Physics and Math behind metal detecting?

[GWestphal]

Hi guys,

I've been thinking about jumping into metal detecting, but I'd like to understand the mathematics behind it so I can better compare different detectors potential depth and recognition characteristics based on things like the detector frequency and such.

Anybody know which equations I could reference? Main things would an equation that would relate coil size, field strength, frequency, and depth and perhaps another that does coil size, field strength, frequency and conductivity/detection strength/magnetic field?

From what I understand the premise is the detector transmits an electric field which will induce a current and associated magnetic field in conductive metals, which then is picked up by a receiver coil.

The reason I ask is because I'm interested in the Gold Bug DP (19kHz) and the Fisher F70 (13kHz), maybe others as well. Higher frequency picks up gold better, but lower frequency penetrates better, so I'm trying to figure out where the best compromise is mathematically speaking.

 

[AD5MB]

more accurately:

• an oscillator generates an electric current in a coil
• this current is also fed to one side of a differential amplifier;
• said current is received by a concentric coil
• which feeds the other input to the differential amp in phase with the oscillator
• you manually adjust the metal detector so both inputs are the same voltage
• nulling the perceived audio oscillation

• if the metal detector passes over a metal object
• some of the current is induced into the skin of that object, developing eddy currents
• which reduces the current in the receptor coil
• unbalancing the diff amp inputs
• resulting in audio in your headphones

different metals result in different phase angle changes, which is how high end detectors can differentiate silver coins from aluminum pull tabs

 

[DrPizza]

Related question: can a metal detector *very accurately* determine if there's a nail embedded somewhere inside a 3 foot diameter maple tree? (Passing the metal detector, of course, over the surface of the trunk after the tree has been cut down.)

I have access to a few big maple trees that have to come down this spring. Enough maple trees, by far, to make 3/4" hardwood flooring for my entire house @ roughly $1 per square foot, including all cutting, kiln drying, and milling.

The reason I ask is that the lumber mill is worried about the possibility of the presence of some hardware inside the tree. Seems that it wouldn't be an issue if the metal detectors worked well enough.

 

[herm0016]

mills usually have a machine that does this already. I am sure a metal detector would work for you also.

 

[GWestphal]

Depends how big the nail is and what the exact alloy is too. Most detectors under $1500 will do about 12-14" on a coin sized piece of metal. The bigger the metal the deeper you can detect it though, I picked out some t fence posts at about 3 feet. Considering the low background noise of a tree, you might be able to pick up a nail, but if it's in the center it would be pretty faint. 12" should be no problem though.

 

[AD5MB]

if a metal object is buried long enough, metal particles migrate from the source to the surrounding soil. acid in the soil frees the metal, which sort of electroplates the soil. so you get a metal cloud around the buried coin.

orientation of the coin also has an effect. a coin buried flat presents a bigger target than a coin buried edge up.

a nail will not be in acidic soil and will inherently be edge-on to the tree. so a nail in a tree is a difficult target compared to a silver dollar in a city park

 

[exdeath]

Spectrum analyzer? Detector varies frequencies in the coil and does a fourier transform on the return signal. Different shaped geometric solids produce known mean frequency response spectrums, and by filtering and correlating you can tell the difference between a toroid and a sphere, a plane, etc. So if you have a phase angle that looks like gold with a frequency spectrum of a toroid, the metal detector shows you a picture of a gold ring. Not sure how it detects the diamond though

 

[Evadman]

The reason I ask is that the lumber mill is worried about the possibility of the presence of some hardware inside the tree. Seems that it wouldn't be an issue if the metal detectors worked well enough.

Then have the mill exclude the bottom 6' of the trunk.