Mines the 81A style ('39-'48) with the hand crank teeth.
Definitely not 7/8", bigger than that. 1 1/8" seemed close.
1949-53 plain bolt 7/8"
1939-48 all with long crank 1 1/8. I use an old Craftsman 12 point deep, as the 6 points are thicker and clumsier and space is limited in the tubular part of 1940-48 pulleys.
1928-38...supposed to be 1 3/8, but they vary. Most sockets that size are 3/4 drive and are collossal heavy things...you can get a 26 mm that is 1/2 drive and not too bulky that will do the job. I think these nuts are very irregular...