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Going Faster Than the Wind In a Wind-Powered Cart
Shawnconna writes "Can a wind cart travel faster than the wind? A group of makers say, 'Yes!' Make: Online has published a story about the Blackbird wind cart that just set a record. This is a follow-up to an earlier story in which Charles Platt built a cart based on a viral video where a guy claimed he'd built a wind-powered vehicle that could travel downwind faster than the windspeed. Charles built one and said it didn't work. Heated debates broke out in forums, on BB, and elsewhere on the Net. In the ensuing time, a number of people have built carts and claimed success, most principally, Rick Cavallaro. He got funding from Google and JOBY to build and test a human-piloted cart. They claim success, with multiple sensor systems on board, impartial judges and experts in attendance."
Not necessary to store energy to go faster than the wind.
The reason this works is that the propeller is able to "push off" against the tail wind. Think of it like sitting on a skateboard and pushing off from a moving wall behind you with your arm. The difficulty in making it work is that you need very little drag and a very efficient propeller. But the energy equations for traveling faster than the wind do balance and there is no violation of energy conservation.
When all else fails, run.
They can, but not directly downwind - which is what the article claims the cart can do.
They don't do it directly downwind, however -- they do it at an angle to the wind. This guy says he's doing it directly downwind.
I'm skeptical of this claim -- though I'd like to see their analysis of why they say it works.
I think they are overcoming that particular limitation with the propellor which is technically approaching the wind indirectly.
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it is possible, if what you do is to extract energy from the speed difference between the wind and the ground instead of that between the wind and the vehicle. Consider this greatly simplified concept: Build an enormous wheel, and set it up so that it has large sails around its circumference, between the thread and the shaft. Sat things up so that the sail will be closed or parallel to the wind when on top of the wheel, and perpendicular to it when on the bottom. The wind will push the sail, that will lever against the ground and cause the wheel to roll forward. Since the shaft is above the sail, it can travel faster than the wind even if the sail is slower,, and if the resistance of all the setup is small enough, you have something that travels faster than the wind, even if it's actually pushed by it
It extracts energy from the potential energy difference between kinetic energy of the atoms in the wind and the atoms on the ground. A sail does this too, but a sail has a lot of drag. In fact, it has so much drag that you will never end up going faster than the wind.
A propellor has very little drag. That's the whole point of a propellor. In fact, a propellor can provide negative drag (aka thrust). So the cart's speed stabilizes when the total drag of the cart exceeds the thrust on the cart from the wind and the propellor.
That's why the treadmill example works perfectly. The energy is no longer being extracted from the air, it's being extracted from the treadmill. If you were to measure the total work being done by the treadmill when the cart is moving forward on it, you would discover it was doing a lot more work when the cart was moving than when it wasn't. With a treadmill that has no extra power capacity this will result in the treadmill slowing down when the cart is moving forward.
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Right, but I just cannot see what keeps the propeller turning once the cart hits windspeed, as at that point the apparent wind would be 0.
In a sailboat or iceboat, to travel faster than the wind you head about 45 degrees off of the direction from which the wind is coming (called 'reaching'). The sails then work as airfoils, creating lower pressure on the outside of the sails, which in conjunction with the keel propel you forward damn fast if you choose (iceboats sometime 4-5 times the speed of the wind). However, when you are 'running' (heading directly downwind) the sails are not working as airfoils, but function merely as a wall the wind hits that propels you forward. You don't go faster than the wind in this case. The article specifically mentions heading directly downwind.
You are just adding a complicated energy storage mechanism and then having the energy collection mechanism disable itself for part of the time. It would be slower.
You could get the car up to speed faster by having a sail that folded itself as soon as the amount of energy it was extracting dropped off. Maybe a triangle sail with the base of the triangle along the bed of the vehicle and the tip at the propellor axis. Then have it spring loaded in such a way that when wind was pushing into the sail it also resisted the spring that was trying to fold it up.
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For the more visual people: http://www.youtube.com/watch?v=k-trDF8Yldc
Actually, the opposite is the case: The propeller is used to take energy from the wind, which is then used to drive the wheels and move the vehicle forward. This is most easily seen if looking at it on its own frame of reference. At stationary speed the wind comes from the front (because it's moving faster than the wind), while the road underneath goes backwards. The propeller takes energy from that wind and uses that energy to drive the wheels, which then keep the vehicle in place, against the forces of the wind and the road, which both try to move it backwards.
The Tao of math: The numbers you can count are not the real numbers.
The math is not too bad, but it does involve propeller theory which is where the magic happens. The goal is to make a propeller and cart that requires less energy than is provided by the wind pushing against the prop thrust. The energy supplied is:
E = (wind speed * prop thrust) - (cart drag * ground speed).
So if the energy required by the prop is less than E, the system works. You use the difference between cart speed - wind speed for the velocity of the air thru the prop.
When all else fails, run.
Here's an analysis performed by Mark Drela of MIT (http://web.mit.edu/aeroastro/people/drela.html)
http://www.boatdesign.net/forums/attachments/propulsion/28167d1231128492-ddwfttw-directly-downwind-faster-than-wind-ddw2.pdf
The achievement here is going faster than the wind in the direction of the wind. This is something sailboats cannot do. Sailboats can only travel faster then the wind when they are at an angle to the wind (usually going against the wind).
Nope, you've got it backwards, the GP got it right, and this is absolutely the key to understanding how this works.
The car isn't using the propeller as a turbine as a source of energy to power the wheels. That, indeed, would be impossible, because once you reach wind speed the force exerted on the propeller is zero.
Instead, it works the other way around, as a fan to push air backwards and accelerate the car. The energy is transfered from the wheels to the fan.
Assume that, to begin with, the car is moving at wind speed. The wheels are spinning (because the car is moving) and you can use that energy (i.e. brake the car) to push the propeller. The propeller blows air backwards, which propels the car forwards. If your mechanism is efficient enough, that push more than counteracts the braking action on the wheels and the car actually accelerates forwards. As it accelerates, the efficiency drops and it eventually stabilizes at some speed, faster than the wind.
Now everyone is shouting "Perpetual motion! You're producing more energy with the fan than you're getting out of the wheels!". Nope. That's the final bit. Let's say that wind speed is 10km/h. If the car is moving at 11km/h (faster than the wind), then the motion on the wheels relative to the ground is 11km/h. However, the fan only has to push air backwards at 1km/h, as the wind is doing the rest and providing the base 10km/h of forward motion. This difference in velocity is what offsets the inevitable energy losses: the ground speed is whatever you're generating with the fan plus the velocity of the wind "for free". This "free velocity" goes down (as a fraction of total velocity) as you accelerate, until it matches the (in)efficiency of the system (energy loss), and this is the stable velocity that the car achieves, faster than the wind.
This really isn't an issue with perpetual motion. It's easy to see that you could use a stationary turbine to generate (say, electric) power from the wind, and then use that power to accelerate a car (say, powered by a laser, so it is not tethered) in a different (windless) location faster than the original wind. Output velocity can be greater than input velocity. The difficulty lies in grasping the interesting mechanics and interactions of the downwind-faster-than-the-wind car uses to achieve this within the original wind itself. It's a mechanics puzzle, not an energy conservation puzzle. Another way to look at it is that the energy lies in the difference between the velocity of the wind and the ground, and the car always has access to both of these moving entities via friction (friction with the wind, and friction of the wheels with the ground), and thus can harness that power regardless of what its own velocity is.
On a treadmill, if the vehicle is moving forward (relative to the observer, not the treadmill belt), then it is moving faster than the wind (which is moving at velocity zero relative to the observer). It is simply a change of frame of reference. If you place the observer on the treadmill's belt, then the wind is blowing forwards as fast as the outside world is moving forwards, and the vehicle is moving forwards faster than that. On the flip side, if you take the real-world DWFTTW vehicle example, and place the observer on a balloon moving with the wind, then (just as in the treadmill scenario) the wind is moving at zero velocity relative to you, the ground is moving backwards (just like a giant treadmill), and the vehicle is moving forwards faster than you (just like in the treadmill example the car moves forwards relative to an outside observer, even though the treadmill moves backwards).
To answer the GP, see my post above. Everyone (including myself at first) immediately assumes this is a turbine-powered car using a wind turbine to drive the wheels. That's backwards, it's a sailcar (simply pushed by the wind) which in addition to that uses the wheels as generators to drive a fan (not a turbine) to push air backwards and increase thrust, thus actually achieving faster than wind speed.
So you're saying the North American Land Sailing Association is in the business of rigging official land speed record tests eh?
For Christ's sake, land sails already go 2-3 times faster than the wind using the exact same principles used in these carts. This is not some kind of voodoo physics, it's simply maximizing the available energy.
I'll break it down for you, since you obviously didn't bother to read the article where they already explained it and since I'm such a nice guy:
At a dead stop, the propeller acts like a sail. The wind pushes against it, pushing the cart forward. As the cart moves forward the wheels turn the propeller. The cart continues to accelerate, which in turn spins the prop faster. Well before the cart reaches wind-speed, the propeller is providing a significant amount of pull, which continues to accelerate the cart, which continues to drive the wheels which continues to drive the propeller faster. The cart stops accelerating when drag and wind-speed cancel out the propeller's pull.
Here's the math for you: tail-wind = 10mph, cart speed = 28 mph. 28mph/10mph = 2.8 times wind-speed.
Better?
In case you are interested, the land sailing speed record was set the same day with 126mph in a 40mph cross-wind. That's 3.15 times wind-speed. I can do the math again for you, if you like.
The physics work just fine, and they have for a couple hundred years now. It's the whole reason triangular sails were invented for heaven's sake! The sailing folks have it rough though, so much drag means the world sailing speed record is only about 20% faster than wind speed.
This is just a new application of old, well known and well established physics.
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It's simple: the vehicle must be able to move forwards faster than the wind forever, as long as the wind keeps blowing. In other words, the energy stored in the moving parts must not decrease and eventually cause it to stop working. Or in yet other words: the system must achieve a steady state where energy is flowing in and out at a constant rate, while traveling faster than the wind.
For a race where time matters, energy input initially into the system is relevant. However, for the purposes of proving that DWFTTW is possible, it isn't. Any amount of energy added initially will by necessity be dissipated in the friction losses of the system - you can't run a car forever on a fixed amount of energy. If it can, in fact, run forever on a steady wind, then you can discount any initially applied or stored energy, and conclude that it is being powered solely by the wind. If it does that while going faster than the wind, then you can conclude that DWFTTW is possible.
At first blush you would say if the lift/drag ratio of the sail/wing/apparatus is > 1 (plus a bit for drag) then a wind vehicle can go faster then the absolute flow speed.
The complication is that the range of possible angles of attack you can achieve gets dictated to you by trigonometry. Example, if you are on a beam reach (traveling 90 deg to the prevailing wind) and your speed is equal to the prevailing wind, the apparent flow is rotated 45 deg fwd of abeam. Now, a typical wing might give you an L/D of 20 at something like 10 degres AoA, so you would set your wing (sail) at 55 degrees from abeam. Your lift vector would be 55+90+atan(1/20) ~ 148 degrees from abeam, or 58 degrees off your bow.
Well, that's forward of abeam (90 degrees off the bow), so you have a component of lift pushing forward. It's then just a matter of getting the drag of your superstructure and rolling components down low enough to make that component sufficient to accelerate you just a bit, whereupon you are going faster than the wind.
For a boat, the "rolling components" are another wing in the water (the keel) which imposes more trigonometric limitations that make it tricky but not impossible to achieve this. Normally if it is possible it happens on a broad reach. With rolling vehicles it should be easier.
I don't know why people argue about this.
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You do realize that NALSA certified it, right? As in they checked all these things?
They installed a bracket on the shaft to ensure the propeller never drives the wheels, so all the momentum of the propeller is going to be able to do is allow the propeller to continue spinning. It never, ever, drives the wheels.
Anyway, it's way beyond theoretical. The current land sailing speed record is 3.15 times wind speed 126mph in a 40mph crosswind, fast!), set with a traditional land sail in a crosswind. It was set the same day NALSA certified the first DDWFTTW record.
Here's the explanation of the physics: http://en.wikipedia.org/wiki/Sailing_faster_than_the_wind
Security is mostly a superstition... Avoiding danger is no safer in the long run than outright exposure. - Helen Keller
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The vehicle accelerates to a a speed faster than the wind, then stays at that speed forever (as long as the speed of the wind is constant) and does not oscillate. It really will get you to your destination faster than e.g. a balloon traveling at precisely the speed of the wind.
There is a feedback loop, but it works like this: there is a wind velocity X, and a stable velocity Y for said X, where Y>X (for a properly designed vehicle using this technique). If the velocity momentarily exceeds Y, the friction losses of the wheels will be greater than the gain in push from the fan, and the car will slow down. If the velocity momentarily drops below Y, the friction losses of the wheels will be lower than the push from the fan, and the car will accelerate forward. It stabilizes at Y, faster than X. The feedback loop keeps it at that stable Y.
So here's a question for everyone: could you make it work in a boat?
Yes.
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You know, if you read the "fasterthanthewind" website, the story is that the math actually came first, and the first one of these vehicles was built later on, because -- guess what -- there were skeptics who refused to believe the math. In the modern era I'd argue it's rare for something to get invented without the physics having been done before that.
We learned today that Andrew Bauer passed on Sept 6. As our blog followers will recall, Andrew Bauer was not the original inventor of the concept, but did build the first successful DDWFTTW cart that anyone seems to know of. He did this to settle a friendly wager with colleague and notable aero engineer A.M.O. Smith in 1969. As we understand, the wager was based on a claim in a student's paper, written 20 years before, that DDWFTTW should in fact be possible. In some small way JB and I have tried to model ourselves after Andrew by doing the engineering and demonstrating the principle - rather than simply proving it on paper.
http://www.fasterthanthewind.org/
We know where leadership by an anti-intellectual "strongman" who scapegoats minorities and likes boisterous rallies goes
Exactly what everyone wants to see, a mathematical proof. Of course if you look at his free body diagram and his second equation. You'll see that he has his force vector Fp going the wrong way.
Fp is pointing in the correct direction, you merely misinterpreted the meaning of it.
Ft is the drag force on the underwater turbine. It is a drag which tends to slow down the vehicle, but the important point is that we are actively drawing energy from it. And yes, it is preforming exactly the same function as the wheels on a bike. We put a load on the wheels to extract energy.
Pt is the power that comes out f the turbine (or equivalently, the power we receive from putting a load on the wheels).
Pp is the power we supply to the prop. This is the same as the power we obtained from Pt, less some negligible percentage of loss.
Fp is the force CREATED by the power-driven prop.
The Fp pointing forwards is greater than the Ft pointing backwards, which indicates a net acceleration.
does not hold up to more than casual scrutiny.
It fails under "casual scrutiny" because the overall operation is extremely counter intuitive. However the math does work out once I managed to wrap my brain around the strange arrangement of forces and energy flow.
Your gut reaction is probably screaming that there MUST be a net energy loss in trying to extract energy from the turbine to drive the prop and that the prop's forward force MUST be less than the turbine's backwards drag. But you must remember that the wind is a source of energy relative to the water (or relative to the ground). That wind-water difference is an energy source, and that energy exists no matter how the vehicle might be moving. The trick is how to access that energy source while you're moving faster than the wind.
Note that force and power are not equivalent. Power is energy over time, and energy is force through distance. The turbine is moving through the water while the prop moves through the air. There is a speed difference (and an energy difference) between the water and the air. The turbine moves a large distance through the water. A large distance times a small force generates one unit of power. The prop is moving in the air, and even though the vehicle is moving faster than the wind the wind greatly DECREASES the apparent speed of the prop relative to the air. Because of the wind, the prop only moves a relatively small distance through the air. The prop generates a large force over a relatively small distance, which costs one unit of power.
Turbine extracting energy: small force * large distance = 1 energy extracted
Prop consuming energy: large force * small distance = 1 energy consumed
The equations balance. The large prop force accelerates the vehicle. The wind-water difference is the energy source. It's a very unintuitive arrangement, but it does successfully tap into the energy available in the wind-water difference, even when traveling faster than the wind. That energy source covers the inevitable inefficiencies in power transfer and it the pays the cost of accelerating the vehicle.
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Too bad I haven't got any mod points left. Yours is the best comment in this thread by far, illuminating the essential point :
harvesting energy from the velocity difference between the wind and the ground, not the velocity difference between the wind and the vehicle
It really is simple. It's an engine that works on the principle that a differential boundary exists between the two media upon which it is in contact with. Since water wheels work (exact same principle) and the stirling cycle works (the thermal variation of the concept), there's no reason why this shouldn't. The fact that engineering and physics didn't consider the frame of reference problem is what's hilarious. (Or rather sad, depending on your perspective.)
In this case the principle is being exploited in the velocity differential between a fluid and a solid. (air & ground) It has also been proven to work with a fluid and fluid, as various boats have been built using the same concept. This concept could very easily be exploited for things that crawl along inside pipes, etc.
Now if somebody want's a real engineering challenge, try making an aircraft designed to work specifically at a wind shear boundary. THAT would be interesting.