Undergrad DDWFTTW: Looking for the least confusing explanation

[Vanadium 50]

I've avoided these discussions thus far - I find them confusing force and energy, and the use of a boating analogy to people who have never sailed (I know that's not you, @anorlunda ) isn't helpful. I also think treadmill analogies are not helpful either.

I maintain that thinking of this in terms of wind energy is unhelpful, because with an infinite volume of air, there's an infinite amount of energy that can be extracted from it. (In real life, replace "infinite" with "very large")

1. Consider a cart with a sail, going exactly as fast as the wind. Do the wheels have to be frictionless? The answer is no, the requirement is that the thrust from the wind is equal to the drag from air plus from the wheels. If I have more wheel friction, I need a larger sail, to be sure. Agree?

If you think you understand, answer this: You are riding in this cart at the speed of the wind, and the brakes are partially engaged. What happens when you release the brakes? The answer is - nothing.

2. Consider a cart with a sail, going exactly as fast as the wind. A battery-powered fan is mounted on it, to move air from the front to the rear, but avoiding the sail. The fan is switched on. What happens to the cart? It accelerates forward. Agree?

Our cart is now going downwind faster than the wind. No problem here - it has its own power source.

3. Now we put the two together. The wheel brakes are taken from a Toyota Prius, and so generate electricity. I remove the battery and use this electricity to power my electric fan. And there we go.

Of course we can then replace the electrical system with a purely mechanical one.

 

[jbriggs444]

3. Now we put the two together. The wheel brakes are taken from a Toyota Prius, and so generate electricity. I remove the battery and use this electricity to power my electric fan. And there we go.

Key, of course, is that the power generated by the one exceeds the power requirements of the other.

From the craft-relative frame, the ground is moving fast and the air slow. So powering a generator with a given force from the ground generates more energy than is required for a propeller to apply the same force to the slowly moving air.

 

[A.T.]

1. Consider a cart with a sail, going exactly as fast as the wind. Do the wheels have to be frictionless? The answer is no, the requirement is that the thrust from the wind is equal to the drag from air plus from the wheels. If I have more wheel friction, I need a larger sail, to be sure. Agree?

At exactly wind speed (going parallel to it) the force on the sail would be zero, no matter how large you make the sail. So a passive sail cart could only stay at windspeed if the drag from the wheels was zero. For a non-zero drag you can approach windspeed from below by making the sail larger, but never quite reach it.

You are riding in this cart at the speed of the wind, and the brakes are partially engaged. What happens when you release the brakes? The answer is - nothing.

Not nothing. It would get closer to windspeed.

3. Now we put the two together. The wheel brakes are taken from a Toyota Prius, and so generate electricity. I remove the battery and use this electricity to power my electric fan. And there we go.

As @jbriggs444 points out: This will only work if the fan produces more thrust than the wheel drag needed to power the fan. And the key point that makes this possible is the difference in cart-relative-velocity of ground and air, as the video mentions briefly.

 

[A.T.]

Key, of course, is that the power generated by the one exceeds the power requirements of the other.

From the craft-relative frame, the ground is moving fast and the air slow. So powering a generator with a given force from the ground generates more energy than is required for a propeller to apply the same force to the slowly moving air.

Derek just added a pinned comment to emphasize this point:

"The key is that we're harvesting power at higher speed, lower force, and deploying it at lower speed, higher force (which is only possible because we have a tailwind - in still air this wouldn't work because the relative velocity of the wheels over the ground would be exactly the same as the relative velocity of the prop through the air)."

 

[rcgldr]

Derek just added a pinned comment to emphasize this point:

"The key is that we're harvesting power at higher speed, lower force, and deploying it at lower speed, higher force (which is only possible because we have a tailwind - in still air this wouldn't work because the relative velocity of the wheels over the ground would be exactly the same as the relative velocity of the prop through the air)."

This also works for upwind faster than the wind. A propeller like windmill is used to drive the wheels, harvesting power from the air at higher speed, lower force, and deploying it to the ground at lower speed, higher force. The Blackbird was modified to do a DUWFTTW run.

I don't like the propeller acting as a pair of tacking sailboats analogy, as the key is interacting between two media moving at different speeds with respect to each other. A propeller just happens to be an efficient way to generate thrust. There is also a significant difference. At high speed on a tacking sailboat, the apparent wind is almost a headwind (small Beta angle), and most of the lift force is perpendicular to the boat, coexistent with an opposing force from the water | land | ice, with no contribution to the boats speed, and only a small component of the lift is in the direction of the boat's heading that contributes to the boats speed. For the blades of a propeller, the apparent wind is even closer to a headwind, but in this case, the lateral component of lift is contributing to almost all the thrust, while the "forwards" direction of lift and drag combine to produce a rotating air column behind the propeller.

In the case of a geared device interacting between two moving surfaces, power losses aren't an issue, and there is nothing that could be construed to be similar to tacking. Similar to a DDWFTTW cart, the gear ratio is setup so that table speed is greater than ruler speed, resulting in the cart moving under the ruler faster than the ruler. Skip to 1:47 into the video to see the movement.

This concept isn't new. It was used in the 1877 Brennan Torpedo. On the dock, there were two steam driven spools that pulled in wire, while on the torpedo, there were two spools that geared down and drove a propeller as the wires were unspooled. Same principle, power is harvested from the wires at higher speed, lower force, and deployed to the torpedo propellers at lower speed, higher force. If the wires were instead attached to posts on a bridge above a stream, then a Brennan Torpedo would move downstream faster than the stream.

https://en.wikipedia.org/wiki/Brennan_torpedo

As noted in Veritasium's video, there's also another requirement. From a ground frame of reference, the true wind has to be slowed down in order to provide an energy source, which occurs due to the backwards thrust from the DDWFTTW propeller. From the cart's frame of reference, the surface of the Earth is slowed down a very tiny amount (huge mass), in order to provide an energy source, which occurs due to the forward force the wheels exert on the Earth's surface.

 

[A.T.]

I don't like the propeller acting as a pair of tacking sailboats analogy, as the key is interacting between two media moving at different speeds with respect to each other.

You need a relative velocity between air and surface in both cases: tacking boat and DDWFTTW cart.

There is also a significant difference. At high speed on a tacking sailboat, the apparent wind is almost a headwind (small Beta angle), and most of the lift force is perpendicular to the boat, coexistent with an opposing force from the water | land | ice, with no contribution to the boats speed, and only a small component of the lift is in the direction of the boat's heading that contributes to the boats speed. For the blades of a propeller, the apparent wind is even closer to a headwind, but in this case, the lateral component of lift is contributing to almost all the thrust, while the "forwards" direction of lift and drag combine to produce a rotating air column behind the propeller.

There is no significant difference if you compare them correctly: The motion of the boat corresponds to the motion a propeller blade section, not to the motion of the cart chassis.

Here the vectors for tacking downwind with VMG > WS:

And here the same vectors for a section of the DDWFTTW propeller blade:

Not in the diagram but easy to see: Both (sail force, blade force) have substantial DDW components, which are partially canceled by the DUW components of the forces from the keel or the wheel coupling.

 

[rcgldr]

> You need a relative velocity between air and surface in both cases: tacking boat and DDWFTTW cart.

I've always agreed with this and noted in prior posts that the vehicles exploit this since the relative velocity of the free stream and ground remain constant regardless of the vehicle's speed (also noting that the apparent crosswind component for a fixed heading and constant true wind remains constant regardless of the taking boats speed).

Not in the diagram but easy to see: Both (sail force, blade force) have substantial DDW components, which are partially canceled by the DUW components of the forces from the keel or the wheel coupling.

True, but what propels the boat is the relatively small forward component of lift (opposed by drag from the air and water, or in the case of an ice boat mostly from the air, since there is very little drag friction with ice), while what propels the DDWFTTW cart is the relatively large DDW component of lift, although this is opposed by the DUW force from the wheels.

The other issue is that if not for efficiency issues, there could be a method of DDWFTTW thrust that does not resemble tacking, such as a turbine with it's main axis perpendicular to the cart, that in theory could work if somehow it was efficient enough. The key as posted earlier is energy is extracted at higher speed, lower force, and geared down to deploy energy at lower speed, higher force, despite the losses in conversion. This part of the concept doesn't require something similar to tacking.

 

[A.T.]

True, but what propels the boat is the relatively small forward component of lift (opposed by drag from the air and water, or in the case of an ice boat mostly from the air, since there is very little drag friction with ice), while what propels the DDWFTTW cart is the relatively large DDW component of lift, although this is opposed by the DUW force from the wheels.

You are again using the wrong correspondence:

"Propelling the boat along its diagonal heading" corresponds to "propelling the prop blade along its helical path", not to "propelling the cart DDW".

There is no substantial difference, if you decompose the vectors in a consistent manner for both cases. For example: parallel and orthogonal to the true wind.

 

[rcgldr]

You are again using the wrong correspondence:

"Propelling the boat along its diagonal heading" corresponds to "propelling the prop blade along its helical path", not to "propelling the cart DDW".

There is no substantial difference, if you decompose the vectors in a consistent manner for both cases. For example: parallel and orthogonal to the true wind.

Part of the issue is that unlike a wing or sail, the propeller is operating in the induced wash ahead of the propeller. If the DDWFTTW cart is moving at true wind speed, then the situation is similar to a helicopter in hover, zero relative free stream speed, but an induced wash in the opposite direction of the true wind, before that wash reaches the propeller, which changes the direction of the apparent wind from the perspective of the blades of the propeller. (For a helicopter in a hover, there is a downwards induced wash above the rotor).

Another difference is that a sail is driven by the wind, while a propeller is driven by a torque at it's axis.

 

[A.T.]

Part of the issue is that unlike a wing or sail, the propeller is operating in the induced wash ahead of the propeller.

This is not completely "unlike the sail", because the sail also affects air in front of it. Pressure differences propagate at the speed of sound in all directions. But it is true that the compactification of the wide tack into a helix within a cylindrical volume might increase the impact of this effect.

Another difference is that a sail is driven by the wind, while a propeller is driven by a torque at it's axis.

That is wrong correspondence again. The torque/rotation corresponds to the forces/motion along the cross-wind direction. And along the cross-wind direction the boat is driven by the keel force, not by the sail force. The cross-wind sail force component (pointing right in the diagram) opposes the cross-wind motion (pointing left in the diagram) .

Again: There is no substantial difference, if you decompose the vectors in a consistent manner for both cases.

 

[rcgldr]

Again: There is no substantial difference, if you decompose the vectors in a consistent manner for both cases.

OK, but say the propeller on the DDWFTTW cart is replaced by an efficient turbine with an axis perpendicular to the true wind and direction of the cart? Other than the issue of efficiency, it should still work.

On a side note, a helicopter in a hover requires much more power than a helicopter in forward level flight due to operating in the induced wash while in a hover.

 

[A.T.]

OK, but say the propeller on the DDWFTTW cart is replaced by an efficient turbine with an axis perpendicular to the true wind and direction of the cart? Other than the issue of efficiency, it should still work.

Not sure I understand what you are proposing here.

 

[A.T.]

On a side note, a helicopter in a hover requires much more power than a helicopter in forward level flight due to operating in the induced wash while in a hover.

This might indeed impact the performance of the DDWFTTW cart at WS, more than it impacts the performance of the boat at downind VMG = WS. But for steady state above WS it makes no substantial difference to the boat at downind VMG > WS.

 

[rcgldr]

This might indeed impact the performance of the DDWFTTW cart at WS, more than it impacts the performance of the boat at downind VMG = WS. But for steady state above WS it makes no substantial difference to the boat at downind VMG > WS.

There's still an induced wash ahead of the prop, say short of 0.6 mach which might slow down the reaction.

I guess my issue is I view the DDWFTTW cart as just one example of the principle of interacting with two media moving at different speeds, for the DDWFTTW car, the two media are air and land, for the Brennan torpedo, the two media are wires and water, for a yoyo being pulled, the two media are the string and table top, for the under the ruler cart, the two media are ruler and table top, and for the last two examples, you just have rolling motion that doesn't resemble tacking.

 

[A.T.]

There's still an induced wash ahead of the prop, say short of 0.6 mach which might slow down the reaction.

The same applies to the sail. Pressure differences that the sail induces also propagate faster than the boat.

I guess my issue is I view the DDWFTTW cart as just one example of the principle of interacting with two media moving at different speeds, for the DDWFTTW car, the two media are air and land, for the Brennan torpedo, the two media are wires and water, for a yoyo being pulled, the two media are the string and table top, for the under the ruler cart, the two media are ruler and table top, and for the last two examples, you just have rolling motion that doesn't resemble tacking.

Nobody claims that the tacking analogy explains some general principle. In fact, for most people it explains nothing, because they don't understand downwind VMG > WS (and that includes many sailors). The point of the analogy is rather that we already have windpowered vehicles, that can beat a balloon in a downwind race, for decades (in the case of iceboats for a century).

 

[A.T.]

UPDATE: Prof. Alexander Kusenko (UCLA) thinks DDFTTW is impossible and has a 10000$ bet with Derek Mueller (Veritasium):
https://www.vice.com/en/article/pkb...de-a-dollar10000-bet-over-the-laws-of-physics

Kusenko posted his arguments here:
https://docs.google.com/presentatio...sKDkhEfN898K4/edit#slide=id.gdc0eb9892c_0_180

And a key clarification regarding the frame of reference he used for his power analysis here:

Unfortunately they didn't specify how the bet will be settled, so there is now a back and forth:

 

[A.T.]

Derek Mueller has posted his rebuttal to Kusenko's arguments:
https://docs.google.com/presentatio...cobNtY2AEqybY/edit#slide=id.gdc0eb9892c_0_180

Derek also posted the raw footage from his ride:

 

[A.T.]

In the latest version of his slides Prof. Kusenko, has presented his theory of why the DDWFTTW models are advancing against a treadmill belt (even against a slope):

It seems to be based on that single video, and ignoring other similar tests. But even in that specific clip, the cart advances from the very rear of the treadmill (0:43-0:45), so it would be climbing that potential energy hill, he envisions in his slide:

 

[A.T.]

It looks like Prof. Kusenko has conceded the wager:

 

[A.T.]

It looks like Prof. Kusenko has conceded the wager:

After admitting to being wrong about DDWFTTW being possible, Prof. Kusenko still thinks he has a better understanding of how it actually works, than the people who build the Blackbird, or those who published previous analyses correctly predicting its behavior. Here is Prof. Kusenko's explanation:

https://docs.google.com/presentatio...KDkhEfN898K4/edit#slide=id.gb6e540a45a_618_51

When the car is moving faster than the wind, the passing air pushes the propeller in the same direction as the wheels push it. This has been a subject of discussion, and Blackbird has a ratchet to prevent the propeller from actively spinning the wheels, but the ratchet does not keep the propeller’s wind power from spinning the propeller itself, adding the torque in the same direction as the wheels.

 

[A.T.]

After admitting to being wrong about DDWFTTW being possible, Prof. Kusenko still thinks he has a better understanding of how it actually works, than the people who build the Blackbird, or those who published previous analyses correctly predicting its behavior. Here is Prof. Kusenko's explanation:

https://docs.google.com/presentatio...KDkhEfN898K4/edit#slide=id.gb6e540a45a_618_51

Here is why I think Prof. Kusenko's alternative explanation is wrong:

 

[jbriggs444]

Amazing how much blithering one can do talking about a turbine when the relevant mechanism is a propeller.

 

[pbuk]

Amazing how much blithering one can do talking about a turbine when the relevant mechanism is a propeller.

Yes Kusenko talks a lot of nonsense, but to be clear when traveling DDWFTTW the thing that looks like a propeller is not acting as a propeller, it is acting as a turbine: extracting kinetic energy from a fluid and using it to drive the wheels.

 

[jbriggs444]

Yes Kusenko talks a lot of nonsense, but to be clear when traveling DDWFTTW the thing that looks like a propeller is not acting as a propeller, it is acting as a turbine: extracting kinetic energy from a fluid and using it to drive the wheels.

I believe that you have that backward.

In a downwind configuration, the relative headwind is passing slowly and the ground is passing rapidly. You win by using a propeller to gain high thrust from the wind with a low power requirement while the wheels provide high power from the ground at an expense of low drag.

In an upwind configuration, the relative headwind is passing more rapidly then the ground. You win by using a turbine to gain power and the wheels to provide thrust.

The gearing is different for the two configurations and I believe that the blade shape is as well.

 

[pbuk]

I believe that you have that backward.

And of course you are right, what was I thinking?

 

[DaveC426913]

So .. .wait. What are we saying?
The contraption is fake?
The video in post 28 is false, or is it simply that the explanation (propeller) is false?

 

[jbriggs444]

So .. .wait. What are we saying?
The contraption is fake?
The video in post 28 is false, or is it simply that the explanation (propeller) is false?

No, I think we're all good and in agreement. Device works, Propeller explanation is good.

 

[A.T.]

The gearing is different for the two configurations and I believe that the blade shape is as well.

Yes, they made a new pair of blades for upwind to have the correct twist/chamber/leading edge combination.

 

[A.T.]

Yes Kusenko talks a lot of nonsense, but to be clear when traveling DDWFTTW the thing that looks like a propeller is not acting as a propeller, it is acting as a turbine: extracting kinetic energy from a fluid and using it to drive the wheels.

Additionally to the explanation by @jbriggs444 why this wouldn't work, consider this: A turbine moving DDWFTTW would push the air forward (in the downwind direction), thus creating more true wind, instead of extracting wind energy form it.

 

[A.T.]

New explanatory video by a wind power engineer: