What is the thread pitch of the Ender 3's bed leveling screws? The diameter measures about 4mm. Are they M4 0.7 (coarse) pitch or 0.5 (fine) pitch? I'd like to develop rigorous formulas for the amount to turn the knobs by after measuring (or visually inspecting, since I can see an accurate 0.2 mm first layer decently well) leveling-test patterns in the corners rather than using a closed-loop tune-and-retry approach.
I measured mine with a thread gauge and it says the pitch is 0.7 mm.
I can't speak for anyone else's, but due to the availability of replacement height adjustment wheels which don't specify alternative thread pitches, I guess that's the only one in use. I encourage you to verify my finding before relying on it.
Possibly tongue in cheek here, but if you can detect a 0.2 mm change, you may be able to determine visually the thread pitch, although it means de-tuning your bed for the experiment. Keeping close count is part of the experiment and you can reverse the count easily enough.
Make contact with the nozzle at the location of one screw. Count the turns in order to set the screw back to original location (or don't worry, re-tune later).
If the pitch is 0.5 mm, two complete turns would give you a millimeter, while the 0.7 mm pitch will give you 1.4 mm. Make it four turns and the difference is more apparent. That would present a 2.0 mm compared to 2.8 mm for the two types of threads.
I don't know what the value is, but there are a few ways to find out. It is very hard to measure this with a caliper, but it can be done, mark the upper and bottom of e.g. 10 windings and measure this with a caliper. Alternatively measure how much the screw drops after 10 full turns.
There are special tools that give you the answer directly, they cost a few Euros/bucks but can be very handy; a thread gauge, just place the 0.5 mm and the 0.7 mm beside the screw and you will instantly see which is the correct one.
I bought mine at a typical Chinese vendor site.