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Brain teaser: travelling faster than the wind.


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On 1/11/2022 at 6:41 PM, TheVat said:

Is it just me, or is this doing it the hard way.  Many sail configurations can give some advantage, as pulleys and other types of leverage do when they concentrate a force, and thus allow a sailed vehicle like a boat to exceed the windspeed.  Look up racing yachts.   If this can happen on water, it seems like it could happen on land with a large efficient sail and wheels with low rolling resistance and a smooth surface.  This method also skips over conversion problems where you convert a mechanical force into an electrical one, which is bound to be lossy.  

 

 

DDWFTTW discussions have happened  and  often became heated since Rick Cavallaro became obsessed by the brain teaser. The issue was never whether there was a practical application. Different folks have proposed different analogies to model the effect. Imagine an airship floating in wind trailing an cable pulling an electrical generator on wheels which drive the generator, the generated electricity used to power a propellor mounted at the pointy end of the airship.  Can the additional power supplied by the movement of the generator be enough to accelerate the airship above windspeed?

Me, I take the empirical view. The various demos convince me. Seeing a bumblebee fly is a stronger argument for me than sheets of calculation proving a bumblebee can't fly.

PS, I see your name has cropped up in another very-similarly-named forum in connection with the moderator, Oceanbreeze.

PPS

Some impressive footage of racing yachts exceeding windspeed:

 

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This did mess with my head - mostly I kept getting to what I named the "wind barrier" - the point at which the speed of the yacht equals speed of the wind - and thinking it can't be right; how can it accelerate through the wind lull? The explanations i read tended to leave me more bewildered, not less. Even now I'm not sure I really understand, although Genady's bike video example helped - with me mentally converting the rising "deflector" into a rotating vane; at "wind barrier" speed it still interacts with the (moving) vane - okay - but in my own head I'm not quite there. In a more vague, intellectual sense I see that there can be different ways to tap the energy from two bodies with momentum moving past each other,

On 1/14/2022 at 10:38 PM, Arthur Smith said:

The various demos convince me.

As for "seeing is believing" - up to a point, sure, but I note that that is what illusionists rely upon to have people believe what isn't true, or else we'd all be pulling coins out of our kid's ears for them to spend instead of our wallets. Many a scam has worked because appearances can be deceptive, like the chess playing "Mechanical Turk" as an historical example.

I note there were demos of this long before Blackbird - but I'm surprised I wasn't aware of it.

I think we may yet see practical applications - some boats are using these kinds of rotors, more experimental and novelty so far but decarbonising shipping is a real issue. There are the vertical turbine types but... how about Flettner Rotors?

DWFTTW messes with my head but so do Flettner Rotors; how does spinning a tube make it move sideways in the wind?

Wärtsilä will include Anemoi Marine Technologies’ Rotor Sails as part of its propulsion offering © Anemoi Marine Technologies

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13 hours ago, Ken Fabian said:

This did mess with my head - mostly I kept getting to what I named the "wind barrier" - the point at which the speed of the yacht equals speed of the wind - and thinking it can't be right; how can it accelerate through the wind lull? The explanations i read tended to leave me more bewildered, not less. Even now I'm not sure I really understand, although Genady's bike video example helped - with me mentally converting the rising "deflector" into a rotating vane; at "wind barrier" speed it still interacts with the (moving) vane - okay - but in my own head I'm not quite there. In a more vague, intellectual sense I see that there can be different ways to tap the energy from two bodies with momentum moving past each other,

As for "seeing is believing" - up to a point, sure, but I note that that is what illusionists rely upon to have people believe what isn't true, or else we'd all be pulling coins out of our kid's ears for them to spend instead of our wallets. Many a scam has worked because appearances can be deceptive, like the chess playing "Mechanical Turk" as an historical example.

I note there were demos of this long before Blackbird - but I'm surprised I wasn't aware of it.

I think we may yet see practical applications - some boats are using these kinds of rotors, more experimental and novelty so far but decarbonising shipping is a real issue. There are the vertical turbine types but... how about Flettner Rotors?

DWFTTW messes with my head but so do Flettner Rotors; how does spinning a tube make it move sideways in the wind?

Wärtsilä will include Anemoi Marine Technologies’ Rotor Sails as part of its propulsion offering © Anemoi Marine Technologies

The important point to be aware of is Blackbird in its downwind mode is using a propellor, not a turbine. The propellor is being powered by a chain driven from the wheels, it is not driving the wheels. Until the vehicle nears windspeed it is not contributing to the vehicle's motion. The propellor pitch is variable. Imagine pitch set to zero thrust (blades at right angles to wind direction). The vehicle approaches wind speed more quickly, then stabilized at just under windspeed (due to rolling resistance). Then pitch is set to achieve maximum thrust. The question is can that thrust exceed the wheel drag and that larger force cause the vehicle to accelerate beyond windspeed. The pro-argument is that gearing allows a smaller force times larger distance to produce a larger force times smaller distance.

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The principle behind this isn't really that amazing. At first sight, how can the vehicle get thrust from a wind that is effectively against it? The answer is that the propeller is forcing a large volume of air backwards at high speed to meet the following wind. So the following wind is able to apply force to the propeller, through the air that the propeller is shooting backwards. The air from the propeller hits the following wind, and pressure backs up, all the way to the propeller. The energy is coming from the wind. It's actually being slowed by the earth, through the wheels, gears and propeller, and it's the loss of kinetic energy in the wind, that provides the raised kinetic energy of the vehicle. 

A wind turbine allows the Earth to slow the wind, and reaps the kinetic energy. This does the same. 

Well, that's how I see it anyway.

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14 hours ago, Arthur Smith said:

The important point to be aware of is Blackbird in its downwind mode is using a propellor, not a turbine. The propellor is being powered by a chain driven from the wheels, it is not driving the wheels. Until the vehicle nears windspeed it is not contributing to the vehicle's motion. The propellor pitch is variable. Imagine pitch set to zero thrust (blades at right angles to wind direction). The vehicle approaches wind speed more quickly, then stabilized at just under windspeed (due to rolling resistance). Then pitch is set to achieve maximum thrust. The question is can that thrust exceed the wheel drag and that larger force cause the vehicle to accelerate beyond windspeed. The pro-argument is that gearing allows a smaller force times larger distance to produce a larger force times smaller distance.

Like the other explanations, that didn't help.

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4 hours ago, Ken Fabian said:

Like the other explanations, that didn't help.

I know, having read it myself, it was pretty garbled. ;) I'm not much better with Lorenz transformation.

I might be able to invite someone here for a decent explanation if that would help or be of interest.

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It might be easier to understand how it works by considering it in the vehicle's reference frame at the moment when it moves with the wind at the wind's speed.

At this moment, in the vehicle's RF, there is no wind, the air stands still, and the ground moves under the vehicle backward. This movement of the ground rotates vehicle's wheels. The rotating wheels rotate the propeller. Propeller pushes the air backward and the vehicle forward. This accelerates the vehicle and it starts moving relative to air.

In the ground RF, it starts moving faster than wind.

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I'll have another go. 

The spinning propeller is designed to that there is a pressure difference between the front and rear surfaces, and that's what gives thrust, in any propeller. 

Now consider the spinning propeller with no wind. Yes, there is a pressure difference, and therefore a resultant force on the propeller. So there is a forward thrust on the vehicle. BUT, it's not enough to drive the vehicle forwards, because of drag and friction losses. So in still air, the vehicle when running at speed would slow down and stop.

But now consider the spinning propeller with a following wind. The air from the propeller meets the following wind, and you get a greater pressure build up, all the way back to the propeller. So in this case, there is a greater pressure difference front to rear on the propeller blade, than in the no-wind case. 

So with a following wind, even if it's slower than the vehicle speed, you will still get more thrust on the propeller blades, than in no wind. So instead of slowing to a stop, the vehicle can accelerate. So it's the back up pressure that's giving the extra thrust. 

So even though the wind is not keeping up with the vehicle, it's still providing energy, through the raised back up pressure. 

The kinetic energy of the wind is being transferred through all of the tiny collisions, between the propeller air molecules, and the wind air molecules. So the wind slows, and the vehicle accelerates. 

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59 minutes ago, mistermack said:

I'll have another go. 

The spinning propeller is designed to that there is a pressure difference between the front and rear surfaces, and that's what gives thrust, in any propeller. 

Now consider the spinning propeller with no wind. Yes, there is a pressure difference, and therefore a resultant force on the propeller. So there is a forward thrust on the vehicle. BUT, it's not enough to drive the vehicle forwards, because of drag and friction losses. So in still air, the vehicle when running at speed would slow down and stop.

But now consider the spinning propeller with a following wind. The air from the propeller meets the following wind, and you get a greater pressure build up, all the way back to the propeller. So in this case, there is a greater pressure difference front to rear on the propeller blade, than in the no-wind case. 

So with a following wind, even if it's slower than the vehicle speed, you will still get more thrust on the propeller blades, than in no wind. So instead of slowing to a stop, the vehicle can accelerate. So it's the back up pressure that's giving the extra thrust. 

So even though the wind is not keeping up with the vehicle, it's still providing energy, through the raised back up pressure. 

The kinetic energy of the wind is being transferred through all of the tiny collisions, between the propeller air molecules, and the wind air molecules. So the wind slows, and the vehicle accelerates. 

Bravo! +1 I think it nails it. In other words, without a wind a vehicle with a speed V relative to the ground would have to have the same speed V relative to the wind. While with the wind having a speed v < V, the same vehicle has to have only V - v relative to the wind! 

Edited by Genady
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Another helping factor, although lesser, is the fact that there is less drag on the actual vehicle with a following wind. 

Even when the following wind is slower than the vehicle speed, drag is still reduced by having a following wind, as opposed to still air. 

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13 hours ago, Genady said:

This movement of the ground rotates vehicle's wheels. The rotating wheels rotate the propeller. Propeller pushes the air backward and the vehicle forward. This accelerates the vehicle and it starts moving relative to air.

Um, if the ground rotates the wheels using vehicle momentum to turn the propeller it will slow the yacht/vehicle down in direct proportion to the (ideal) thrust. To me that doesn't appear to explain it.

The bike vid example you provided did a better job, showing that there is still wind interaction with the moving vane as it passes through still air, and in the correct direction. I think it got me thinking in the right direction but it hasn't got me to the finish line. Unless that IS the finish line?

The notion that those vanes are acting much like a keel/centreboard keeps coming to mind - like the way the wheels prevent a sideways motion so a tangential force only produces motion along a predetermined line rather than principally a means of providing power; not sure that is helpful or not. It is fundamental to conventional sailing of course but in this case the vane's motion is connected to the ground, not the yacht... and I may be just circling back on myself...

12 hours ago, mistermack said:

I'll have another go. 

And that didn't really help either - which could be more about my comprehension than the quality of explanation.

I may yet encounter an explanation that better suits my comprehension and I expect I'll keep coming back to this until I have understood it..

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I don't remember if this link has been mentioned already -- I think this Wikipedia article summarizes the principle quite well:

A vehicle with a bladed rotor mechanically connected to the wheels can be designed to go at a speed faster than that of the wind, both directly into the wind and directly downwind. Upwind, the rotor works as a wind turbine driving the wheels. Downwind, it works as a propeller, driven by the wheels. In both cases, power comes from the difference in velocity between the air mass and the ground, as received by the vehicle's rotor or wheels.[7]

Relative to the vehicle, both the air and the ground are passing backwards. However, travelling upwind, the air is coming at the vehicle faster than the ground, whereas travelling downwind faster than the wind speed, the air is coming at the vehicle more slowly than the ground. The vehicle draws power from the faster of the two media in each case and imparts it to the slower of the two: upwind, drawing power from the wind and imparting it to the wheels and, downwind, drawing power from the wheels and imparting it to the rotor—in each case in proportion to the velocity of the medium, relative to the vehicle.[7]

In summary:[7]

  • Upwind, the rotor harvests the power from the oncoming air and drives the wheels, as would a wind turbine.
  • Downwind, when the vehicle is traveling faster than the windspeed, the ground is the fastest-moving medium relative to the vehicle, so the wheels harvest the power and impart it to the rotor, which propels the vehicle.

Blackbird (wind-powered vehicle) - Wikipedia

 

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7 hours ago, Ken Fabian said:

Um, if the ground rotates the wheels using vehicle momentum to turn the propeller it will slow the yacht/vehicle down in direct proportion to the (ideal) thrust. To me that doesn't appear to explain it.

The bike vid example you provided did a better job, showing that there is still wind interaction with the moving vane as it passes through still air, and in the correct direction. I think it got me thinking in the right direction but it hasn't got me to the finish line. Unless that IS the finish line?

The notion that those vanes are acting much like a keel/centreboard keeps coming to mind - like the way the wheels prevent a sideways motion so a tangential force only produces motion along a predetermined line rather than principally a means of providing power; not sure that is helpful or not. It is fundamental to conventional sailing of course but in this case the vane's motion is connected to the ground, not the yacht... and I may be just circling back on myself...

And that didn't really help either - which could be more about my comprehension than the quality of explanation.

I may yet encounter an explanation that better suits my comprehension and I expect I'll keep coming back to this until I have understood it..

Imagine a change of inertial frame. Instead of wind, the vehicle is in still air on a roadway that is an endless belt that can be static or moving powered by an external source. When the belt is static, nothing happens. When the belt begins to move, accelerate and reach some arbitrary velocity (say 10 m/s), what happens to the cart? If we first consider the propellor set with blades parallel to direction of movement (zero thrust), there will be an interplay between the force exerted on the vehicle wheels by the belt and the rolling and wind resistance of the vehicle including the blades. I suggest the equilibrium position will be that the cart will end up at just under belt velocity (wrt to air).

Does that make sense so far? 

If the propellor blades then are set to produce maximum thrust, will that make any difference. It seems to me the propellor thrust will tend to "pull" the cart in the direction of belt travel, resisted by rolling resistance and retarding force at the wheel. The pro lobby argues that gearing will result in a greater force from the propellor than the retarding forces. It seems counter-intuitive but it is not perpetual motion. There is an external source of energy: supplied by wind movement or belt movement. All Blackbird (and all the different models) does is exploit and redirect the energy extracted.

ETA

It just occurs to me, a simple illustration of the power of leverage. I came across it while doing some electrical work. There was a stock of flex I'd bought, supplied rolled around a cardboard tube with cardboard "wheels" at each end of the tube. There was perhaps 40 metres of flex on the originally 50 metre roll.The roll was needed and nearby and the end of the flex was nearer so I pulled it. The flex roll moved rapidly away from me even though I was exerting a force towards me. You can do the same thing with cotton on a reel on a suitable surface. 

ETA2

For amusement and to show there is still strong skepticism against the flight of bumblebees:

I posted the Blackbird brain teaser in another science forum, here.

A final response here! ;)

ETA3

A previous discussion on scienceforums.com that got buried!

Edited by Arthur Smith
Not my choice
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2 hours ago, Arthur Smith said:

Imagine a change of inertial frame. Instead of wind, the vehicle is in still air on a roadway that is an endless belt that can be static or moving powered by an external source. When the belt is static, nothing happens. When the belt begins to move, accelerate and reach some arbitrary velocity (say 10 m/s), what happens to the cart? If we first consider the propellor set with blades parallel to direction of movement (zero thrust), there will be an interplay between the force exerted on the vehicle wheels by the belt and the rolling and wind resistance of the vehicle including the blades. I suggest the equilibrium position will be that the cart will end up at just under belt velocity (wrt to air).

Does that make sense so far? 

If the propellor blades then are set to produce maximum thrust, will that make any difference. It seems to me the propellor thrust will tend to "pull" the cart in the direction of belt travel, resisted by rolling resistance and retarding force at the wheel. The pro lobby argues that gearing will result in a greater force from the propellor than the retarding forces. It seems counter-intuitive but it is not perpetual motion. There is an external source of energy: supplied by wind movement or belt movement. All Blackbird (and all the different models) does is exploit and redirect the energy extracted.

ETA

It just occurs to me, a simple illustration of the power of leverage. I came across it while doing some electrical work. There was a stock of flex I'd bought, supplied rolled around a cardboard tube with cardboard "wheels" at each end of the tube. There was perhaps 40 metres of flex on the originally 50 metre roll.The roll was needed and nearby and the end of the flex was nearer so I pulled it. The flex roll moved rapidly away from me even though I was exerting a force towards me. You can do the same thing with cotton on a reel on a suitable surface. 

ETA2

For amusement and to show there is still strong skepticism against the flight of bumblebees:

I posted the Blackbird brain teaser in another science forum, here.

A final response here! ;)

ETA3

A previous discussion on scienceforums.com that got buried!

Oops! I just noticed an error (not to say there aren't others) in  my comment above.

The sentence "It seems to me the propellor thrust will tend to "pull" the cart in the direction of belt travel, resisted by rolling resistance and retarding force at the wheel" is wrong.

It should say "It seems to me the propellor thrust will tend to "pull" the cart against the direction of belt travel, resisted by rolling resistance and retarding force at the wheel.

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If you have difficulty imagining how a 5mph wind could drive a vehicle to 10mph, think about a golf club hitting a ball.

If you take a big heavy object, like a golf club head, and swing it at 100mph, it can transfer some of it's momentum to a golf ball, and cause it to fly forward at nearly 200 mph. So momentum from a big heavy object can be transferred and concentrated causing a smaller and lighter object to travel faster than the big one. 

In this case, the big heavy object is the great mass of air, that is being sucked into the propeller, and forced out backwards. And the small object is the vehicle. 

On a still day, if you push the vehicle up to 10 mph, the air that's being sucked into the propeller (or technically pushed) has no momentum, in the frame of the static Earth.  It's then driven out of the rear, and there is a change of momentum, so there is a force on the propeller. But it's not enough to keep the vehicle going. 

Now in a second case, if you push the vehicle again up to 10 mph, but this time with a following wind of 5mph, then this time the air has momentum, relative to the static earth. So when the air passes through the propeller, and out of the rear at high speed, it experiences a much greater momentum change than in the first instance. 

Because of the propeller action, it's driving a great volume of air backwards. Not just the air directly in front of the propeller, but air from the sides a well. So the mass of air moving through the propeller is a lot, and it all has momentum because it's moving at 5mph. 

So what the vehicle is doing, is causing a momentum change in a big volume of air, and that momentum is concentrated into a smaller body, just like the golf club and the ball. 

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