curvedsky,
Many thanks for that very interesting link.
And no, it was not an F-16 I was remembering, more like a large twin jet. Might have been a DC-9, a 737, or a large business jet.
Slightly O/T, but IIRC NASA has a few T-38s that can be reconfigured to "fly like a space shuttle" and that the shuttle pilots used to "stay current" and practise the approach.
Maybe they're for sale now?