Anchor chain

[RupertW]

It is not circular logic, not in any way. I only assumed all boats would have a chain that was related in the same logical manner to breaking strength. Read my post again. Plug the values into the model, and you will get matching results. When the chain is at given % of BS, the curve is always the same. True? This is a very simple, obvious artifact of the math. It is a defining characteristic of the catenary.

No you are still circular - now you are saying that a curve that matches force to breaking strain is the same as the same curve that matches a different force to a different braking strain. Obviously but that is nothing to do with the breaking strain required for boats of different sizes and strengths which will not vary in the same linear manner.

I am also a qualified engineer with a background in applied mathematics but that doesn't stop me from acknowledging that I am sometimes wrong or state things in a way that is unclear.

 

[RupertW]

Like you I hate urban legends, and do the maths. By which I mean compose and solve the differential equations, and plot the results. You can see a calculator here: http://www.awelina.co.uk/anchor_rode/rode_length_graph_only.html

Over some years of observing quite rational and experienced people disagreeing so vehemently (on this and other forums) about whether the chain's weight does anything, despite the maths being common to all, the penny eventually dropped (maybe I was a bit slow): size matters and we are all correct, despite disagrreeing, but are coming from a different perspective. The windage of a boat scales roughly as length squared but the weight of the boat, and so what is a reasonable weight of chain to carry, scales roughly as length cubed. So those with smaller or lighter boats always say that the chain will end up bar-taught whereas those with heavy boats and lots of heavy chain say 'no it doesn't, my chain's always got some curve'. I suggest that you play around with the calculator linked to above to see this effect. The source code of the javascript is visible, so if you spot an error do let me know.

I think the calculator is great apart from the mad suggestion on acceptable angle - proposing 0% for CQR and 5% for Rocna is a long way out as both are designed to allow much greater angles and still be digging in rather than coming out - 20 or 30 degrees is more like it with I think the Mantus having less tolerance than the Rocna, and even a CQR copes with a reasonable but lesser angle.

Putting in a sensible angle like that shows that there is absolutely no difference in the length of chain needed for a 6.5mm versus a 19mm chain. You need to create the highly artificial scenario of zero or three degrees requirement to need catenary rather than scope and the length of chain needed in an F10 become ridiculous because it's trying to achieve a curve that is neither necessary or useful.

 

[thinwater]

... but that is nothing to do with the breaking strain required for boats of different sizes and strengths which will not vary in the same linear manner....

And this goes back to how are chain sizes selected in the UK? In the US chain size is proportional to load via established tables. Where are the tables? Is there a calculation basis for chain selection based on something other than wind plus dynamic load? That is what I infer from this statement.

I'm struggling with why you would size a chain based on anything other than a fixed ratio of expected strain to breaking (or working) strength. Answer that if you will. Any other assumption means that the safety factor has intentionally been selected as different, which you can simply state, and I could accept that.

But otherwise, the ratio of BS to strain is a constant. Otherwise, the chain is either over- or under-sized, from a point of view.

---

The observation that chain is bar tight on small boats vs. curved on large boats is counter to my experience, all things being equal. There is one possible reason why people believe that; smaller boats anchor in shallower water and thus have less chain out. Obviously, that changes everything, since "all things" are no longer equal.

 

[jdc]

Glad to have the suggestion of a different default set of angles. This parameter ('angulation' in Alain Fraysse's excellent work) is a key parameter for an anchor, yet, astonishingly, to me at least, never seems to be investigated. Alain says that he models it as a simple cos(theta) correction to the anchor's holding power. I think angulation may be a significant factor between different types of anchor, and it seems clear that the modern generation of anchors are designed with this in mind, and perform better in many situations as a result - Peter Smith himself makes exactly that point.

But I'm not entirely convinced that 30 degrees is acceptable and I would gladly receive quantitative and/or theoretical guidance on what's acceptable. It may of course itself be a function of the force applied, but algebra can handle that! I don't think it can be a simple '21.23 degrees is allowed' type number else why would putting out more chain ever have a point? I do think a more horizontal pull must, in general, improve performance to some extent. I have tried analysing this from a soil mechanics perspective, which gives what looks a reasonable shape to a curve which has higher holding power the more horizontal the force applied, but am not yet happy enough with it to build it in to my model.

 

[noelex]

A very interesting analysis JDC.

However, I think the idea of an "allowable angle of chain at the anchor" is not the right way of looking at the problem.

As the angle of the chain at the anchor is increased the anchors holding ability will decrease, but there is no fixed "allowable angle". The maximum holding ability will be generated with the chain parallel to the seabed but this does not mean the anchor will not work and hold the boat at other angles.

This example of an Ultra shows the anchor holding despite a much higher chain angle than 3°. The anchors ultimate holding ability would be increased if the scope was increased causing the chain angle to reduce, but the chain angle does not necessarily need to be very low for the anchor to generate enough holding ability to overcome the wind force on the boat and to stay stationary.

Note the chain angle to seabed is not the same as the shanks angle to the seabed. People often imagine the shank angle will always rise to match the chain angle and this leads to incorect assumptions about how anchors will work, especially at shorter scopes.

 

[Neeves]

JDC,

I think the idea that every 40' yacht performs the same way is too simple. A yacht geared up for a circumnavigation will have more windage (and weight), I would have thought, than a cruiser/racer out for the weekend. Similarly a Catana and a Lagoon, of the same length, will perform differently.

It would be my observation that dragging is a function of hold, of the anchor, but that hold is modified by the movement of the yacht, yawing and hobby horsing have very significant impacts. Consequently a deep set anchor that has buried chain would be better than a shallow set anchor, with no chain buried - as chain contributes to the hold of the anchor (and used by the US Navy in their calculations of anchor specifications).

At lower rode/depth ratios lack of buried chain will become increasingly significant and any movement of the yacht will directly impact the anchor, reducing shear strength in the immediate vicinity of the fluke and increasing the potential for dragging.

Because increased buried chain is advantageous then bulky items, like overly large shackles but especially swivels and bigger chain rather than smaller chain will all impact performance. And of course the biggest unknown is the seabed itself and how the anchor you have actually performs in that seabed - most testing is conducted in nice, clean sand).

Unless we are specifying for a new yacht, or answering the query the OP posed, then most of us have fixed chain (and we are not going to change it - as it costs too much). For the individual the calculations then become simpler, as the yacht and chain are fixed. But considering factors or multipliers to modify the initial results to accomodate, biminis, twins furling headsails, larger windage cats (or any vessels), dinghies on davits etc would be a boon. Considering chop or the impact of unstable winds, causing yawing, would also be useful.

The other factor missing from the calculator is the impact that snubbers might have as they, if correctly specified, will factorially improve 'anchor performance'.

JDC - your calculator is of considerable value but it could be added to, I think, with simple multipliers - how much windage does a typical furling headsail add etc, how much for a dinghy on davits, what impact does a regular veer of 50 degrees have, what impact does a snubber add etc

Finally as there are many unknowns any calculator is only going to indicative - as even good anchors are prone to dragging even when used by owners with many seamiles.

Jonathan

 

[GHA]

as chain contributes to the hold of the anchor (and used by the US Navy in their calculations of anchor specifications).

From memory this came up a while ago with some links and wasn't as simple as that, you can't just scale up. A ship that size can't realistically carry an anchor big enough not to drag so chain friction was factored in because they will drag when the wind gets up long before the chain gets lifted off the sea bed.
Our little ships behave differently, a decent anchor in a half decent bottom shouldn't be dragging before the chain gets lifted off the seabed. Don't most of the new gen give allowable angles?

 

[Neeves]

Its not the friction on the seabed but the resistance of the chain to dragging. movement up and down and side to side, when a metre or more has been buried.

You can test this yourself.

Simply dive on your anchor when the conditions are a bit frisky and touch any exposed part of your anchor - it will be twitching. The more chain you have buried the less it will twitch, because the transmission of movement causing the twitch is reduced because the chain is buried. Now go to the seashore and stand in shallow water and twitch your toes/feet and you will reduce the shear strength of the shank immediately round your feet. If you jiggle a trowel in wet concrete - same effect you liquify the concrete, reduce its shear strength. Every time your anchor twitches it impact the shear strength of the seabed.

So - go back to our chains, bury some chain and you will reduce the opportunity for yacht movement to impose on the chain - at the anchor - that movement will be reduced and shear strength remain higher.

The US Navy test results, data and calculations are on mooring (not anchors and chain for ships) where chain lengths are short - its not only the chain on the seabed (which might be lifted) but the chain IN the seabed which will resist lateral and vertical movement.

Of course its not simple - if it was, anchors would not drag as we would have all the answers.

If you are in a tight or busy anchorage you may not have room to deploy more chain, without moving and where you are might be as good as its gets. Having buried chain, as opposed to not having buried chain, is advantageous - as I say - go and dive on a few anchors and check it out. Anchors with no, or little, buried chain twitch more than those with buried chain.

Its also a reason to use 2 anchors in a 'V' it reduces veering and thus the 2 anchors do not twitch as much as one single anchor.

It also a reason to use a snubber with good elasticity - negating the importance of catenary - as stretch of snubber occurs instead of catenary straightening. A saggy chain, where the snubber has stretched (rather than the catenary straightening), will impose less on the anchor - and reduce that twitching.

Obviously the chain and snubber work together - but the catenary has finite limits but the snubber will continue to stretch at roughly the same 'rate' until it fails. You obviously don't want to approach anywhere near failure, 25% of UTS would be a common limit, - but you can manage that by deploying more or a stronger snubber.

This is where Thinwater's (largely ignored) query on what source of tensions of anchors has relevance - as if you have a decent appreciation of the loads you can then devise your snubber system to accomodate.

Jonathan

 

[Tranona]

If the the chain is sized properly in all cases, the tension per pound of chain will be equal. Strength in tension is proportional to weight because it is proportional to cross sectional area. A chain that is twice as strong is roughly twice as heavy. I assume we can all agree to this.

The problem i have with this idea of "properly sized" according to a chart is that boats are infinitely variable in weight and windage (the two main factors that contribute to loads on an anchor, but chain sizes are not. We only effectively have 4 chain sizes covering boats from around 30-50' and weights between say 3 and 15 tons. So, how can you have properly sized chain for all these boats.

You state that strength is proportional to weight in your second sentence which is simply not true, and you can get chain of the same size (and therefore weight) with significantly difference strengths. As weight is often a negative from both the chain handling point of view and from trim of the boat there has been a move in recent years toward smaller, stronger chain. So your "chart" may say 10mm but you can get equal strength with a better 8mm chain at a substantial weight saving, or an increase in length for the same weight.

 

[GHA]

A saggy chain, where the snubber has stretched (rather than the catenary straightening), will impose less on the anchor - and reduce that twitching.

If you have a saggy chain then it ain't very windy

 

[Neeves]

I stand corrected - a less saggy chain.

Now (picking up on Tranona's point of lighter but stronger) that we use 6mm G80 chain its always less saggy (than it would have been were it the original G30 8mm) - but we have oodles of stretch in hand with our 30m snubbers. The 6mm is the same strength as the 8mm it replaced, but is lighter and takes up less room (and is easier to handle - come over the bow roller more smoothly and that lightness).

Now there are 2 terms that are ambiguous, for the pedants - 'less saggy' and 'oodles'

Jonathan

 

[Neeves]

The problem i have with this idea of "properly sized" according to a chart is that boats are infinitely variable in weight and windage (the two main factors that contribute to loads on an anchor, but chain sizes are not. We only effectively have 4 chain sizes covering boats from around 30-50' and weights between say 3 and 15 tons. So, how can you have properly sized chain for all these boats.

You state that strength is proportional to weight in your second sentence which is simply not true, and you can get chain of the same size (and therefore weight) with significantly difference strengths. As weight is often a negative from both the chain handling point of view and from trim of the boat there has been a move in recent years toward smaller, stronger chain. So your "chart" may say 10mm but you can get equal strength with a better 8mm chain at a substantial weight saving, or an increase in length for the same weight.

In defense of Thinwater

I had assumed and interpreted that he was referring to those using G30 - weight is proportional to strength - which for most people here is correct as the numbers of people who claim to buy G40 or G70 chain are a bit like hen's teeth.

You are correct other qualities are available but as long as Chinese chain is available to its 'recent' historic quality (G30) and it remains 'cheap' then motivation to use G40 does not appear evident and G70 is viewed very much as an exotic and therefore questionable. Reports of chain failure, over the last, say, 10 years, are non existent and as long as this remains true the need to move to G40 simply does not exist (especially as a major supplier of G40 in Europe has a poor reputation for galvanising longevity).

As a proponent of high tensile smaller chain I don't quite understand the overwhelming reluctance to use G70, G80 or G100 - particularly now that there is better acceptance (and importantly usage) of sensible snubbers. But then I am biased

Tranona, you are quite correct there are other qualities but 95% of people here use G30, oddly where Thinwater is located the default quality is G43 - so the same is true - but for a different quality.

Jonathan

 

[Zing]

Like you I hate urban legends, and do the maths. By which I mean compose and solve the differential equations, and plot the results. You can see a calculator here: http://www.awelina.co.uk/anchor_rode/rode_length_graph_only.html

Over some years of observing quite rational and experienced people disagreeing so vehemently (on this and other forums) about whether the chain's weight does anything, despite the maths being common to all, the penny eventually dropped (maybe I was a bit slow): size matters and we are all correct, despite disagrreeing, but are coming from a different perspective. The windage of a boat scales roughly as length squared but the weight of the boat, and so what is a reasonable weight of chain to carry, scales roughly as length cubed. So those with smaller or lighter boats always say that the chain will end up bar-taught whereas those with heavy boats and lots of heavy chain say 'no it doesn't, my chain's always got some curve'. I suggest that you play around with the calculator linked to above to see this effect. The source code of the javascript is visible, so if you spot an error do let me know.

Why measure water depth. It is surely anchor to bow roller height that counts?

 

[GHA]

Some more python fun - this based around the equation below, can't even find the website it came off now but seems to tally up with JDCs chart above so might be rightish, or close enough. Only a bit of hopefully interesting fun at the end of the day.

>length of chain needed so the last link just lifts off the bottom = square root of (2 x depth x horizontal force on chain / chain weight per metre x depth x depth. ) x depth
(Depth is to bow roller)


http://www.moondogmoving.co.uk/catenary.html

 

[KellysEye]

I would fit and had all chain, my view is the weight of the catenary holds the boat and the anchor is the back up when the wind picks up.

 

[GHA]

I would fit and had all chain, my view is the weight of the catenary holds the boat and the anchor is the back up when the wind picks up.

A catenary doesn't have any weight, it's a curve.

 

[jdc]

Some more python fun - this based around the equation below, can't even find the website it came off now but seems to tally up with JDCs chart above so might be rightish, or close enough. Only a bit of hopefully interesting fun at the end of the day.

>length of chain needed so the last link just lifts off the bottom = square root of (2 x depth x horizontal force on chain / chain weight per metre x depth x depth. ) x depth
(Depth is to bow roller)


http://www.moondogmoving.co.uk/catenary.html

Formula is

s = sqrt(y^2 + 2 * lambda * y)
where s = length to let out
y = depth of water (from bow roller to be pedantic)
lambda = wind force / weight of chain per unit length

This has the obviously desirable property that ds/dy tends to one as y tends to infinity, and is dimensionally correct.

It's a pedantic point about depth from bow roller or depth of the water. I do it for depth of water, but only start 'counting' the length of rode from where it just enters the water.

 

[GHA]

Formula is

s = sqrt(y^2 + 2 * lambda * y)
where s = length to let out
y = depth of water (from bow roller to be pedantic)
lambda = wind force / weight of chain per unit length

This has the obviously desirable property that ds/dy tends to one as y tends to infinity, and is dimensionally correct.

It's a pedantic point about depth from bow roller or depth of the water. I do it for depth of water, but only start 'counting' the length of rode from where it just enters the water.

Ta. Just plotted both equations side by side, close at the depths we anchor in, yours a little bit higher up to about 50m.
And looks like a nicer equation

Very impressed how quick python can create web friendly graphs even for a non programmer like meself.

import numpy as np

from bokeh.layouts import row, widgetbox
from bokeh.models import CustomJS, Slider, HoverTool, Range1d
from bokeh.plotting import figure, output_file, show, ColumnDataSource
from bokeh.io import output_notebook






# Set x to array from 0 to 100 with 500 steps
x = np.linspace(1, 100, 500)
y = np.sqrt((2*x*240)/(2.2*0.87*0.98*x*x))*x
scope = y/x
source = ColumnDataSource(data=dict(x=x, y=y, scope = scope))




hover_tool = HoverTool(tooltips=[
    ("Depth", "@x{0.0}"),("Chain Length", "@y{0.0}"), ("Scope", "@scope{0.0} :1")
])
TOOLS="pan,wheel_zoom,box_zoom,reset, save"








plot = figure( x_axis_label='Water Depth', y_axis_label='Chain Length', 
              plot_width=1100, plot_height=600,  tools=TOOLS, title = "Force in Kg required to just lift the last link of chain off the sea bed. ")
plot.add_tools(hover_tool)
# set a range using a Range1d
plot.x_range = Range1d(0,30 , bounds=(0,None))
plot.y_range = Range1d(0,80, bounds=(0,None))






callback = CustomJS(args=dict(source=source), code="""
    var data = source.data;
    var c = chain_weight.value;
    var f = force.value;
    x = data['x']
    y = data['y']
    scope = data['scope']
    for (i = 0; i < x.length; i++) {
        y[i] = Math.sqrt((2*x[i]*f)/(c*0.87*0.98*x[i]*x[i]))*x[i];
        scope[i]=y[i]/x[i];
    }
    source.change.emit();
""")


 #for (i = 0; i < x.length; i++) {*c+f
  #      y[i] = Math.sin(f*x[i]+c);


chain_weight_slider = Slider(start=0.1, end=20, value=2.3, step=.1,
                    title="Chain Weight (Kg)", callback=callback)
callback.args["chain_weight"] = chain_weight_slider


force_slider = Slider(start=1, end=1000, value=240, step=1,
                     title="Force (Kg)", callback=callback)
callback.args["force"] = force_slider






plot.line('x', 'y' , source=source,legend="Chain length", line_width=3, line_alpha=0.6, color = 'red')
plot.line('x', 'scope' , source=source, legend="Scope. (Chain length:depth)", line_width=3, line_alpha=0.6)




plot.legend.click_policy="hide"
#print(x)


layout = row(
    plot,
    widgetbox(chain_weight_slider, force_slider),
)


#output_notebook()
output_file("catenary.html", title="Catenary force")


show(layout)

 

[Neeves]

I would fit and had all chain, my view is the weight of the catenary holds the boat and the anchor is the back up when the wind picks up.

I'd agree with GHA

But also.

If you do the maths - some of the equations are on this thread

but unless you have infinite lengths of chain of more and more weight then usage of chain has limits.

Under normal chain lengths carried and using recommended chain size then at about 30 knots the effective catenary is no longer effective and you may as well be anchored by a steel rod. Beyond 30 knots the snatch loads will be increasingly traumatic - you may have catenary (it never disappears) but what is left is of no value.

I can assure you (unless you carry excessive lengths of chain and anchor only anchor in a maximum of 3m of water - its the anchor that hold you (or not).

I can speak from some experience - see earlier post - we are using 6mm chain, maximum of 75m, 7t x 38' (LOA) and 22'6" beam and if its not the anchor holding us I have to ask - what is it! We have never deployed more than 50m.

Jonathan

 

[Neeves]

[QUOTE


It's a pedantic point about depth from bow roller or depth of the water. I do it for depth of water, but only start 'counting' the length of rode from where it just enters the water.[/QUOTE]

Interesting reasoning.

It might be pedantic - but why not length of chain from bow roller (and depth from bow roller) - it is so much easier and it does not vary (for the given situation). Whereas as - as thew wind increases the length of chain 'before' the water will increase as wind increases.

Having said that 'weight' will vary air and water?

And as we use a bridle the length of slack chain, between bow roller and bridle hook, makes calculating the length from where it enters the water slightly more complex.

I just use length from bow roller, including slack, and depth from bow roller - but then I'm lazy.

Jonathan