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

[Geotech]

Here's the equation I came up with for an effective diameter:

Using nominal dimensions the 5x10 is 6.32 and the 7x11 is 8.35, both remarkably close to GB's numbers.

To add to Jason's post, increasing coil diameter has a double effect, both on the TX side (which Jason covered) and on the RX side. The two are similar, in that curvature of the B-field limits the effectiveness of the coil depending on diameter vs target size. If the target is small enough, its eddy B-field presents both the positive and negative flux to the RX coil, resulting in cancellation and no detection. But right at the edge of the coil, geometry works in your favor and you can detect it.

Eric Foster made a chart of coil size vs optimum detection depth:

"Here are the curves I have used for many years. The range reaches a maximum when it is equal to the radius of the coil. Coils larger or smaller than this optimum will result in less range. To show how this works, along the bottom axis you see coil diameter, which is obviously 2 x the radius. So for an 11in coil, if we go up the vertical scale to A, we have 5.5in. Also note the diagonal line and the series of ever increasing semicircles. Everything to the left of this line shows increasing detection range up to the maximum where it intersects the line, then decreasing range to the right, where the semicircles are shown dashed.
If a certain metal object is just detected at 5.5in with the 11in coil, then going larger in coil size will cause a reduction (going down the dashed side), and going smaller in coil size will have a similar effect. Initially, it won’t be much, i.e. going from an 11in to an 8in coil will only make 0.5in difference but below 4in diameter, the range will drop rapidly.
Now, suppose with the 11in coil, you can detect an object at about 12.5in (B on the vertical scale. This indicates that the coil is not an optimum size for that particular object. If we carry on up the curve (direction of arrow) we can see that by using a 20in coil, we could gain another 2.5in (C). The curve peaks at 15in with a 30in coil. But the extra inch gained hardly makes such an unwieldy coil worth while.
Other factors come into play of course. The curves assume that the number of turns and the coil current is the same in all cases; which it isn’t necessarily. For the same inductance value, a smaller coil has more turns, which counteracts to some degree the loss in range. Also a smaller coil will pick up less electromagnetic noise, earth’s field noise and ground effect, which make for a smoother threshold.
The end result is, that with a small nugget that can be detected at between 5 and 7in with the 11in coil, so that it is on the top part of the curve, an 8in coil may well give a similar range. That is not to say that smaller coils do not have other advantages. Small coils and probes are very useful in rocky areas or searching in undergrowth. They have less drag too for water hunting, and less pickup from mineralised soil or conductive sea water plus better signal separation on close or multiple objects.
One other point regarding PI, is that the small object sensitivity is largely determined by the sample pulse delay. If an object is so small, or thin, or made of high grade stainless steel, such that all the signal has decayed before sampling takes place, it would not matter how small a coil you made, it would never be picked up.
Eric."

Jason, I'm curious what FEM software you were using.

- Carl

Edit: Thanks (Steve, I presume) for embedding the chart, I've deleted the link. Didn't occur to me that the link only works for Geotech members.

 

[Steve Herschbach]

Wow Carl,

I was thinking of exactly the post and chart from Eric, and it was on my list to track it down and post here. Here is another quote from Eric - I used this tidbit as a general rule for a long time:

Coil/target optimisation can be quite complicated, but it can be broken down into a number of separate considerations. I will deal with just one, at the moment.

The diameter of the coil in relation to the target size is perhaps the most dominant characteristic. If we look at a mono coil, which is the simplest to understand, the optimum coil size is one that detects the target at a distance equal to the coil radius. e.g. if you have a 10in coil that just detects a target at 5in, then going either up or down in coil size will result in less range. If, however, your 10in coil detects a target at 10in, then the coil is not optimum, and going to a larger size will give more range on that target. In fact, the optimum coil for that target is 27.5in diameter, and it will detect the target at 13.7in. Say your target was big enough to detect at 15in with the 10in coil. The optimum coil size would then be 46in diameter and the target range 23in.

Coil sizes get bigger quite rapidly, and more cumbersome, but because the coil radius/range curve is very flat as you approach the optimum, you could reduce to a 30in coil and still get just under 23in.

All this assumes that everything else stays constant. i.e. TX current, inductance etc, and also pickup noise.

If I can find it, I will post a graph of coil radius/range curves.

Eric.

Anyway, thanks for posting that Carl, saved me a little time searching my hard drive archive. 

All ways of saying that for each target there is an optimum coil size, and going too much smaller or larger loses depth. But that is air tests - the caveat always is ground conditions. We have target masking, extreme mineralization, and EMI to deal with, and very often the solution is a smaller coil. Yet manufacturers have tended to cater to the burgeoning number of amateur testers that quote air tests or tests in clean low mineral soil, leading to machines actually optimized for those conditions with larger coils. White's move from the 9.5" coil on the MXT to the 12" coil on the "new" MXT 300 was that kind of a head fake. Same detector, but "new, improved model with more depth!" Well yeah, because the coil is larger. And frankly not exactly true. Depth actually was worse under some of the conditions I have described by going to the larger coil. I think new detectorists in particular would benefit from using more moderate coil sizes when starting out.

[jasong]

11 hours ago, Geotech said:

Jason, I'm curious what FEM software you were using.

It was the only free FE software I could find on the internet back then (2004) called FEMM (Finite Element Method Magnetics) which amazingly is still around it seems: http://www.femm.info/wiki/HomePage 

It was a static modeller but had a scripting language which could make it calculate a series of hundreds of static "pictures" to get a rough idea of what was happening in dynamic systems numerically where the math was too complex to calculate by hand. It'll calculate B, H, force, etc at every point in a 3d system with a little creativity using 2 cross sections. Problem was non-axially symmetric coils were not possible to model, maybe that changed now though.

[Steve Herschbach]

To summarize:

For every target there is an optimum coil size, and going to a larger or smaller coil than that optimum will get you less depth. To repeat, going to a larger coil can lose depth if the coil you have is already best for your target. People swinging super large coil sizes are losing depth on the most common targets sizes and only winning with the largest.

Conversely, there is an optimum target size for each coil, and both larger and smaller targets than the optimum will lose depth compared to using a coil optimized for that size.

Most detectors are optimized for coin size targets using an 11" coil. Smaller targets benefit from smaller coils, and larger targets from larger coils.

I should mention mineralization and EMI also. Large coils see more of both relative to target size. These two factors work against larger coil sizes and can negate some or all of the theoretical gains.

[Digalicious]

3 hours ago, Steve Herschbach said:

 

Most detectors are optimized for coin size targets using an 11" coil. Smaller targets benefit from smaller coils, and larger targets from larger coils.

 

That's why my go to coil for just about every coin shooting site is around a 9x5. Compared to the typical 11" round stock coils, it's much lighter, far less prone to EMI and ground noise, has superior unmasking and separation characteristics, and much more sensitive to all those angled coins and other small targets. In addition, there is much less need to reduce depth by having to significantly reduce the sensitivity to compensate for EMI noise. Ditto for having to add more filtering for the extra ground noise. When all that is taken into account, then the depth difference on coin sized targets between those coils, is minimal, and can often be better on the smaller coil for weak signals like coins that aren't lying flat...and I suspect most coins in the ground aren't lying flat 🙂

With all that said, how is it that the smaller coils perform much better on smaller targets? Is it because the field is compressed more, thus allowing for more eddy currents to be produced on the target?

[Steve Herschbach]

The coil output is fixed, so you get a more intense small field with small coils, and a larger weaker field with big coils. Keep in mind also that when comparing concentric and DD coils with mono coils, it’s the area of the receive coil that matters most, not the physical size of the entire coil.

This chart shows how medium coil sizes are the happy medium, and the benefits of going smaller or larger. In this case they should have tested a half pennyweight nugget, which would have done best with the 10” coil.

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

[CPT_GhostLight]

So in a semi-related question, looking at X-rays of double D coils, I noticed one coil winding is physically larger than the other. Which side of the DD coil is the transmitter and which is the receiver?

[GB_Amateur]

1 hour ago, CPT_GhostLight said:

...Looking at X-rays of double D coils, I noticed one coil winding is physically larger than the other. Which side of the DD coil is the transmitter and which is the receiver?

There's probably a way to reason this out with sufficient knowledge of how detectors work.  The easy solution is to look it up in the book I've touted here a bunch of times over the years (cf. p55):

Note the heavy gauge wire used in the TX coil versus the much smaller gauge RX coil wire.

 

[CPT_GhostLight]

8 minutes ago, GB_Amateur said:

There's probably a way to reason this out with sufficient knowledge of how detectors work.  The easy solution is to look it up in the book I've touted here a bunch of times over the years (cf. p55):

Note the heavy gauge wire used in the TX coil versus the much smaller gauge RX coil wire.

 

Thank you GB, that's what I was thinking and thanks for the link to the book!

[kac]

Good book to pick up is Carl's and Georges "Inside the Metal Detector" found on Amazon.