[hamdani yusuf (OP)]

You need to learn to read. I never suggested the need for an additional power source for the car between the conveyors.

You haven't retracted your claim that the land yacht needs a battery to go faster than the wind.

[Halc]

You need to learn to read. I never suggested the need for an additional power source for the car between the conveyors.

You haven't retracted your claim that the land yacht needs a battery to go faster than the wind.

You need to learn to read.  See post 31.

When the size of the pulleys are equal, we get back to my previous picture. Tip speed of bottom wheels are 1 m/s. The car would be stationary wrt observer, or 1 m/s relative to bottom conveyor.
With 2:1 ratio, the car would move 2 m/s relative to bottom conveyor, or 0 m/s relative to top conveyor.

If it's moving at 0 m/sec relative to the top conveyor, the wheel would not be turning at all, which contradicts a 2:1 ratio between the turn rates of the two wheels. Your algebra is off.

With 3:1 ratio, the car would move 3 m/s relative to bottom conveyor, or 1 m/s relative to top conveyor.

It will not.  It will move at 1.5 m/sec right relative to the bottom conveyor and 0.5 left relative to the bottom. Only then is the ratio 3:1 with the wheels turning in the same direction as you have it pictured. If you figure-8 the belt, the wheels will turn with a ratio of 3:1, but in the opposite direction, which gets the car going at 3 m/s as you indicate. The 2:1 ratio makes it go even faster.

When the ratio is negative, like in 8 figure V-belt, the car would move backward.

Your assertion contradicts the algebra. If you want the assembly to move left, the lower pulley needs to be the larger one, regardless of regular or figure-8 looping of the belt.

[hamdani yusuf (OP)]

You need to learn to read.  See post 31.

Do you mean this one?

I read the line in the article: "the rotor (acting like a wind turbine)" to mean that the air drove the propeller, the energy of which was sent to the wheels, which violates energy conservation per my post above. But reading closer, the opposite is what is going on. The rotor acts as a propeller, not a turbine. The wheels apply a braking action and the propeller applies thrust. Thus energy is taken from the air movement and no violation of energy conservation takes place.

I'm sorry for missing this one. I guess I didn't count it since it says nothing about battery.
My analogy shows that bottom wheel always act to push the conveyor belt to the left. It never acts as a brake. It can have tip speed higher than the wind because of the speed multiplication effect provided by the pulley ratio. In the case of land yacht, it's also determined by angle of the blades in the turbine, as explained in Steve Mould's video.

[hamdani yusuf (OP)]

If it's moving at 0 m/sec relative to the top conveyor, the wheel would not be turning at all, which contradicts a 2:1 ratio between the turn rates of the two wheels. Your algebra is off.

Remember that the bright wheel is slippery, hence it can spin in any speed without much problem.  On the other hand, dark wheels always spin according to speed difference between car and conveyor. So, if the car speed is +1 m/s, bottom wheels must spin at 2 m/s tip speed. Bright wheel is then spin at 1m/s tip speed. But that means that its top surface is moving at 2 m/s, which is faster than the top conveyor.

You made me realize that before achieving 1 m/s, the car must accelerate from 0 and gradually increase the speed. At some point, it can't absorb kinetic energy from the top conveyor anymore.
But the experiment shows that the car can move faster than the wind, so there must be something else at play.

[hamdani yusuf (OP)]

Let's analyze the process more thoroughly, for both straight and inverting pulleys. I used spreadsheet to generate the trend.

The left image shows straight pulleys with positive ratio, while right image shows inverting pulleys with negative ratio.
vc : speed of the car
vbc : tip speed of bottom wheels relative to the car
vtc : tip speed of bright wheel relative to the car
vt : tip speed of bright wheel touching top conveyor
dvt : speed difference between highest point of bright wheel and top conveyor

dvt determines the force acted to the car. Negative values means the car is pushed to the right, while positive value means it is pushed to the left.

[hamdani yusuf (OP)]

vc : speed of the car
vbc : tip speed of bottom wheels relative to the car
vtc : tip speed of bright wheel relative to the car
vt : tip speed of bright wheel touching top conveyor
dvt : speed difference between highest point of bright wheel and top conveyor

For those who want to reproduce the table, just use following formula.
vbc = vc - v1
vtc = vbc / ratio
vt = vtc + vc
dvt = vt - v2

Here is an interesting thing. With ratio=-1, dvt is constant. No matter how fast the car is running, it will always feel a push to the right by top conveyor. It seems like the only force countering it is friction. Traction between bottom wheels and conveyor can be a limiting factor. So does the slipperiness of the bright wheel.

[hamdani yusuf (OP)]

Your assertion contradicts the algebra. If you want the assembly to move left, the lower pulley needs to be the larger one, regardless of regular or figure-8 looping of the belt.

Thanks for pointing this out. I guess my intuition is not a good guidance for problems I'm not familiar with.

[hamdani yusuf (OP)]

Here is an interesting thing. With ratio=-1, dvt is constant. No matter how fast the car is running, it will always feel a push to the right by top conveyor. It seems like the only force countering it is friction. Traction between bottom wheels and conveyor can be a limiting factor. So does the slipperiness of the bright wheel.

With ratio of -0.3, the car gets even bigger force as it gets faster.
 

[hamdani yusuf (OP)]

The twisted belt can be replaced by gears to achieve the same effects.

[hamdani yusuf (OP)]

Unless there's some error in my formula, it should be clear beyond a reasonable doubt that the answer to the OP question is yes. My analogy confirms the conclusion of Blackbird team that there is no inherent theoretical limit for going faster than the wind.

[Halc]

The twisted belt can be replaced by gears to achieve the same effects.

This is equivalent to the twisted belt with identical size pulleys top and bottom.
In such an arrangement, there is no speed at which the one wheel will not forever slip at dvt=2.
The size of the yellow idler gears has no effect on the relative rate of turn of the wheels. The only size that matters is the red gears, and you drew those the same.

You also drew the arrow for the large yellow gear larger than the smaller one. The smaller one will turn faster, but indeed, the actual wheels with the red gears will turn the fastest as you have drawn them.

[hamdani yusuf (OP)]

This is equivalent to the twisted belt with identical size pulleys top and bottom.
In such an arrangement, there is no speed at which the one wheel will not forever slip at dvt=2.
The size of the yellow idler gears has no effect on the relative rate of turn of the wheels. The only size that matters is the red gears, and you drew those the same.

You also drew the arrow for the large yellow gear larger than the smaller one. The smaller one will turn faster, but indeed, the actual wheels with the red gears will turn the fastest as you have drawn them.

Thanks for pointing out those facts. Looks like we can solve problems better by collaboration.

[hamdani yusuf (OP)]

The left image shows straight pulleys with positive ratio, while right image shows inverting pulleys with negative ratio.

It seems counter-intuitive that both straight and negative ratio push the car to the right. So, it's understandable that many of us got it wrong. Only after thorough analysis the whole process becomes clear.

[hamdani yusuf (OP)]

Someone from twitter shared an old video demonstrating this experiment in simplified version.

[hamdani yusuf (OP)]

Here is a diagram showing the setup from the video. No slippery wheel is used. Instead, to simulate wind, the top conveyor can be made slippery. All wheels are non-slippery type. The ratio is inverting.

[hamdani yusuf (OP)]

The result of the wager.

Professor @alexkusenko has graciously conceded the wager.
Changing your mind in light of new evidence is the hallmark of a great scientist.
I want to thank Alex for the many good points he raised, which have sharpened my thinking about this problem. https://t.co/UEzYHsYjd9

https://twitter.com/veritasium/status/1407566432699781126?s=19

[MarkV]

Here is a diagram showing the setup from the video. No slippery wheel is used. Instead, to simulate wind, the top conveyor can be made slippery. All wheels are non-slippery type. The ratio is inverting.

Not quite. Note the two different radii of the spools used in the video. The are key to have it move faster than the ruler. I'm attaching the diagrams for various examples, including the formula to compute their speed.

[hamdani yusuf (OP)]

Not quite. Note the two different radii of the spools used in the video. The are key to have it move faster than the ruler. I'm attaching the diagrams for various examples, including the formula to compute their speed.

What would happen if R=r?

[MarkV]

Not quite. Note the two different radii of the spools used in the video. The are key to have it move faster than the ruler. I'm attaching the diagrams for various examples, including the formula to compute their speed.

What would happen if R=r?

Then Coco from the video would be right: It can't work at all. It would slide or lock or break.

[MarkV]

In the frame of Earth, the rotor accelerates the air since it is pushing from behind.

When going downwind faster than the wind, the rotor speeds up the air relative to the cart, which implies slowing down the air relative to the ground. It extracts wind energy by reducing the velocity difference between air & ground.