# 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?

• Why do you think the airspeed here is any different from the airspeed of a "true" wind when the vehicle is on a road rather than a moving belt? Jul 2, 2021 at 12:00
• The maximum speed of these DDWFTTW vehicles is a direct function of the gear ratio from wheels to propellor (aside from various friction things). Jul 2, 2021 at 12:01
• The same applies for true wind, I am not saying it is different. This helps with the concept of constant wind which outdoors is more difficult to achieve. Jul 2, 2021 at 12:53
• @VincentThacker No, that is not true. It is not wind to propeller to gears to wheels. The propeller is being driven by the wheels. SO it is wheels to gears to propeller. So, in essence , the wind is not pushing the propellers or the vehicle. Rather, the propellers is "pushing off" on the wind. Imagine a rope being pulled by some car. If you held on to the rope, then you could never go faster than the velocity of the vehicle. But if you pulled on the rope ( which in this analogy is what the blackbird is doing), then u can go faster than the car Jul 2, 2021 at 13:11
• The treadmill test is in the linked video. It doesn’t work until their fourth prototype; skip to timestamp 15:00.
– rob
Jul 2, 2021 at 13:25

## 3 Answers

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

• They keep the car at a point to gain speed on the wheels until it is steady compared to the ground (with a fork). Then they release it. Jul 2, 2021 at 13:25
• Yes, then what you are asking can be done, is what they show in the actual vehicle video . There they did not do the equivalent of keeping the car at a point on the treadmill to gain speed on the wheels. There the vehicle started from much lower than the windspeed. So, we can say that what you are asking can be done. Jul 2, 2021 at 13:45
• @Sanandrea I know that in the treadmill video, that is what they do. That is because , they do not have a long enough treadmill to do what you suggested. Which is why to see them do what you require to be done, look at the original video, there they do not have any such distance constraints at that large dry lake. If you understand why the treadmill is an analogy of the real thing, then you should be able to understand , why the hypothetical situation that you are asking to be done on the treadmill is equivalent to what they did with the actual vehicle. Jul 2, 2021 at 14:00
• The question is to quantify SUPER WINDY! Jul 2, 2021 at 14:30
• @Sanandrea Obviously , it is. If this cutoff speed was lower than the downwind speed, then they would not have needed to give him the initial push Jul 2, 2021 at 18:09

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)

• my question is: is that minimum velocity bigger than the speed of wind? Jul 2, 2021 at 21:05

There are three possibilities for how a craft like this could interact with the wind while sitting stationary on the ground.

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

2. 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.

3. 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.

• going up wind and and goind downwind with speed v > w is the same case. In both cases the wind comes in front of the propeller. Jul 2, 2021 at 21:03
• @Sanandrea I am not sure that is correct. There is at the very least a difference in (optimal) gearing. The more I think about this problem, the less I trust my intuition about "obvious" symmetries.
– rob
Jul 2, 2021 at 22:37
• @rob - believe the understanding is that the 'blade' is pushing the vehicle. So that way its a fan/propeller than a turbine. Jul 19, 2021 at 21:16