Can a Wind-Powered Vehicle Travel Downwind Faster Than the Wind?

[my_wan]

I'm interested in the theoretical limits from an engineering perspective but I'm having trouble setting up the problem. Here are some thoughts on it that may also help convince people that are still skeptical. From a theoretical perspective, ignoring relativistic speeds, assuming perfect efficiency there is no limit to the velocity that can be achieved, i.e., Newton's first law. The limit is the energy available for acceleration, not velocity. The theoretical limit to the acceleration achievable is given by the energy differential between relative air speed to the ground and the cross section of air used, regardless of the motion of the craft. This available energy remains a constant at a given relative air to ground speed and cross section. The differential between relative air and ground speed is an absolute regardless of the motion of the craft under Galilean relativity, i.e., neglecting Special Relativity. The engineering limits to the maximum ground velocity is defined by the air resistance of the crafts frame, the friction in the drive train components, and the efficiency/cross-section of the prop. This available energy remains a constant due to the fact that as ground speed of the craft increases so does the prop speed. It is the efficiency that eventually limits the crafts speed as this efficiency drop off exponentially with craft to air and ground speed or friction.

From engineering perspective a maximal reduction in drive train and aerodynamic drag is trivial, the more efficiency the better. Prop design is vastly more complex. The prop efficiency has a theoretical limit of about 59% due to Betz' law. Ideally maximum efficiency of acceleration is achieved when air and craft speed closely match, assuming drive train friction can be ignored. However, this is not the speed you want the props "design point" engineered for. The "design point" is the speed at which the prop is at peak efficiency and drops off at higher or lower speeds. The "design point" should be set as close to maximum craft ground velocity, not maximum acceleration, as possible. This is further complicated by the fact that maximum craft ground velocity is extremely sensitive to air to ground velocity. The props "design point" must therefore be chosen on the assumption of a given air to ground speed. Equally as important to the props "design point" is the drag from all sources and the effect on maximum velocity.

Anybody want to tackle this analytically? It should be somewhat similar to the derivation of Betz' law with a few more variables.

 

[spork]

The "design point" should be set as close to maximum craft ground velocity...

I'm not sure I agree with this. I think the design point for the prop should be as close as possible to the cart's velocity minus the wind velocity. But I'm open to hear your theory.

Consider the cart operating at exactly the speed of the wind downwind. At this speed you would have a prop of 0 pitch if you were operating with zero losses.

 

[rcgldr]

Betz' law.

I'm not sure how Betz law applies here. Betz law relates the amount of power that can be extracted from a flow of fluid or gas. Betz laws applies to power extracted from the air by a propeller, which is different than power inserted into the air by a propeller, which is more efficient based on articles I've read about prop efficiency.

Also the goal here isn't to maximize extracted power, but to maximize downwind speed of the cart. It's probable that maximum speed occurs with a power extraction and consumption rate well below the maximum possible for a given wind speed and propeller size. As an extreme example, a 1500lb glider with a 60 to 1 glide ratio at 60mph, only consumes 4hp in the process.

Referring back to my landsail analogy, the apparent crosswind on a landsail is wind speed times sin(angle between wind and vehicle direction), and independent of vehicle speed. For these propeller carts, the apparent crosswind at any point on the propeller is equal to the angular velocity times the radius at that point, minus any induced wash rotation of the air before it reaches the blades of the propeller. The angular velocity is a function of gearing and forwards speed and the radius goes from the hub to the blade tips. Note that the apparent crosswind for the propeller is not independent of cart speed, which is different than a landsail or icesail. In the case of a cart, the apparent crosswind speed increases with the carts forward speed. Drag also increases with speed, and the situation is more complicated.

 

[atyy]

This is very cool to watch. But could you explain what "downwind" means? Also I know it's been explained, but can the physics be put in simple terms for us who non-schroders and non-heavyweight mathematical physicists?

 

[spork]

This is very cool to watch. But could you explain what "downwind" means? Also I know it's been explained, but can the physics be put in simple terms for us who non-schroders and non-heavyweight mathematical physicists?

I think it can be explained in a fairly straightforward manner. But as you can see, it's not necessarily intuitive even to the big-brains - so don't be surprised if some of it doesn't initially sound quite right.

First of all - downwind... This simply means we're going in the exact same direction as the real or "true" wind is going. We're not talking about the wind we'd feel if we were riding on the cart. So if the wind was coming from the North and heading south, this cart would also be heading south. However - it ends up going faster than the very wind that propels it (yes - I know that doesn't sound right). So if you were riding on this cart, you'd *feel* no wind when the cart reached the wind speed. Then you'd feel a wind in your face when the cart surpassed the wind speed. But in any event, we still say we're going downwind, because to an outside observer the cart is still headed in the downwind direction.

So - how does it work?

Well, when we think of a sailboat sailing straight downwind, we realize it can never go faster than the wind, because it relies on the wind hitting its sail to push it along. But this cart doesn't use a static sail to get pushed along. Instead it uses a clever arrangement of propeller, simple transmission, and wheels to extract the energy of the wind moving over the ground - not the wind moving relative to the cart. This is the secret to the whole thing. When the cart reaches the wind speed, it's no longer possible to extract energy from the wind relative to the cart - because there is no wind relative to the cart. But there *IS* still wind relative to the ground. So if we can come up with a clever way to slow that wind down *relative to the ground*, we can use it's energy to keep accelerating us beyond the speed of the wind.

Now, I'm not asking if this makes perfect sense just yet - but let me know if you understand what I'm getting at. If so I'll go into exactly how the cart pulls off this clever feat. Otherwise let's first make sure we're starting on the same page.

 

[atyy]

Now, I'm not asking if this makes perfect sense just yet - but let me know if you understand what I'm getting at. If so I'll go into exactly how the cart pulls off this clever feat. Otherwise let's first make sure we're starting on the same page.

Thanks! Let's see, my intuition says we should be able to go downwind as fast as we want. The wind provides a force which provides an acceleration, so as long as the force is present, the thing will get faster. So friction due to of the internal parts, and the air drag would be the factors limiting the acceleration. I would guess friction approximately proportional to velocity so there would be a terminal velocity relative to the ground, but it's not obvious to me this is less than the wind speed relative to the ground. What am I doing wrong?

The second thing I don't understand is it doesn't look like there's any wind in the videos. It looks like the treadmill is turning the wheels and this is being used to turn the propeller which pushes the vehicle forward against the direction of the treadmill.

 

[my_wan]

I'm not sure how Betz law applies here. Betz law relates the amount of power that can be extracted from a flow of fluid or gas. Betz laws applies to power extracted from the air by a propeller, which is different than power inserted into the air by a propeller, which is more efficient based on articles I've read about prop efficiency.

I think you are probably right here. In fact the more I think about it the more sure I am that you are right.

Also the goal here isn't to maximize extracted power, but to maximize downwind speed of the cart. It's probable that maximum speed occurs with a power extraction and consumption rate well below the maximum possible for a given wind speed and propeller size. As an extreme example, a 1500lb glider with a 60 to 1 glide ratio at 60mph, only consumes 4hp in the process.

This relates to spork's objection also.

I'm not sure I agree with this. I think the design point for the prop should be as close as possible to the cart's velocity minus the wind velocity. But I'm open to hear your theory.

I tried to be real careful to distinguish between ground air speed and craft air speed. The point was that the available power is defined by the ground air speed. The design itself is geared toward getting the highest possible craft ground speed. The "design point" of the prop, being on the craft, would naturally have the be set for the air speed as measured by the craft at maximum velocity. The intended meaning was that the "design point" should not be the air speed as measured by the craft while the craft was at zero air speed (maximum thrust efficiency), but the air speed as measured by the craft at maximum craft velocity. Admittedly the singular statement of mine as quoted failed to make that distinction but in no way was I suggesting the props "design point" be set by air speed as measured from the ground. Ground air speed simply determines available horse power regardless of the motion of the craft and nothing else.

Maximizing extracted power and minimizing resistance maximizes the downwind speed of the craft. They go hand in hand. The more craft speed you get through efficiency and extracted power the higher the wind speed needs to be for the "design point" of the prop. This is simply because you want everything at its maximum efficiency when the craft is at its maximum possible ground velocity. Obviously this also determines the gear ratio of the prop to wheels at that velocity also.

Referring back to my landsail analogy, the apparent crosswind on a landsail is wind speed times sin(angle between wind and vehicle direction), and independent of vehicle speed. For these propeller carts, the apparent crosswind at any point on the propeller is equal to the angular velocity times the radius at that point, minus any induced wash rotation of the air before it reaches the blades of the propeller. The angular velocity is a function of gearing and forwards speed and the radius goes from the hub to the blade tips. Note that the apparent crosswind for the propeller is not independent of cart speed, which is different than a landsail or icesail. In the case of a cart, the apparent crosswind speed increases with the carts forward speed. Drag also increases with speed, and the situation is more complicated.

Yes agreed, "apparent crosswind for the propeller is not independent of cart speed". Again my point was that the "design point" of the prop should be set for when the craft is at maximum velocity, whatever the apparent wind speed relative to the prop is at that craft velocity. The reason I brought up the issue of what "design point" to engineer for is because once we know what "design point" we are after then designing the prop is standard well known engineering. If the "design point" is too high or too low you are giving up quiet a bit of thrust at the highest craft velocity. This "design point" also sets a sweet spot where when the wind is blowing at this certain speed your efficency and speed is greatly maximized.

I will have to rethink the role of Betz' law.

 

[spork]

We took this video of JB's new DDWFTTW cart last night. We plan on making some improvements today - but it works quite well as it is:

http://www.youtube.com/watch?v=1BRvYZd81AQ&fmt=18

https://www.youtube.com/watch?v=1BRvYZd81AQ&fmt=18

 

[my_wan]

I will have to rethink the role of Betz' law.

I thought it over and it appears I was originally right, with qualifications.

At first glance it would appear that under Galilean relativity the treadmill speed is equivalent to wind speed. Although wrt showing that the speed at which the craft matches equilibrium speed does not correspond to wind speed remains valid it does not hold strictly true.

This is best illustrated by considering how entropy propogates through the system. The so called thermodynamic arrow of time. In the powered treadmill case the enthalpy is supplied by the treadmill itself with the surrounding air at high entropy. When the craft is held in contact with the treadmill the energy goes from wheel to prop and the dissipation of enthalpy get paid for by a slightly increased use of electricity to maintain the differential. There is a directionality to the flow of entropy that is determined by the source of enthalpy. When Jeff said;

Betz laws applies to power extracted from the air by a propeller, which is different than power inserted into the air by a propeller, which is more efficient based on articles I've read about prop efficiency.

he was correct for essentially the same reason articulated here. This would also mean that the treadmill craft is more efficient than the wind craft.

In the case of the wind craft the enthalpy is provided by thermal disequilibrium in the atmosphere. When you extract energy to operate your wind craft the enthalpy is paid for by an increase in the entropy of the air, i.e., paid for by reducing the overall atmospheric disequilibrium. The increase in entropy has a direction and the direction is important to efficiency as Jeff pointed out in the above quote. Betz' law would then be applicable in the wind case but not the treadmill case.

 

[spork]

This would also mean that the treadmill craft is more efficient than the wind craft.

The two are identical. How does the cart know if the road is moving or the air is moving? What if I put the cart down on an east-west facing road with a 10 mph tailwind? the road is moving about 1000 mph (due to the Earth's spin on its axis). But the cart doesn't know this.

 

[my_wan]

The two are identical. How does the cart know if the road is moving or the air is moving? What if I put the cart down on an east-west facing road with a 10 mph tailwind? the road is moving about 1000 mph (due to the Earth's spin on its axis). But the cart doesn't know this.

By the manner in which energy dissipates through the system. All energy systems have an energy source and a sink for that energy to dissipate into. The differential between the source and the sink must be maintained to have useable energy (enthalpy). Drawing energy from the sink and back into the source is not the same. The same way a prop propelled by the air is different from a prop to propel things through the air. It in no way invalidates your treadmill proof but it does effect efficiency.

 

[spork]

The same way a prop propelled by the air is different from a prop to propel things through the air. It in no way invalidates your treadmill proof but it does effect efficiency.

Again, I have to disagree. One of the most basic principles of physics is the equivalency of inertial frames of reference. Whether the cart is on a roadway that's moving backward at 10mph in still air, or on a "stationary" road with a 10 mph tailwind cannot be determined through experiment - this is true by definition.

In point of fact, I imagine you must see the irony in even describing the road as moving or stationary as there is no such objective concept in physics.

 

[my_wan]

Again, I have to disagree. One of the most basic principles of physics is the equivalency of inertial frames of reference. Whether the cart is on a roadway that's moving backward at 10mph in still air, or on a "stationary" road with a 10 mph tailwind cannot be determined through experiment - this is true by definition.

In point of fact, I imagine you must see the irony in even describing the road as moving or stationary as there is no such objective concept in physics.

No I see no irony in the equivalence of road speed to air speed. The issue is the source and sink for the energy you are using. You certainly must be drawing energy from somewhere and sinking it somewhere else or it would constitute a perpetual motion machine. Consider what happens when you drop a rock in water. You see a wave pattern spread out from the point of contact. Now try and produce a wave that comes in from all directions and disappears a point. Try unstirring cool aid.

The fact is, regardless of the equivalency of motion, your craft requires an energy source and a direction to dissipate that energy through the craft itself. The reverse is not always as easy as the forward. A thermocouple does not convert heat to electricity at the same efficiency as it converts electricity to heat. The energy source and energy sink doesn't change as a result of the frame of reference of the observer.

http://plato.stanford.edu/entries/time-thermo/

 

[spork]

You certainly must be drawing energy from somewhere and sinking it somewhere else or it would constitute a perpetual motion machine.

Of course it's drawing energy from somewhere. It's drawing energy from the interface between the air and road surface. And in either scenario that interface is identical.

Consider what happens when you drop a rock in water. You see a wave pattern spread out from the point of contact. Now try and produce a wave that comes in from all directions and disappears a point. Try unstirring cool aid.

That's all fine and dandy, but not relevant.

The fact is, regardless of the equivalency of motion, your craft requires an energy source and a direction to dissipate that energy through the craft itself. The reverse is not always as easy as the forward. A thermocouple does not convert heat to electricity at the same efficiency as it converts electricity to heat.

You're confusing the question of an irreversible process with the question of equivalency of inertial frames. If what you're telling me were true, you would have discovered an experiment (namely the efficiency of this vehicle) that distinguishes between different inertial frames. And we know no such experiment exists.

 

[atyy]

The two are identical. How does the cart know if the road is moving or the air is moving? What if I put the cart down on an east-west facing road with a 10 mph tailwind? the road is moving about 1000 mph (due to the Earth's spin on its axis). But the cart doesn't know this.

Ok, now I see why the treadmill is related to the wind. But in the case of the wind, there's no need for you to hold the vehicle in place at start up, and the wind will push it along. As long as the wind is present and friction is not too great, the vehicle will move downwind. Can the vehicle move up the treadmill, or at least remain stationary relative to the treadmill, all the time?

 

[spork]

Ok, now I see why the treadmill is related to the wind. But in the case of the wind, there's no need for you to hold the vehicle in place at start up, and the wind will push it along.

That's correct. If our treadmill were long enough we could start the vehicle moving backward at the speed of the belt (equivalent to setting it down on a road with a tailwind). Eventually the relative wind would get the vehicle up to speed and it would finally outpace the wind and advance on the treadmill

Can the vehicle move up the treadmill, or at least remain stationary relative to the treadmill, all the time?

The vehicle will advance on the treadmill. It can even go up a small incline.

This video shows the vehicle advancing on the treadmill:

http://www.youtube.com/watch?v=1BRvYZd81AQ&fmt=18

1BRvYZd81AQ&fmt=18[/youtube]

 

[my_wan]

Of course it's drawing energy from somewhere. It's drawing energy from the interface between the air and road surface. And in either scenario, that interface is identical.

Agreed, but in what direction is this energy being propagated through the craft? Either the prop is powering the wheel or the wheel is powering the prop. The two cases are not equivalent. Trying to describe it like that is like saying it is physically equivalent to say the road is tuning the motor in an automobile. Energy consumption/dissipation always has an absolute direction. Even in General Relativity the curvature of space is an absolute.

That's all fine and dandy, but not relevant.

It's more relevant than what you may think.

You're confusing the question of an irreversible process with the question of equivalency of inertial frames. If what you're telling me were true, you would have discovered an experiment (namely the efficiency of this vehicle) that distinguishes between different inertial frames. And we know no such experiment exists.

It is not a distinction between inertial frames. Your craft is accelerating which is an absolute in both Galilean and Special Relativity. The absolute is determined by what system lost energy and what system that energy was dissipated into. In the treadmill case the treadmill lost energy for every possible observer in any frame of reference and the air gained energy for all observers. If it weren't true you would be getting the electricity for your craft from the treadmill for free. The reverse is true for the air craft case. It is not a difference in inertial frames but what system the energy was dissipated from which then determines the direction the energy propagates through your craft.

 

[my_wan]

There is a simple way to determine unambiguously whether the prop is powering the wheel or the wheel is powering the prop. Run the shaft from the prop to a ring with a peg. The shaft can rotate freely in the ring until a flange on the shaft meets the peg. If the wheel is doing the powering the flange will be on one side of the peg and if the prop is doing the powering it will be on the other side. Surely it can't be on both sides at the same time.

 

[OmCheeto]

Yes it was. We were attacked as charlatans when we presented perfectly valid analyses and analogies. In the end it comes down to this - we were told no such vehicle could be built. We have now built and demonstrated it.

Despite your theory - no transient conditions are involved - nor is any "greater than unity effect". We take the laws of physics pretty seriously where I come from. I wouldn't break even one.

You may not be convinced by the performance in that video. But I assure you there will be no room for doubt with the video we will post within the next day or two.

I think the reason they don't lock these threads immediately is because they want to see how much time and money you can waste trying to convince us that these things work in a way that is not obvious from watching them. This new one seems to operate on a different principle from the outdoor device, that of the wind up toy.

 

[spork]

Either the prop is powering the wheel or the wheel is powering the prop.

That is not true. Just as a sailboat is like a watermelon seed being squeezed between thumb and forefinger, this cart is being "squeezed" between road and wind. The prop pushes on the wheels in the longitudinal sense, and the wheels push on the prop in the rotational sense. The wheels and trasmission provide the equivalent kinematic constraint as the skates on the ice boat.

Trying to describe it like that is like saying it is physically equivalent to say the road is tuning the motor in an automobile.

Your badly mistaken.

Energy consumption/dissipation always has an absolute direction.

Of course. Just as it does on this cart. And that direction is the same whether the road moves or the wind moves. You continue to fail to answer the question of how you can have been the first to discover an experiment that distinquishes between equivalent inertial frames.

It's more relevant than what you may think.

I assure you it's not relevant to this problem.

It is not a distinction between inertial frames. Your craft is accelerating which is an absolute in both Galilean and Special Relativity.

It will accelerate in either case. Just as it will reach equilibrium - faster than the wind - in either case. The two cases are identical.

If it weren't true you would be getting the electricity for your craft from the treadmill for free. The reverse is true for the air craft case.

You're not understanding how this craft works.

There is a simple way to determine unambiguously whether the prop is powering the wheel or the wheel is powering the prop. Run the shaft from the prop to a ring with a peg. The shaft can rotate freely in the ring until a flange on the shaft meets the peg. If the wheel is doing the powering the flange will be on one side of the peg and if the prop is doing the powering it will be on the other side. Surely it can't be on both sides at the same time.

No - it can't. The prop pushes the wheels. The wheels rotate the prop.

I think the reason they don't lock these threads immediately is because they want to see how much time and money you can waste trying to convince us that these things work in a way that is not obvious from watching them. This new one seems to operate on a different principle from the outdoor device, that of the wind up toy.

Before the insults were aimed at me claiming perpetual motion. I should never have been able to make this thing. I'm glad to see you have a new line of insults - equally invalid - at the ready.

 

[OmCheeto]

Before the insults were aimed at me claiming perpetual motion. I should never have been able to make this thing. I'm glad to see you have a new line of insults - equally invalid - at the ready.

hmmm... I thought I'd deleted my statement that the reason they called you charlatans was because you are charlatans.

 

[my_wan]

To this:

There is a simple way to determine unambiguously whether the prop is powering the wheel or the wheel is powering the prop. Run the shaft from the prop to a ring with a peg. The shaft can rotate freely in the ring until a flange on the shaft meets the peg. If the wheel is doing the powering the flange will be on one side of the peg and if the prop is doing the powering it will be on the other side. Surely it can't be on both sides at the same time.

You responded with this:

No - it can't. The prop pushes the wheels. The wheels rotate the prop.

So does that mean that by adding the limiting ring the craft will no longer work? Does the shaft jump back and forth in the ring? Does it go to one side of the ring yet still get powered from both wheel and prop? If such a slip ring can't distinguish between them give me a clue what effects the slip ring should be expected to have.

I had no doubt the principle was sound when you first posted the OP on this thread. I commend you for sticking with your guns and actually building a demonstration. Something many people would do well to emulate. You deserve a lot of credit. That said with the manner in which you are describing the physics there wasn't much choice but to lock the previous thread. It wasn't then nor is it now an insult of any sort. The fundamental problems with the description remain the same. Sorry, that's how science works. Some people unfortunately don't have the stomach for it. Claiming you were attacked for your ideas goes against the very methods we depend on in science. You even got a direct apology from Russ even though he didn't technically owe it. So hold your head up and avoid these claims of personal attacks lest you force what you claim. The science will speak for itself.

 

[spork]

I had no doubt the principle was sound when you first posted the OP on this thread.

Perhaps so, but you didn't speak up. I was being called out as a charlatan and told I was proposing a perpetual motion machine when that was clearly never the case. I was being told I knew nothing of physics or aerodynamics by a group of people that didn't even understand the equivalency of inertial frames.

That said with the manner in which you are describing the physics there wasn't much choice but to lock the previous thread.

It had nothing to do with how I described the physics. People claimed I was a charlatan and a fool. They claimed this thing could never work. I defended myself against these spurious claims, as I now have to defend against people that are telling me it doesn't work for the reasons I know it does - quite possibly the same people who thought it could not work in the first place. I hope you can understand how that gets old. The thread was closed either because the administrators, like the other participants of the thread, thought this was tantamount to perpetual motion OR becuase I defended myself against personal attacks. It was NOT closed because of how I described the physics.

It wasn't then nor is it now an insult of any sort.

If the original thread is still there I recommend you go back and read it.

The fundamental problems with the description remain the same.

The problem being that you're not able to follow them?

Sorry, that's how science works.

It kills me when someone like yourself tells me "how science works". Let's not pull our johnsons out - you won't like how it ends up.

Some people unfortunately don't have the stomach for it.

Grow up.

Claiming you were attacked for your ideas goes against the very methods we depend on in science.

Oh, now we depend on calling people idiots and charlatans? When they're RIGHT!?

You even got a direct apology from Russ even though he didn't technically owe it.

You didn't see what Russ posted. He deleted some of his posts before you could. You don't know what my responses would have been - the thread was locked so that only the moderators could get their licks in - and they did.

So hold your head up and avoid these claims of personal attacks lest you force what you claim. The science will speak for itself.

The science DOES speak for itself - unfortunately too many people can't seem to follow it.

You don't really even see the slightest bit of irony in this, do you? The members of this forum called me a charlatan and a fool, and locked my threads, because I claimed I could do EXACTLY what I did go and do. What I did works for EXACTLY the reasons I said it would. And NOW you want to tell me that it doesn't work like I think it does. But I've got news for you - it does. I conceived of this thing (although others had also done so independently), I built it, and I demonstrated it does what I said it would. How about you actually *do* something rather than tell me "how science works" and how I don't understand the thing I concieved of, built, and demonstrated.

hmmm... I thought I'd deleted my statement that the reason they called you charlatans was because you are charlatans.

And this is AFTER I proved him wrong. So tell me my_wan - this is how science works?

 

[spork]

I had no doubt the principle was sound when you first posted the OP on this thread.

When you think about it, that's not such a leap since the post included a video of a vehicle doing exactly what I claimed. What was your opinion when people were piling on me BEFORE I built one - and was simply explaining that it was quite doable?

 

[spork]

In response to... "How can a vehicle move faster than the wind that is powering it?"

OmCheeto wrote:
"It cannot go faster than the wind when going directly downwind."

Then I built a cart that does exactly that, made a video, and posted it.

Now OmCheeto incredulously writes:

hmmm... I thought I'd deleted my statement that the reason they called you charlatans was because you are charlatans.

and my_wan tells me I haven't been insulted, I may not have the stomach for this, and this is "how science works".

There's a kind of twilight-zone sort of entertainment to this I suppose.

 

[atyy]

That's correct. If our treadmill were long enough we could start the vehicle moving backward at the speed of the belt (equivalent to setting it down on a road with a tailwind). Eventually the relative wind would get the vehicle up to speed and it would finally outpace the wind and advance on the treadmill

It' not obvious to me this is like the wind. A vehicle in the wind doesn't need wheels, and the wind will just blow it along. The less friction between the ground and the vehicle, the easier it is for the wind to get the vehicle moving.

This seems more devious (I mean that as a compliment!) to me. Here friction between the vehicle and the treadmill is essential. With wheels there is the ability to make friction useful. The treadmill exerts a torque on the wheels and this is converted into the propellor movement which pushes the vehicle up. The question is how do you get friction to point in the right direction? Is holding the vehicle in place at the start necessary to do this? Does the propeller sort of "replace the hand" once it has sufficient speed?

 

[rcgldr]

Either the prop is powering the wheel or the wheel is powering the prop.

The wheels are turning the prop. The prop is generating a small amount of thrust, enough to allow the cart to move slightly faster than the wind.

 

[spork]

It' not obvious to me this is like the wind.

But it is. Imagine you were on your sailboat in the middle of the ocean. You wake up, go up on deck, and feel a 10 knot breeze on your face. How do you know if that's "real" wind? You don't. Maybe there is no current and the wind is blowing 10 knots, or maybe there is actually no wind, and there's a 10 knot current. To the boat (and to your face) it's all the same thing. And that's all we're doing here, we move the road and let the air sit still. This makes it much easier to prove the concept indoors with very controlled conditions.

A vehicle in the wind doesn't need wheels, and the wind will just blow it along. The less friction between the ground and the vehicle, the easier it is for the wind to get the vehicle moving.

Yes, but that vehicle can never go directly downwind faster than the wind. Because this vehicle extracts the needed energy from the air/ground interface, it must have a way of working against the ground. You could use skate blades, wheels, or other things.

The treadmill exerts a torque on the wheels and this is converted into the propellor movement which pushes the vehicle up.

You could look at it that way, but it's probably better to see it as the treadmill (or ground) holding the bottom of the wheel still so the cart can produce a torque on the wheels by pushing them forward at the hub.

Is holding the vehicle in place at the start necessary to do this?

No, but our treadmill would probably have to be over 100' long if we just set it on the belt. It would be going backward until it reached wind speed. It then starts advancing on the treadmill when it exceeds wind speed.

The wheels are turning the prop. The prop is generating a small amount of thrust, enough to allow the cart to move slightly faster than the wind.

To say the wheels are turning the prop oversimplifies it slightly (in my opinion). Not only does the prop have to create the thrust to overcome rolling friction and other transmission losses - it also has to create enough additional thrust to cause the wheels to turn.

The whole thing is simply caught between the ground and the wind. The prop pushes the wheels forward so they have to turn, and the wheels are geared to the prop so it has to turn when the cart moves forward. I know, it sounds like perpetual motion, but it's extracting that energy from the ground/air interface. Wouldn't do a thing without it.

 

[rcgldr]

The wheels are turning the prop. The prop is generating a small amount of thrust, enough to allow the cart to move slightly faster than the wind.

To say the wheels are turning the prop oversimplifies it slightly (in my opinion). Not only does the prop have to create the thrust to overcome rolling friction and other transmission losses - it also has to create enough additional thrust to cause the wheels to turn.

The wheels interact with the ground and turn the prop. The prop interacts with the air to generate thrust that affects the entire cart. The drive train torque from the wheels is opposed by an equal an opposite drag torque from the prop. This should answer my_wan's question.

simple explanation of the DDWFTTW cart

Ignore the land sail comparason for these carts, here's a much simpler explantion. Power input = equals the force at the driving wheels times the speed of the cart relative to the ground, because the wheels interact with the ground. Power output equals the thrust at the prop times the speed of the cart relative to the air, because the prop interacts with the air. The ratio of (power output) / (power input) = (thrust times air speed) / (force times ground speed) and with a ratio well less than unity, the cart can still go DDWFTTW.

To compensate for rolling resistance and other drag factors, the thrust from the prop is greater than the force at the driving wheels, but as long as the speed between prop and air is relatively smaller than the speed between wheels and ground, the power output is less than the power input, and the cart works.

Given this perspective, a rotating prop isn't required. Any thrust producing device would work as long as it was similarly efficient to a prop. Regarding the prop, a range of pitches will probably work, changing the pitch changes both the thrust and drag torque from the prop, and these are offsetting, depending on the lift to drag ratio of the prop.

 

[spork]

The wheels interact with the ground and turn the prop. The prop interacts with the air to generate thrust that affects the entire cart. The drive train torque from the wheels is opposed by an equal an opposite drag torque from the prop.

That's a perfectly fair characterization.

This should answer my_wan's question.

I will be surprised and impressed if it does.

Ignore the land sail comparason for these carts, here's a much simpler explantion.

Everyone's got a "simpler" explanation, because everyone had a different point where it clicked for them. For me the land sail explanation is the most accurate and intuitive given. If another explanation works better for you - that's great - as long as it's accurate.

Power input = equals the force at the driving wheels times the speed of the cart relative to the ground, because the wheels interact with the ground. Power output equals the thrust at the prop times the speed of the cart relative to the air...

This suggests there is no power output when it's going downwind at exactly wind speed. Depending on how you define your system this can be true. Is this how you're looking at it? I would be more inclined to say the power output is equal to the work the prop actually does on the air (which will be greater than thrust * speed of cart relative to air).

...but as long as the speed between prop and air is relatively smaller than the speed between wheels and ground, the power output is less than the power input, and the cart works.

True - as long as that difference is enough to allow for the inefficiencies of the prop, rolling resistance, and drivetrain losses.

Given this perspective, a rotating prop isn't required. Any thrust producing device would work as long as it was similarly efficient to a prop...

...and indexed to the ground in a way similar to the prop. This is required to extract the energy from the ground/air interface so that we can go faster than the wind.

Regarding the prop, a range of pitches will probably work, changing the pitch changes both the thrust and drag torque from the prop, and these are offsetting, depending on the lift to drag ratio of the prop.

Agreed - as long as the efficiency is still sufficient and the advance ratio of the prop vs. wheels is less than 1.

 

[ThinAirDesign]

Ignore the land sail comparason for these carts, here's a much simpler explantion.

Ok, let's hear your simpler explanation:

Power input = equals the force at the driving wheels times the speed of the cart relative to the ground, because the wheels interact with the ground. Power output equals the thrust at the prop times the speed of the cart relative to the air, because the prop interacts with the air. The ratio of (power output) / (power input) = (thrust times air speed) / (force times ground speed) and with a ratio well less than unity, the cart can still go DDWFTTW.

You didn't pass the "simpler" test ... my girlfriend says the above is all gibberish. :-)

JB

PS Meant in good fun Jeff.

 

[schroder]

It has taken me a while, but for what it’s worth, I finally understand the principle of this thing. It is not a pmm at all. I won’t apologize for being dense, but if I directly insulted anyone I sincerely apologize for that. As I understand it now, the cart is employing positive feedback, not unlike a turbo charger, from output device (propeller) to input device (wheels). In that sense, the cart is being driven by both the wheels and the prop at the same time. My mental block concerned advancing against the treadmill, while drawing all its power from the treadmill. If the device were using two wheels to extract power from the tread and an additional set of wheels working against the tread, clearly that would not work. What finally convinced me was to imagine a threaded rod run parallel to the treadmill, and instead of a propeller a worm gear was used to drive the cart along the threaded rod. That would certainly work, and the cart would accelerate until it either burned itself up from friction and heat, or it reached some terminal velocity dictated by the available energy, mass and friction forces. I then extrapolated that idea to the propeller drive and found it is not much different. Of course, saying all this after seeing the very convincing video does not establish me as a good intuitionalist but at least my brand of formalism does allow some flexibility. But all of these concessions are to the machine on the treadmill. As a formalist, I still have reservations about the ability to outrun the wind, going directly downwind. As Atyy pointed out, any contact with the ground must introduce friction forces which would not be present with the wind alone, but those same friction forces can be used to advantage as well. In that case, from both an intuitionalist and a formalist point of view, it does seem rather questionable as to which of the forces would be greater. However, having been proven wrong about the treadmill I concede that I may well be wrong about the wind as well.

 

[spork]

I won’t apologize for being dense

An apology is never required or expected for simply not quickly understanding unintuitive things.

..but if I directly insulted anyone I sincerely apologize for that.

Thank you. I accept.

If the device were using two wheels to extract power from the tread and an additional set of wheels working against the tread, clearly that would not work.

Agreed. The cart extracts its energy from the road/air interface. As such it has to have something working against the air.

What finally convinced me was to imagine a threaded rod run parallel to the treadmill, and instead of a propeller a worm gear was used to drive the cart along the threaded rod. That would certainly work, and the cart would accelerate until it either burned itself up from friction and heat, or it reached some terminal velocity dictated by the available energy, mass and friction forces.

Perfectly accurate.

I then extrapolated that idea to the propeller drive and found it is not much different.

Also true.

Of course, saying all this after seeing the very convincing video does not establish me as a good intuitionalist but at least my brand of formalism does allow some flexibility. But all of these concessions are to the machine on the treadmill. As a formalist, I still have reservations about the ability to outrun the wind, going directly downwind.

But the two cases are identical. The same experiment is being performed in two different inertial frames. As such the results must be identical.

However, having been proven wrong about the treadmill I concede that I may well be wrong about the wind as well.

It *has* to work in the wind - because wind across a stationary road is identical to a road moving beneath a stationary mass of air.

 

[ThinAirDesign]

Schroder, I commend not only your ability to learn and in return model and describe your observations, but even more so your ability to stand up and apologize -- that demonstrates a quality that really matters.

Kudos.

JB

 

[ThinAirDesign]

my_wan, I respect knowledge and you clearly hold more physics knowledge than I. I must say however that if you are correct, the Physics world will be rocked by your discovery and you will likely get a Nobel.

You are holding that there is now a test which can be performed which will yield varying results based on differing 'amounts' of purely linear motion.

I'm quite surprised frankly that there are not more folks on a physics forum piping up and taking a position on a debate so fundamental to one of the most basic and long-standing physics principles.

JB