In 1931 Ford introduced the use of cast nodular iron front and rear brake drums, replacing the earlier drums which were assemblies of stamped steel drums mounted on steel hubs.
The pic above shows a comparison of the 1931 Model A front brake drum on the left, and the 1932 - 1934 Model B front brake drum on the right.
The drums are similar in appearance but the Model A drum is 11 inch internal diameter, whereas all 1932 and later drums were 12 inch internal diameter (larger on some trucks).
Note the visual difference of the dimension between the spokes and the outer diameter near the wheel flange surface.
This pic shows the inner construction of the one piece 1931 cast iron front drum. 1932 - 1934 front drums are similar.
The 1935 cast iron front drums are similar but have several small rib grooves on the outside diameter, rather than one large rib.
If you can't find them NOS, then look for the A or B prefix part number cast into the drum surface. This Model A drum is A-1106-C2.
The pic above shows the 1-3/4 inch shoe surface width of 1931 - 1934 original drums.
This pic above shows the dimension from the wheel stud mounting surface to the wheel flange contact surface of 1-11/32 inch.
The last pic above shows two methods of accurately measuring drum ID. The upper tool is an Ammco drum micrometer, and the lower tool is a Starrett 12 inch dial calipers.
For swap meets, you can also carry a Starrett 12 inch precision rule. If it won't fit in the drum, then the drum is 11 inch. If it fits loose it is oversize 12 inch and you can eyeball the approximate oversize.
Follow this link for more information about 1931 cast iron rear drum details on Ford Garage.