Are you talking about Raptor, or that one where you could red out or black out, depending on if you were climbing or diving, had tons of missles, an
incredibly hard time landing, etc?
F-15 Strike Eagle. I used to play version 3 all the time. I think this is the one you are thinking of. Most of the time you took off from land, but I
think there was a carrier mission built in there somewhere.
I have been searching for this game too. I actually do have a copy of the game, it's called JetFighter I: The Adventure. A company called Velocity
Development designed it. I remember having a lot of fun playing it. Unfortunately the 3.5" diskette it was stored on got corrupt. I managed to
pull all the files off of it, but I get errors when I try to run it.
During my search, I found this website which is a flight sim game museum page. Here is the link to the JetFighter I page:
He apparently has copies of all the actual flight sim games on his page. I emailed him to see if he would help me get my copy to work by giving me
good copies of the files I have that are corrupted.
I actually found a copy of this game on ebay, I can't believe my luck! There is actually still another 'buy it now' auction for another one but
that one is on a 5.25 disk and is pricey. I paid $15 for an original game 3.5" diskette and manual, no box unfortunately but still a great find.
Most of the really good flight sims back then were Microprose..so just surf the Microprose titles in the last link.
You'll most likely find it in there.
You can also try Jane's F-18. Never tried it myself, but I had Jane's USAF, no longer works properly in Windows XP and latest Nvidia drivers
For civilian flight sim that features realistic carrier landings, try X-Plane. You even try to land any aircraft into a carrier or land a helicopter
in high seas in a frigate.