sophiecentaur said:
QUOTE "You seem to misunderstand the method of operation. The prop is not acting like a wind turbine - it is never extracting energy from the air, so to speak. It is acting as a propeller, pulling the cart forwards against the air. The energy source is the wheels - they are rolling against the ground. "
"Wheels" are not an energy source. Something must be pushing them along the ground, making them rotate, for power to be available. What is that 'something'? You need a Force X a Speed for power to be developed. Where does the Force come from? If the action of the prop were just like a conventional 'driven' propellor, you could do at least as well by driving the wheels - and that would be nonsensical, you must agree.
The force to drive the wheels comes from the propeller. The propeller is pushing the cart (and the wheels) forward along the ground. That's the force. The reason that the propeller can generate enough force to drive the wheels even despite losses is because of the speed differential between the ground and the air.
Effectively, the energy the wheels generate is equal to the force required to turn them multiplied by the distance they move along the ground (this is a simple statement of work). The energy the propeller puts into the air is equal to the force it exerts on the air multiplied by the distance it moves through the air (again, a simple statement of work). When the cart is in steady state operation, the force generated by the propeller and the force on the wheels is the same (ignoring friction losses), so there is enough energy to drive the prop so long as the distance that the prop moves through the air is shorter than the distance the wheels move along the ground.
This condition is satisfied so long as there is a tailwind (and the way I've worded it, it makes the most sense if you consider the cart already moving faster than the wind). If the cart is moving at twice the windspeed, then the wheels will actually generate twice as much energy as the prop would require (if it were 100% efficient), since the force is the same and the wheels move twice as far along the ground as the prop does through the air. If the cart is moving at triple the wind speed, then the wheels generate 150% of the energy the prop requires, again ignoring losses.
Note that this only works because the prop moves a shorter distance through the air than the wheels do along the ground. This is why your assertion about being able to do at least as well by driving the wheels is wrong.
sophiecentaur said:
QUOTE "The airflow around it will be very much like the airflow around any propeller. As the cart moves, it will leave a cylinder of air behind it which is moving slower (relative to the ground) than the surrounding air."
I think you would have to agree that, if your cart were inside a tunnel (tube) with the same CSA as the cart, then it wouldn't go any faster than the airflow in the tunnel (how could it do better than a well fitting piston).
Wrong. In a tunnel, the cart would do significantly better than a well fitting piston, and (perhaps more surprisingly), the cart would do better in a tunnel with a relatively close fit between the prop blade and the wall of the tunnel than it would in free air. This is because ducted propellers are more efficient than free ones.
sophiecentaur said:
Therefore there must be another source of momentum to transfer to the cart to explain how it goes faster than the air flow. The cylinder to which you refer must be much larger than the cylinder immediately around the cart or where is the momentum / velocity difference / power coming from? You can't transfer momentum if there is no (positive) velocity difference so the system has to produce one in some way.
The cylinder to which I refer will be roughly the size of the propeller, though airflow through a prop disk is quite complicated. You're overthinking things here - the airflow around the cart behaves exactly as if it were a simple, propeller driven cart with an electric (or other) motor driving the propeller. Relative to the cart, the air flows smoothly around it with some velocity, with the air moving faster behind the propeller due to the propwash. Do you agree that a propeller is capable of transferring (rearwards) momentum to air even if the propeller is moving forwards through the air? If so, then you agree to the basic principle that allows this cart to work.
sophiecentaur said:
Just because you have a system that works (and very impressive it is too!) it doesn't necessarily mean that your explanation is correct. I can find nothing in your explanation that goes further than a 'by its own bootstraps' argument and that won't do, will it? I am trying to look at the system in more depth and to explain what's happening in terms of possible energy transfers.
The energy transfers are fairly straightforward, so long as you understand that the propeller is doing work on the air and the wheels are having work done on them by the ground (and therefore, they have different effective velocities). Once you see that, everything else basically falls into place.
sophiecentaur said:
I can't really accept that your use of the term "ground frame" is relevant. I feel that it could probably also work for an airship, using some sort of drogue, possibly.
An airship could not go directly downwind faster than the wind unless it were dragging something along the ground (or in some other medium with a different velocity than the air). The whole reason the cart works is because the airspeed of the cart is slower than the groundspeed. Without it being in contact with both the air and the ground, it could not work.
Oh, and it also might help to visualize the opposite case. The cart as shown here is effectively extracting energy from its groundspeed and using it to drive the vehicle by pushing against the air. Many people find it easier to visualize a cart extracting energy from its airspeed, and using it to drive the vehicle by pushing against the ground. This would be a cart driving directly upwind powered by a wind turbine. With appropriate gearing, the turbine can extract more energy from the air than is required to drive the wheels, and the cart could go directly upwind. It's exactly the same principle, but easier to visualize.
In the case of the downwind cart, the correct "gearing" has to do with the prop pitch. With the correct prop pitch, the cart can generate more force than is required at the wheels to turn the propeller, since the propeller is acting as both the method of pushing against the air and the method of altering the force/velocity balance (like a gearbox would in a car driven by the wheels).