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In some of the photos I saw of the MiG-21, the nose cone was extended and in others it was shortened. So, is the nose cone of the MiG-21 adjustable in-flight to allow for increased/decreased air flow?

I noticed on a video yesterday from another question regarding the nose cone of the MiG that the SR-71's engine cones are adjustable, so that led me to believe the MiG's might be as well, though nobody mentioned it specifically in that particular question.

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Yes, it moves forward as the speed increases. Its purpose is "to slow the flow of air from supersonic flight speed to a subsonic speed before it enters the engine."

From Wikipedia:

The air flow to the engine is regulated by an inlet cone in the air intake. On early model MiG-21s, the cone has three positions. For speeds up to Mach 1.5 the cone is fully retracted to the maximum aft position. For speeds between Mach 1.5 and Mach 1.9 the cone moves to the middle position. For speeds higher than Mach 1.9 the cone moves to the maximum forward position.

On the later model MiG-21PF, the intake cone moves to a position based on the actual speed. The cone position for a given speed is calculated by the UVD-2M system using air pressures from in front and behind the compressor of the engine. On both sides of the nose there are gills to supply the engine with more air while on the ground and during takeoff.

You can watch it move on YouTube. You can see two different positions below plus the aforementioned "gills":

two different positions plus the aforementioned "gills"
Left: wikimedia.org; Right: worldwide-military.com

Related:

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    $\begingroup$ On the later MiG-21s (with UVD-2M), it's actually more complicated. At supersonic speeds, the cone also moves forward in anticipation of the higher angle of attack (sourced from the stick position). This is to prevent the shockwave from entering the intake. In perfect conditions, the cone is regulated such that the shockwave cone just about touches the lips of the intake. But non-axial flow distorts that picture. $\endgroup$
    – Zeus
    May 16, 2022 at 0:50

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