I believe the "1BA" designation was required by the slight change required to the crankshaft to accommodate the new for 1951 Ford-a-Matic transmission.
@Flathead Freddie Mercury flathead engines from 1949 through 1953 had 4" stroke cranks. As I recall, they were 1CM and 8CM and were 255 cubic inches. The only 'BA' engines I am aware of are 8BA, found in 1949 thru 1951 Ford cars. Ford Pickups beginning in 1948 had an 8RT engine designation. Essentially the same as an 8BA car engine with minor external differences. The Ford versions were 3 3/4" stroke and 239 cubic inches. Ray
I've never seen one, but I'd bet there is a "1CM" crankshaft used in '51 Mercury's. The engine in my '51 is a '51 Mercury and some parts did have a "1CM" prefix. I didn't have the forethought to check the crankshaft, though.
The change in 1951 for both the Ford and the Mercury crankshafts was the enlargement of the pocket on the flywheel end of the crankshaft flange to accommodate the larger diameter of the input on the new automatic transmissions offered in 1951. This change did not affect the manual transmissions at all so the same crank was used for both auto and manual transmissions. The 1BA was the Ford crank with the 3.75” stroke and the 1CM crank was the Mercury crank with the 4” stroke.