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(I have read the other question related to this topics here on physics.stackexchange, but the answer there is too general and I want to address some details about the vehicle and the validity of the test run so I ask a new one)

I have recently come across a land vehicle called Blackbird, the inventor of which claims that it can run directly downwind faster than wind. It is sponsored by Google and there were some tests which showed that the vehicle can run up to 2.8 times the windspeed.

I find it really interesting so I did some search about the topic on the internet. After reading several articles and forum threads related to the topic, I am still confused about how it exactly works.

To begin with, the explanation of the team that built the vehicle can be summed up as follows: wind pushes the frame of the car, which makes the wheels roll, the wheels then rotate the propeller, the propeller extract wind power to produce thrust that drives the car forward. How can a propeller do such thing? How can it use power out of the wind to create thrust in a direction opposite to the wind (when it has already exceeded wind speed)?

Secondly, I have also looked at some formulas that are claimed to be the description of how the vehicle works. One formula (from a professor named Mark Drela, link at the end) shows zero propeller power when the vehicle speed equals wind speed, so apparently the vehicle could not exceed wind speed, but it could still accelerates given it is already at a speed greater than wind speed. How could it reach 2.8 times the wind speed from zero velocity in the test?

This confusion also led me to doubt the actual test itself, so I searched further and found a thread on international skeptics forum, in which there are some who critized the way the data was measured and processed. In particular, the measurement data was processed by the inventors, not by a third party, which raises doubts about transparency, the placement of measurement instrument and data processing after the test could also hide gust and change in wind direction (making it not directly downwind). Why couldn't they just test in a wind tunnel?

Could someone explain whether this works. If so, what is wrong in my understanding of the way it works?

Link to Mark Drela formula: https://www.boatdesign.net/attachments/ddw2-pdf.28167/

tlong
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Yes this does work, but the blades work opposite of, say a windmill which is turned by the wind. Initially the wind blows on the blades, which act more like a sail, to begin pushing the craft forward. This causes the wheels to rotate, the wheels are connected to the blades to turn them to push air back against the wind. this creates a higher pressure on the blades than a flat sail would get as it approached wind speed. This higher pressure can push it past the wind speed.

Adrian Howard
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The blackbird, initially imagined by aerospace engineer Rick Cavallaro, was co-developed by the aeronautics departments of an university, the San Jose state university, and supervised and recognized by the North American Land Sailing Association (NALSA). Furthermore the calculations of MIT professor Dr. Mark Drela (as well as of a research group of the Technical University of Denmark) showed already in 2009 in quite a straight-forward manner for both water and land vehicles in a downwind configuration how this is possible even before the actual full-size vehicle was test driven for the first time in 2010. Additionally there have been similar efforts previously (see Aeolus Racing and Greenbird). An exhaustive article on the topic by Wired can be found here and a good video report by Discovery Channel here.

There are two different configurations for each water and land vehicles depending on the rotor design of the rotor ("propeller"): Up- and downwind. In the upwind configuration the vehicle harvests the energy like a wind turbine and transfers it to the wheels. In the downwind configuration on the other hand the flow and the vehicle move into the same direction. The former is rather intuitive (basically a wind turbine on wheels) while the latter might seem unphysical at first.

Downwind configuration

In the end it boils down to the fact that the power generator experiences a different velocity than the power consumer and that the wheels and the rotor are coupled to some sort of feedback loop. Disk actuator theory (as a model for the propeller) can be used to estimate the efficiencies for the propeller and then the resulting equation is put into a dimensionless form (something common in fluid mechanics as it makes the results somewhat independent of the problem size). The resulting force (from thrust and drag) must compensate the resistance forces (roll and air resistance). The curves given at the end of the linked document describe the ratio of terminal velocity (steady-state) to wind speed depending on the dimensionless thrust coefficient. The results for water and land vehicles are different due to different efficiencies and resistance coefficients. As you can see the results for land vehicles with $\eta_{net} = 0.8$ are pretty similar to what was actually achieved in the test run.

According to the articles listed above several people have already designed working small-scale prototypes going faster than the wind but a large group of individuals still believed these to be hoaxes. Additionally as you can see from the curves in the document the whole experiment relies on the efficiencies: It is questionable how a model performs compared to full-size model. The reason why they did not test the full-size prototype it in a wind tunnel are its operating conditions: The thing seems to be approximately 6 m tall, is operating at only 16 km/h and needs the speed of the wheels to be synced to the wind speed. Finding an appropriate wind tunnel fulfilling the size requirements of an actual full-size prototype is already challenging (only leaving a hand full world-wide, most wind tunnels are intended for small-scale models) and I don't think there even exists a moving ground wind tunnel (such as used for Formula 1 cars) of that size. A real-world test on the other hand is quite straight-forward and offers real insight into achievable efficiencies.

I think you are misunderstanding formulas \eqref{1}-\eqref{3} given in the document:

$$P_t = F_t \, V \, \eta_t \tag{1}\label{1}$$

$$P_p = \frac{F_p \, (V-W)}{\eta_p} \tag{2}\label{2}$$

$$P_p = P_t \, \eta_g \tag{3}\label{3}$$

Formula \eqref{3} states that the power generated by the turbine or wheels $P_t$ must be consumed by the propeller $P_p$ in steady-state. The shafts and gears are assumed to move with a constant rotational speed meaning there is no energy required to accelerate the entire drivetrain (which would require a certain moment of inertia) but it is not assumed completely loss-less, the efficiency $\eta_g$ takes into account mechanical losses due to friction. As a result the propeller is only supplied a fraction of the power of the power generated by water turbine/wheels.

For $V = W$ indeed the propeller consumes no power even though the turbine/wheels supply a certain amount $P_t > 0$. This means that this power will be used to accelerate the drive-train and the propeller which increases $F_p$ and as a consequence accelerates the vehicle to a higher velocity $V$ resulting in a larger relative velocity $V - W$. A steady-state operation at this point is not possible (for this particular setup and $P_t > 0$); this is why the curves in the document end before the vertical value $\frac{V}{W} = 1$. The entire concept is based on a feedback loop (coupling) between wheels and rotor as well as clever design.

In the end the whole setup indeed works but lacks real practical applications: You would have to change the setup depending on the wind direction. Nonetheless I think this is really an interesting concept from a theoretical view similar to the Flettner rotor working with the Magnus effect (check it out if you have never heard of it!). It sounds like magic at first but is only a clever use of physics!

2b-t
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    This is a great answer that ought to silence all the critics (but of course it won't). – D. Halsey Dec 26 '19 at 16:06
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    how can the wheel generate power at v=w? the wind is not pushing anymore. Please explain it in the frame of reference of the ground – tlong Dec 26 '19 at 16:22
  • @tlong The translational velocity of the vehicle $V$ is correlated with the rotational speed $\omega$ of a wheel of radius $R$ by $V = \omega , R$. So similarly to the translational power $P = F , V$ (which is used for the water vehicle) for a torque $T$ the power is given by $P = T , \omega$. – 2b-t Dec 26 '19 at 16:53
  • I think you misread my question, at v=w, in the RoF of the ground, what gives power to the wheel? – tlong Dec 26 '19 at 17:04
  • @tlong Simply watch this: https://www.youtube.com/watch?v=LjLPPInzSzI – 2b-t Dec 26 '19 at 20:19
  • this is just a brief explanation and does not provide further detail or answer anything related to what I have asked – tlong Dec 27 '19 at 00:39
  • @tlong I thought the explanation with the feedback loop and the part where you see the orange ribbons move depending on the speed of the vehicle would help: The rotor first acts like a turbine, harvests energy to power the wheels then when you come close to $V = W$ the wheels will start to power the rotor acting as a propeller until you reach the equilibrium between thrust, drag, air resistance given by the steady-state calculations we have discussed at length already. – 2b-t Dec 27 '19 at 00:49
  • I think you've got it wrong, what the inventor said (I've summed it up in my original post) is that wind pushes the frame of the car, which makes the wheels roll, the wheels then rotate the propeller, the propeller extract wind power to produce thrust that drives the car forward, the prop does not turn in the direction of a turbine (if you look at the footage of the test run, it is easy to see). And the discussion of the formula is not finished as none has answer my question: what push the wheel when v=w? – tlong Dec 27 '19 at 00:58
  • @tlong Have a look at the Veratasium video about this that came out some day ago in case you are still interested: https://www.youtube.com/watch?v=jyQwgBAaBag – 2b-t Jun 02 '21 at 14:26
  • @2b-t Do you happen to know of any reference which derives a theoretical maximum terminal velocity irrespective of efficiencies? Say, in terms of the gear ratio coupling the propeller to the wheels and the pitch angle of the propeller? I'm trying to determine if such a bound I believe I've worked out is known. – jawheele Jun 23 '21 at 20:56
  • @jawheele I don't know about any but you should be able to derive it pretty easily by analogy with draft in the link given above. As you have air resistance there will be some limit to it... – 2b-t Jun 24 '21 at 19:09
  • Hmm, I had taken a look at that, and it doesn't seem quite what I was looking for. Or, at least, if it does imply something equivalent, a good bit of translating is required. Thanks for your insight! – jawheele Jun 25 '21 at 06:49
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If you want a simple intuitive way to understand it, try this.

You know how you can squeeze a wet watermelon seed and make it shoot out from between your fingers? It's based on wedge action.

Now let it be a sailboat with a centerboard, so the boat can only go in one direction. The sail is at an angle to the centerboard, and that angle forms a wedge, like this:

enter image description here

The boat is like the watermelon seed, and it's being squeezed between the centerboard and the wind. So that way, the boat can sail across the wind at virtually limitless speed.

Now let the direction of the boat turn downwind. Not completely downwind, but only 45 degrees or so. You can still get the same effect.

enter image description here

As you can see, it depends on there being a narrow angle between the sail and the centerboard of the boat.

In the car, instead of a sail on a mast you have a propeller blade on a stick, and instead of a centerboard you have wheels and gears that constrain the direction traveled by the blade. Since the "sail" is rotating, it is not going directly downwind, but at an angle like maybe 45 degrees off of downwind. You still get the squeezed watermelon-seed effect.

Mike Dunlavey
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  • analogies can be misleading, what you are saying the prop simultaneously harvests wind power and generates forward thrust against the wind when vehicle speed > wind speed, correct? If that is the case then I think this would violate conservation of momentum, because if wind power is extracted, wind slow down, and so the momentum vector of wind after passing through the prop has smaller magnitude but still points in the same direction compared to itself before pasing through the prop. By conservation of momentum the momentum of the prop would also points backward, not forward. – tlong Dec 27 '19 at 00:37
  • @tlong True - analogies can be misleading but it clearly demonstrates that depending on the physical mechanisms involved you can indeed go significantly faster than the speed of the wind, something that seems counter-intuitive to most at first. Furthermore as already pointed out by Adrian Howard it is the pressure difference that keeps the propeller going faster, not the wind. You have to look at the system as a whole not at the isolated phenomena. Furthermore there are several universities that have replicated this with their own vehicles. – 2b-t Dec 27 '19 at 01:03
  • @tlong: Try to look at it a little differently. A single propeller blade is following a diagonal path downwind, not a direct path. It is angled in such a way that when the wind hits it, the wind is slowed down, transferring momentum to the blade. Another way to think of it: the propeller acts as a fan blowing backward faster than the wind. Another explanation, which you should have seen before, but if you didn't here it is again. – Mike Dunlavey Dec 27 '19 at 02:02
  • @2b-t no matter how you look at the system, as a whole or at each part of it, conservation of momentum, and energy cannot be violated, but here if the vehicle works as what the inventor decribes, then the it violates conservation of momentum. – tlong Dec 27 '19 at 02:18
  • @Mike Dunlavey as I said, if the wind slow down after passing the prop, and the prop gain forward momentum then conservation of momentum is violated. – tlong Dec 27 '19 at 02:20
  • @tlong: No, conservation of momentum is not violated. Regardless of how fast the car goes, each parcel of air (in the wind) encounters a surface which is not moving as fast as the air is, so the air pushes it. – Mike Dunlavey Dec 27 '19 at 02:23
  • I am talking about the conservation of mometum considering the interaction between wind and prop. If wind power is extracted, wind slows down, and so the momentum vector of wind after passing through the prop has smaller magnitude but still points in the same direction compared to itself before pasing through the prop. By conservation of momentum, the prop momentum vector needs to point backward, not forward. – tlong Dec 27 '19 at 02:40
  • @tlong Figure 2 on page 5: http://projects.m-qp-m.us/donkeypuss/wp-content/uploads/2009/06/Bauer-Faster-Than-The-Wind-The-Ancient-Interface.pdf – 2b-t Dec 27 '19 at 02:47
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    @tlong: Yes, the wind slows down, because the propeller blades beat back against it. That does not mean the propeller as a whole is moving slower than the wind. Rather *the surface that the wind sees* is moving slower than the wind. If you would, please examine again the second image here. I edited the answer to try to make the point. – Mike Dunlavey Dec 27 '19 at 17:02
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Your confusion is understandable. The gist: there is nothing special¹⁾ in the situation when the speed of the vehicle is exactly the same as the speed of the wind. Indeed, to accelerate, you need to “push against the wind”. However, pushing does not take any energy as far as you are not moving against what you push!

¹⁾ Well, there is something special: you can achieve arbitrarily large acceleration. (See below!)

With a big enough (well-designed) propeller, you can push-against-the-wind arbitrarily strongly with a tiny energy spent — as far as the wind velocity is close to 0. So take some energy from the wheels (e.g., attach a generator to the wheels); this would put some breaking force on your vehicle — but using the obtained energy, you can overpower an arbitrary strong breaking force — and accelerate your vehicle beyond the wind speed!

I explain in another answer how “the gear ratio” between the wheels and the propeller affects the speed one can achieve.

Ilya Zakharevich
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