Helicopters and operational height limits

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I know that helicopters cannot fly arbitrary high and 5,000 m are considered as the average limit. In a quick search I also found out, that a AS 350 B3+ has been landed on the Everest (8,848 m, 2005) and another AS 350 has (unofficially) reached 12,954 m in 2012 (official record: 12,442 m by a SA-315 in 1972).

Now the question: What runs out first: oxygen for the engines or air for the rotors?
 
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It's largely irrelevant deciding which parameter would "run out first," I'd say they both limit the operational altitude for a helicopter. Rotors would have to spin at higher speeds in the thin air (or operate at a higher angle of attack potentially reducing efficiency), and oxygen availability for the engine will become a problem as well.

Here is some useful reading on the topic: https://www.quora.com/Whats-the-highest-altitude-an-average-helicopter-can-fly

Some points brought up in the above page:
  • There isn't going to be a set altitude that a helicopter can get to. There are numerous charts in helicopter performance planning manuals that allow pilots to figure out a maximum altitude. This altitude will be a function of aircraft gross weight, Mean Sea Level elevation and temperature. Engines and Rotor systems are less efficient at higher temperatures/altitude and they have work harder when the aircraft weighs more. Temperature and Altitude factored together gives you density altitude. Most aircraft's service ceilings are based on density altitude.
  • For level flight most helicopters can fly up over 10000 feet MSL. Without a pressurized cabin the FAA requires oxygen for flights above 12000 MSL longer than 30 minutes and all flights above 14000 MSL.
 
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