Thanks for the additional advice. I was planning to make a capacitor out of foil and newspaper interleaved. One day when I've finished all the other things I want to play around with...
Newpaper will be 'fun' to work with as its moisture content will vary with environmental conditions, making its dielectric constant not very..erm..constant - unless you impregnate it with wax or a lacquer.
(Made plenty of crystal sets during my teen years in the mid 70s-80s)
There are lots of ways to homebrew variable capacitors. A sheet of glass and two pieces of scrap copper does well.
I have a "crystal" radio (uses a modern diode) all built on a paper towel tube. The coil is wound on the tube like usual but at the other end of the tube there's also a layer of foil and a smaller tube with a layer of foil that slides inside that to make a variable capacitor.
Also, I find that inserting a ferrite rod into the coil (or winding the coil around the ferrite rod to begin with) makes tuning much more effective (sharper) and makes the audio signal much stronger. A steel or iron 6" nail also works if you want to dispense with the ferrite rod.
I live very close to the BBC regional broadcast transmitters (100KW apiece) and since boyhood I've made loads of crystal sets as well. A few feet of wire often being quite sufficient as an antenna and the radiator pipe as an earth connection. A good earth connection is very important to the effectiveness of a crystal set.
I made a single transistor regenerative set next and because the local BBC signal was so powerful I literally didn't even need an antenna at all!
Another single transistor was all that was required to drive a speaker loud and clear.
