Re: Hi Eric, about coil size

[Anonymous]

Hi Eric,
Some time back there was a discussion about coil size and size of objects detected.
I was wondering if you could post your findings in regards to your experience with different coil sizes and their depth of detection.
Hopefully, the information will provide what advantages a person might see using a smaller coil versus a larger coil to look for small gold nuggets.
Thank you in advance,
Reg

 

[Anonymous]

This is a 3D plot of what I think the response of a family of coils would look like.
The assumptions are:
The coils are all of the same mono design but with different diameters.
The coils all have the same inductance. That means the larger diameter coils have fewer turns to make the inductance come out the same.
The target is much smaller than any of the coils.
The horizontal axis of the graph is coil diameter. So each of the mesh lines that are nearly vertical represents one coil size.
The axis that comes toward you is depth. So each of the mesh lines that are nearly horizontal represents a different target depth.
The vertical axis is signal strength (actually the log of signal strength). The signal strength is represented by the height of the point above the gray plane and by color. Red is the strongest signal and blue is the weakest.
The thing to notice is that for each target depth there is a coil size that gives the strongest signal. For a depth of 0 the smallest coil gives the strongest signal. But for a depth of 4 the signal first gets stronger as the coil size gets larger and then starts to drop off. The maximum signal for each depth occurs when the coil diameter is about twice the depth (when the radius is equal to the depth). For the 24 inch depth the maximum signal would be from a 48 inch diameter coil.
The formula used to make this graph was :
signal = radius^3/(radius^2 + depth^2)^3
The ground signal does not follow the same formula.
Robert

 

[Anonymous]

Hi Robert,
Interesting chart, but I would be inclined to think the chart would be like you have posted if the diameter of the target is directly proportional to the diameter of the coil.
In other words, lets say the diameter of the object is 1/10 of the diameter of the coil, or some similar ratio, then I would think the chart would apply more accurately.
Just my thoughts.
Reg

 

[Anonymous]

Eric said he was going to answer about the coil questions as soon as he can.
As I remember correctly what he told me about it, as the distance to the target approaches the radius of the coil, your reaching the limits of the depth with that given size coil. (hmm. I think I said that right).
Take a 11" coil, and a nugget can be detected at about 5.5", that would be about the optimum size coil for that object. If you only could detect it at, say 4", then a larger coil would give you a improvement in detection depth of that object. This is when your dealing with small size objects. He made a chart up to make it easier to figure out the distance, perhaps he will post it here ???
To improve the sensitivity of the PI detector, one needs to shorten the pulse delay. Changing to a smaller coil will not make it more sensitive, although it "may" improve performance.
Eric, If I screwed this up, jump in and let me know. <IMG SRC="/forums/images/smile.gif" BORDER=0 ALT=""> <IMG SRC="/forums/images/smile.gif" BORDER=0 ALT="">
Mr. Bill

 

[Anonymous]

Reg
My equation assumes that the target size is negligible compared to the coil size (even less than 10%). If the target size is not negligible then the equation becomes more complicated. For one thing every place I have "radius" would have to be replaced with something like "coil radius - effective target radius", where the effective target radius is a bit less than the physical radius. The effective target radius would depend on the distribution of currents in the target, and I don't know how to calculate that.
Also if the target size is taken into account it would have to appear in another place in the numerator because more of the magnetic lines would intercept a larger target. For targets less than half the coil size I think it would be approximately target radius squared in the numerator. And if the target radius is a fraction of the coil radius, that would be replaced by coil radius squared which would change the shape of the plot.
Robert

 

[Anonymous]

Here are the curves I have used for many years. As Robert said, 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

 

[Anonymous]

Hi Eric,
Thanks for the chart. As I look at it, I have to assume the ever increasing semicircles reflect different sized targets with the larger semicircles indicating an increase in target size (providing all other factors are kept constant).
If that is the case, then the diag line indicates the maximum depth for a particular sized object and its relationship to the diameter of the coil.
My remarks to Mr. Hoolko were based upon that assumption.
I am also assuming that the effective semicircle for a particular object of a particular mass can change, either increase or decrease, depending upon its shape, orientation and composition.
I hope this is correct. If so, then I would assume the relationship between the peak of the semicircle, coil, and target size, would indicate there is a relationship between target size/coil size such that a simple rule of thumb might apply. This goes back to my statement in an earlier post where something like a ratio of target to coil size of 1/10 or so might generate the diag line you have indicated.
If I am incorrect in my thinking please tell me.
Thanks again,
Reg

 

[Anonymous]

Hi Eric,
I agree whole heartedly about the advantages of using a smaller coil. They are much easier to get closer to the ground or into tight places which can make the difference in being able to detect a small shallow nugget.
My coil of choice when I was using a VLF for nugget hunting was a 7" coil. The reason was for the purposes you mentioned, getting closer to the ground.
As for a PI, one might not be able to really see any great increase in depth or be able to see smaller nuggets when testing or comparing the two coils, but normally testing is done under ideal conditions where the surface is level, etc. Running the same test in a rocky or brushy area similar to the ground conditions that will be encountered in many areas can easily show a significant advantage of using a smaller coil.
One more point, the open center design of your coils does offset the advangage of smaller coil in some cases. I have used the open center to my advantage by sliding the coil over rocks and clumps smaller than the inside diameter of the coil This gives me an edge to get closer to the ground under certain conditions. Yes, this open center does allow the coil to get hung up on brush at times, but overall, I find the open center to be an advantage.
Reg

 

[Anonymous]

My problem is a productive wet sand area that gathers 1/8-1/4 inch bits of copper. With a VLF I could go to a larger more insensitive coil but what about with a P.I. If I thinking correctly I could de-sensitise by increasing pulse delay and perhaps ignore tiny fragments but then I am shifting away from the detectors most sensitive setting for gold and gold rings are what I'm searching for.
Any suggestions welcomed
Brian

 

[Anonymous]

Reg
This is my version of Eric's chart. Starting with my formula for signal strength, I added target size to the formula. I made the simplest approximation I could. I assumed that the target size is small enough compared to coil size that I could ignore its effects on distance from the winding to the target. I also assumed that it is small enough that the magnetic field is uniform across the target and the signal strength is proportional to the target cross sectional area. So all I did was put target size squared in the numerator of the formula.
Then I picked a value for the minimum signal strength needed and solved for distance as a function of coil size and target size.
The left graph is for fixed target sizes. The ratio of target sizes used was 1:2:3:4. I get the same results as Eric, the maximum depth occurs when the coil diameter is twice the target depth. Also notice that the maximum depth does not go up linearly with target size, and the optimum coil size does not go up linearly with target size.
The right graph is for targets that are a fixed percentage of coil size. Each curve is for a different percentage of coil size. In this case the target size automatically increases when the coil size increases. Notice that now the maximum depth occurs when the coil diameter is 4 times the target depth. But I don't think you should look at this graph to get a feel for how coil size affects depth. It creates a misleading impression because targets do not magically get larger when you put a larger coil on.
Robert

 

[Anonymous]

Hi Robert,
I stand corrected about the possibility of a direct ratio of target size and the coil diameter. Your graph on the right clearly displays that the relationship is not a linear function.
However, I guess I am not making my point. There is some relationship between coil size, depth and maximum depth as it relates to the target size. I just am not sure what it is, but it is getting clearer.
If I understand your statement about the left graph correctly, the different colored semicircles indicate proportional increases in target size. The smallest curve having a 1 unit size, the second having a 2 unit size, the third a 3 unit size, and the fourth and largest semicircle having a 4 unit size. By this I mean, for the sake of argument, a unit is 1" sq, then the first semicircle is a 1" sq object, the second might be a 1" by 2", or about a 1.424" sq object etc. Is that correct?
The reason for the questions is to try to determine in greater detail the advantages and disadvangages when trying to find nuggets of different sizes, by changing from, lets say, an 8" coil to a 11" coil, or from a 11" coil to a 14" coil.
Obviously, nuggets vary in size and shape and there certainly isn't a concrete answer that will hold true for all cases, but when a person elects to increase the coil size, it would be nice to have a better idea of which size nuggets will give a stronger response and which will give a weaker response.
So, I guess the question might be what is the relationship of target to coil size that produces the peak signals on the semicircles on the left graph holding all factors but size constant.
Reg

 

[Anonymous]

Reg
When I said the ratio of target sizes was 1:2:3:4 I was using a linear measure of target size. So if the red curve is a 1 x 1 target then the blue curve is 2x2, the green is 3x3, and the magenta is 4x4.
As for the bottom line question of what coil size is best for a particular target size I don't think you will get the answer from any single equation. Under the assumptions I have been making the best coil size is proportional to the two thirds power of the target size. That is: best coil size = K * target size ^ 2/3. The problem with that is that K depends on everything, such as target shape, orientation, composition, coil on time, delay, amplifier gain. Even if you gave me the schematic for a detector I could not tell you what K is.
One way to get at it would be to use Eric's procedure. For one target find the maximum distance at which you can hear it. Then use Eric's chart to find the best coil size for that target. Then for other targets of the same shape but different sizes use target size ^ 2/3.
But target size ^ 2/3 is based on my assumptions that this is a family of coils that all have the same inductance. Which means that the larger coils have fewer turns. I thought this was a reasonable assumption.
An alternate assumption would be that all the coils have the same number of turns. In that case the inductance would increase with coil size. If you increased supply voltage in proportion to coil size then I think you would get the best coil size being proportional to target size. I think that is what you were looking for originally. But you would still have to determine K experimentally, and I do not think having the supply voltage depend on coil size is reasonable.
If the number of turns was constant and the supply voltage was constant then the coil current would be different for different sized coils and would depend on the details of the drive circuit.
And all of this is for targets in air with no external noise. As soon as you put the target in the ground the situation changes and you want a smaller coil. Maybe a lot smaller for really bad ground.
Robert

 

[Anonymous]

I must say I did not lose any sleep over the answer but here is my best guess.

 

[Anonymous]

Hi Rober,
Thanks for clearing up my misunderstanding on the ratio of target sizes. Your explanation makes things clearer.
This discussion has cleared a few things up for me. It also has also help clear up what Eric mentioned at the onset when he discussed his graph. Somehow, I was having a difficult time grasping his clear explanation.
I guess old age is having its affect on me. Couple that with a computer that deliberately misspells my words, and I just don't make much sense at times. Got to get a new computer to at least minimize one of the problems. I just hope I don't get one that is worse at spelling. <IMG SRC="/forums/images/smile.gif" BORDER=0 ALT="">
Reg

 

[Anonymous]

Well done Robert. I was half hoping that you would

 

[Anonymous]

Hi Robert and Reg
To make the coil current independent of coil characteristics you could use a constant current TX, as described by Thomas Breuer a while back. One problem though, if you keep the turns the same on all coils, the higher inductance of the larger sizes will slow the switch off and receiver sampling will have to be set back to suit.
Eric.