PROTOTYPICAL DIAMETERS varied with wear, commonly up to 1½" was allowed off the tyre thickness (=3" off the diameter) from new.
At 10 mm/ft that allows your wheels to be up to 1.8 mm diameter under nominal size.
The diagram is based on an early design. A large amount of lip or overlap gives the impression of a thick tread. In this example the overlap allows for a rivet or bolt to pass right through the tyre lip and the wheel centre from the front to the back (as in a GER Claud). Other designs such as those using Gibson rings show different amounts of overlap - and a different apparent tread for the same actual tyre tread.