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

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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.

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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.


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

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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.

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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 ..

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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.

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This all is consistent with how I very often nugget hunt. Either VLF small coil, or PI big coil. My favorite VLF nugget coils have been 6” or smaller concentrics. My favorite PI nugget coils were 16” and 18” rounds. Very often I am hunting for small gold, or hunting for large gold, and optimized for either. Some places there simply is no large gold, and if you are not set up for the tiny stuff, you get nothing. But if larger gold does exist, it adds up faster than chasing tiny bits, and it’s best to set up for that.

The GPZ in my experience was the best of both worlds, finding a wider range of all sizes with one medium size coil.


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