I often fly in the Swiss mountains at 12’000 - 13’500ft without oxygen. It’s ok, but you shouldn’t stay there for hours. I believe the legal limit (at least in Europe) without oxygen is max 30min above 12’500ft and not above 14’000. Also, I’m extra careful when carrying “older” and unexperienced passengers and with high outside temps. Besides the impact on aerodynamics and engine performance the higher density altitude impacts the breathing performance.
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