Helicopters and operational height limits

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Helicopters typically have an operational height limit around 5,000 meters, but notable exceptions exist, such as the AS 350 B3+ landing on Everest at 8,848 meters. The primary limitations for helicopter altitude are the efficiency of rotor systems and engine oxygen availability, both of which diminish in thinner air. Performance planning manuals indicate that maximum altitude is influenced by factors like aircraft weight, temperature, and density altitude. Most helicopters can operate above 10,000 feet MSL, but regulations require supplemental oxygen for flights above 12,000 feet MSL for extended durations. Understanding these limitations is crucial for safe helicopter operations at high altitudes.
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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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