Any Mathematicians

[davidhand]

I think we have all heard the textbook statement that one of the disadvantages of an all chain rode is that has little give (ie no elasticity). However I have often wondered if that is true. Would not the deeper catenery in itself act as a cushion? chain being heavy it would be almost impossible to pull it taught. I think it would need a mathematician to solve this one.

<hr width=100% size=1>

 

[qsiv]

One formula says that

F = W x (L)^2/(2 x D)

Where F is force in Kg
W is weight of chain / metre
L is length of chain
D is depth

So if we take a weight of 3.5 Kg/Metre, 30 metres in 7 metres of water we get about 225 Kg. Increase the length of chain to 60 metres and the figure rises to 900KgF.

These figures correspond to approximately 35 and and 65 knots of windspeed respectively.

The catenary forces are NOT for a 'flat catenary', rather rhey are an estimation of the point at which there is no meaningful elongation left in the catenary to absorb snatch loads from wave action - which is what is likely to break the anchor out, and also be most uncomfortable!

One estimate for boats around the 10 metre mark, is that the scope should equal the windspeed in knots, in 5 metres of water.

<hr width=100% size=1>

 

[bedouin]

Where oh where is Mr Charlesworth when you need him

I think the effectiveness of a catenary must depend on the depth of the water rather than the length of the rode - so it is possible that with light chain in swallow water it may be less effective than a nylon rode.

Note that the issue is not so much how much force it takes to pull the chain taut but how much force it takes to move the boat back a specific distance (e.g. 1 metre).

<hr width=100% size=1>

 

[Birdseye]

if you had an infinite length of chain available to you, then you could always let out enough to form a catenary and the shock wind and wave loads loads on the boat will be at least partially be absorbed by the chain being pulled towards the straight. however, this is not practical. you cannot carry an infinite chain, your boat cleats couldnt support it anyway, there wouldnt be enough swinging room, and the chain would be too heavy for the boat - and no doubt another few reasons i havent thought of.

when the boat starts yawing under the effect of wind and waves, the energy of movement of the boat is first absorbed into raising the chain ie reducing the catenary. when there is no catenary left, you start trying to stretch the steel chain like a rubber band - and it takes a lot of energy to stretch steel only a small amount. so the boat comes to a stop with a jerk. you can absorb the same energy with nylon rope, but because it is much more stretchy, it absorbs the energy over a greater stretch and you feel less of a jerk if any at all.

in this situation where there is no catenary left, the jerk you feel on the boat is the jerk that the anchor feels. if you wanted to pull an anchor out, would you apply a steady force or would you jerk at it? if you have any doubts, just imagine doing a bungy jump first with a bungy, and the second on the end of a chain



<hr width=100% size=1>

 

[MainlySteam]

Unless in very shallow water with a short scope you are very unlikely to pull the catenary even close to being straight. For example, we have 1.4 m of freeboard at the bow roller so in 20 m of water with 70 m of chain (bit over 3:1 scope) if the catenary is pulled close to straight the chain is pulled to a 16 degree angle to the sea surface and will enter the water 5 m in front of the boat. For us, that is almost half a boatlength forward of the bow (we are approx 40 foot). With 10 mm chain I have never seen that even close to happen under those depth and scope circumstances even in a sustained F9. In lesser conditions, in a long 40 knot gust, say, the boat will ride back and slowly stop but I have never seen the chain at less than around 45 degree angle to the water surface in that type of circumstance. Despite all the talk about shock loads with chain, we have never, best I can recall, ever experienced anything that could be called a shock load. Most times, even in strong gusty conditions with changing wind direction (as in hilly inlets) if down below one does not even know the boat is riding around if one is not looking outside.

Of course, long before the catenary is pulled straight the anchor shank will be lifted from the bottom. However, despite many words to the effect that a nylon cable is best in this respect, for a given cable length and depth of water the load at which point the stock will lift is entirely dependant on the weight of the cable. It is obvious which is the heaviest cable material (furthermore, nylon is essentially weightless in water).

In very shallow water one should use as much scope as possible given the proximity of dangers and other boats. Despite the common opinion, the elastic properties of a nylon cable do not allow you to use a shorter scope in shallow water because the stretch in a short length of cable sized to take the full anchoring loads will be insignificant. The use of a long piece of light nylon brace roller hitched to the cable (whether of chain or nylon) and brought to the anchor bollard has merit in my opionion, but I personally have never felt any need for it and certainly would not wish to sit out heavy weather under such an arrangement due to the likelihood of the brace failing (both a recoil danger if long enough to stretch and shock load to anchoring system danger). I suspect that the most use of such a brace is simply to reduce the transfer of dragging noises from the chain on a hard bottom and that the lengths I have seen typically used are next to useless from a elasticity point of view.

Looking forward to the next 150 posts on this /forums/images/icons/smile.gif.

John

<hr width=100% size=1>

 

[Chris_Stannard]

I just looked up my seaman's pocket book (1952) to see what it says on anchoring. The basis of anchoring is that the anchor chain should lead along the bottom to the anchor to prevent it breaking out. For this purpose chain, with its weight, is obviously better than a warp.

I also guess the object is to prevent the anchor dragging when the wind gets up. This is usually caused by the boat sailing from side to side, which tends to break out the anchor. It can be prevented by dropping a kedge anchor under foot. You have to pick the kedge up on the turn of the tide of course to prevent it winding round your main anchor.

I tend to use 1.5 times the depth of water to get the chain to the bottom and at least the boats length on the bottom. So in 10 metres I would use about 20 metres of chain.



<hr width=100% size=1>Chris Stannard

 

[OzGirl]

You guys make me feel quite humble................../forums/images/icons/smile.gif

<hr width=100% size=1>

 

[davidhand]

Your practical observations seem to bear out my intuitive feeling. But wait I just found my old HNC maths book and it has a chapter on the "catenary" I must spend a couple of hours over the hols sorting this one out. That should please SWMBO.

<hr width=100% size=1>

 

[SlowlyButSurely]

John,

I agree with all you have said here.

Am I right in thinking that it is only people with new-fangled anchors and those advocating nylon warp have strong views about this, and that those of us with a hefty CQR and plenty of chain are quite happy with what we have?



<hr width=100% size=1>

 

[hugh_nightingale]

You will never be able to pull the chain "straight".

Using a washing line analogy:
the tension in the line is proportional to the weight say at the centre (obviously) and on the tangent of the angle of deflection. As this angle approaches 90 degrees (i.e. just off staight, its the half angle at the centre) the tangent approaches infinity and so does the line or chain tension. You can't even pull a washing line absolutely straight.
The chain doesn't take a true catenary anyway and I believe and there are probably too many variables to sort it out (I have just been advised).
You do not want to lift the last bit of chain off the bottom either.
I think we add some nice elastic rope to, yes, have a bit of give, but mainly to stop the noise.


<hr width=100% size=1>

 

[DeeGee]

Double trouble

In all these long threads, we have this theory and that about length of scope and so on, but almost never does the thread develop theories about putting out second anchors, or putting a second anchor in series with the first? Yet my heavy weather anchoring books (not much h/w anchoring experience, I'm afraid) suggest either or both of these. Certainly, my intention, if the h/w anchoring experience is going to be kindly provided at some point - will be to deploy my second anchor on chain and rope rode. I am not geared up for series anchoring but would be interested in anyone commenting on using it.

<hr width=100% size=1>Black Sugar - the sweetest of all

 

[Talbot]

Re: Double trouble

I do not like the concept of series anchoring (all the eggs in one basket) the second anchor being deployed makes more sense to me especially as the biggest cause of break out is pulling on the anchor at an angle (i.e. when the boat veers around the anchor). This is would be minimised with a second anchor. It will also make breaking out the anchor afterwards a tad easier.

Does anyone else recall the article in PBO some few years ago that took a mathmatical look at anchoring and IIRC concluded that it was better to have 10metres of 10mm chain than 20m of smaller as the resultant forces were much better for remaining attached to the bottom. Its conclusion was that 20m of chain was optimum, and that if you had this then you could then calculate anchor cable length at a different ratio to normal 5:1. It also concluded that 20m was the minimum length of cable to be used regardless of depth.

<hr width=100% size=1>

 

[penfold]

Re: Double trouble

Theoretically series anchoring offers the best performance, but relies on nothing breaking, and the wind direction staying the same or changing only very slowly.

Apropos the chain catenary, If it is windy enough to straighten it and start jerking, it must be getting on for Hurricane force. In these circumstances it is likely the sea state will become a bigger concern. Use of an angel or chum weight and/or motoring to take some of the strain off is usually advocated in the event of extreme conditions. Or maybe finding religion!

cheers,
david

<hr width=100% size=1>Gosh darn it, Mr. Lamarr, you use your tongue purttier than a twenty dollar whore!

 

[peterb]

Re: Double trouble

I suspect that the real problem here isn't wind loading. As most people know, thw water doesn't move with the wave. Float a small buoy on the water and watch the waves go past it; the buoy stays roughly where it is. But only roughly. Theory (and experiment) say that in a deep-water wave system (but not a breaking wave), each particle of water is moving in a circle. For a particle on the surface, the diameter of the circle is the same as the valley-to-crest height of the wave.

But for the motion to be circular, it's not just up and down; it must be back and forth as well. The top of the wave is moving in the same direction as the wave, while the bottom is moving in the opposite direction. To some extent, the boat will be trying to do the same. Since an anchored boat will usually be facing into the waves, this means that at the crest of the wave, when the scope is least, the boat is trying to move backwards, whilst in the valley of the wave there is a tendency for the boat to move forward, or at least for the cable load to decrease. As a result the cable is likely to come taut at the crest of each wave. This may not mean that the anchor cable becomes straight, but it does mean that the cable load is not steady and may have peaks far above the steady wind loading.

As some of you may remember, I said a little time ago that I was trying to investigate the best position for an anchor 'Chum'. I haven't done so yet, because I've been sidetracked by the dynamics of the movement of the Chum in a wave system. In fact, I suspect that the main advantage of a Chum may lie in in its energy absorption in a dynamic system rather than in its effects under steady load. Watch this space.

<hr width=100% size=1>

 

[Guest]

Wait till HYlas starts !!

nm

<hr width=100% size=1>Nigel ...
Bilge Keelers get up further ! I came - cos they said was FREE Guinness !
/forums/images/icons/cool.gif

 

[Guest]

Of course it will be harder to bring cahin to near straight .... even rope rode will not go straight, but will approach it faster than the heavier chain.
Using a Chum will delay it even further and increase the damping effect.

As many have seen from my arguments with Hylas on this very subject .... I am an advocate of all chain ... with possibly a rope rider securing over bow to reduce noise ....... I would not like to ride to all rope or be next to a boat with such in a real blow.


<hr width=100% size=1>Nigel ...
Bilge Keelers get up further ! I came - cos they said was FREE Guinness !
/forums/images/icons/cool.gif

 

[Guest]

But this assumes

that you only put limited scope out .....

I have about 120ft of chain stowed in the bow of my 25ft boat .... it does not ride bow-down and I have yet to experience the boat pull the anchor out by jerking on it in a sea ..... To break it out and lift I usually have to motor up to the anchor and then over it to pull exactly opposite to its lay.


<hr width=100% size=1>Nigel ...
Bilge Keelers get up further ! I came - cos they said was FREE Guinness !
/forums/images/icons/cool.gif

 

[Guest]

QED ....

Stick to KG's and plenty of it and you cannot go worng.


<hr width=100% size=1>Nigel ...
Bilge Keelers get up further ! I came - cos they said was FREE Guinness !
/forums/images/icons/cool.gif