Blackbird debate: Case when speed of car smaller than speed of downwind I am puzzling my head around the Veritasium famous video right now: https://www.youtube.com/watch?v=yCsgoLc_fzI
Also the Physics Olympiad problem Part B1 https://www.aapt.org/physicsteam/2019/upload/USAPhO-2013-Solutions.pdf
I fully understand (I hope) the case when the car has a speed v higher than the speed of wind w it will accelerate until it reaches an constant speed where the power transferred from the wheels is bigger than the power of the propeller.
What is puzzling me is the following experiment: Suppose we have a very long treadmill (so we can simulate the case of constant wind). If we were to just place the car in the treadmill without rolling the wheels. The car would go initially backwards with constant speed the one of the belt backwards. It will create some drag with the air of the room which will cause the car to slowly start rolling forward. When it starts rolloing forward the propeller will rotate as well, but the air is still coming from behind the propeller.
Is it possible that the car exceeds the one of the belt (assuming the aerodynamic shape of the car does not change)?
Will it start rolling forward with speed v greater than w, for any speed w of the belt?
 A: 
Is it possible that the car exceeds the one of the belt

Yes, that is possible. Check out the treadmill videos that they have made, where the small model they built, was able to do this
A: In a follow-up video published on the 30th of June Derek shows a mechanical analog of how the Blackbird vehicle can move downwind faster than the wind.
I will refer to the device that Derek demonstrates there as the 'difference cart'
The two screenshots show how the difference cart is operated.



The difference cart has traction contact both with the floor and the wooden beam.
When pushed from left-to-right (as seen from the camera view in the video), the lower wheels turn clockwise, and the upper wheel turns counter-clockwise.
The difference cart is driven by the difference in velocity between the floor and the moving beam.
The ratios of the wheels determine the ratio between device velocity and the relative velocity of floor and moving beam.
If you would have perfect traction, and no loss to friction, then there would be no upper limit to the velocity that the difference cart can reach as you move to ever more extreme ratio of wheel diameters.

In the case of the Blackbird vehicle (and the small treadmill version) the efficiency is much lower because a lot of the power output of the propeller is lost to creating turbulence. Still, the Blackbird vehicle can harvest enough energy from the difference between air velocity and ground velocity that it can sustain a velocity that is higher than the wind velocity itself.

Minimum velocity
To your question: is there a minimum velocity for the vehicle in order to harvest energy from the difference in velocity between air and ground?
I believe there is indeed a minimum velocity.
In order to be pushed forward the Blackbird vehicle must create an air cushion behind itself. That air cushion behind the propellor must be replenished with sufficient air velocity to make that air cushion collide with the wind coming up from behind. When the propellor is moving slow then pretty much all of the air just escapes and there is next to no buildup of air cushion. Above a certain rotation rate of the propellor the air has less time to escape, resulting in better efficiency. (Still low efficiency, but sufficient)
A: There are three possibilities for how a craft like this could interact with the wind while sitting stationary on the ground.


*Friction prevents the object from moving, upwind or downwind.


*The stationary propellor could act like a sail, pushing the cart downwind. In this case the action of the wheels would engage the propellor and set it spinning, sending the cart off into its faster-than-downwind mode.


*The wind could turn the stationary propellor the wrong way, so that it works as a turbine†. The turbine would drive the wheels the wrong way, pulling the cart upwind.
Which of these actually occurs seems to be a question of wind speed, gear ratios, propellor pitch angles, and efficiencies, rather than any fundamental physics.
Note that the Blackbird has set records not only for traveling downwind at nearly three times windspeed, as discussed in these videos, but also for traveling upwind at twice windspeed.  Adding in the fact that it has brakes, the Blackbird demonstrates that all three travel modes are possible.  This interesting analysis becomes ill-conditioned as the vehicle speed approaches zero.

† I don’t know if I knew this before I encountered this problem a month ago, so I’ll define the terms here: it’s a “turbine” if the fluid flow causes the rotor to turn; it’s a “propellor” if the rotor is causing fluid flow.
