[RedDevil]

In hindsight I really like the treadmill experiment.
Because it is so simple, and because it so obviously seems to violate 'logic'.

Here is a thought.
If you put the car model on the treadmill but remove the pusher propeller, what would happen?

The cars wheels would turn (given it is held in a steady position) but once released it would gradually lose speed and move to the end of the treadmill.
However, assuming internal friction is low, it would stay on the tread for a few seconds.
If you hold the car steady it would require very little force to do so.

If we re-attach the fan and still hold it by the axle, then the fan will spin. But with the fan spinning it pushes the air backwards, creating a force that pushes the car forward.

In order to move the car forward, the force on the propeller must be larger than the drag on the wheels.
So it needs its gearing set up in a way that the propeller moves the air backwards slower than the speed of the treadmill.

As the treadmill moves the wheels over a greater distance than the prop moves the air, it requires less energy to create the same force that allows the wheels to generate it.
It is a negative feedback loop, but not a full negative feedback loop.
The air is pushed over a smaller distance than the tread travels in the same time.

Suppose the propeller generates 1 Newton of force blowing the air aside at 1 meter per second, and the tread is moving at 2 meter per second.
The propeller would require 1 Watt of energy to maintain the airflow and force (bar losses).
It derives that power from the wheels that move at 2 meter per second.

It only takes half a Newton to generate 1 Watt worth of energy over 2 meter per second.
So the wheels only feel half the resistance on the thread that the propeller provides by milling the air.

Hence, strange as it may seem, the propeller pushes the car forward against the rolling tread because the wheels offer less resistance than the thrust of the propeller!