|Quoting WPIAeroGuy (Reply 5):|
What do you mean by "zero equivalent"? Is that the speed where the turbine is extracting as much energy from the wind as it take to move the cart into the wind
The turbine is being spun so that it's effectively at rest in the airflow created by the speed of the cart. Imagine the cart going 10kts on a completely calm day. It's being spun so that it's creating a nominally 10kt forward bite into the airstream, which is exactly canceled out by the 10kt forward speed of the cart. So the turbine is spinning at a 10kt rate, but it's producing zero thrust or drag because its also being moved through the air at exactly that speed.
IOW, you've factored out (more or less) the airspeed caused by the forward motion of the cart, and the airspeed the turbine is seeing at that point is effectively zero.
Put another way, the screw that is the turbine, is advancing into its medium (the air) at exactly the same rate as the threads (aka blades) are advancing, and so is generating no force at all (thus requiring little energy).
Now toss in a tailwind, and the turbine will see a force from the tailwind. Assume the tailwind is 5kts. If the cart is at rest, the turbine (which is also be stationary), will directly see the 5kt breeze, and extract energy from the wind based on that. If the cart is moving at 10kts, because the turbine has been pre-spun to cancel out the 10kts of the cart, the turbine will *still* see a tailwind of 5kts.
You can thing of that as (sort of ) producing two forces on the turbine, one is basically torque in the wrong direction (since it’s a tailwind it will be trying to spin the turbine in the wrong direction, thus slowing down the wheels), and a forward force from the wind blowing on the turbine blades. So long as the later is greater than the former, you get net energy input.
In truth you cannot separate the two forces like that, but these are the lift and drag components of the airflow over the turbine blades – the drag trying to slow down the rotation of the turbine, and the lift pushing the cart forwards. With calm winds the turbine is at zero degrees angle of attack (and zero lift), once the tailwind hit, the AoA increases, increasing lift. Just like pitching up in an airplane increases the lift from the wings. So long as the L/D is over 1.0, you’ll be getting a push from the turbine.
There’s no perpetual motion here – the cart’s airspeed is not driving the turbine, the cart’s speed is only used to zero out the effective airflow through the turbine (and to cancel out the drag component from the turbine – but so long as that, plus the drag of the cart itself, are less than the lift, you’ll get acceleration).