Back to the loses of aircraft we have suffered most were due to pilot error.
Sorry fly boys someone has to crash the plane.
ie.. trying to fly through a cloud with a rock in it has littered the westcoast with fighters.
Now we have aerospace controllers, GPS, Radar altimeters, collision avoidance radar and the ability to fly in and land in conditions well beyond IFR. Plus we train our pilots in the flat lands now, go figure.
But if you want to take the credit feel free.
Now back to the problem of those F-86 Sabres. Would you believe that one little bolt brought a ton of them down? Yup the wing would flex in a high G turn and the aileron would catch on the bolt head. Once someone figured out what was going on they changed the bolt and voila germans have less to fear of the Canadian airforce falling on them. Well in reality all users of this aircraft suffered this initial flaw.
Now as for the power versus lift, thingy.
Do you remember when they were teaching you how an airplane works?
They had that cross made up of four arrows. Lift at the top, drag at the rear, weight at the bottom and to get it all moving thrust at the front.
Now weight is the only constant (less fuel consumed smart ass).
So now you have a plane that flies and want to make it generate more lift. How do you do that?
You could increase the angle of attack or you could put a bigger/higher lift wing on it. These work but increase drag. Now so your plane can maintain all that new lift you have to give it power lots of power. Because your plane now has more lift it now has more drag. I did not go into the if you want more lift just go faster side because that usually requires more power and fast landings create hard landings and that is the big problem now isn't it.
So to tie this down for the night, if you want more lift you "need" more power.
And the UH-60 is good to 5 800 meters which might explain why the US uses them for mountain rescue and they have not crashed all of their choppers, just a few of them
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post note:
In your altitude calculations did you take the humidity into account?
Last I heard it was low.