The "F" is a chassis model designation, going back to the vehicle type chassis standard with Ford assembly lines of the 20's, 30's, 40's and into the early 50's. Ford used to label their assembly lines by letter designation, and the aptly nicknamed vehicle produced on the line sometimes stuck. Model T, Model A, Model B, Model 18, and Model "F" for trucks, as example. The "F" series vehicles began post-WWII in 1948 starting with the Model F-1, and are now on their 9th generation line of trucks.
Boom done!