The correct size of tire for a '36 tire cover is 600 x 16 on a 4 or 4.5 inch wheel.
The stock 36-39 wheels with a 16" tire fit just fine, as does the '40 and later 4.5" wheels.
Contrary to what has been written in many publications, the standard '36 Ford did reputedly come with 550 x 16 tires on a 3.5 inch wheel and the "Standard Tire cover", i.e. August cover, will only fit a 550 x 16 tire on a 3.5" wheel.
As I have stated in many other treads about this topic, the printed info about the August cover tire size is incorrect, a 600 x 16 tire on a 4" wheel will fit the August cover..
It just could be that Ford specified the 550 x 16 on the 3.5 wheel, their thinking being unknown, however, in the real world the consumer opted for a 600 x 16 because the 550's were not a mainstream size of tire..