I own a copy of this movie, as I have been a x plane/space buff since a child. I lived just outside Wash DC and was able to visit the Air and Space Museum and see the x15 and other planes close up.
I think the scene with Bronson and his young Son has to be one of the best acting performances by Bronson, tender, and yet shows a bit of his machismo as well.
This scene is heartbreaking for me, too. It represents the potential of Father-to-Son communication that many of us never get to experience.
My Mom & Dad were in the USAF at this time, too (1954-1964), and while I don't claim that they were 'like' any of the characters in this movie, the whole picture reminds me of "The Acme of the American Empire" as J. Hoberman put it in an essay he wrote for Arlen Schumer's 1990 book "Visions from Twilight Zone" . . . . an empire that is never coming back.