I probably mentioned that I bought an FCC discarded but fully working calibrated FIM-41 a couple years ago. One watt might be heard for some distance with ground wave if radiated from a licensed station's antenna and very little cochannel interference. I heard a station on Silent STA that had it's oscillator stage leaking to the antenna system. I had measured the signal at my location at about 5 mV/m with 1000 watts before it went silent. I got a 25 uV/m unmodulated carrier about 20 miles away, which corresponds to about 25 milliwatts radiated from the antenna. Figure it out if you doubt my calculations. There was another station about 200 miles away that put about a 5 uV/m signal during critical hours interfering with the unmodulated oscillator carrier. When I go a few miles from the silent station, it is definitely stronger. I plan to take the FIM-41 close to the transmitting antenna to further verify the FI and approximate inverse field. When I get about one mile from it, it stops the scan on my car radio.
So if there is little or no cochannel interference, no electrical interference, and a good antenna, you could probably hear 1 watt quite a bit further. That's not to say the station was operating with only one watt. Look at the 0.5 mV/m 50% skywave contour of a 5000 watt station on fccdata.org. With no other skywave or ground wave interference, 50 watts would put 50 microvolts per meter. 0.5 watts would be 5 uV/m, essentially unmeasurable with a barefoot FIM-41. So 50 watts may be believable, not 1 watt in my estimates.
When KSL 1160 was unduplicated, the year they had DST very early due to the energy crisis, WJJD 1160 was allowed 50 watts presunrise. I heard it and recorded it about 220 miles away in Genesee County, MI. KSL and WJJD faded in and out at about the same field intensity, which corresponded to the skywave curves in the 1960 NAB Engineering Handbook. My antenna was a 100 foot longwire.