Oh, excellent the altitudes that 99% of aircraft fly at, unaffecting the ultra rich who fly private jets at 40,000k-50,000k+.
I didn't realize private jets fly so high. What's the reason for the difference in elevations?
Most private jets aren't someone flying a billionaire around in a $60M Gulfstream, they're $3M toys being flown around by the owner to go to their ski trip.
I recently flew from NYC to Lisbon, Portugal and it was 6.5 hours there (flying east) and 7.5 hours back (flying west) because you go with and against the jet stream.
I wonder if there's a noticeable difference if you fly at a lower altitude against the wind. It didn't seem like the plane adjusted for that, it cruised at the same altitude both ways from what I remember. Both flights used the same exact plane type (A330neo).
They're also looking at fuel economy so even if it takes longer if the air is thinner and they burn less fuel they may still save money. I imagine there's a certain distance where those two lines cross that is probably baked into the dispatch software for each plane model.
Basically, with aircraft mass and angle of attack unchanged, \rho v^2 must be constant, so smaller density \rho -> higher air speed.