First note that the DDWFTTW vehicles actually work, videos have been posted in previous threads. Here's an older video before the aerodynamic frame was added to the "blackbird", reaching 37.5 mph in about a 15 mph wind. Note the change in direction of the streamers attached to the poles on the vehicle. Intially the propeller acts as a bluff body, but as speed picks up it then acts as a true propeller.
Tom_K said:
propeller operating in a tailwind
As posted previously, the propeller operates wtih a relative headwind. The example I used was a 10 mph tail wind and a DDWFTTW vehicle moving at 30 mph tail wind. From the frame of reference of the vehicle, the propeller operates with a 20 mph headwind, and the ground moves backwards under the vehicle at 30 mph. (Note the actual vehicle with aerodynamic frame achieved about 35 mph with a 10 mph tailwind).
Tom_K said:
You seem to be saying the propeller on the car is producing thrust above wind speed yet all of the power to produce thrust is coming from the wind. Or are you saying the surface moving under the wheels is somehow transferring energy to the car, like a belt drive turning the wheels?
The axle for the wheels is connected via a chain drive to drive the propeller to produce thrust, and the propeller generates an opposing torque eventually onto the wheels, which in turn apply a forwards force onto the ground, part of a Newton third law pair where the ground applies a backwards force onto the wheels. As mentioned before, there is an effective reduction gearing of the propeller, so it generates more thrust than the opposing backwards force from the ground, but at a lower speed than the 30 mph that the ground is moving under the vehicle, somewhere between 20 mph and 30 mph, most likely around 23 mph since it's a big prop and a 3 mph relative acceleration of the air (wrt vehicle) will generate enough thrust.
From the ground frame of reference, the propeller slows the affected wind down by 3 mph, which is it's source of energy.
From the vehicle's frame of reference, the forwards force of the wheels on the ground slows down the surface of the Earth (wrt vehicle) by a very tiny amount, since the Earth is massive, but the decrease in kinetic energy of the Earth (wrt vehicle) is a bit larger in magnitude than the increase of kinetic energy of the air accelerated (by about 3 mph in my theorectical example here) by the propeller (wrt vehicle). It is in this frame of reference that energy is extracted from the ground.
Tom_K said:
By my reasoning, once the car is traveling at the same speed as the wind there is no longer any wind force acting on the car since there is no longer any Δ Velocity.
When the vehicle is traveling at wind speed, the wind force acting on the vehicle is zero, but the propeller is producing thrust. The Newton third law pair of forces are the forces related to the deceleration of wind (wrt ground) by the propeller, the propeller exerts a backwards force onto the air, and the air exerts a forwards force onto the propeller.
Again note that this only works when there is a wind relative to the ground. In my example here, at 30 mph ground speed, due to effective gearing, the propeller generates 23 mph thrust speed. Without a tail wind greater than 7 mph, the propeller would not be slowing the wind.
Looking at the external forces, there's a forwards force exerted by the air onto the propeller, which is greater in magnitude than the backwards force exerted by the ground onto the wheels, resulting in a net forwards force that is opposed by aerodynamic drag of the vehice moving against a relative head wind, rolling resistance in the wheels, losses in the drive train, ... . Eventually the vehicle reaches some maximum speed where the net force ends up zero.