chingel said:
Yes in the end the energy can only come from the wind, and since there are videos of it going faster than the wind, it does extract it somehow. What I would like to know is how does it do it, where does the energy come from when the cart is up to wind speed?
Although the cart is moving at or faster than wind speed, the air accelerated by the propeller is moving slower than wind speed, and that air is slowing down part of the wind, and that is the source of the energy. All of this is from a ground based frame of reference.
From the carts frame of reference, the forward force (from the wheels) on the surface of the Earth is slowing down the Earth (relative to the cart) a very tiny bit, and that is the source of energy that allows it to accelerate the relative headwind.
From the air's frame of reference, again the forward force (from the wheels) on the surface of the Earth is slowing down the Earth (relative to the air) a very tiny bit, and that is the source of energy that allows the propeller to accelerate the air.
The DDWFTTW cart is like a hybrid car, except that the braking energy is being used to drive the propeller as opposed to charging a battery. This only works if there's a tailwind to supply more energy than is consumed by the braking energy.
chingel said:
Isn't it that the smaller the diameter of the center part, the faster the yo-yo goes up the string?
If the center part (and string) had zero diameter there would be no winding of the string, and the yo-yo would move at the same speed as the string.
To cover all the cases from a yo-yo like device, imaging that there are two hubs on the outside of the yo-yo and that the hubs rest on a pair of rails, with a rail on each side of the yo-yo, with the yo-yo otherwise suspended in air, only resting on the hub rails. If the string is wound above the center axle and the string is pulled forwards, the yo-yo moves at less than string speed, and this is the equivalent of a negative advance ratio. If the string slides on the center axle, then it's the equivalent of a zero diameter axle, and a zero advance ratio, and the yo-yo moves at the same speed as the string. If the axle diameter is smaller than the hub diameter, the yo-yo moves faster than the string, the equivalent of advance ratio greater than zero and less than one. If the axle and hub diameters are the same, the yo-yo doesn't move unless it slides, this is an advance ratio of 1. If the axle diameter is greater than the hub diameter, but less than double the hub diameter, the yo-yo moves away as the string is pulled, but faster than the string, an advance ratio greater than 1 but less than 2. If the axle diameter is double the hub diameter, the yo-yo moves away at the same speed as the string, advance ratio of 2. If the axle diameter is greater than double the hub diameter, the yo-you moves away, but at less than string speed, an advance ratio greater than 2.
The closer ratio between the axle and hub diameters is to 1, the faster the yo-yo will move relative to the string, until the ratio gets too close to 1 and then the yo-yo "stalls" and won't move without sliding.