test targets

[green]

Was reading some other posts the other day. If I read it right, stated time constant proportional to thickness and size didn't effect time constant. I made some test targets awhile back where time constant is proportional to thickness and length of square targets cut from the side of an aluminum coke can. Charted some data. ITMD states signal strength is proportional to diameter cubed. For the square targets with the same time constant signal strength increased from 8 to 10 times when doubling length, the 10 could be measurement error. Tried to get the target lengths as close as I could. I read, need to increase the coil current 64 times to double the detection distance. I find that to be true for targets that can be just detected at distances greater than coil diameter assuming delay and sample time could remain the same. For a nugget that can just be detected at 1 inch with a 8 inch coil doubling the current should double the distance.

[Skippy]

I've done similar experiments, using a 13KHz VLF machine, with good results. The time-constant is proportional to the linear size of a square 'drinks can' target.
I haven't investigated the variation with metal thickness, it's difficult getting enough significantly different samples to test. I'll have another try.

I'll post up my test results later when I've dug them out...but a summary is:

Sample size 25mm x 25mm has time-contant = 7 microsecs. All other delays are in absolute proportion.

[green]

I've done similar experiments, using a 13KHz VLF machine, with good results. The time-constant is proportional to the linear size of a square 'drinks can' target.
I haven't investigated the variation with metal thickness, it's difficult getting enough significantly different samples to test. I'll have another try.

I'll post up my test results later when I've dug them out...but a summary is:

Sample size 25mm x 25mm has time-contant = 7 microsecs. All other delays are in absolute proportion.

How do you measure time constant with a 13KHz VLF detector.

[Skippy]

It has a good 00 - 99 target ID display, which I have calibrated so target frequency / time-constant can be simply measured. I can also probe internally and do direct measurements, but the point of the calibration was so measurements can be done easily and quickly. Internal probing is a bit laborious, and for tiny targets is also less accurate.

I was also going to point out that the 1/64th / inverse-6th power effect is really applicable when the target is a minimum of 1.5 coil-diameters away from the coil, it's less severe when close to the coil, maybe even as low as inverse 4th power.

[green]

It has a good 00 - 99 target ID display, which I have calibrated so target frequency / time-constant can be simply measured. I can also probe internally and do direct measurements, but the point of the calibration was so measurements can be done easily and quickly. Internal probing is a bit laborious, and for tiny targets is also less accurate.

I was also going to point out that the 1/64th / inverse-6th power effect is really applicable when the target is a minimum of 1.5 coil-diameters away from the coil, it's less severe when close to the coil, maybe even as low as inverse 4th power.

25mm/20mm*4.6(TC)=5.75 not 7 what you stated for the 25mm square. Recorded TC data with 1.5 in. diameter Rx coils(think I used to measure the TC data above)and the 8 in. diameter Rx coils(distance data above). Charted fairly close today but different than what I charted before. Still wondering why my TC data doesn't repeat better. Some of it can be drawing the line thru the charted curve. Was hoping another method of determining TC might help explain why. I used the same targets except for the added 25mm square that were used before. Maybe some of our difference is using different targets, our methods for measuring TC or something else? Maybe the difference we are seeing isn't a problem but I would like to know what the correct TC is. Anyone have any ideas?

What power is double the current double the distance?

[Skippy]

Correct value? There is NO correct value, we've measured different cans, with different metal thicknesses, and possibly slightly different alloys that have somewhat different resistivities. Unless we use the SAME target samples, or IDENTICAL cans, eg. two from the same 6-pack and I post one to you, we're going nowhere. This is why drinks-can metal, (and aluminium foil) are not universal targets. I have some other cans that are thicker (by about 15%) and targets cut from them definitely read lower freq / longer tc value. I think I still have some of this can material in my 'bike stuff' box, (I use it to shim rear gear cassettes on freehubs so they don't move about) , if I get the opportunity, I'll pick up a few random cans off the street, to see if there's any particularly thin/thick ones amongs them. Experience shows they are near-identical across Europe, so even if I get some Polish lager can (my country is littered with Tyskie/Lech/Zubr/Zywiek thanks to migrant workers) it will be from the same Scandinavian factory.

And re:"What power is double the current double the distance?" - I don't understand, and I know little about PI's either, so I can't answer.

[green]

[I was also going to point out that the 1/64th / inverse-6th power effect is really applicable when the target is a minimum of 1.5 coil-diameters away from the coil, it's less severe when close to the coil, maybe even as low as inverse 4th power.]

Charted some data for three different coils, log amplitude and log distance. Added a line for each coil(double distance signal reduces to 1/64). Look like the lines are close to matching the target slopes past the coil diameters. Using a larger target to allow charting at a greater distance would make it better.

[Skippy]

It's a bit subjective, theoretically it NEVER reaches the inverse 6th power slope, even 10 metres away it's probably 5.99 th power, so at which point you decide it's 'close enough' is up to you....when it's beyond 5.75 th power?
The mathematics of it can be found in one of the 'how metal detectors work' articles by Bruce Candy on ML's website (though I believe there's an error in the maths somewhere). There's other online articles that explain the inverse cube field strength drop off effect, which is just 'doubled up' in detector operation, as it's transmit AND receive.

I've done quite a few target strength vs distance measurements, but measurements taken beyond 350mm from a "200mm" coil lack accuracy, so I can't say how close to 6th power they were, but they were evidently heading that way.

[Skippy]

I've sorted out the details of my experiment with the square drinks-can aluminium samples.
Metal was from the middle section of a normal 400 ml (or thereabouts) can. Measured thickness was 0.105 mm, which is a very common value for cans here in the U.K.
Squares from 6mm up to 25mm were measured, readings were as follows:

Square size (mm) / corner freq(KHz) / time-constant (usec)
25 / 24.5 / 6.50
22 / 26 / 6.12
20 / 29 / 5.49
18 / 32 / 4.97
15 / 37 / 4.30
12.5 / 47 / 3.39
10 / 62 / 2.57
8 / 80 / 2.00
6 / 92 / 1.74

Errors in the time-constant vary, but +/- 0.25 usec is probable.
Plotting them, assuming that 0mm / 0 usec is a real reading shows a good linear variation. See attached graph.

[Qiaozhi]

It's a bit subjective, theoretically it NEVER reaches the inverse 6th power slope, even 10 metres away it's probably 5.99 th power, so at which point you decide it's 'close enough' is up to you....when it's beyond 5.75 th power?

I've done quite a few target strength vs distance measurements, but measurements taken beyond 350mm from a "200mm" coil lack accuracy, so I can't say how close to 6th power they were, but they were evidently heading that way.

Here's an LTSpice simulation that shows how the magnetic flux density falls off along the z-axis of the coil.



The equation is:



where:
B = magnetic flux density (Tesla)
(vacuum permeability)
N = number of turns on coil
a = coil radius (m)
I = coil current (A)
z = distance along z-axis of coil

The LTSpice files are attached.
Note that the 6th law doesn't really kick-in until the distance is equal to the coil radius. Before that, the drop-off of B is less severe.

[green]

Here's an LTSpice simulation that shows how the magnetic flux density falls off along the z-axis of the coil.



The equation is:



where:
B = magnetic flux density (Tesla)
(vacuum permeability)
N = number of turns on coil
a = coil radius (m)
I = coil current (A)
z = distance along z-axis of coil

The LTSpice files are attached.
Note that the 6th law doesn't really kick-in until the distance is equal to the coil radius. Before that, the drop-off of B is less severe.

How to convert the time scale to distance? I charted your curve log scales and it didn't get to the 6th law. I'm missing something.

[Skippy]

I don't know why it's labelled in seconds, but I assume 100msec equals 100mm distance.
The fact that the bottom line contains (a*a + z*z) is the reason the 6th power is never reached. There's always the 'a' term stopping it reaching the 1/(z^3). George is just showing the inverse cubic effect at distance, you have to square it to get the round-trip inverse 6th power.
The theoretical analysis also assumes the target is a point-sized one. If you were analysing it correctly, you should take into account the finite size of the target - the kind of item you will find 12 inches from an 8 inch coil is not going to be tiny, more like U.S silver dollar size.

I've failed to find any significantly different thickness drinks can metal, it's all 0.100 - 0.105mm, even the small 'energy drink' size cans. I've made a new set of square targets from a different 0.105mm can, I'll try and fire up my in-bits detector and re-measure.

The good thing about the linear relationship in size vs TC is that you can make up standard TC value test samples, eg 2,4,6,8,10 usec by carefully cutting the correct size square.

[green]

I don't know why it's labelled in seconds, but I assume 100msec equals 100mm distance.
The fact that the bottom line contains (a*a + z*z) is the reason the 6th power is never reached. There's always the 'a' term stopping it reaching the 1/(z^3). George is just showing the inverse cubic effect at distance, you have to square it to get the round-trip inverse 6th power.
The theoretical analysis also assumes the target is a point-sized one. If you were analysing it correctly, you should take into account the finite size of the target - the kind of item you will find 12 inches from an 8 inch coil is not going to be tiny, more like U.S silver dollar size.

I've failed to find any significantly different thickness drinks can metal, it's all 0.100 - 0.105mm, even the small 'energy drink' size cans. I've made a new set of square targets from a different 0.105mm can, I'll try and fire up my in-bits detector and re-measure.

The good thing about the linear relationship in size vs TC is that you can make up standard TC value test samples, eg 2,4,6,8,10 usec by carefully cutting the correct size square.

Thanks. The slope does follow the 3rd law after 200ms(200mm?)

[Qiaozhi]

How to convert the time scale to distance? I charted your curve log scales and it didn't get to the 6th law. I'm missing something.

I meant to say the 3rd Law, as this doesn't show what happens during the return journey.
The x-axis is unfortunately labelled as time, but it's really showing distance in meters. There may be a sneaky way of changing the label on the x-axis from time to meters, but I haven't look into that very closely. If you move the mouse cursor to the x-axis and left-click, a dialog box pops up where you can change "time" to "meters", but the change is not allowed.

I don't know why it's labelled in seconds, but I assume 100msec equals 100mm distance.

Yes, that's correct.

[green]

I don't know why it's labelled in seconds, but I assume 100msec equals 100mm distance.
The fact that the bottom line contains (a*a + z*z) is the reason the 6th power is never reached. There's always the 'a' term stopping it reaching the 1/(z^3). George is just showing the inverse cubic effect at distance, you have to square it to get the round-trip inverse 6th power.
The theoretical analysis also assumes the target is a point-sized one. If you were analysing it correctly, you should take into account the finite size of the target - the kind of item you will find 12 inches from an 8 inch coil is not going to be tiny, more like U.S silver dollar size.

I've failed to find any significantly different thickness drinks can metal, it's all 0.100 - 0.105mm, even the small 'energy drink' size cans. I've made a new set of square targets from a different 0.105mm can, I'll try and fire up my in-bits detector and re-measure.

The good thing about the linear relationship in size vs TC is that you can make up standard TC value test samples, eg 2,4,6,8,10 usec by carefully cutting the correct size square.

Wondering if you have tested the new set of square can targets.