I was wondering if the force generated from the engines of a jet plane would lift it up from the ground if in a free treadmill.
Would it take off?
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Aircrafts, other than a few which could lift vertically, create lift by moving forward in the air and bending the stream of air flow around their wings.
Airplanes create the traction forward by the thrust of their engines not by traction of their wheels, so they will start to move even on water like a sea plane or on a free treadmill, ice, even from a wood carriage on set of rails like the Wright brothers
Hypothetically there is no issues, other than control and breaking in case of aborting a take off.
As a private pilot I have had to take off from glazed, icy tarmacs, or sllippery muddy dirt runways, albeit while following proper pilot's instructions by the manufacturer.
Aircraft fly by the action of air over the wings. That's a simplification, but all that is needed to answer your question.
If the aircraft is not moving with respect to the ground (as would be the case on a treadmill), the only airflow over the wings is local wind.
Accordingly, aircraft will take off if there is wind that meets or exceeds the aircraft's safe speed for conditions. I have flown an ultralight in very smooth, very strong wind and had a zero distance ground roll for take off and landing. No treadmill required.
Many small aircraft pilots will attest to the same circumstances.