The final decision to attend the Air Force Academy culminated
This sentence would be better as "The final decision to attend the Air Force was
made..."
flew fighter planes
There should be a more specific term for planes used in the military."Fighter" sounds,at least to me,too banal.
he academy but to succ
This needs a comma after "academy".
choice but I
Comma after "choice".
with math and these career
Comma after "math".
As for the content of your essay,I think it charts the progression of your interest in the Air Force pretty well.It details your history of discovery and also,of a family legacy.It's honest,open and straightforward.