How does down-wind faster than the wind (over-land) really work?

Question

There has recently been posts on youtube where in a land based propeller/fan driven tricycle (blackbird) has been shown to roll faster than the wind that is behind it.

The youtube channel veritasium covered it recently and the topic has apparently been around for a while.

Although veritasium does provide an answer in terms of formulae and additionally explains based on the power in the wheels (which is counter-intuitive to me as noted in the points able), I have an understanding to cross-validate on this (and hence the question) and wanted a confirmation if it was correct. However if it is incorrect, then am at least looking for an explanation in the same sort of layman's terms that I am trying to describe.

Specifically my understanding is as follows -

1. The wind powers the vehicle initially.

2. The wheel's (through gears and chain) drive the propeller.

3. It would be safe to assume that until the vehicle reaches the wind speed, its powered by the wind and as such builds up inertia (and consequently can accelerate).

4. However the explanations (in the veritasium video) tend to focus on the power generated by the wheels to explain the vehicle going faster than the downwind. The problem with this explanation is that it holds only to the extent that the vehicle has expended (exhausted) the potential energy it initially built (from it rolling when it was slower than the wind). Friction would eventually slow it down back atleast to the same speed as the wind. It does not explain how the vehicle is able to sustain it.

5. The question is - what is the force that is allowing the vehicle to sustain the speed ? It definitely can't be the power from the wheels - its built on inertia and friction would cause it to drain its energy back to zero.

6. My understanding is that there should be some physical 'link' that would be between the wind generated from the propeller (propeller-wash?) that compensates for and allows for the 'link' to be re-established between the downwind and the vehicle - analogous to a boatman pushing the boat in shallow rivers/lakes using a stick, the wash from the propeller is the 'stick' and the downwind forms the 'lakebed/riverbed'.

7. Is my understanding correct? If not then what is wrong with my understanding ?

My question is similar to the question posted here - How to sail downwind faster than the wind?

It also has a fairly good answer in the past few days (which I believe draws insights from the videos linked below) but does not clarify on point #5 (on sustainability) - https://physics.stackexchange.com/a/651106/31729

References

1. (A Physics Prof Bet Me $10,000 I'm Wrong) https://www.youtube.com/watch?v=yCsgoLc_fzI
2. (Risking My Life To Settle A Physics Debate) https://www.youtube.com/watch?v=jyQwgBAaBag
3. (CNN Early Start - Blackbird upwind cart) https://www.youtube.com/watch?v=b8MWCvKIi7E
4. (DDW.mov) https://www.youtube.com/watch?v=5CcgmpBGSCI

Answer 1

In an comment I already linked to the moment in the follow-up video were Derek Muller demonstrates a device.

The following may bring the aerodynamics of the Blackbird vehicle into focus. Imagine the design is not weight constrained at all and the propeller can be built as a ducted fan.

For the purpose of the thought demonstration we make the shroud of that ducted fan very long, we can visualize it as a tube that is longer than it is wide, with the propellor halfway along the length.

The effect of that elongated shroud is that air mass is prevented from escaping sideways.

For its propulsion this ducted fan vehicle needs to have traction both with respect to the ground and with respect to the wind.

In idealized conditions there is a uniform wind speed, and the vehicle has all the space to keep going straight downwind. Under those idealized circumstances, once set in motion, the vehicle will reach the top speed (a sustained speed) that the vehicle can attain under the given circumstances. From here on I will refer to that speed as 'cruising speed'.

When the ducted fan vehicle is at cruising speed:
It is necessary that the propellor is moving air from the front of the duct to the rear of the duct. We assume that at cruising speed the vehicle is going faster than the wind, so the vehicle is overtaking the wind. The propellor must exceed that rate of flow, sustaining a surplus of air pressure in the rear half of the duct.

When the vehicle is at cruising speed:
Even though the vehicle is overtaking the wind, the presence of the rear wind still makes it harder for the air in the rear half of the duct to escape the duct. In that sense the rear wind is essential for sustaining the pressure difference.

That is how the ducted fan vehicle can harvest propulsion from the difference in velocity between air and ground.

(In the case of the actual Blackbird vehicle the propellor isn't ducted, so air can escape sideways, but the Blackbird vehicle does go downwind faster than the wind. Apparently without a duct it is still possible to harvest fairly good propulsion.)

Answer 2

It can go faster than the wind in steady state and doesn't have to slow down. It's not using any stored energy for propulsion, so there is no reason why it would ever have to slow down, unless the wind relative to the ground slows down.

Your mistake is trying to apply sequential cause-effect reasoning to a feedback loop. This approach might be intuitive to you, but fails in situations like this. Instead you have to analyse it quantitatively and find the force and power balance.

For correct analyses see:

• 2013 AAPT United States Physics Olympiad Semifinal Exam Solutions (page 10)

• Drela, Mark "Dead-Downwind Faster Than The Wind (DFTTW) Analysis"

• Gaunaa, Mac; Øye, Stig; Mikkelsen, Robert (2009), "Theory and Design of Flow Driven Vehicles Using Rotors for Energy Conversion"

Answer 3

I think every article that I have read is missing the point entirely. The inventors analogy on sail boats going around a pipe is the best in terms of how the wind spins the propeller and that wind hitting the propeller, drives the cart forward. Now how can it go faster than the wind ? Simply put the propeller vanes are acting like sails and are in fact changing the wind direction so that the wind blows off the sails out sideways to the wind direction. That means that the wind from behind is both pushing the cart and deflecting the wind downstream sideways deflection the generated headwind from slowing down the cart. Think of how an electric fan works, the air comes in from all directions including sideways, but discharges for the most part in the same direction away from the fan. For the fans on the Blackbird the air flow is the reverse. The wheels do NOT turn the fan blade pushing the air to the rear of the cart.

Answer 4

Force is not power

Power is force times velocity. It takes less braking force to extract the same kinetic energy in a faster moving object. Conversely, it takes less power to accelerate a slower moving object.

In cruise, the wheels act like regenerative brakes, slowing the vehicle down but extracting power. The propeller does the opposite, expending energy to push the vehicle forward.

Crucially, in the vehicle's frame the ground is moving faster than the air because of wind.

At cruise, the wheels are extracting slightly more power than the propeller consumes (some is lost to friction). But the propeller is providing more force (extra force is needed to overcome drag).

The vehicle pushes the air against the direction of the wind, stealing kinetic energy from the air. Run enough of these and the wind will slow down.