong."

I think the maths merely backs up what we all knew intuitively anyway, which is a happy ending :D

Scuse the pedantry, but your additional 15kgf in your post aint right. The catenary force is not additional to the frictional force from the chain. It is in fact the same thing , or is the opposite action/reaction force in a Newtony way. So it's 55, not 55+15. But that doesn't change the general conclusion above.
 
jfm said:
Scuse the pedantry, but your additional 15kgf in your post aint right. The catenary force is not additional to the frictional force from the chain. It is in fact the same thing , or is the opposite action/reaction force in a Newtony way. So it's 55, not 55+15. But that doesn't change the general conclusion above.
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Yup, I was wondering about that myself but I looked at it this way. If one end of the chain is fixed, then a certain force is needed to straighten the chain ie overcome the catenary effect and that effectively is what is happening when a boat pulls on an anchor chain. Certainly the catenary effect absorbs some of the shock loading from a boat shearing around so I would argue that the catenary effect assists in keeping the boat anchored and hence can be added to the frictional resistance
 
Deleted User said:
Yup, I was wondering about that myself but I looked at it this way. If one end of the chain is fixed, then a certain force is needed to straighten the chain ie overcome the catenary effect and that effectively is what is happening when a boat pulls on an anchor chain. Certainly the catenary effect absorbs some of the shock loading from a boat shearing around so I would argue that the catenary effect assists in keeping the boat anchored and hence can be added to the frictional resistance
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Um, I can't see a way to say this delicately(!) I've read that a few times but don't see any logic in there at all Deleted User. I mean, nothing that says Newton is wrong and that the force needed to make the chain slip is 55+15 :D

The catenary thing does help absorb the shock loads from the boat shearing around, agreed, but that's something different. The benefit is that there is a reduction in the pulling force on the anchor+chain, rather than an increase in the force that the anchor+chain can take before slipping.
 
jfm said:
Um, I can't see a way to say this delicately(!) I've read that a few times but don't see any logic in there at all Deleted User. I mean, nothing that says Newton is wrong and that the force needed to make the chain slip is 55+15 :D

The catenary thing does help absorb the shock loads from the boat shearing around, agreed, but that's something different. The benefit is that there is a reduction in the pulling force on the anchor+chain, rather than an increase in the force that the anchor+chain can take before slipping.
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Umm, if you accept that the catenary effect absorbs shock loads, then you are saying you accept that those shock loads are not transmitted to the part of the chain that is sitting on the seabed and the anchor. Therefore, the chain is providing a holding force which is in addition to that provided by friction with the sea bed and that additional holding force comes from overcoming the catenary effect IMHO
 
Deleted User said:
Umm, if you accept that the catenary effect absorbs shock loads, then you are saying you accept that those shock loads are not transmitted to the part of the chain that is sitting on the seabed and the anchor. Therefore, the chain is providing a holding force which is in addition to that provided by friction with the sea bed and that additional holding force comes from overcoming the catenary effect IMHO
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No. The bit before the "therefore" is fine, and the bit after is pure single malt bollox.

When we say the shock loads are "absorbed" by the catenary, we really mean they are reduced. "Absorbed" is a bit colloquial. As the boat shears it moves, and let's say it is moving 2 knots down wind and about to snatch on the anchor. If the anchor chain is bar taught the snatch consists of the boat going from 2 knots to zero in virtually no time, which is a very high acceleration (or deceleration, if you are using colloquial terms). High acceleration means high force. The catenary, in contrast, exerts a force that decelerates the boat from 2 knots to zero over say 3metres, hence a much slower acceleration, and hence a much smaller force

You see, the force required to accelerate a mass from 2 knots to zero can be anything between 0.0000000Kgf and 1 billion kgf, depending on how quickly you want to go from 2 to zero. The catenary makes it go from 2 to zero nice n slowly, hence little force required hence you hopefully dont exceed that 55kg (or whatever) limit at which the chain breaks free

So the catenary doesn't exert an additional force of its own. It causes the forces exerted by the boat's movement (for any given change in speed of the boat, like the 2kts to zero in my example) on the chain+anchor to be less, aotbe. You'd get exactly the same effect if you had chain lying flat on the seabed then elastic for the bit that rises up to the boat
 
Deleted User said:
Some of us have observed that often the anchor doesn't dig into the seabed
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I must have missed the specific posts where this was mentioned.
But I can't see how that can happen - other than doing it as a sort of experiment, which is somehow contraddicting with having observed that "often".
I mean, don't you (or anyone else who experienced that) make the anchor dig purposedly, as part of the normal anchoring maneuver routine?
 
MapisM said:
I mean, don't you (or anyone else who experienced that) make the anchor dig purposedly, as part of the normal anchoring maneuver routine?
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Certainly if I'm staying overnight, I'll choose an anchorage where I can be as sure as possible that I can get the anchor to set but if I'm just stopping for a swim or for lunch and the wind is light, frankly I'm not that bothered about setting the anchor properly because in my experience the weight of the chain and anchor on the sea bed is sufficient to hold the boat. In any case, I've had a few bad experiences getting anchors stuck and I'd rather avoid that. In Croatia as you are aware there are many anchorages with rocky seabeds and its very easy to get the anchor stuck under a rock if you try to set it into the seabed by going astern too hard.
 
jfm said:
You see, the force required to accelerate a mass from 2 knots to zero can be anything between 0.0000000Kgf and 1 billion kgf, depending on how quickly you want to go from 2 to zero. The catenary makes it go from 2 to zero nice n slowly, hence little force required hence you hopefully dont exceed that 55kg (or whatever) limit at which the chain breaks free

So the catenary doesn't exert an additional force of its own. It causes the forces exerted by the boat's movement (for any given change in speed of the boat, like the 2kts to zero in my example) on the chain+anchor to be less, aotbe. You'd get exactly the same effect if you had chain lying flat on the seabed then elastic for the bit that rises up to the boat
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Yup won't argue with that but you address only one feature of the catenary and that is its ability to damp the acceleration of the mass of the boat as it responds to wind and current forces. But you don't mention the ability of the catenary to apply a horizontal load to the boat as well. In fact the website you linked to mentions this very fact
The chain performs two functions. It exerts a horizontal force on the yacht which resists the force produced by wind and waves, and it absorbs energy when the yacht surges backwards in response to gusts and waves.
 
Deleted User said:
In Croatia as you are aware there are many anchorages with rocky seabeds and its very easy to get the anchor stuck under a rock if you try to set it into the seabed by going astern too hard.
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Yep, in Croatia I used to deploy also a signaling buoy. It was worth the hassle, in a few occasions where I actually had to use its line and the winch to recover a stuck anchor.
But I still preferred to properly set the anchor also when not overnighting (though not necessarily going so hard astern - just a little).
In some bays with many boats around, it was nice to be reasonably sure that the boat was not going to interfere with the neighbours right in the middle of a lunch...
 
Great post guys. A few observations...

It's clear to me that enough chain could equal the holding of the anchor, but why would we want to carry say 400M of extra chain weighing 600kg (?) in preference to a 20kg anchor? (Particularly with a planing hull and especially with MY planing hull - which would undoubtedly sink under the weight of this example! :eek:)

Is a mooring much different to a heavyweight anchor with no chain?

The suspended chain's catenary is surely applying force against the anchor/seabed chain as well as the boat? If you take a 20M length of chain and fix it to your roof, then grab t'other end and walk away, it will get heavier until you can't pull any more! Granted there will be more force pulling the boat than the anchor/chain, but only because of gravity...
 
Deleted User said:
you address only one feature of the catenary and that is ...
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:? :? That's because I was replying to your post in which you disputed Newton's 3rd law. The horizontalisation benefit of the catenary is a completely separate point which I commented on several posts above, agreeing that it was v important benefit of the chain
 
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