What I have eliminated is the windmill.
IMPORTANT: There is no windmill.
This is a roadblock to understanding that trips up most people. As long as you look at the cart and you think you see a windmill.... as long as the word "windmill" pops to mind... you aren't going to be able to get a handle on how the cart works. There is no windmill. The propeller is a fan, always a fan, only a fan.
Note that you have completely eliminated the wind from the system.
No, the wind is still blowing. What I have eliminated is the windmill.
I didn't say the wind ceased to exist. I said you eliminated it from the system. The sun exists. But if the cart doesn't have solar panels, the sun obviously isn't a part of the system
If we're talking about a battery-powered machine, and you eliminate the battery wires, and I point out that you have "removed the batteries from the system", I hope you can see that it comes across as a little silly when you object that the batteries still exist.
This is a wind powered cart. If you are having trouble seeing how the cart taps into that energy, I'll happily do my best to explain it. But simply disconnecting the power source very quickly sends things in a very simple and obvious direction. No magic, no free energy, no perpetual motion... a machine which is not connected to a power source simply and inevitably winds down to a halt. A machine which is connected to a power source can run as long as it's connected, it can accelerate within the bounds of available power, it can tapdance and whistle dixie if it wants. Grin.
Check the "Thrust at Constant Power vs. Airspeed" chart here, where the thrust initially increases with airspeed This is presented as a typical case, not a special or corner one.
It is presented as a "typical case" for aircraft, the graph labels show between a quarter-million horse power and a half million horse power, and the intended performance range is obviously in the 100+ MPH region.
I think you'll agree that it's not very surprising that the left side of the graph, that down-left slope going from 50 MPH to 0 MPH, shows an aircraft prop going into an obvious "fail" region outside the intended operation range. A prop designed for low speed efficiency would have a significantly higher thrust at 50 MPH, and the thrust graph would continue to rise as velocity decreased below 50 MPH.
And you mentioned corner cases - that is exactly what we're examining here. We're looking at what happens at zero MPH, which is an extreme corner case. According to the laws of physics for an ideal 100% efficient device we have:
power = force * velocity
If we flip that to isolate force we get:
force = power / velocity
To simplify lets define a constant power input of 1 unit:
force = 1 / velocity
We are examining the extreme corner case where velocity goes to zero, and in that corner case an ideal prop can generate infinite force. Obviously no real machine is 100 percent efficient, no real machine can generate infinite forces. So as we approach zero a prop or other machine can provide increasing force, but we're running into a corner case and at some point we hit a design limit. At some design point the force generated reaches a maximum and anything more gets lost into inefficiencies.
We obviously don't need ideal infinite force for the cart to successfully work at zero air velocity. All we need is for prop thrust to be greater than wheel drag. A prop designed for low speeds can easily generate double, triple, or several more times as much force in low-velocity or zero-velocity air.
Consider a cart going 30 feet per second in a 20 foot per second MPH wind. The car is going 10 feet per second faster than the wind, so there's 10 feet per second of air going through the prop. Lets put one pound of drag on the wheels. Again, power = force * velocity. Power = 1 pound * 30 feet per second. The drag at the wheels generates 30 foot-pounds per second of power. We feed that 30 foot-pounds per second of power into the prop. Power = force * distance. The distance is 10 feet per second of air through the prop, so we have 30 foot-pounds per second = force * 10 feet per second. Solving that we get Force = 3 pounds. The prop can covert that power into up to 3 pounds of thrust. Even if the prop is only 50% efficient, it's still generating 1.5 pounds of thrust. The cart is going faster than the wind, and accelerating.
It works like a lever. One side of the lever is long, you apply a small force pushing that side down a long distance. The other side of the level is short, and a large force pushes upwards a short distance. The laws of physics allow you to use leverage, trading off a large-distance-small-force to obtain a small-distance-large-force.
The wind and the propeller are blowing at each other, pushing against each other.
This looks like the bogus "the exhaust pushes against the air" explanation of how a rocket works
Yeah, the way I phrased it was a pretty crummy attempt to translate the physics equations into "plain English". A better way to make that point is to look at the air going into the front of the prop. A prop can easily grab onto still air and forcefully shove it out the back (where "easy" means with small power input).... but if 100 mph headwind is coming into the prop it needs to spin crazy fast attempting to grab onto it, and it has a really difficult time (where "difficult" means large power input) trying to push it any faster out the back.
The propellers of airplanes efficiently generate thrust in a 100 mph airflow, and well above
The prop-thrust graph you linked was citing props using between a quarter million and a half million horsepower. How "difficult" something is is relative, and this stretches it to humorous proportions. You're casually tossing off a half million horsepower as easy and efficient.
An aircraft flying with a 10 MPH airflow could generate the ten times as much thrust using that same horsepower. Or, alternately, a plane in a 10 MPH airflow choose to only use one tenth as much horse power to generate the same thrust as your plane in the 100 mph airflow.
If the plane were in a 200 MPH airflow you would need twice as much horsepower for the same thrust. Its so difficult for a prop to push against a 200 MPH wind that we now need a million horsepower to obtain the same force.
The power generated by a drag at the wheels depends on the speed of the cart and the size of the drag force. The power we extract from the wheels is not affected by the windspeed. When we use that power to drive the prop, the force we can generate from that power depends crucially upon the speed of the air through the prop. The existence of a wind can reduce that velocity, which directly impacts the size of the force generated at the prop. The existence of wind can and does modify the drag-thrust ratio of the cart.
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