Fortress scaling plot

[Neeves]

This is me keeping my head below the parapet . .....

I posted this screen shot - and no-one took any notice (or if they did they were distracted).

But the data is 'odd'

It represents most of the tests, or all of the tests, on multiple anchors of the same design. There is an unhealthy spread of data for some of the anchors but that is partially or completely ironed out by the number of tests. Calculating the average for each anchor size looks sensible and the plot, the straight line looks 'about right'.

The problem is that the line should pass through the origin, zero capacity, zero anchor weight. The line, that looks about right suggests that an imaginary anchor or zero weight will have a hold of about 450lbs. Why doesn't the line pass through zero, or at least close to zero?

I have my ideas, in fact I'm pretty sure - but I've spent too much time already exposed, I'm going down to my bunker.

Suggestions?

Jonathan

 

[AntarcticPilot]

Well, my reaction to that plot is that although there's not enough data to justify it, the relationship is not best described by a linear fit. A polynomial of order 2 or three constrained to go through zero might well be a better fit, or an exponential.

Statisticians often use a process called winsorizing to remove outliers; that might be useful here.

Incidentally, thanks for the data from the other thread; I had a look at it and it seemed to me that the force exerted by the wind was best fit by a cubic equation.

 

[lustyd]

It's likely that the relationship is between the capacity and anchor fluke area rather than anchor weight. It's also probably due to starting the Y axis at 1000

 

[vyv_cox]

Well, my reaction to that plot is that although there's not enough data to justify it, the relationship is not best described by a linear fit. A polynomial of order 2 or three constrained to go through zero might well be a better fit, or an exponential.

Statisticians often use a process called winsorizing to remove outliers; that might be useful here.

Incidentally, thanks for the data from the other thread; I had a look at it and it seemed to me that the force exerted by the wind was best fit by a cubic equation.

I agree. A straight line relationship seems highly unlikely in these circumstances.

 

[Tranona]

It's likely that the relationship is between the capacity and anchor fluke area rather than anchor weight. It's also probably due to starting the Y axis at 1000

Agree completely - but some posters here are obsessed with weight (unsurprising as anchors are sold by weight!) and assume that hold is directly related to weight while at the same time posting test data that clearly shows the relationship is not linear, nor even consistent from one weight interval to another.

 

[lustyd]

In theory the relationship shouldn't be linear with weight since weight and area won't generally be a linear relationship (weight being based on volume of the metal rather than area)

 

[Tranona]

Well, my reaction to that plot is that although there's not enough data to justify it, the relationship is not best described by a linear fit. A polynomial of order 2 or three constrained to go through zero might well be a better fit, or an exponential.

Statisticians often use a process called winsorizing to remove outliers; that might be useful here.

Incidentally, thanks for the data from the other thread; I had a look at it and it seemed to me that the force exerted by the wind was best fit by a cubic equation.

The plot is confusing as it includes a range of data for each size but the plot seems to be just a visual line based on the average for each weight (the red squares) I expect if you did a simple regression on the six sets of data the line would be similar to the eye ball one. On average there is a linear correlation between size and hold.

 

[AntarcticPilot]

I agree. A straight line relationship seems highly unlikely in these circumstances.

Another, perhaps more subtle point is that the anchor weight is not a continuous variable; anchors only come in specific weights, and each weight is probably different in important ways from the others. Scaling of a complex design is NOT simple or intuitive! And the Fortress is specifically designed to rely more on the geometry of the anchor than on its weight; the weight is a consequence of important design parameters, not the driver.

 

[AntarcticPilot]

The plot is confusing as it includes a range of data for each size but the plot seems to be just a visual line based on the average for each weight (the red squares) I expect if you did a simple regression on the six sets of data the line would be similar to the eye ball one. On average there is a linear correlation between size and hold.

It states that it's a linear fit (presumably linear regression) to the average, so you are correct about that. Given how easy it is to get a regression line from software like Excel, I'd be surprised if it was a visual fit, though it might be more convincing if they gave the parameters of the fit, including R (a measure of the goodness of fit)

 

[doug748]

Since weight and area are firmly linked in any one design of anchor, apart from a parlour game, almost nobody cares which is the final arbiter. You can't have one without the other.

We do have some clues:

.

 

[lustyd]

weight and area are firmly linked

They are, but usually in 3d objects the weight isn't a linear link to the area since it's based on volume so will be area x thickness and we know that the thickness increases with anchor size. I imagine that here, because it's aluminium the difference is small for the given sizes so it's not obvious how bad the graph is, but it will certainly be bad, even setting aside the vertical axis

 

[AntarcticPilot]

Since weight and area are firmly linked in any one design of anchor, apart from a parlour game, almost nobody cares which is the final arbiter. You can't have one without the other.

We do have some clues:

.

But the point is that the relationship between weight and area is not straightforward, and is definitely non-linear. Simple dimensional analysis indicates that area scales as the square of the linear dimensions, but weight as the cube. So an anchor that is twice the weight might only have about 1.6 times the area of fluke.

@lustyd got there first!

 

[noelex]

Fortress list the holding power of their anchors on their website:
Anchor Selection Guide - Fortress Anchors

Only a few anchor manufacturers do this, and personally I don’t think it is of much value. Many manufacturers don't even specify what type of substrate will produce these holding figures.

For most anchor manufacturers I think the numbers are made up by the marketing department .

However, Fortress do a much better job than most. They publish the expected holding power for different substrates and Fortress have actually done some good holding power tests (these are very expensive to do well) so presumably the numbers are far more realistic than most. With their extensive testing, Fortress should be aware of their anchors’ capabilities.

Out of interest, I have plotted in green dots on the graph the published holding figures for "soft mud" that Fortress have on their website.

The gradient of a best fit line between these points is much steeper than the original graph.

The Chesapeake Bay area has a very unusual soupy soft mud substrate that can produce atypical anchor holding results, so this is likely why the anchors were not behaving as Fortress would expect in a more conventional soft mud substrate.

Most substrates become rapidly firmer as the anchor penetrates deeper. This characteristic particularly benefits larger anchors. At the limit of holding larger anchors can penetrate deeper than smaller anchors of the same design. I have never anchored in the Chesapeake Bay area, but I understand that in this particular area the substrate can remain very soft even a long way below the surface. This would have the effect of flattening the gradient of the best fit line, which is exactly what we are seeing.

 

[Neeves]

It's likely that the relationship is between the capacity and anchor fluke area rather than anchor weight. It's also probably due to starting the Y axis at 1000

I agree with this.

But if you assume the plotted line is about right, and the data is actual - real anchors, real seabeds - lots of money involved - then the imaginary anchor of zero weight has a hold of 450lbs.

If this is correct then all the holding capacities - might be overstated.

Why?

There is the assumption that the scaling of the anchors is correct. Fortress I understand have their own dies for the extrusion of the various components - have they modified the dies to address scaling issues as increased data has been produced? My thought is why bother - the market place has a fixation with weight, why invest money fine tuning the dies when no-one will appreciate the difference - but maybe I'm a cynic.

If I invested money in fine tuning the dies every time the Navy did some tests I would want the world to know - and I'd use may investment as part of my advertising...

However the holds of Fortress models are so high fine tuning the dies to ensure that the hold was an accurate linear progression against weight - would be a bit of a waste - as the the holds are so high no-one would really care - they would still buy on weight.

But going back to why does the plotted line pass through, approx, 450lbs.

When Fortress anchors set - they set with the fluke at 30 or 45 degrees and the shank is not pulled into the substrate until the all the fluke is buried. Most other anchors (none of which are optimised for mud) set at, approx, 30 degrees and the shank buries with the toe.

Once the fluke of either design of anchor is fully buried the fluke, as tension is increased, continues to bury and the complete anchor - disappears. As tension is increased further the shank - and the chain, attached to the shank, is increasingly buried.

The shank is an obstruction to burial (which is why shanks are thin) and the chain that is pulled down, as the anchor dives further, is also an increased obstruction to burial. As the resistance to burial increases the fluke rotates toward the horizontal from that 45 or 30 degrees and at about 10 degrees the anchor pulls horizontally - it drags. As tension is maintained the fluke clogs, meets a contaminant - and breaks out.

If you look at, primarily, oil rig anchor websites the buried chain is always represented as the reverse catenary.

The makers of large commercial anchors have recognised all of this, and its important to them, and they have developed the maths to determine when the anchor has reached optimum hold.

An analysis of Fortress performance at Chesapeake was conducted and this is a summary:

Fortress at ultimate hold was 10' below the seabed surface. Test were conducted at different scopes, between 5:1 and 8:1 - and the depth of ultimate burial remained the same. At a 500lb load, 20' of 3/8th chain the angle at the anchor was 35 degrees and varied by 1.5 degrees (whether it was 5:1 or 8:1 - so extrapolating this - if the rode was flat on the seabed it would make no difference to the tension angle at the anchor. At 2100lb tension the tension angle at the shackle with 3/8th" chain was 49 degrees whether 5:1 or 8:1.

If all of this is correct then at 500lbs, not a very unusual setting tension the shackle, or tension angle, is 35 degrees - a far cry from zero if your chain is lying on the seabed. Is this correct - I'm not so arrogant that I think Vryhof, Acteon and the world's Navies are not as clever as me.

Repeating - this is in Chesapeake mud.

My conclusion is - if you can ensure your anchor engages, the toe starts to grab the seabed, then the anchor will dive at the angle designed (by chance or analysis) at its characteristic performance (say 30 degrees) and it matters not what scope you use but the anchor will dive - and the tension angle at the shackle will increase (because the chain is resisting burial from zero 10:1 scope or 5:1 scope to around 35 degrees (in mud) - for a 10mm chain at 500lb of tension. Scope does not matter, within reason, for anchor setting. If you increase tension the anchor will drag at around a 10 degree fluke angle. For the Chesapeake tests the chain rode was 20' - the rest 5/16th" wire.

If you are burying chain its resistance to burial is being measured as part of hold - and that's why the plotted line does not pass through zero.

Extrapolating - if you set you anchor at 5:1, or maybe 3:1. your anchor (assuming it performs) will set as deeply as if you have set at 10:1. It will have the same hold, 5:1 or 10:1. At 5:1 you will have less usage of catenary than at 10:1 - but you can replace catenary with a snubber. In a tight anchorage you don't need catenary (but you do need a snubber. In a 'large' anchorage you can use both.

The test were conducted in mud - but the concepts will hold true for other seabeds to a greater for lesser degree.

Chain reduces the depth to which your anchor will dive, so use as small a chain as is safe. Adding a big swivel or oversized or more shackles will reduce the ability of the rode to bury. Slim is good. Shear strength increases by the square of depth, the deeper you anchor can set - the higher the hold. An anchor you cannot see has a higher hold than one that can still be seen.

I have some photographic evidence of some of this - but am reluctant to post. I'll go back to my bunker and drink some more red wine.

Jonathan

 

[Neeves]

Interrupted by the absence of wine, temporarily I thought this would be useful:

Defense Technical Information Center

Jonathan

edit

I like to show both sides of an equation - If you think I'm a heretic - I have not managed to persuade an editor that this is actually relevant - so you might be among friends.

end edit

 

[Tranona]

I agree with this.

But if you assume the plotted line is about right, and the data is actual - real anchors, real seabeds - lots of money involved - then the imaginary anchor of zero weight has a hold of 450lbs.

If this is correct then all the holding capacities - might be overstated.

Why?


Jonathan

Basic caveat when using line of best fit methods like linear regression. It is only valid within the range of data points used. While interpolation (points between 2 recorded data points) is OK extrapolation either below or above recorded data points is not. You have answered your own question - extrapolation downwards results in an absurdity.

As mentioned by AP earlier R in the linear regression gives you a measure of goodness of fit and I would guess it is very high as all 6 data points are close to the line - ignore all the other data points as they are what underpin the average which is used for the regression.

 

[AntarcticPilot]

Basic caveat when using line of best fit methods like linear regression. It is only valid within the range of data points used. While interpolation (points between 2 recorded data points) is OK extrapolation either below or above recorded data points is not. You have answered your own question - extrapolation downwards results in an absurdity.

As mentioned by AP earlier R in the linear regression gives you a measure of goodness of fit and I would guess it is very high as all 6 data points are close to the line - ignore all the other data points as they are what underpin the average which is used for the regression.

I agree that R is probably high. But I actually suspect that a linear equation is inappropriate; the dimensional analysis in my earlier post suggests that it should be an equation of the form F = W^0.6666 to reflect the change in fluke area rather than the weight (^ indicates exponentiation). I'm also not convinced that averaging the values is the right approach; the curve in soft mud might be quite different from that in hard sand. But for comparable substrates, I'd expect the relationship between force and weight to be as given here, not a linear equation.

 

[boomerangben]

Since the science of how an anchor holds is dependent on many variables, even in the same substrate, I’d be very surprised if there was a linear relationship. Straight lines are nice to look at and make the maths easier, but Nolex’s green dot plot indicates a curve to my eye, with hold reducing per increment in anchor weight. It wouldn’t surprise me if there’s a stepped relationship as material thicknesses are discrete meaning a switch to thicker materials means a step change in weight for area. I personally think it is more complicated than just area since large areas might inhibit deeper setting and there by accessing stringer substrate, but I have not thoroughly investigated it.

But anchor manufactures have to differentiate between models somehow and weight is simple to use for their range. Fluke Area might also work, perhaps better, but if a single manufacturer ignores weight for area, how are buyers going to cope with the different metric? Possibly by ignoring that brand. Not good marketing.

 

[thinwater]

I don't think you can pull data together from different sets of tests and derive this sort of correlation.

• The setting procedures differ. For example, some tests you a steady rate of pull (x feet per minute) and record tension. Others increase tension at a stead rate (pounds per minute). Other use combinations. Some record the max load, and other record the max static load (did not creap down of the cable pull stopped). These differences in method could easily cause a 50% or greater difference in results (I have used these methods, and they can be VERY different in soft mud).
• The rate at which the substrate becomes more dense is very important. Is there firm mud 2 feet under the soupy surface, or are there scatter shells, or is it soft down many feet? These seem similar at first examination, but can give very, very different results.

I think it is well established that most anchors, with the metal thickness increased as needed to match hard sand holding capacity, tested in uniform sand, follow the model Hold = Mass^(about 1.1). The density of the substrate increases at a predictable rate with depth. But in soft mud, the layers are so variable that moving just a few meters can change the result, let alone to a different continent. I think Neeves is not far off on his plot and exponent, and I am sure you could get a very different exponent on some other bottom. I'm pretty sure, for example, that with a thin layer of sand over hardpan the exponent would be less than 1. If there was a layer that was hard to penetrate, perhaps several feet down, then greater than 1.

All we really learned is that comparing anchor test results is like herding cats. Neeves did as well as could be done IMO.

---

I did test several size Fortress anchors, including a 2.5-pound Guardian (very similar to Fortress). The holding in soft mud was 80-200 pounds, depending on the area and setting protecole. So yes, the data go through the origin. The low numbers were from real Chesapeake soup that was barely mud (holding from a 35-pound NG anchor was less than 400 pounds) and the higher numbers from what most people would call soft mud.

 

[noelex]

I think it is well established that most anchors, with the metal thickness increased as needed to match hard sand holding capacity, tested in uniform sand, follow the model Hold = Mass^(about 1.1).

Thanks Thinwater.

Expressing the formula with a variable exponential is great way of simplifying the relationship between anchor weight and the maximium holding ability.

Hold = Mass^(about 1.1).

The above formula means if we double the weight of a particular design of anchor we slightly more than double the hold (the hold will increases by 2.1). That is my conclusion as well looking at all the data we have.

You can also apply this formula to work out the maximium holding power gain produced by increasing the weight of a particular anchor design by, for example 60%. ( There was a recent thread on this subject :
https://forums.ybw.com/threads/lewmar-epsilon.612374/ ). In this case the increase in the maximium holding ability is likely to be around:

1.6 ^1.1 = 1.68 so a 60% increase in weight increases holding by 68%

Many on this forum have pointed out that if you double an anchor’s weight you do not double the fluke area and this is perfectly true, but they are forgetting that an anchor’s holding ability is not just influenced by weight, but also significantly by the depth of bury (as well as other factors). The maximum depth of bury a specific anchor design is capable of achieving in any particular substrate increases as the size increases. This plays a significant role in increasing the holding power of larger anchors.

However, while I do feel that while the general rule that if you double the weight of an anchor you will approximately double its hold (or increase it by 2.1 ) is a well proven rule, this rule has been established mainly by experiments on steel anchors of a conventional design. I don’t think this can necessarily be extrapolated to very atypical anchor designs, for example the steel XYZ anchor, or even an aluminium fluke anchor such as Fortress. As Thinwater points out, I also don’t think it applies in unusual substrates such as soft soupy mud that does not become firmer with depth or to very hard to penetrate substrates such as thick weed or cobblestones.