# Focussing on the Treadmill of Veritasium's Blackbird faster than wind

• I
• peanutaxis
In summary: and in this case the toy cart gets energy from the ground in the wind frame and the real cart gets energy from the wind in the ground frame.

#### peanutaxis

TL;DR Summary
The treadmill test case DOES break physics.
Hi,

Like many here I watched Veritasium's awesome videos on this*. And like many I found myself having to drag my mind into understanding why it works.
The energy explanation makes the most sense to me. Derek explains that the fan is taking energy out of the existing wind - slowing it down - and using that energy to speed up the cart. Just like a heat pump can heat your house on a cold day - you might ask, where is the heat coming from, it's cold outside! Well, just because it's cold outside doesn't mean you can't cool that air down further and pull energy from it. Similarly with the cart, just because you are going faster than the wind doesn't mean that the wind that you are going faster than doesn't have any energy left in it which you can harvest.

But because of this energy explanation the part that really bothered me about the Veritasium vidoes is when they use a treadmill as a test case. The builder/owner of the cart comments about the treadmill test case as valid because it doesn't matter your inertial frame. And Derek gets the treadmill test case 'working' in the second video. But this is completely wrong as follows:
Your initial condition is a resting test cart and still air (energy = 0). Your final condition is a moving cart that has accelerated itself by accelerating air in the opposite direction (positive energy). Not possible.

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Dale
peanutaxis said:
Summary: The treadmill test case DOES break physics.

Your initial condition is a resting test cart and still air (energy = 0). Your final condition is a moving cart that has accelerated itself by accelerating air in the opposite direction (positive energy). Not possible.
The air is moving in the inertial frame of the threadmill, so it has energy that can be given to the cart.

topsquark
willem2 said:
The air is moving in the inertial frame of the threadmill, so it has energy that can be given to the cart.
Hi.
I know this is invalid/wrong because:
In the frame of me looking on: Cart = 0, Air = 0. And then suddenly the cart moves. Either the cart gains energy from the treadmill or you have a perpetual motion machine. No way out of that, I'm afraid.

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peanutaxis said:
Hi.
I know this is invalid/wrong because:
In the frame of me looking on: Cart = 0, Air = 0. And then suddenly the cart moves. Either the cart gains energy from the treadmill or you have a perpetual motion machine. No way out of that, I'm afraid.
In the ground frame the cart does gain energy from the treadmill. In the ground frame the treadmill is moving at ##\vec v## which is pointed “backwards”. The force ##\vec F## on the cart from the treadmill is also backwards. So ##P=\vec F \cdot \vec v>0## is the power delivered from the treadmill to the cart in the ground frame. That power is used both to increase the energy of the cart as well as the energy of the air (plus some heat for friction and drag)

Physics is not broken in any frame, although the explanations differ in different frames, as usual

topsquark
Dale said:
In the ground frame the cart does gain energy from the treadmill. In the ground frame the treadmill is moving at ##\vec v## which is pointed “backwards”. The force ##\vec F## on the cart from the treadmill is also backwards. So ##P=\vec F \cdot \vec v>0## is the power delivered from the treadmill to the cart in the ground frame. That power is used both to increase the energy of the cart as well as the energy of the air (plus some heat for friction and drag)

Physics is not broken in any frame, although the explanations differ in different frames, as usual
Right, so the treadmill scenario is not a good demonstration of the real cart. One is gaining energy from the ground, the other the wind.

No, I know physics isn't broken, that was...a purposefully provocative statement in the OP.

peanutaxis said:
Right, so the treadmill scenario is not a good demonstration of the real cart. One is gaining energy from the ground, the other the wind.
It is a good demonstration. The real cart gets energy from the ground in the wind frame and the toy cart gets energy from the treadmill in the air frame. The real cart gets energy from the wind in the ground frame and the toy cart gets energy from the air in the treadmill frame. The toy is an accurate and complete demonstration.

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One way to look at a system like this, regardless of its initial conditions or history is to just examine its current state and the state trajectory, i.e how the state is changing. Regardless of how energy was "put into" the object you can look at what it does next, what is the state behavior after the ICs have settled down, or what is the steady state. This isn't broken physics, it's just an initially complex set-up where we have to mindful of the reference frames. For example, how would it have worked if there was no propeller, if the pitch of the blades was reversed, or if it was a brick.

It actually does do what it does. The fact that we may think it's paradoxical or just complicated can't be blamed on physics.

Some related airfoil questions to ponder:
- How can sailboat sail faster than the wind speed?
- How can an airplane fly when the engine thrust is much less the the force of gravity on the plane?

Dale said:
It is a good demonstration. The real cart gets energy from the ground in the wind frame and the toy cart gets energy from the treadmill in the air frame. The real cart gets energy from the wind in the ground frame and the toy cart gets energy from the air in the treadmill frame. The toy is an accurate and complete demonstration.
Hmmmm.

To me - standing stationary on the side watching the real cart - it is ... intuitive that the wind is actually slowed by the propellor which actually transfers energy to the cart.
From the frame of the passing wind what ... intuition/reason would there be for the ground to actually give the cart energy? (So surely in actuality it is not ?)

p.s. Another observation. It seems obvious to me that the hard limit for the real cart is that it can't accelerate air past zero ground speed; it can't (net) accelerate air backwards(from the frame of the ground), because to do so would be to be putting energy into the very energy source that it is taking from: the difference btw ground and air/wind speed.
But from the passing wind perspective I can't see that there is any limit. The ground is accelerating the cart and also accelerating air backwards. Why can't this just continue without bound?
Surely, then, the frame of the ground is the superior perspective.

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peanutaxis said:
To me - standing stationary on the side watching the real cart - it is ... intuitive that the wind is actually slowed by the propellor which actually transfers energy to the cart.
From the frame of the passing wind what ... intuition/reason would there be for the ground to actually give the cart energy? (So surely in actuality it is not ?)
Energy is a frame variant concept. It is conserved in all frames but it is not equal in all frames.

You used the word “actually” a lot with italics. I don’t know exactly what you mean by that, but I guess that you mean some frame independent truth. In which case there is no "actually" about the energy transfer. Using the same laws of physics to analyze the same scenario in two different frames simply results in different explanations for the same outcome.

In the ground/treadmill frame energy is transferred from the wind/air to the cart. In the wind/air frame energy is transferred from the ground/treadmill to the cart. Both frames are perfectly valid perspectives and both use the same laws of physics to produce the same measurable outcome: DDWFTTW.

peanutaxis said:
Surely, then, the frame of the ground is the superior perspective.
If you feel it is superior then use that frame. But then the superior frame for the toy would be the treadmill frame for the same reason. The laws of physics don’t discriminate between the frames, but you are free to.

peanutaxis said:
It seems obvious to me
Indeed, obviousness of some feature is a good reason to pick one frame. The same feature will exist (in an appropriately transformed sense) in the other frame, but indeed it is not obvious. Picking a convenient frame often is based on such features. But inconvenient/not-obvious frames are still valid

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Dale said:
You used the word “actually” a lot with italics. I don’t know exactly what you mean by that, but I guess that you mean some frame independent truth. In which case there is no "actually" about the energy transfer...
Yes, I understand that but I am pushing up against this; trying to bend it to try to understand it better.

Dale said:
If you feel it is superior then use that frame. But then the superior frame for the toy would be the treadmill frame for the same reason. The laws of physics don’t discriminate between the frames, but you are free to.
No! Or rather, you have missed the crux of my point - my previous point about 'wrong' frames of reference being without bound. I'm wondering if you can correct me how I am wrong on this challenge:

- For the real cart, the perspective of the wind is inferior because when considering energy there is no obvious bound on how much energy the cart can get from the ground - why can't it just gain more and more and more energy from the ground and keep accelerating more and more and more air backwards as fast as it wants? I can't see any reason why not.
The ground perspective is superior because it tells me more information when considering energy. When considering energy it tells me that the fan can't decelerate the air further than groundspeed=zero.

peanutaxis said:
I can't see any reason why not.
It is not obvious to me either. But there is guaranteed to be such a reason, even if it is not obvious.

peanutaxis said:
The ground perspective is superior because it tells me more information when considering energy.
And by that exact same criterion the treadmill frame is superior for the toy. This is the correct point made in the Veritasium video. They were not recommending using the inferior frame. They were identifying the superior frame as the treadmill frame, wherein the air is moving and has KE that can be extracted, just as in the ground frame for the real cart. Their point is correct.

peanutaxis said:
I'm wondering if you can correct me how I am wrong on this challenge:

- For the real cart, the perspective of the wind is inferior because when considering energy there is no obvious bound on how much energy the cart can get from the ground - why can't it just gain more and more and more energy from the ground and keep accelerating more and more and more air backwards as fast as it wants? I can't see any reason why not.
For your specific question, assuming that the ground is not affected by the force from the cart is not valid.

This is easier to understand, if you replace the huge Earth, with a less massive floating barge that the cart runs on. The cart's wheels exert a forward force on the barge, accelerating the barge downwind. In the inertial rest frame of the freestream airmass the backwards moving barge is slowing down, so you can see why the energy from the barge in this frame is limited.

But even assuming the ground-airmass-system is resupplied with energy, so the ground-airmass-motion remains constant, the cart won't accelerate forever due to practical engineering limits on efficiency. It will reach a constant speed greater than wind.

peanutaxis said:
The ground perspective is superior because it tells me more information when considering energy. When considering energy it tells me that the fan can't decelerate the air further than groundspeed=zero.
The ground that the cart interacts with, if otherwise isolated, is not an inertial object, so energy conservation doesn't hold in its rest frame.

But in the version with the barge, we can use the initial inertial rest frame of the barge (like the rest frame of the lake that the barge floats in). In this frame the air losses energy, and transfers it to the barge via the cart.

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@peanutaxis
"Another observation. It seems obvious to me that the hard limit for the real cart is that it can't accelerate air past zero ground speed; it can't (net) accelerate air backwards(from the frame of the ground), because to do so would be to be putting energy into the very energy source that it is taking from: the difference btw ground and air/wind speed."

That is the Mark Twain thing for you --'it's not what you don't know that gets you in trouble, it's what you know that just ain't so.'

Think about whirlpools and eddies. Fluid flow is going one direction, and yet somehow some of that fluid winds up going backward relative to the fluid flow. Fluid flow is NOT an infinite series of particle collisions. That is where intuition fails you--and the prof that lost \$10,000 betting that DWFTTW was impossible. If you have a means of leverage over a fluid flow, you can construct an object that can move faster than the fluid flow. The more leverage you have, the greater differential you can attain (ice boats and land-yachts can go faster DWFTTW than sailboats can.) But you will never believe it until you stop thinking of fluid flow as a series of collisions.

Think too about a constriction in a pipe. That results in higher fluid velocity--but no one would say that it is adding energy to the fluid.

Dale
The explanation that works for me may not be the explanation that works for you. I suspect that the explanation that works is the one that most effectively attacks one's personal, seemingly ironclad intuition that the darned thing cannot work.

Preaching to the choir here, I am sure. But the argument that satisfies my intuition is...

I picture a stationary cart on a moving treadmill. Maybe there is a slight upward slant to the treadmill. The belt of the treadmill is moving downward toward the front of the cart. The cart has excellent wheels, lubed up perfectly, tires pumped up fully, maybe steel wheels. Maybe radial tires. Whatever it takes to have near zero rolling resistance. The cart has a huge sail.

The huge sail can almost hold the cart in place. Almost. But that is not good enough. We want the cart to be able to climb the treadmill. No matter how big we make the sail and no matter how good the wheels are, we just cannot make the thing move forward relative to the ground. It inevitably slips backward instead under the combination of gravity and friction at the wheels. Drat!

So we stop and think. We have this belt moving rearward beneath our wheels. It is passing us at a pretty good clip. We could put generators on our wheels and harvest some energy. Sure, that would increase the drag from our wheels. From near zero to something decidedly non-zero. But the sail will still nearly hold us in place. We'll be moving downhill faster than before, but we will have a power source that we may be able to utilize.

Let us utilize that power source.

What if, instead of a huge sail, we use a huge propeller? We are nearly stationary in the air, so we do not have to make the propeller spin very fast or use much power to generate a large thrust. We can use the power harvested from our wheels to drive the propeller.

The obvious objection against this scheme is conservation of energy. Surely one cannot generate enough energy from the wheels to power the propeller that is driving the craft?! But actually, one can. The trick is leverage. Or gear ratio. Or power. Or work. Or however you want to think about it. We are generating power at the wheels with a small drag and a high relative velocity. We are consuming power at the propeller with a large thrust and a small relative velocity. The net thrust can be forward while the net energy balance can also be positive. We can get net forward thrust and still have an energy surplus.

The next objection is still conservation of energy. We have an energy surplus seemingly from thin air. Surely we cannot get something for nothing. Where did this energy come from? In the frame of reference of the cart, the answer is that we are exerting a forward force (from the tires) against the rearward moving belt. This causes whatever motor is driving the belt to have to produce more power to keep the belt moving. So we did not get the surplus energy for free. We got it from the motor driving the treadmill. (Duh -- of course we did. That's the only place where energy is injected into the system).

[I've long since come to terms with the fact that energy, energy flow and even energy flow direction are frame relative concepts. It does not bother me that an explanation focused on another frame of reference may seem significantly different than this one. So I do not bother to present an explanation in a frame-independent way. I just pick a frame and use it]

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peanutaxis said:
It seems obvious to me that the hard limit for the real cart is that it can't accelerate air past zero ground speed; it can't (net) accelerate air backwards(from the frame of the ground), because to do so would be to be putting energy into the very energy source that it is taking from: the difference btw ground and air/wind speed.
This limit is not relevant for the DDWFTTW cart, because the goal is not to extract as much energy per air volume as possible. The goal is to extract just enough energy to offset the losses and continue to accelerate. The goal is to be efficient, and for propellers that means: Accelerate a lot of air by a little bit. So the optimum is not to stop the air relative to the ground, but the opposite: disturb it as little as possible.

There is no hard theoretical limit on how efficient the cart can be made, and how many wind-speed multiples it can achieve.

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jbriggs444