I need to determine what cog/lockring size for a wheel. I don't know much about these. I found on the hub the name Dachang. I don't know a size but it is a roadmaster bike.
As usual Sheldon Brown has the answer, in his glossary of all places:
Fixed-gear hubs use a left (reverse) threaded lock ring to keep the sprocket from unscrewing when the cyclist resists the motion of the pedals. Fixed-Gear (Track) Hub Lockring Threading (Left-hand thread):
English/ISO 1.29" x 24 TPI Campagnolo/Phil Wood 1.32" x 24 TPI Old French 33 mm x 1.0 mm
It's most likely that your bike takes the first of those options, and the difference is small enough that unless you have both in front of you telling them apart is hard (it's only 1/30th of an inch)