Escape timelines for my interstellar ark

Peter Lynch wrote:

My understanding of orion engines is that they use atomic/nuclear
detonations as the energy source to (explosively) heat air uunder
the vehicle. It's the rapid expansion of the heated air that actually
provides the thrust, not the detonation itself.

Your understanding is mistaken. The mechanism was direct transfer of
momentum: a shaped nuclear charge would blast a propellant plasma
against the "pusher" plate. No air required; if anything it might even
reduce thrust a bit, and would certainly complicate the modeling.