Time to see if I can build myself a crystal radio set. Or two. Or three.
I decided rather than demonstrate building a radio at the Charleston Library's DIYFest, it would be easier to bring in some examples of some simple crystal radios that could be built using stuff easily obtained around the house. Found three nice cylindrical objects and started winding magnet wire.
The inductance of an air wound coil, according to Section 2.12.1 of the 2014 ARRL Handbook, is approximately
L (μH) = d2n2/(18d + 40l)
where d is the coil diameter in inches, l is the coil length in inches and n is the number of turns. Converting it to use more sensible metric units, it becomes
L (μH) = d2n2/(45.72d + 101.6l)
where d and l are in centimeters.
The first coil is 182 turns around a toilet paper tube. d = 4.5 cm, l = 6.7 cm, n = 182, and L = 757 μH.
Coil #2 is 110 turns around the cardboard core of a packing tape roll. d = 8 cm, l = 4 cm, n = 110, and L = 1003 μH.
Coil #3 is 118 turns around an empty plastic pill bottle. d = 4.8 cm, l = 4.1 cm, n = 118, and L = 504 μH.
This is the basic schematic I'm planning on using.
I want the radios to be able to tune in the AM broadcast band (540-1710 kHz) so the capacitance I'll need for coils #1 and #2 is around 10 pF and around 17 pF for coil #3.
Since I have three coils, I think I'll make one with a variable inductor, one with a variable capacitor, and one with a variable inductor and capacitor.
I don't have any high impedance earpieces (I've seen some builds say you can use a telephone handset though), so I might add an amplifier or impedance matching transformer and see if I can get regular headphones to work.
Normally, to cover the AM broadcast band, an inductance of around 250uH is used, along with a 365pF variable capacitor (or somewhere in this range) A variable capacitor that swings from 20pF to 365pF, with a 250uH inductor, will cover from about 520KHz to 1700KHZ, allowing for stray capacitances of about 15pF. That's a very rough guess, and I'm thinking that the self-capacitance of a coil like that, and the stray capacitances in the circuit could add up to be quite a bit higher than 15pF. All that capacitance will have quite a limiting effect on your top frequency.
Anyway, do consider the self-capacitance of your coil, and stray capacitances in the circuit when making these calculations. As I said, if you want to cover the AM BC band, a coil of 250 - 300uH along with a 365 or 400pF variable capacitor will put you in the ballpark.
Eugene Mah replied to comment from aa7ee
Thomas/LA3PNA also warned me about the self capacitance of the coils. I haven't gotten around to putting anything together yet, but I'm fully expecting to have to make some adjustments.
I've gathered a few different ideas to try, including the foxhole type configuration with just a coil and diode.
I'll probably end up taking a bunch of turns off one of them to get closer to the inductance values you mentioned.