UCLA physics professor loses $10k bet about downwind kart

Sure they do.

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As long as there’s a differential between the speed of the air and the surface then that differential can be exploited to harness energy without breaking any laws of physics.

Using energy from the initial push to maintain constant speed indefinitely is another matter entirely unless you’re in a frictionless environment.

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fair enough. I should have been more specific: most boats, and definitely not downwind

Jesus, I need new glasses. When I read this title while scanning the recent Boings, I thought it read:

UCLA physics professor loses $10k bet about downwind fart

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I don’t think that’s what I said exactly. I apologise if I was unclear.

This is a slight derail, but bear with me. It takes more power to get something moving, than it does to keep something moving. And then after that that friction increases with speed. In other words, when you move a shopping trolley, you give it a push to get it moving and once its moving, its easy to keep it moving.

So initially the vehicle is stationary, with the wind at its back. Static friction (and inertia) hold it in place even though there is a gentle breeze trying to blow it forward. The breeze increases in speed enough to overcome static friction and the vehicle starts to move and accelerate just a little.

You could think of this as the drag on the vehicle pulling it forward, but it would be better to use a different word, because drag in the aerodynamic sense usually means the resistance to forward motion. In this instance, maybe just call it windforce cos Thrust has a different meaning and we need that word later.

With the treadmill example, there is no windforce to speak of, because the treadmill is operating indoors in still air.

The treadmill is running from front to back. If the propeller is disconnected from the wheels so its not spinning, and the kart is held in place on the treadmill until the wheels are running at the same speed as the belt, and then the kart is released, pretty abruptly the kart will go backward off the treadmill with alacrity.

Now imagine the treadmill is 500 miles long. Reconnect the propeller to the wheels and hold the kart on the moving belt until everything is up to speed. The kart will start moving up the treadmill (exactly like the in the video) and it will keep going at a slow and steady speed for 500 miles until it falls off the treadmill at the other end.

Where is the power coming from? Well from the treadmill and it’s complicated relationship with the mass of the kart and some friction and stuff. But mostly, the treadmill is powering the propeller of the cart to hold and also to gain ground against the belt.

Why does the kart maintain a constant speed? Because all the forces are in equilibrium. The thrust of the prop is equal to the friction of the wheels. Increase the speed of the belt and the kart will accelerate until it finds equilibrium again.

Keep increasing the speed and eventually you will reach a point where the Kart will slow, and eventually it will start losing ground to the treadmill ( I think, this is pure speculation on my part)

And if you turn the speed of the belt down? Initially the kart might move faster due to its own momentum but eventually it will get slower and slower and at some point the propeller won’t be able to produce enough thrust and then the whole system will fail, and the kart will stop on the belt.

Inittially, the cart may acc

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Easy, the prop slows down the wind. That is a reduction of kinetic energy, that is energy harvesting, that is what drives the wheels who can then accelerate.

For that to work all you need is a speed difference between the surface the yacht drives on and the air the prop works on. (See relativity) That is why the thing works on a treadmill as well, it doesn’t matter if the surface is going backwards or the wind is going forwards.

The confusing bit is the relativity. From the view of a spectator there is a point the speed of the yacht is equal to that of the wind, that is weird, right? But from the point of the driver there will never be a point where the airspeed is equal to the road speed. There will always be a difference, so there will always be a potential for acceleration.

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I can’t believe people keep having the same arguments that we did… what was it… about 13 years ago (BTW, about nine months after this classic and very relevant XKCD came out).

My explanation is still the same from 13 years ago. The long version is here, the short version is here and below:

There is a “braking” force on the wheels (i.e. they offer resistance, the ground pulls back on them), and the prop provides propulsive power (it is not a turbine). These forces are the same in any reference frame. The prop pulls the cart downwind, the wheels try to hold it back upwind.

To show that this is not perpetual motion: The power into the wheels is wheel traction force (the aforementioned “braking force” on the ground) times the ground speed. The power out the prop is the prop thrust times the air speed (be it the air in the wind or the air blown by the prop; Pick either). In order for this to not be perpetual motion, the power out the prop must be less than the power in the wheels. And in order for this to move DDWFTTW, the thrust from the prop must be greater than the traction in the wheels (since the thrust is also opposing drag, etc). This is doable since the airspeed past the prop is lower than then ground-speed past the wheels. If there were no wind, airspeed would be the same or grater than ground speed, and the vehicle would not work. Only when airspeed is lower than ground-speed (i.e. when there is wind) can prop power (airspeed x prop thrust) be lower than wheel power (ground-speed x wheel traction force) with prop thrust still being greater than wheel traction.

The treadmill cart is absolutely equivalent to being outside in the wind. Sure, the treadmill cart takes energy from the treadmill, but from an equivalent frame of reference outside (e.g. from a balloon) the DDWFTTW car takes KE from the Earth (since that braking force slows down, by just a tiny bit, the speed at which the Earth goes by under the balloon). Where the energy comes from (the air or the Earth) does depend on your frame of reference (which is why, to say something that should make sense from any frame, we say the energy comes from the difference in velocity between the air and the Earth).

Right?

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Ah, but it does add power. The propeller generates more thrust when there is a tailwind than when there isn’t.

For example, imagine the treadmill cart: If you turned on a fan that is blasting air at the treadmill card from the front, i.e. if the air moved similarly to the treadmill, the propeller would make less thrust, causing the vehicle to move backwards on the treadmill, not only due to increased drag but also due to decreased thrust.

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I think there are actually two different (but interconnected) things that’re causing confusion here. First, as a number of people have discussed, is the relativity angle: things look different depending on which reference frame you decide to use (but they only look different, they’re actually the same). The second source of confusion is that there are two different paths for energy to pass between the wheels and the propeller: linear work (propeller pushes on thrust bearing, which pushes on kart’s frame, which pushes the axle and wheels) and rotational (“shaft”) work (wheels spin, turning axle, turning various gears and shafts, turning the propeller).

lava’s fundamental question is about whether it’s the propeller powering the wheels or the wheels powering the propeller, and the answer (at least in the Earth-stationary reference frame) is that it’s both. This is not a contradiction because there are two power paths, and they’re carrying power in opposite directions.

The propeller does linear work on the thrust bearing, adding energy to the kart’s frame/body. The frame/body in turn does work on the front wheels, pushing them along the ground. Some (but not all) of that energy goes into forcing the wheels to turn, which does shaft work on the axle, gears, etc… which is then fed back to do rotational work on the propeller, turning it against the wind. And because the propeller is turning against the wind, it continues to push on the thrust bearing (continuing the linear work that started this loop) even when going faster than the wind.

This power loop does not violate conservation of energy because the shaft work (wheels → propeller) is less than the linear work (propeller → wheels). (The difference goes toward accelerating the kart and/or overcoming friction.) Overall, energy is conserved because by pushing against the direction the wind is moving, the propeller slows the air, which decreases the air’s kinetic energy. As long as the increase in the kart’s kinetic energy (and losses due to friction) are less than the decrease in the air’s kinetic energy, conservation is satisfied.

At least, that’s the case in the Earth’s reference frame; in other reference frames you’ll find that the linear work portion is different, and even that energy is moving in different directions. But that’s normal, because they’re different reference frames.

(When Derek does the analysis in the video, he does it in the reference frame where the cart is instantaneously stationary – he mentions this at 11:28. Linear work is proportional to velocity, so in this frame the linear work vanishes and the analysis is much easier and less confusing because he only has to deal with the parts related to shaft work. In this frame, the Earth’s motion is the ultimate source of energy, and the propeller is actually doing work on the air. But that only applies in this reference frame.)

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(14 hours later)

unnamed

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It’s not an assumption; it’s a thoroughly repeatedly proven fact.

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…and totally irrelevant to the question.

Elves don’t exist either, so what?

What question? I was rebutting @lava’s (quite possibly sarcastic) characterization of the fact that perpetual motions can’t work as an assumption which it most certainly is not. :man_shrugging:

ETA: Okay, I finished the entire thread of people trying to explain to lava why the Blackbird isn’t a perpetual motion machine, and realized you probably just assumed my very particular comment to lava about one very particular thing lava said was somehow about your attempt to explain classical relativity to lava.

This is why Felix Hoffman invented aspirin.

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Really I think the most intuitive explanation is when he got out the two wooden beams and showed how with a cleverly made gearing, he could get a thingiemajig to slide out faster than both beams by rubbing them against each other. The downwind kart is just a version of this where one wooden beam is a gas.

Another thought experiment: imagine if the kart operated by another principle - as the wind blows against the ground, it generates heat from friction. A little collector on the kart collects this radiant heat and uses it to generate electricity, which it uses to move forwards. If the kart is made more efficient at collecting this heat, and there’s less air resistance/friction loss in the wheel bearings, the faster the kart can go. Assume a frictionless kart, and in this thought experiment the kart can accelerate effectively without limit!

Of course in real life this would be an incredibly impractical way to make this work, but I think it makes clear that there really needs to be no connection between the relative speed of the kart and the wind and how fast the kart is driven. The deciding factor is the efficiency with which the kart collects power from the difference in ground/air speed, and how much is lost through friction/air resistance.

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I think this is what confused a lot of people: the idea that even moving at windspeed implies being so fast that the vessel is in stasis with the wind as such.

You quite rightly point out that the kart (or a boat, for that matter) isn’t moving with the air, it’s moving with the ground, so the friction with the ground (or water) is the vehicle’s friend this time, not its enemy. Friendly friction is what we call traction.

It’s just a reversal of the famous “airplane on a treadmill” mental exercise, which only serves to remind us that friction/traction with the ground is irrelevant, because the airplane is only concerned with airspeed and doesn’t use its wheels.

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From that article though, they had their best results at medium wind speeds because at higher speeds the chain snapped. He also mentions that the torque on the propeller shaft is ~700lbft (900Nm)! That’s fast car/medium sized lorry levels for torque, and frankly makes me more impressed that they managed to do this without the entire thing ripping itself to bits, given that half of it seems to be made of bicycle parts.
What I’m saying is, the engineering is almost as interesting as the physics.

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Look what popped up in my youtube suggestions :slight_smile:

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apologies to everybody’s sincere efforts when I was not taking it all that seriously.

As far as classifying it as “wind powered” I still have a hard time considering leveraging the differential as the same as wind powered. But opinions on this don’t matter much unless you are betting 10k on it.

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much better than the original video.

There must be a better way to express in easy terms what is going on here. Like:

The kart is not being pushed by the wind, rather the kart is pushing against the wind.

or this:

The wind is not pushing the kart, rather the wind is pushing the column of air thrust back by the propeller.

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I mean, I like a cash windfall as much as the next person, but I couldn’t in good conscious take 10K bucks from someone who didn’t do his homework like the UCLA prof. (Maybe 1K to a good cause?)

Think of it this way. The Blackbird is a mechanism for extracting the potential kinetic energy of the difference between the momentum of the air and the ground. It doesn’t matter that you can arbitrarily define the ground as stationary, because in reality only the relative motion of the ground to the wind generates the potential kinetic energy. That’s the cornerstone of relativity, that there’s no preferred frame of reference (hence the name). If you abandon the incorrect notion of an absolute rest frame, then you’re left with forces between frames of reference. A machine extracting energy from the potential kinetic energy of the masses moving in these different frames of reference can do work, and isn’t limited to extracting them from only the direction in which one source of momentum (in this case wind) is moving.

The Blackbird is fundamentally a mechanical engine for converting the potential kinetic energy of the relative motion of the wind to the ground into motion in a “forward” direction (a vector). Even when it’s moving at the same speed as the wind relative to the ground, it can still extract that energy until it’s own aerodynamic drag balances the work that difference can do, which in the case of the Blackbird is 2.86 times the wind speed relative to the ground.

I hope that helps explain. I promise it’s all just vector analysis.

[Edited for accuracy with compliments to @Otherbrother.]

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