Sticky coil calculator: how to calculate inductance of a D-shaped coil?

[Mullihaka]

What value should I use as inner radius for a D-shaped coil? Should I measure the length of one full turn, assume it a circle and divide by (pi * 2) ?

[Qiaozhi]

What value should I use as inner radius for a D-shaped coil? Should I measure the length of one full turn, assume it a circle and divide by (pi * 2) ?

The best way I have found to calculate the inductance of DD coils, is to measure the narrow and long diameters, add these together and divide by 2. Then (of course) divide by 2 again to get the radius. Use this value in the calculator.

In order to get a good value for the narrow diameter, you will also need to estimate the coil overlap. There is a discussion on this subject somewhere in the forum.

The formula is: x = pi * r * k / 2
where:
x = the coil overlap
r = the radius of the overall DD coil
k = 0.1 (empirically determined)

For example:
For a 27cm DD coil shell, the actual overall search head diameter is 255mm, which requires an overlap of 20mm.

[Skippy]

This thread contains useful information:http://www.geotech1.com/forums/showthread.php?t=17786

[Qiaozhi]

This thread contains useful information:http://www.geotech1.com/forums/showthread.php?t=17786

In the tests I have performed, the most accurate result is obtained by using the average of the two diameters, rather than converting the circumference of the D-shape into a circle. Also, Wheeler's equation is for solenoids, not for the type of air core coils used in metal detectors.

[golfnut]

Id try in % terms perhaps.

I did one that was appox a round it was 6.5mH
I forced the corners to get a D and the L dropped to about 5.5mH

first order - its 1 in 6 reduction

~ 18% less as a D

Steve

[Skippy]

Qioazhi: There appears to be more than one 'Wheeler's Formula'. The one mentioned in the article you linked to does seem to apply to solenoids. I've used a different variant, which seemed better suited to the 'search-coil' arrangement. I can't remember where I got my copy from, but here's another pdf version I've located:
http://techdoc.kvindesland.no/radio/...3155331811.pdf
This is simpler than your 'coil-calculator' formula, (which I agree is accurate), but this does make it easier to mathematically rearrange, to suit the various practicalities of the design process.

[Qiaozhi]

Qioazhi: There appears to be more than one 'Wheeler's Formula'. The one mentioned in the article you linked to does seem to apply to solenoids. I've used a different variant, which seemed better suited to the 'search-coil' arrangement. I can't remember where I got my copy from, but here's another pdf version I've located:
http://techdoc.kvindesland.no/radio/...3155331811.pdf
This is simpler than your 'coil-calculator' formula, (which I agree is accurate), but this does make it easier to mathematically rearrange, to suit the various practicalities of the design process.

The other problem with Wheelers equation is that it does not take account of the wire diameter.

I did once write a version of the Coil Calculator where any of the parameters could be determined from the other values, but I don't seem to have that any more. It was just easier to alter the input parameters until you got the desired value of inductance.