As a matter of interest, I have recently built a very adaptable crystal set and measured some voltages and currents that can be obtained in the St Albans area. By adaptable, I mean that I can tap the aerial, tuning capacitor and crystal almost anywhere on the tuning coil as well as being able to either series or parallel tune it. The best results were achieved when receiving Radio 5 Live on 909kHz using series tuning with maximum inductance and maximum capacitance in series, when the voltage on modulation peaks across the unloaded inductance reached 80V peak to peak. This high open circuit voltage collapsed of course when any current was drawn. The detected voltage, using a small signal germanium diode (the sort where you can see the cat’s whisker through the glass), was 3.3V when 0.7 mA was drawn, which was sufficient to power the HF and reaction stages of a simple straight receiver – but more of that anon.
Circuit diagrams of crystal sets often show an RF bypass capacitor across the audio output, but I found that this made no difference to the loudness of the received signal, or to the selectivity, whether headphones or a small cabinet loudspeaker were used (via a suitable matching transformer). The signal strength from Radio 5 Live was quite adequate for comfortable listening by loudspeaker at a distance of about 3 feet.