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:
https://steampunk.wonderhowto.com/how-to/complete-guide-build-crystal-radio-plus-they-work-0141117/
https://en.wikipedia.org/wiki/Crystal_radio
hackaday.com/2020/01/28/eric-talks-crystal-radios/
https://www.mtcradio.com/the-pickard-crystal-set-radio-kit/
This is the equation I was using to calculate the frequency:
https://www.elprocus.com/lc-oscillator-circuit-working-and-its-applications/
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)
https://www.allaboutcircuits.com/uploads/articles/round-wire-formula.jpg