Update:
tristes_tigres finally decided to become acute while observing the prop in a cart video. lol

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Downwind, below windspeed, you can do it either way. But in this region it also works to hoist a moose on a pole and call it a sail, chuckle.

Downwind, at exactly windspeed, the cart feels dead air. A windmill in dead air collects zero energy to drive the wheels. As you get above windspeed downwind you feel an apparent headwind, but trying to stick a windmill in it is a net drag. The energy of the headwind is your own motion *minus* the true wind. That headwind effectively contains negative-energy as far as wheel drive is concerned.

Downwind faster than the wind only works with the wheels driving a prop.

For an equivalent reason, an upwind cart only works with a windmill driving the wheels. Upwind faster than the wind presents no special issue.

In both directions your windspeed-multiple is capped only by design efficiency, factoring in aerodynamic drag and whatnot. Blackbird gets over 3x downwind and (with a propeller swap and gear change) it gets over 2x upwind.

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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.

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.

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.

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 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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Right...

Nope. Going downwind-faster-than-the-wind requires the wheels to drive the prop. The easiest way to see this is to consider the cart traveling downwind at exactly windspeed. The cart feels like it's sitting in dead air. A windmill in still air collects zero energy. Nothing to drive the wheels. The math gets worse when traveling downwind faster than windspeed. Above windspeed you feel a headwind which can spin a windmill, but any attempt to stick a windmill in this headwind ends up dragging the cart slower.

You can use windmill to drive the wheels for a cart that goes upwind, and it can even go upwind faster than the wind. In fact an upwind cart can only work with the prop driving the wheels for basically the same reason we couldn't use a windmill to drive the downwind cart.

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I'm the article submitter. I say those people are wrong. They are describing a false or broken design, one which is incapable of going downwind-faster-than-wind. The math states that going downwind-faster-than-wind require wheel powering a propeller. The math also states that going upwind requires a windmill powering the wheels (That's not directly relevant here, but hopefully it's an easier to understand and illuminating mirror image case).

Furthermore, I included in the story a link to the Wikipedia entry on the cart, which states the downwind-windmill idea is wrong.

And I included a link to a physics analysis paper from MIT professor Mark Drela which shows the downwind-windmill idea is wrong

And I included a link to the International Physics Olympiad test with this cart as a sample problem, which includes and answer section explaining the downwind-windmill idea is wrong

And if you like, I can google up a link to the Blackbird builders themselves repeatedly and firmly insisting it's not a windmill cart.

And if you like there are countless videos on line, videos of the large Blackbird as well as videos of small model carts, and a causal visual inspection will easily reveal that propellers on downwind carts always rotate in a fan-like direction, never in a windmill-like direction.

Anywhoo:

Yep, I'm in the "later group"...

Okey dokey. We strip off the prop and attach the generator directly to the wheels. This is the power we would ordinarily be using to run the prop, but we direct it to a linear induction motor. No prob, simple enough.

Note that you have completely eliminated the wind from the system. The wind was our power source. So the end result is going to be pretty much what you would expect from any cart lacking a power source:

(A) If it's not moving, it simply sits there. It's not going to start moving on it's own.
(B) If you give it a shove, it will be ruled by the basic principals of inertia and frictional-style energy losses. It's coasting at the shove-speed, and over time slows to a stop. The only question is how quickly it's going to slow down. That's determined by friction and inefficiencies and any other losses.

Having a generator at the wheels driving an induction motor does not change that, other than potentially contributing additional energy losses which make it slow down faster. In the ideal case the trust at the induction motor will equal the drag at the wheel-generator, for zero net effect on the coasting-slowing cart.

The reason it does work with the propeller is because of the presence of the wind. (Without the wind, the thrust generated at the prop can only be equal to or less than the drag at the wheels, exactly like in your linear accelerator question.) The wind and the propeller are blowing at each other, pushing against each other. The thrust generated at the prop is effectively the combined effect of the energy driving the prop PLUS the effect of the wind.

Note that this additive effect applies even when the cart is going at or above wind speed. Consider a cart going 100 MPH in zero wind. There is going to be a 100 MPH apparent headwind flowing over the cart. The power-driven prop is going to to be very inefficient and it will struggle trying to generate any significant thrust to the rear in a 100 MPH airflow already heading to the rear The prop would have to spin crazy fast and it's going to yield squat thrust. Now consider a cart going 100 MPH, downwind, in a 100MPH wind. The prop now feels like it's sitting in still air. Propellers are extremely efficient at generating a thrust against still air. Any power going into the prop is going to generate a very large thrust force. The fact that the 100 MPH wind exists greatly magnifies the force that can be generated at that prop, even when the cart is at windspeed. Things are similar, but less extreme, when the cart is going above windspeed. The existence of the true wind reduces the apparent headwind that the prop feels, which increases the efficiency and thrust that it can generate for a given energy input. Any wind, even wind slower than the cart, adds to the prop thrust.

The power extracted at the wheels and driving the prop can, on it's own, at best, break even and produce zero net thrust. Any positive net thrust at the prop is entirely due to the wind blowing towards the prop and increasing the force appearing at the prop.

When we're parked, the blowing wind obviously contains available energy. The key point to not that that it exists, and that it cannot magically cease to exist due simply to where we stand or what direction we move or how fast we move. The wind blowing over the ground contains energy, and it has independent irrevocable existence. When we're traveling at or above windspeed, figuring out how to tap into that existing energy source is merely an engineering problem, not any sort of laws-of-physics problem or perpetual-motion problem. This cart connects to the ground via the wheels, and connects to the wind via the prop. That enables it to place itself in between the wind and ground and tap into the existing wind-vs-ground energy source.

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Yeah. Because on Mythbusters they would never do anything stupid. lol

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The Blackbird and similar carts are notorious for starting up very slowly. The initial start is from simple wind drag, with the large non-rotating prop acting much like a simple crappy sail increasing the basic wind drag.

Once the prop starts to turn, and while below windspeed, the cart slowly gains speed from a combination of simple wind drag augmented by the wheel-prop-thrust system working at a very low efficiency. I think at low rotation speed the prop blades are like an airplane wing in a stall condition... it can't generate aerodynamic lift when the air is just hitting the flat side of the blade and turbulently swirling over the edges. Anywho.... starting up from a dead stop is crap.

In the Blackbird test runs there's a point, I think in the ballpark of 75% of windspeedish, where it crosses a threshold and the prop gets a better bite on the air. I think at this point the prop blades are escaping the stall condition and they start generating true wing-type aerodynamic lift. The efficiency jumps and the cart starts to accelerate briskly. It then powers through windspeed and aggressively surges to either peak speed or until the drive chain snaps, whichever comes first. They generally run in a windspeed less than 20 MPH, and even with those light winds the peak torque in the driveshaft is comparable to the torque put out by a V8 engine, several hundred footpounds. The conflict between the prop pushing forwards against the wheels actively dragging backwards means that the drive shaft is under several times higher torque and power transfer than a simple car would experience at the same speed. As it picks up speed the prop is able to harvest the wind energy more rapidly from a greater volume of air, so as the speed picks up it starts cranking out pretty massive horsepower.

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At the risk of beating a dead analogy horse, the wheel/prop_axle system can be considered reasonable analogous to a keel. The function of a keel is to constrain the available path of motion of the sail when the wind pushes on it. In particular the sail, via the keel, pushes against the water-medium in such a way as to constrain the sail to moving nearly 90-degrees off from the direction of the wind force. Equivalently, the wind force on the prop gets transferred through the keel (the axles and wheels) such that that force presses against the ground-medium in such a way as to constrain the sail to moving nearly 90-degrees off from the direction of the wind force. The cart transfers this force from the prop to the ground along a more complicated path than a ship keel transferring sail force against the water, but the the force transfer is equivalent, and the result is the same. The keel constrains the sail to sideways across the wind, and the cart keep constrains the prop blade to sliding sideways (where that sideways is bent in a circle).

In both cases the keel causes the wind-on-wing-force on the wing to reflect back at the wing in a sideways direction.

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Ahh, now I'm looking at the source equations in the International Physics Olympiad and I see I misinterpreted the reference frames of the equations you posted. (You translated the variable "v" into "v_land", which threw me off. Writing it as v_cart would have been much clearer.)

So, trying again.

quoteSo evidently this equation only holds in steady state not in development.

Yeah. They state "the force due to air and the force due to ground must balance", so they are specifically analyzing the cart at steady-state peak speed, where prop force and wheel force sum to zero.

You appear to have mis-copied that one. The equation should read:

F * (v_land - v_wind) = (1-alpha) * F * v_land

put in that magic moment when V_land-V_wind = 0, for another silly result.

V_land-V_wind = 0 puts the cart at windspeed, at which time it is accelerating. Acceleration means that the prop force and wheel force are out of balance. Any such equation will involve two differing F values.

I inserted a < in there, which I assume you intended but which Slashdot eats unless you type &lt; to get <

Anywho, again you're looking at a case of an accelerating cart involving different wheel and prop forces. Any equation with a single F value is going to be nonsensical.

That's the mis-copied equation again. I'm pretty sure you wanted:

F * (v_land - v_wind) = (1-alpha) * F * v_land

In any case, it's an equation doe a faster-than-wind-cart at peak speed. Therefore v_land > v_wind, and v_land-v_wind > 0. In other words both sides have the same sign as F, and therefore have the same sign as each other. (Unless of course alpha is > 1, which would be a machine with greater than 100% energy loss, chuckle.)

I'm not sure if this will answer what you want, but some time ago I worked out the complete force and energy calculations for an accelerating cart. If you can follow it you can (hopefully) see where and why the propeller thrust turns out larger than the wheel drag. The short answer is that work = force * distance. The wheels roll a long distance over the ground, in comparison to a shorter distance of air through the prop. The differences in distances can trade off against a difference in forces. A small force at the wheels (pushing against a long distance of ground) can do enough work to generate a large force at the prop (pushing against a short distance of air).

http://talkrational.org/showpost.php?p=1278991&postcount=311

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I'm not sure if we fundamentally disagree on the operation of the cart, or if you're quibbling over a reference-frame-dependent inherent ambiguity of "how energy gets into the cart". So lets see if you agree with this:

Rip out the dive shaft. I say we can attach an electric generator to the wheel axle. This generator provides us with a several kilowatt powerline. We then attach that to an electric motor driving the propeller and consuming the several kilowatts of power

If you agree with that, then we're merely discussing a reference frame ambiguity of "how power gets into the cart". From the point of view of an observer nailed to the ground, you're right.... the forwards force of the air on the prop is adding kinetic energy to the cart, and that energy is obtained by the equal-and-opposite force slowing the air (and reducing the air's kinetic energy).

However from the point of view of an observer "nailed to the airmass", energy is entering the cart through the force of the earth applying a torque to rotate the wheels, and that energy is obtained by the equal-and-opposite force slowing down the earth (and reducing earth's kinetic energy).

In my opinion the second version is often an extremely useful way to explain things. It helps nail down for people the crucial direction of the internal energy flow: The wheels are being used to drive the prop to rotate, and that it's the resulting air-vs-prop force pushing the cart forwards. There's nothing fundamentally incorrect about viewing the energy as coming in through the wheels. It's a frame-dependent interpretation.

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Agreed, and agreed.

I'm not a sailor, but I've seen numerous knowledgeable sailors declaring that a tacking sail can be the equivalent of either a turbine or a propeller, depending upon the particular tack. You're mistaken that a sail tack can only be equated to a turbine. I could be mistaken on the following detail, but I think downwind tacks have the sail operating like a propeller, and upwind tacks have the sail operating like a turbine. I haven't really focused on that aspect though.

All the sailors I've seen have found it acceptable and extremely illuminating to have the cart-prop explained as a sail on downwind tack, with the wheels acting as the keel. Sailors seem to find that to be an extremely intuitive setup extracting energy from the true-wind.

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I'm the article submitter. All of those statements are incorrect. I suggest you look at the MIT analysis paper I linked in the article. You'll see he has force of the air on the propeller pushing the cart forwards. In the paper he drew an underwater turbine, but that fulfills the same role as the wheels. The wheel-ground force is a drag, pulling the cart backwards. This is where the torque is generated to power the rotation of the propeller (fan) in the air.

And to reply to your other post:

Again, downwind faster than the wind is impossible using a turbine. One reason is that, at the moment you equal windspeed, there is zero apparent wind which means zero torque can be generated by a turbine. If a "turbine" is rotating while sitting in still air, it in fact expends energy pushing the air in a direction, and this expenditure of energy shows up as a drag (negative torque) slowing down the drive shaft.

However the more fundamental reason that downwind-faster-than-the-wind is impossible using a turbine is that at above windspeed you're trying to use the apparent headwind to drive the turbine. The energy content of this apparent headwind is diminished by the existence of the true-wind, whereas the force of the driven prop is augmented by the existence of the true wind. This means that attempting to use a turbine to extract energy from the apparent headwind imposes a drag, with an energy return deficit equal to true wind.

Energy equals force times distance.

Any attempt to extract power from the slow apparent headwind and expend it driving the fast wheels is a losing proposition. Slow apparent headwind means you have a force times a short air distance in that energy formula. You either obtain little energy or a large drag force. Spending the energy at the fast wheels means a force times a long ground distance in the energy formula. For a given energy, you obtain a small drive force over a long distance at the wheels.

An upwind cart uses a turbine to gather energy(torque) to drive the wheels. A downwind faster than wind cart uses the wheels to gather energy(torque) to drive a propeller like a fan.

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You're close to getting it, except the propeller is turning like a fan, not a turbine. (Because it's a fan, the cart doesn't notice anything unusual or even interesting as you pass though the apparent "dead air" when you equal windspeed.)

Each blade of the prop is in a constant corkscrew tack, spiraling downwind. The wheels are like the keel, *forcing* the prop-blades to stay on that particular tack. The cart moves forwards forcing the wheels to turn, with the wheels forcing (powering) the prop to rotate. Note that the keel is essentially a drag force.... the wheels experience a large force trying to drag the cart backwards. The existence of the wind ensures that the lift at the prop(sails) is greater than the drag at the wheels(keel). The net force is forwards. And yeah, you nailed it that it all works because attaching to the ground and the air enables us to tap into the energy of the true wind.

I kind hate sailors and the sailing analogy though. For me it ruins all the fun of debating the "energy problem" a physics perspective. The "How the #$%@! does the wind energy get into the cart when you're sitting in dead air" issue, chuckle.

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I prominently stated it when I submitted this article:
Directly Downwind Faster Than The Wind, Powered Only By The Wind, Steady State

No cheats. No tricks. Just a very simple machine which is connected in the reverse of the way people expect, and which produces a surprising result that seems impossible, but which isn't.

Understanding it is a fun brainbender. However a caution: It's very common for people to think "that can't be right", and try to "correct the miscommunication" by dismissing or reversing a direct statement such as "Directly Downwind" into "not directly downwind".

Caution: It's also a major stumbling block to understanding when people commonly make that sort of reversal "fixing" parts of the explanation that sound wrong. The way it works is very counterintuitive, and until you pull the whole picture together each of the individual parts of the explanation can sound backwards.

The propeller is not a windmill. The prop is a fan. Always a fan, only a fan.
The prop pushes the cart forwards.
The prop does not drive the wheels. The wheels drive the prop.
The wheels don't push the cart forwards. The wheels try to drag it backwards.

If you miss any of those points, or even worse mentally reverse any of them, it can become very difficult to grok the explanation. To avoid redundancy I'll just note that explained in detail elsewhere, but I'm happy to help with any questions or confusion.

Yeah, if you use a sailing analogy the wheels are like the keel, the prop blades are sails on a constant corkscrew tack, and the drag at the wheels(keel) is what forces the the prop(sail) to travel along that tack.

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It's unclear whether this is merely a language quibble, or you don't yet understand how it works.

The propeller is exerting a rearward force on the air. Newtons Laws: for every action there is an equal and opposite reaction. If a force exists from the prop towards the air, there also exists and equal and opposite force from the air towards the prop. The air *is* exerting a forwards force on the cart, even when the cart is going above windspeed. And assuming we're not getting into some linguistic quibble distinguishing "the air" from "the wind", then "the air" is the same thing as "the wind", and "the wind" is indeed pushing forwards on the propeller. And again, assuming we're not getting into some linguistic quibbling, "the propeller" is a part of "the craft".

So the net force on the craft, from the wind, is a forwards acceleration. Even when the craft is above windspeed.
That's true because the prop is turning (and it's turning like a fan, not a windmill).

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