What was the diameter of the screws (the propellers that drive the
ship) on any WW II battleship or full size carrier?

Hello squareroot1-ga and thank you for your question.

The South Dakota class all had propeller diameters of 17'8" (seventeen
feet, eight inches)
"SOUTH DAKOTA (BB-57)
INDIANA (BB-58)
MASSACHUSETTS (BB-59)
ALABAMA (BB-60)"
http://www.voodoo.cz/battleships/usa/sdclass.html


The Iowa class all had propeller diameters of 18'3" (eighteen feet three inches)
IOWA (BB-61)
NEW JERSEY (BB-62)
MISSOURI (BB-63)
WISCONSIN(BB-64)
ILLINOIS (BB-65)
KENTUCKY (BB-66)
http://www.voodoo.cz/battleships/usa/iowa.html


The Pennsylvania Class all had propeller diameters of 12'7" (twelve
feet seven inches)
PENNSYLVANIA (BB-38)
ARIZONA (BB-39) 
http://www.voodoo.cz/battleships/usa/arizona_penn.html


The Tennessee class also had propeller diameters of 12'7" (twelve feet
seven inches)
TENNESSEE (BB-43)
CALIFORNIA (BB-44)
http://www.voodoo.cz/battleships/usa/tenclass.html

and

The New York Class had propeller diameters of 18'8" (eighteen feet eight inches)
NEW YORK (BB-34)
TEXAS (BB-35)
http://www.voodoo.cz/battleships/usa/nyclass.html

Thank you for your question, and if you need any clarification of my
answer, do not hesitate to ask before rating my answer.

Very best regards,

THX1138

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