Well... Not to be a nitpicker, but the NYC didn't use F units on passenger trains (much), the "F" is for "freight".
Actually, I believe the "F" designations used by the builder Electromotive Division of GM started with the F-3s predecessor, the FT. The "F" stood for "Fourteen hundred," the horsepower of the prime mover of that engine. "F" worked for the F-3 as well, it having been equipped with a Fifteen hundred horsepower prime mover. It had nothing to do with "freight."
The "F" for freight designation had some meaning with some engines made by ALCO (American Locomotive Co.). In the designation of their FA series of diesel engines the F stood for freight, and with their PA series of diesel engines the P stood for passenger.
I'm sure we'll be corrected a billion times, but in FT103 (the movie), it was said that the F = freight, and T = 2700hp. In addition, the four-wheeled passenger power was called the "TA" (twelve-hundred HP / A-unit), and was delivered before FT (1937). If they were going to continue this naming line, then it would have been the T2 (Thirteen-hundred fifty HP / A unit-2nd version of the TA) or FA (fourteen hundred HP / A-unit). Since ALCo didn't release it's FA until 1946, then EMD would have already named its units FA. Their RS' (the "1" was added after the war) wasn't until 1941, a full 2 years after the EMC 103.
References:
Readingmodeler.com - The EMD FT
Americanrails.com - The EMD FT
we shall see...
Thanks,
- Mario