Can you explain to me how this little vehicle goes uphill
faster than the treadmill speed. Please!
Certainly...
Consider a cart with a generator hooked to the rear axle. We'll
attach the propeller (it IS a propeller - not a turbine) to an
electric motor.
For the sake of argument I'm going to assume the following
efficiencies:
generator: 85%
electric motor: 85%
propeller: 85%
And just for now...
rolling resistance: 0 lbs
aerodynamic drag: 0 lbs
(we'll come back to these).
Now let's tow this cart up to 20 mph in a 15 mph tail-wind and let it
loose. That means it will feel a relative head-wind of 5 mph over the
cart. Now I'll adust my generator output until it produces 20 lbs of
drag at the wheels. This means I'm putting power in at a rate of 20
mph x 20 lbs (400 mph-lbs). But I only get 340 mph-lbs out of the
generator due to its limited efficiency. I deliver that power to the
electric motor. But I only get 289 mph-lbs at the motor's shaft due
to the motor's innefficiency. So I'm putting 289 mph-lbs into the
prop - but it's only doing about 245 mph-lbs work on the air due to
it's innefficiency.
So now lets see how much thrust I'm getting from my prop...
245 mph-lbs / 5 mph (the speed I'm moving through the air) gives 49
lbs.
So we're producing 49 lbs of thrust and only 20 lbs of drag. But we
haven't yet accounted for the rolling resistance and aero drag. If we
can get both of those numbers to come in at a total of less than 29
lbs (which should be a piece of cake) we'll be going 5 mph faster than
the wind and still accelerating. But why?
Simple. The car acts as a force multiplier (i.e. lever) between two
media (the ground and the air). Just like any lever, I can get more
force out of one end if I put more distance in the other. Force x
distance = work, so those will nominally be the same on both sides.
But my car is going over the ground at 20 mph while it's only going
through the air at 5 mph. This means the ground side of my lever
moves 20 miles in one hour while the air end of my lever moves only 5
miles in that same hour. With no losses I can get four times the
thrust as the drag I produce.