Over at Good Math, Bad Math, Mark has a takedown of a device purported to move directly downwind, faster than the wind. Wind-Powered Perpetual Motion (and Dave Munger thinks he’s wrong.)

Here’s the video

The objection is simple: when you are traveling at the wind speed, there is no more wind in the cart reference frame, so there’s no force. The treadmill analysis is flawed.

If you’re testing a wind powered vehicle, then in a closed, windless room, putting the vehicle on a treadmill moving at 10mph is not the same thing as putting the vehicle on a stationary surface in a 10mph wind.

By putting it on a treadmill, you haven’t recreated the real-world situation — you always have your wind, and the treadmill doesn’t remove that. You never test the condition of having the wind relative to the cart drop to zero. So while it’s not faked, it’s still a sham.

It shouldn’t be hard to engineer a device such that the wheels rotate faster than the propeller, i.e. whatever the propeller’s rotation rate is for a wind of speed X, the wheel edges move faster than X. Since the wind is always present, the cart will move forward on the treadmill moving at X. Even uphill.

My question is this: if this works, at what speed does the cart stop accelerating?

UPDATE: Or with no wind present, as in the test (On the first viewing I thought they had a fan turned on) what you’re doing is converting treadmill kinetic energy into propulsion by turning the propeller. But you don’t need to have much propulsion to move forward, even uphill. Not a valid test.

Update, Mark II. See the comments — I was viewing this from the mistaken notion that the propeller was acting as a turbine while on the ground and at low speed, which isn’t the case.

This has the implication, I think, that the cart must have enough mass to ensure that the propeller acts as a propeller. My question of what the maximum speed is still stands, because I’m sure it involves fluid mechanics and that’s not something I’ll win should I tangle with it.