sol invictus
Philosopher
- Joined
- Oct 21, 2007
- Messages
- 8,613
By the way in this thread I have not seen an aerodynamic approach to the issues at all. Here I am referring to the conceptual frameworks and grammer as used in such a discussion, as opposed to physics and vectors. Humber comes close with his noting that air close to the cart on the treadmill is stationary, and this is not the same as airflow in the open field.
Et tu, Brute?
I'm truly shocked by the lack of even rudimentary physics knowledge displayed here, especially by self-styled engineers.
Here's an analysis of the forces, since so many of you seem incapable of doing it yourself.
Use the frame in which the cart is stationary, the air is stationary, the ground is moving, and the wheels are spinning. That frame and initial condition are physically identical in every way to a situation in which the cart starts off rolling along the ground at exactly the speed of a steady wind. We'll ignore friction, air resistance other than what is relevant to the propeller, and assume the wheels and connection from wheels to propeller can't slip. We want to know if the cart can go faster than the wind, which would mean it accelerates from this initial condition in a direction such that it increases its speed relative to the ground (and its wheels spin faster).
The physics is simple. If the wheels weren't connected to the propeller, Newton's first tells us the cart would remain stationary in this frame (no friction, and no wind force on the propeller since the air is still). When the wheels are connected the propeller spins and generates a force. There is also a force from the torque on the wheels (which is now non-zero since there is resistance from the propeller).
To see what happens next, consider re-orienting the propeller. If you aim it up, like a helicopter, there will be a force up from that, and a force back from the wheels, so the cart will start to fall back (i.e. move with the ground, with its wheels spinning slower). If you orient it so it pushes back, the cart will fall back faster. But if you orient it so it pushes forward, opposite to the ground motion, there are two forces acting in opposite directions and one must check their magnitudes. There is no principle which says one must be bigger than the other - and given some assumptions about the propeller and the gearing one could easily estimate them. If the propeller force is larger, the cart will move forward against the direction of the ground motion - which means faster than the wind.
I have not done the estimate of the forces, which is why (as I have said all along) I don't consider it obvious that this particular design will work. However there is no reason why it shouldn't, and the videos are convincing. The burden of proof is fully on anyone that doubts it - there is no legitimate reason given by anyone here why it shouldn't work.
That's it.
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