Detecting Depth Vs. Coil Size And Shape (long, Detailed)

[GB_Amateur]

With the official announcement on May 15 of the (hopefully) mid-summer release of the Garrett Apex there was considerable discussion of the (only) stock coil planned for release and its affects on depth.  Within that discussion Chase gave me incentive to do some testing.  This post is a result of that, but since I think my testing is applicable to more than just the Garrett Apex I'm creating this post in the general DetectorProspector forum.

The gist of the topic there was how much compromise the 6" (wide) X 11" (tall/high - my choice of word) Apex stock would have on depth.  As I mentioned I have quite a few coils for each of my detectors, but subsequently I realized there was one detector (Fisher Gold Bug Pro) and coil combinations (5" DD round and 5" X 10" DD elliptical) which would best address this issue.  (I also have some other options -- White's TDI SPP and Minelab X-Terra 705 -- but those are a bit less ideal as will be discussed later.  Since I have two other coils for the GB Pro I decided to include those for completeness although they add more variables/concerns and thus don't fit quite as neatly as the other two.

I initally started with my variable depth test stand which allows me to vary the depth of small targets in 1/2 inch increments from ~ 1" down to 12" depth in the ground.  However, in the midst of that part of the study I realized that I have some (likely iron) trash targets in the field-of-view which compromise the tones/measurements.  Fortunately I also have two cleanly placed buried coins -- a copper alloy Lincoln Memorial USA penny buried at 5" depth and a Jefferson nickel alloy 5 cent piece at 6 inch depth.  Neither of these currently suffers from nearby trash targets.  I subsequently altered my study to use those targets for the coil performance tests.  Unfortunately these also aren't ideal since under the conditions of testing they are too shallow to determine in-ground depth limits.  What I did as a hybrid compromise is to carefully (i.e. measurably, with shims) raise the coil above the ground until the signal disappeared.  For a second (more/less confirmation) test, and one that should be easily repeatable by anyone with the same/similar detector and coils, was to then perform a standard air test.

Let's start with the conditions of the tests:

1) Ground conditions -- moist ground (we've had a typical wet Spring season), Fe3O4 mineralization measure of 2.5 bars on both the Fisher Gold Bug and Fisher F75 (2.5 meaning that about half the time I see 2 bars and half the time 3 bars).

2) Gold Bug Pro running in "all metal" ("motion all metal" in USA terminology which I like to call minimally filtered), max gain, threshold at 11 (which is about where Kevin Hoagland calls "mosquito buzzing in your ear"), no headphones (so detector's speaker).

3) My precision for "depth" is 1/2 inch.  That coincidentally was the height of the shims I used in the hybrid test and also my ability to control the hand-held coin distance in the air test.

4) My determination of (maximum) depth limit was simple.  I increased the depth until I thought I could barely detect an audio signal.  I then decreased the target-->detector distance by 1/2 inch and required that I subsequently heard a clear signal.  If not I reduced the depth/distance and repeated.

Here are the raw data results.  I'll explain the meaning of the columns shortly.

You can see the four coils I tested.  The first three are all Fisher manufactured and the last is the NEL Tornado.  Rather than to use the nominal product quoted dimensions ('dim' short for 'dimension' in the column headings) I actually measured the coils and interpolated to account for the fact that a coil doesn't typically have a single extent but rather is a bundle, and further that the bundle obviously fits inside the housing.  For the closed coils this is obviously more vague but in those cases I just used half an inch less than the housing dimension.  An addition oddity is that DD coils aren't really simple ellipses but some overlap of two independent elliptical coils.   'geom mu' is the geometric mean of the two just determined transverse dimensions -- more specifically the square root of their product.  Hopefully you'll see later why I calculated that quantity.  It's not really relevant for the main conclusions I draw.  The last two columns are the actual distances between the target and coil for the limiting distance (see item 4 above).  In the case of the air test that is obvious.  In the 'part ground' test that is the sum of the depth of the coin in the ground and the height of the coil above the ground for both coins.

At this point I think it's worth discussing some caveats/assumptions/limitations of this test.  Then if you've stayed with me I'll go a bit farther and hypothesize on how to use these data to draw conclusions for other coils.

1) Although I chose a detector/coils combination that was as consistent as I could be (same manufacturer and same 'width' coil), it has been discussed on this forum previously (sorry, no link) that the quality control of coil manufacture is a difficult task.  It's certainly possible, although not necessarily likely, that my 5" x 10" elliptical coil is a high end tail performer among its peers and/or my 5" round is a low end performer.

2) With any measurement, there are in particular systematic errors and biases.  I can't "double blind" my method.  That is, I do know which coil I'm testing at a given time and if I have a prejudice for or against a certain coil that could show up in the results.  Also, statistical uncertainties (more succinctly, how repeatable are my data) can contribute to errors.

It is worth pointing out that swinging the heavy NEL 15" coil effectivly makes taking in-ground measurements with it difficult.  As a result I was unable to confidently get a max depth reading for the penny using that coil, which is why that cell is blank.  No problem with air tests because there, as is standard (?) I mounted the detector in a stationary horizontal position and just 'swung' the targets to determine the (max) limit distances.

Again, it's really the 5" round DD and 5" x 10" elliptical DD that are most relevant.  The others are include for information purposes but also to add to the plots I show later.  As you can see, in these tests there is a clear and significant advantage for the 5" x 10" elliptical over the 5" round in both the hybrid test and in the air test.

OK, I now go a bit deeper.  Is there a mathematical relationship which can predict coil depth performance if I know the coil dimensions?  Compared to above this is another leap into the unknown with additional uncertainties.  However, here are a couple plots which seem to indicate relationships between the potential maximum detectable depth and the geometric mean of the coils width and height dimensions.

(Sorry for the confusion but the Blue dots in both plots are for the 1 cent piece and the red dots are for the 5 cent piece.)  It's better to look first at the 2nd plot -- air test.  There appears to be nearly linear relationship between max depth and the geometric mean of the coil's dimensions, although it appears to trail off with the large (NEL) coil.  Superimpose upon that the effects of ground noise and you see a further deterioration both in absolute depth and also in the trend which is shown in the first plot.  Simply put, it is well known that mineralized ground, even moderately mineralized as in my back yard, negatively affects attainable depth.  The larger the coil, the more ground it "sees", and thus the more ground interferes with performance.

I'll finish by pointing out that this isn't the first study I've made.  Back 3 years ago when DetectorProspector member Karelian made detailed measurements of a large collection of mono coils on a White's TDI in both ground and air, I noticed the depth vs. geometric mean relationship.  However, without a theoretical (physics/engineering) reason to expect this relationship, at this point it's merely a convenient correlation.  Karelian's data are further muddied by the fact that the coils studied have many manufacturers:  Coiltek, White's, Miner John, Nugget Finder, Minelab,...  I could show those results but I think I'll await the reactions to the above.  I can also do more tests (e.g. with the X-Terra although there is not clean comparison of round vs. eliptical coils with the same width, at least in my collection) or repeat these.  I await your posted reactions (including yawns ?).

 

[jasong]

14 hours ago, GB_Amateur said:

Is there a mathematical relationship which can predict coil depth performance if I know the coil dimensions? 

Relatively speaking, yes there is a simple relationship. At least for PI's. B = Φ /Area. Where B is magnetic flux density and Phi is magnetic flux. Notice this is a linear relationship as long as Phi remains constant, Phi may change non linearly when other stuff starts changing though, but I assume detectors keep energy to the coil constant no matter what coil you use.

This probably applies to VLFs too though. Ignoring the detector electronics and just looking at a coil loop, sensitivity is a function of flux density since more flux cutting a target means more inductive effects.  If the total energy of the coil stays the same (IE, the impulse or driving current stays the same) when you change coils then the flux density must increase or decrease in different parts of space around the coil since the total flux stays the same but area is changing. This is based on conservation of energy, which is an immutable law, however detector electronics can be more or less efficient and cause this relationship to be non linear between different machines.

When you increase area, the flux distribution (magnetic field) increases in size. Since the energy in the magnetic field stays the same, what this means is the flux density which is concentrated around the windings gets scavenged out to provide flux further away from the coil as the loop area increases. This is why bigger coils get greater depth, but experience less sensitivity to tiny targets close to the coil.

Conversely, small coils have a smaller overall magnetic field size, which means the flux density is greater closer to the windings. This means less overall depth, but more overall sensitivity to small targets close to the windings. 

In dynamic EM systems often the only way to see what's happening is via numerical analysis (think, creating a model, not a formula). I modelled this all and produced some 3D plots to demonstrate this effect (and also disprove the "V" shaped myth, which is actually more "U" shaped) in a finite element analysis program. But some childish mods on the Nuggetshooter forum deleted my account and years worth of posts so it's unfortunately gone now. I've forgotten a lot since then, but at the time I was more or less fresh out of school where I did my research, coincidentally, on modelling dynamic EM fields in solenoids for the purpose of creating mass accelerators to transport ore from asteroids. 

I did this with mono coils (mono coils are basically very skinny solenoids) and PI detectors in mind. But I think the general principle can be applied to VLF's as long as one compares like coil geometry to like coil geometry (ie, no concentric to DD). But I don't know enough about VLF's to say for certain there. Also, as you mentioned, the actual windings may differ from manufacturer to manufacturer, so it's just a rough gauge.

Simply put - for non-extreme cases of ellipticity, and using the same detector, one can get a pretty good comparison of coil performance by comparing their total areas, which isn't far off from what it looks like you also determined experimentally.

[AZ Jim]

I'd have to agree.

 

 

[Steve Herschbach]

Random comments. I’d certainly expect the 5x10 elliptical to outperform the 5” (actually 4.5” round), with the much larger coil area, on coin size targets. Too bad there is not a 10” round in the mix, which would complete the picture. However, on a sufficiently small target I would expect the difference between the small round and the elliptical coil to close and the 5” round to possibly pull ahead. Target size also matters in coil comparisons, and using the appropriate coil for the appropriate possible target size is one of the tricks in detecting. Small target, small coil, large target, large coil.

Notice in the chart below that the medium coil actually does not give the best depth on any of the test targets. It would if the right target was picked, maybe a half pennyweight nugget. The right half pennyweight nugget might show 5” with the 10” coil and 4” with the other two coils. The chart shows how setting the target size actually determines which coil is best.

Coil Size vs Depth Fisher Gold Bug 2
Source - Field Testing the Gold Bug 2 by Gordon Zahara

The difference you found in the air versus ground test on the 5x10 versus 7x11 is interesting. The larger coil has a clear advantage in the air test, that all but disappears in the ground test. Nice illustration of how air tests can mislead once ground effects are added to the equation. In extreme ground the smaller elliptical may actually outperform the larger coil.

[GB_Amateur]

13 hours ago, jasong said:

Simply put - for non-extreme cases of ellipticity, and using the same detector, one can get a pretty good comparison of coil performance by comparing their total areas, which isn't far off from what it looks like you also determined experimentally.

Yes, the square root of the area is the geometric mean of the long and short dimensions with a constant thrown in.  You don't need to take the square root but I like the more/less linear relationship that results.

I can appreciate your finite element analysis effort and it's too bad your work was lost.  I'm not willing to go that far, though.  I can probably work through some of my old texts to get the static field strength on the axis (where we care, at least ideally) for circular and maybe eliptical coils, but as you note, real detectors use changing (dynamic) currents, etc.  So the static solution may not be sufficiently meaningful.

I'll look at Karelian's data and my analysis of it again.  They are 'noisy' but that isn't surprising given that he meassured depths for coils from multiple manufacturers meaning in some cases different designs (e.g. "folded mono") and almost certainly different coil winding parameters.  Again, those are mono coils on the White's TDI (Pulse Induction detector) so may not be as meaningful to the discussion which instigated my study -- the new Garrett Apex simultaneous multifrequency IB/VLF with 6" x 11" DD -- neither the same detector type nor the same coil configuration.

 

[Bash]

Thanks for the post GB.  Since I trade options, I loves me some quantitative analysis!

[Chase Goldman]

Thanks for your analysis, Chuck.  Glad I inspired you to do the deep dive, I have to think about coil dimensions some more regarding elliptical coils.  For a normal coin sized target my main takeaway is that we are not talking a large delta in depth along the entire range of coil sizes.  I find Steve's small vs. large target depth crossover point to be a very interesting table.

[palzynski]

On 6/8/2020 at 7:36 AM, Steve Herschbach said:

...Target size also matters in coil comparisons, and using the appropriate coil for the appropriate possible target size is one of the tricks in detecting. Small target, small coil, large target, large coil.

Yes I agree with you Steve there is an optimum coil for a given target size. Concerning the air tests they are too far from the field results, so I do not do them any more it is a waste of time to my opinion. So I just keep on doing ground tests with my boxes filled with mild ground .  I have been doing these tests since several years now , and the max depth I measured with VLFs for a big coin is around 11/12 inches , so very similar results as GB_amateur's and yours ...

Btw from what I saw in other threads , only PIs go deeper , 15/16inches for a big coin with a TDI GB off . And it looks like the impulse AQ will be rather in the 20inches range for such a big coin  We will know very soon now .. . ?

Of course with reduced iron disc capabilities for the PIs ..

[GB_Amateur]

On 6/8/2020 at 10:36 AM, Steve Herschbach said:

Notice in the chart below that the medium coil actually does not give the best depth on any of the test targets. It would if the right target was picked, maybe a half pennyweight nugget. The right half pennyweight nugget might show 5” with the 10” coil and 4” with the other two coils. The chart shows how setting the target size actually determines which coil is best.

Coil Size vs Depth Fisher Gold Bug 2
Source - Field Testing the Gold Bug 2 by Gordon Zahara

Here are those data plotted (leaving off the largest = 1 oz to preserve a linear horizontal scale):

I've taken the liberty of drawing curves through the sparse data (four datapoints for each coil).  With that caveat, note that Steve's prediction that the medium coil would perform best around 1/2 pennyweight (12 grains) is spot on.

Spurred by Jason's mention of physics theoretical principles I dug into one of my textbooks for the ideal magnetic field strength, on axis, for coil of known diameter.  The equation I found was 'ideal' in that it was a single wire (not a bundle as in a real coil).  There was no dielectric -- what we effectively think of as the ground mineralization -- so the plot below is analagous to an air test.  I used my equivalency hypothesis (geometric mean of long and short coil dimensions determines the equivalent circular coil diameter) to choose these ideal coils as analogous to the real Fisher Gold Bug 2 coils.

It's important to note that the equation I used to plot the data assumes a constant current.  Electronic detectors require a changing current (that's actually physics that requires it) so this further distances the literal interpretation of the plot.  (Jason mentioned needing to use advanced numerical techniques to simulate dynamic fields for better real world predictions.)  Also, I left off multiplication factors which include current, number of turns, and some physical constants.  Thus I labeled the vertical axis as having arbitrary units.  In the real world the target plays a significant roll (see first plot above).  Simplistically you can think of a target at detection limit represented by a horizontal line cutting across the second plot.  Where that horizontal line intersects the various curves is that target's detection limit.  I likely could have done better in my plotting so the two graphs could be better compared, but given that the first is of real data and the second an overly simplified ideal case it's probably better this way.

One feature of this ideal case worth pointing out, though, is the various regions where one coil has an advantage over the others.  Similar to the plot of the Zahara data (first one above), you can see a small region where the middle-sized coil is best, but that in most cases it is intermediate between the small coil performance and the large coil performance.  Further, consistent with real world tests, for small targets where larger magnetic field is required to get the return signal above electrionics noise, the small coil wins but as target size increases, the larger coils win.  Again, this is because properties of the target play a role in the return signal, not just the magnetic field strength.