I've been looking at crystal radios recently, and I noticed that many of them had quite big coils (maybe around 5cm on average from what I can see), but wouldn't they want quite a low value inductor to get the right frequency without using an absolutely miniscule capacitor? I know the size would have been quite useful for tapping, but wouldn't they have still wanted them as small as possible?
These are some of the images I found, they are all modern recreations and kits, but ones made to look like the old ones:
This is the equation I was using to calculate the frequency:
These were the formulas I was using as a reference for inductors (I know they're air-core, but they showed me that increasing the radius of the coil increases the inductance, which should be the same for a ferrite-core inductor as well)