No claim to the contrary. The only claim is that it will move faster than the air around it. That it does when the ground is stationary and the air is stationary and it moves forward wrt the ground. I hope that isn't too hard to see that it does exactly that!
Well. I do admit to expending a fair bit of energy when I run on my treadmill at 10 mph. All that just to attain "wind speed" - which I do in my basement.
You can Google to find the differences between treadmill exercise and real running. However, the treadmill's motion is not responsible for your expenditure of energy. It provides a reactive force to your muscles. In fact, you don't want the motor to do your exercise for you.
The body absorbs some of the KE generate while running, or stores it in ligaments, to be later returned. When walking, the leg is raised against gravity, and returns much as a pendulum. We need a make a bit of 'gap' to ground, so there is a lateral waddle to our gait. The belt simply moves back to accommodate those and other actions of ambulation, and our balance mechanism. Your are also your own dummy load, so to speak.
You can see that running is no more than a simple repetitive cycle, and if that is
once possible, the length of the belt makes no difference.
Quite different ideas there.
Somehow I am unable to "hover", even on roller skates, especially when the treadmill is inclined. To duplicate the motion that my cart achieves on my treadmill I would need add little motors to my roller skates.
No, the power will fall to almost zero.
I'll bet that the treadmill motor would show an increase in power demand if I were to use little electric motors in my roller skates to move up the treadmill. What do you think?
I think that the amount of energy consumed by the motor by the addition of the cart is negligible.
Talk of resonance is overwrought.
The belt is passing under the wheels at exactly the rate that the wheels are rotating in the opposite direction. That is the the equivalent of a
fixed point w.r.t the ground. (they subtract to produce zero w.r.t the ground).
All motion is therefore w.r.t the ground. That motion is nothing more than a slight imbalance in that subtraction. In principle, the cart cannot move.