DDWFTTW Turntable Test: 5 Min Video - Is It Conclusive?

[rcgldr]

This needs clarification in my mind. The "We've been calling..." means you have adapted this term from aeronautics to apply to the DDW vehicles?

As you just mentioned, and I explained in an earlier post, advance ratio for propellers is ratio of (prop speed in the direction of wind) / (tip speed perpendicular to the wind), and it's also generally less than 1.

correction - What I was calling "advance ratio" is called "slip" in the case of propellers. For propellers, "advance ratio" is the apparent head wind speed / (prop diameter x rate of rotation) = (apparent wind speed / (2 x prop tip speed)) acheived in steady (non-accelerating) flight. Propeller "slip" is (effective pitch) / (geometric pitch).

However slip ratio isn't correct either. Another ratio is prop pitch / prop diameter, but that's also not a good analogy.

Who does "we" refer to

The people that posted in the earlier threads here and at the wiki web site. Spork was the one that defined the term advance ratio so it was less than 1 for a DDWFTTW cart, and the particpants in those threads at the time agreed so there was a "community standard" for the term "advance ratio" The term "advance ratio" seems generic enough to apply to objects that move at different speed, which is why Spork and others started using it for DDWFTTW carts, even though it's meaning is different in the case for propellers.

Another term used for propellers and tires is slip ratio, actual speed / gemotric speed, but this is a slippage factor, not an effective gearing factor that Spork and others wanted to convey with the term advance ratio.

I didn't start the precedent of using "advance ratio" in reference to DDWFTTW carts, but I did re-introduce it in this thread so if members here read the older threads here or at wiki (and a few other places), the usage of the term "advance ratio" will be consistent, and it's a relatively easy concept to understand.

I attempted to explain "advance ratio" in post #237.

 

[zoobyshoe]

As you just mentioned, and I explained in an earlier post, advance ratio for propellers is ratio of (prop speed in the direction of wind) / (tip speed perpendicular to the wind), and it's also generally less than 1.

However slip ratio isn't correct either. Another ratio is prop pitch / prop diameter, but that's also not a good analogy.

The people that posted in the earlier threads here and at the wiki web site. Spork was the one that defined the term advance ratio so it was less than 1 for a DDWFTTW cart, and the particpants in those threads at the time agreed so there was a "community standard" for the term "advance ratio" The term "advance ratio" seems generic enough to apply to objects that move at different speed, which is why Spork and others started using it for DDWFTTW carts, even though it's meaning is different than the case for propellers.

Another term used for propellers and tires is slip ratio, actual speed / gemotric speed, but this is a slippage factor, not an effective gearing factor that Spork and others wanted to convey with the term advance ratio.

I didn't start the precedent of using "advance ratio" in reference to DDWFTTW carts, but I did re-introduce it in this thread so if members here read the older threads here or at wiki (and a few other places), the usage of the term "advance ratio" will be consistent, and it's a relatively easy concept to understand.

I attempted to explain "advance ratio" in post #237.

Thanks very much. That completely clears it up for me.

 

[rcgldr]

What about the notion of a vertical shaft rotor such as we see on anemometers which can accept power from wind in any direction?

The problem is that the cart's aerodynamic interface has to produce a thrust while operating in an apparent headwind. I don't know if there is something more efficient than a propeller for doing this. The thrust for minimal DDWFTTW doesn't have to be much, just enough to overcome the small amount of aerodynamic drag, any internal friction related to forward speed, and the opposing force from the ground related to powering the thrust generating device (this last aspect doesn't apply to sailcraft, because the opposing force from the ground is perpendicular to the direction of travel in the case of sailcraft).

An alternative, although not efficient, would be to have a long track in the direction of travel, and have a sail that moved backwards along the track as the cart moved forwards. Once at the end of the track, the sail would be retracted and a second sail deployed at the front of the track. The retracted sail would be moved forward along the track to be redeployed once it reached the front of the track. Sort of a linear paddle wheel.

A ducted paddle wheel (squirrel cage) could also be used, but in the case of water propelled vehicles, propellers are more efficient than paddle wheels (even though in this case the upstream blades move in relatively low drag air).

 

[swerdna]

I'm confused by your description of the situation you offer as a solution. "Simply don’t start it in a wind." If there is no relative motion between your two "surrounding media" (air and ground) then there is no energy for the cart to harvest.

I have dial up (exceptionally primitive, I know) and am waiting for your video to load.

Sorry, I meant that when you push a cart up to the speed of the wind the cart is effectively not experiencing a wind. There is still a wind relative to the ground and propeller thrust. The main point I was trying to make is it is completely unimportant what happens below the speed of the wind as long as it doesn't give any "advantage" to plus wind speeds. The question is only whether plus wind speeds are possible and sustainable.

 

[zoobyshoe]

The problem is that the cart's aerodynamic interface has to produce a thrust while operating in an apparent headwind. I don't know if there is something more efficient than a propeller for doing this. The thrust for minimal DDWFTTW doesn't have to be much, just enough to overcome the small amount of aerodynamic drag, any internal friction related to forward speed, and the opposing force from the ground related to powering the thrust generating device (this last aspect doesn't apply to sailcraft, because the opposing force from the ground is perpendicular to the direction of travel in the case of sailcraft)

Help me analyze it with respect to the priciple: The power from differences of speeds of surrounding media can be extracted rather independently of gearbox`s (=vehicle`s) own speed.

Now in the HH situation where we are trying to harvest the energy from the difference between the wind speed and the ground speed, both moving toward us, we have wind moving toward us at speed A and ground moving toward us at speed B. The wind has a certain amount of power and the ground has a certain amount of power. We need to find the difference to know how much power there might be to harvest. How do we determine the power available from the wind with respect to a particular cart and how do we determine the power available from the ground with respect to a particular cart?

 

[zoobyshoe]

Sorry, I meant that when you push a cart up to the speed of the wind the cart is effectively not experiencing a wind. There is still a wind relative to the ground and propeller thrust. The main point I was trying to make is it is completely unimportant what happens below the speed of the wind as long as it doesn't give any "advantage" to plus wind speeds. The question is only whether plus wind speeds are possible and sustainable.

OK, I understand. This is what I was saying before: the real problem to overcome is to design for an HH situation: one where we can consider both the wind and ground as forms of head wind and design to extract power from the difference in their relative speed.

 

[rcgldr]

We have wind moving toward us at speed A and ground moving toward us at speed B. The wind has a certain amount of power and the ground has a certain amount of power.

The potential power is extremely large. A wind turbine can generate megawatts of power if it's large enough. The goal for a DDWFTTW cart is forward speed, not power conversion.

The key factor here is the difference in speed between ground and air. Power equals force times speed. The power input is the opposing force related to thrust generation from the ground times the carts speed relative to the ground. The power output is the thrust from the prop times the speed of the air through the prop (the classic definition is thrust times apparent headwind, but this ignores the induced wash through prop and indicates zero power output in a static (no wind) situation).

In a tailwind situation, the apparent headwind is less (or zero or negative) than the apparent ground speed. Effective gearing in this case is = 1 / (advance ratio), and without changing the power, can multiply the force while dividing the speed by some factor. Real gearing has a linear relatioship (minus losses), but the force at the prop is subject to prop efficiency, and the speed of the air through the prop is affected by slip ratio, so the power output from the prop is significantly less than the power input from the ground.

The DDWFTTW carts work because the force from the prop only needs to be a bit greater than the related input force from the ground (the bit of extra force is required to compensate for speed related drag factors) and the speed of the air through the prop only needs to be a bit faster than the apparent headwind. The power output versus power input ratio can be much less than 1 because the power output is into a much slower medium (the air in a tailwind situation) than the power input (the ground).

 

[swerdna]

OK, I understand. This is what I was saying before: the real problem to overcome is to design for an HH situation: one where we can consider both the wind and ground as forms of head wind and design to extract power from the difference in their relative speed.

Not sure I understand what you mean by HH (headwind headwind).

A wind moves relative to the ground and a cart. When the cart is traveling with the wind slower than the wind it experiences a tailwind. When the cart reaches wind speed it doesn’t experience any wind. When the cart exceeds the speed of the wind it experiences it as a headwind. Both a headwind and rolling resistance over a surface are frictional forces against forward movement. Where is the second headwind?

ETA - Think I’ve just caught up - are you are meaning moving ground seen as a headwind? If so the ground doesn’t usually move relative to things unless there is a landslide. For the ground to move relative to a cart usually means that the cart has to use some energy (especially if it’s also traveling into a headwind at the same time). A cart moving relative to the ground can’t get more energy from that relative movement than it has put into creating it to start with.

 

[rcgldr]

ETA - Think I’ve just caught up - are you are meaning moving ground seen as a headwind?

yes he is

If so the ground doesn’t usually move relative to things.

It does in your turntable tests. The cart itself is a reasonable frame of reference (ignoring the accelerating frame of reference issues), and relative to a cart going DDWFTTW, both the wind and the ground are moving backwards, which is what he was getting at by using "HH".

The power input (ground wheel interface) versus power output (air prop interface) is also easier to explain using the cart as a frame of reference, since that's the point of application for the forces involved.

 

[schroder]

yes he is
It does in your turntable tests. The cart itself is a reasonable frame of reference (ignoring the accelerating frame of reference issues), and relative to a cart going DDWFTTW, both the wind and the ground are moving backwards, which is what he was getting at by using "HH".

The power input (ground wheel interface) versus power output (air prop interface) is also easier to explain using the cart as a frame of reference, since that's the point of application for the forces involved.

If I may interject something: This is exactly the point I was trying to make earlier, but I guess I did not express it as well as you did here. What you have in your test, and indeed in all treadmill tests, is a Headwind Headwind situation. Then, on the basis of the carts performance in that situation, you interpret what the cart will do in a down wind situation, and the interpretation is that it will go faster than the wind. In fact, this is not a justifiable interpretation as the reference frame in a down wind situation is not equivocal to what is happening on the turn table or treadmill! I tried to demonstrate that by showing the way the cart reacts with a tailwind on the propeller; it tries to go the opposite way to what it does when driven by the table! This shows that the frames of reference are not equivocal at all and therefore you cannot interpret what is happening in the test frame to say what will happen in the down wind frame. I hope that makes some sense. I apologize for pulling out of the discussion prematurely, but I did not want to see another thread get locked because I was disagreeing with a “mentor”.

 

[schroder]

Does this mean you have given up on our step by step evaluation process? I would be very disappointed if so. I don't think it's a waste of time and I'm very keen to continue if you are. You don’t have to respond to the posts of others in the process. Please let me know if you wish to continue or not - thanks.

That is very generous of you to offer both your time and your device to work with me in carrying out testing. It is very rare when such an offer is made, especially since I am attempting to show that DDWFTTW is not happening in these tests. I appreciate your open-mindedness in trying to discover the truth of the matter, whatever that truth may be. I also will accept the results, should they prove DDWFTTW is in fact true. I have considerable experience as a test director, mainly on DOD projects, so I can sometimes come on as a bit “authoritative” and forget my place in a discussion group such as this. Just jump on me whenever that happens!
In the previous test, what I tried to demonstrate is that there is no equivalency in the reference frame of the cart on the turntable to a cart in a downwind. I agree that a moving ground and still air is entirely equivalent to moving air and a still ground. But for a reference frame to be entirely equivocal, all forces and objects must behave in exactly the same way. In other words, one frame must be indistinguishable from the other. When the tailwind (provided by the fan) was blowing on the propeller, the cart should have moved downwind, to demonstrate equivalency. It did not. In fact, it tried to move upwind. Although the forces in the reference frame were equivocal, the result was not! On the basis of that, we cannot take an observation in the test frame and then make a prediction of what will happen in the real down wind frame.
Think about that for a while and see if we can find some common ground to agree on. If so, I have a true test in mind, where the frames will be 100% equivalent, and it should show that DDWFTTW is not happening with this cart, or any other cart. Thanks

 

[rcgldr]

What you have in your test, and indeed in all treadmill tests, is a Headwind Headwind situation.

It's not a HH situation in the second video where cart speed = turntable speed and experiences a relative tailwind until the block is picked up via the fishing line.

Then, on the basis of the carts performance in that situation, you interpret what the cart will do in a down wind situation.

I don't see an issue here, whether on a treadmill, turn table, or outdoors, from the cart's frame of reference, the cart experiences a tailwind when it's speed is less than the wind, and then experiences a headwind when it's speed exceeds that of the wind. The videos have convinced me that a model similar to Sporks (if radio control steering was added) would work outdoors if a large enough flat area could be found. swedna's second video shows a cart starting up, and continuing to accelerate until it's beyond wind speed, good enough for me.

The princple here may be difficult to implement, but not difficult to describe. Going downwind faster than the wind just requires some sort of aerodynamic interface that slows the wind to a speed that is less than the vehicle speed, allowing the wind to be slowed down even though the vehicle is going faster downwind than the true wind. Slowing the wind down is how any wind powered device extracts energy from the wind.

Sailcraft tach at an angle and divert the apparent wind to upwind in order to accomplish this a net downwind speed faster than the wind (VMG). DDWFTTW carts use a propeller to slow the wind down to a speed slower than the cart is moving forwards.

When the tailwind (provided by the fan) was blowing on the propeller, the cart should have moved downwind, to demonstrate equivalency. It did not. In fact, it tried to move upwind.

Is there some video I've missed? Did swerdna post a start up video that resulted in a cart moving upwind as opposed to not moving at all? In both of sporks start up videos the cart went downwind, even in the second video when the prop windmilled, the wheels skidded and spun the wrong way as the cart went downwind. Eventually the wheels recovered traction.

 

[zoobyshoe]

Not sure I understand what you mean by HH (headwind headwind).

A wind moves relative to the ground and a cart. When the cart is traveling with the wind slower than the wind it experiences a tailwind. When the cart reaches wind speed it doesn’t experience any wind. When the cart exceeds the speed of the wind it experiences it as a headwind. Both a headwind and rolling resistance over a surface are frictional forces against forward movement. Where is the second headwind?

ETA - Think I’ve just caught up - are you are meaning moving ground seen as a headwind? If so the ground doesn’t usually move relative to things unless there is a landslide. For the ground to move relative to a cart usually means that the cart has to use some energy (especially if it’s also traveling into a headwind at the same time). A cart moving relative to the ground can’t get more energy from that relative movement than it has put into creating it to start with.

It does in your turntable tests. The cart itself is a reasonable frame of reference (ignoring the accelerating frame of reference issues), and relative to a cart going DDWFTTW, both the wind and the ground are moving backwards, which is what he was getting at by using "HH".

The power input (ground wheel interface) versus power output (air prop interface) is also easier to explain using the cart as a frame of reference, since that's the point of application for the forces involved.

Jeff is correct. For Swerdna's sake I'll repeat the reasoning behind adopting this viewpoint (swerdna, please read this):

If we keep our focus on this vehicle as one which harvests power from relative motion of surrounding media then we have also to contend with the fact that the relative motion of the surrounding media has two separate and distinct configurations to deal with. In the first the cart sees the wind as a tailwind and the ground as a head wind (provided the cart's in motion at all.) In the second the cart sees both the wind and the ground as headwinds. These two headwinds have energy to harvest, in principle, by virtue of the fact they are moving relative to each other at different speeds (according to MGrandin's description of the situation). However, they are still both headwinds, and will require an engineering solution specific to that situation, which must be different than the solution to the tailwind verses headwind situation.

I think it would be very useful to begin analyzing each design according to how it solves for two separate situations 1.) the Tailwind-Headwind (TH) and 2.) the Headwind-Headwind (HH). This would greatly clarify design strategies and discussions.

Personally I think that designing for the HH situation is the critical problem to solve. I would design for that and let the TH solution be direct blowing (DB) i.e. accept and allow for the startup to consist of the wind simply blowing the whole thing physically downwind. Otherwise you have to design transmissions or rotors that change configuration somehow.

 

[zoobyshoe]

The potential power is extremely large. A wind turbine can generate megawatts of power if it's large enough. The goal for a DDWFTTW cart is forward speed, not power conversion.

The key factor here is the difference in speed between ground and air. Power equals force times speed. The power input is the opposing force related to thrust generation from the ground times the carts speed relative to the ground. The power output is the thrust from the prop times the speed of the air through the prop (the classic definition is thrust times apparent headwind, but this ignores the induced wash through prop and indicates zero power output in a static (no wind) situation).

In a tailwind situation, the apparent headwind is less (or zero or negative) than the apparent ground speed. Effective gearing in this case is = 1 / (advance ratio), and without changing the power, can multiply the force while dividing the speed by some factor. Real gearing has a linear relatioship (minus losses), but the force at the prop is subject to prop efficiency, and the speed of the air through the prop is affected by slip ratio, so the power output from the prop is significantly less than the power input from the ground.

The DDWFTTW carts work because the force from the prop only needs to be a bit greater than the related input force from the ground (the bit of extra force is required to compensate for speed related drag factors) and the speed of the air through the prop only needs to be a bit faster than the apparent headwind. The power output versus power input ratio can be much less than 1 because the power output is into a much slower medium (the air in a tailwind situation) than the power input (the ground).

My goal was to convert everything to some common unit so that we can do simple math and see if we have enough to accomplish the task at hand. The prop on swerdna's cart is 12 x 6. Let's find out how much power that prop can collect from a 10 mph wind. Then let's find out how much power we have to expend to drive that cart and propeller into that 10 mph wind at any minimum speed you choose: use some realistic guesses for drag and friction and convenient time periods where necessary. This is the HH situation. The critical one.

 

[swerdna]

That is very generous of you to offer both your time and your device to work with me in carrying out testing. It is very rare when such an offer is made, especially since I am attempting to show that DDWFTTW is not happening in these tests. I appreciate your open-mindedness in trying to discover the truth of the matter, whatever that truth may be. I also will accept the results, should they prove DDWFTTW is in fact true. I have considerable experience as a test director, mainly on DOD projects, so I can sometimes come on as a bit “authoritative” and forget my place in a discussion group such as this. Just jump on me whenever that happens!
In the previous test, what I tried to demonstrate is that there is no equivalency in the reference frame of the cart on the turntable to a cart in a downwind. I agree that a moving ground and still air is entirely equivalent to moving air and a still ground. But for a reference frame to be entirely equivocal, all forces and objects must behave in exactly the same way. In other words, one frame must be indistinguishable from the other. When the tailwind (provided by the fan) was blowing on the propeller, the cart should have moved downwind, to demonstrate equivalency. It did not. In fact, it tried to move upwind. Although the forces in the reference frame were equivocal, the result was not! On the basis of that, we cannot take an observation in the test frame and then make a prediction of what will happen in the real down wind frame.
Think about that for a while and see if we can find some common ground to agree on. If so, I have a true test in mind, where the frames will be 100% equivalent, and it should show that DDWFTTW is not happening with this cart, or any other cart. Thanks

I’m very pleased that you haven’t completely abandoned the thread and if I understand you correctly you are happy to continue with a step by step analysis? As I pretty much now totally (but not quite 100%) think DDWFTTW is possible I prefer it that you don’t believe it is so. I want it vigorously tested not confirmed.

I can’t agree with you when you say “there is no equivalency in the reference frame of the cart on the turntable” and then say that the test you got me to conduct was equivalency. As I said previously, the fan blowing just on the prop isn’t the same as the wind blowing on the total frame of the cart as well as the prop outside. I also thought you had agreed with this. I also can’t understand why you can’t or don’t accept the several video clip examples of carts actually starting in a wind as being proof that they obviously can. Also beyond the start up the carts obviously do move with the wind with the prop spinning the “wrong way”.

The cart in the test I did for you wanted to go away from the fan every bit as much as it want to move toward it yet you still seem to want to claim it only wanted to go toward it. The whole thing about this design is that the prop is not being driven directly by the wind. It is being driven via the wheel(s) and is being made to rotate the opposite way it would if it was being driven directly by the wind. I’m absolutely sure that if I was using a more powerful fan the cart would have moved away from the fan even if it meant the wheel had to initially slip to do so. I have seen a video of a small cart that does move towards a fan but it was very heavily negatively geared to do so.

You had an issue with the tether arm that I really don’t understand. This is not a test of any particular design of cart it’s a test of whether DDWFTTW possible or not. Does it matter at all what happens to the cart before it reaches wind speed as long as it doesn’t gain any lasting faster than the wind advantage in the process? I would be happy if a cart was towed up to close to the speed of the wind then released. Surely the only thing of importance is if a cart can achieve and sustain faster then the wind speed. If you don’t agree with this please say why you don’t. If you do agree I would be happy to move on to your next test.

 

[swerdna]

Jeff is correct. For Swerdna's sake I'll repeat the reasoning behind adopting this viewpoint (swerdna, please read this):

If we keep our focus on this vehicle as one which harvests power from relative motion of surrounding media then we have also to contend with the fact that the relative motion of the surrounding media has two separate and distinct configurations to deal with. In the first the cart sees the wind as a tailwind and the ground as a head wind (provided the cart's in motion at all.) In the second the cart sees both the wind and the ground as headwinds. These two headwinds have energy to harvest, in principle, by virtue of the fact they are moving relative to each other at different speeds (according to MGrandin's description of the situation). However, they are still both headwinds, and will require an engineering solution specific to that situation, which must be different than the solution to the tailwind verses headwind situation.

I think it would be very useful to begin analyzing each design according to how it solves for two separate situations 1.) the Tailwind-Headwind (TH) and 2.) the Headwind-Headwind (HH). This would greatly clarify design strategies and discussions.

Personally I think that designing for the HH situation is the critical problem to solve. I would design for that and let the TH solution be direct blowing (DB) i.e. accept and allow for the startup to consist of the wind simply blowing the whole thing physically downwind. Otherwise you have to design transmissions or rotors that change configuration somehow.

Sorry to be so selfish but I don’t have much time to spend on this forum so would prefer spending the time I do have just evaluating if the DDWFTTW claim is genuine or not, and not how efficient it is or what any other technical details of performance might be (I‘m not trying to win a race). The thing is the carts as they are currently designed appear to work fine so why fix something that isn’t broken? I have read what you said and think I understand it.

 

[zoobyshoe]

Sorry to be so selfish but I don’t have much time to spend on this forum so would prefer spending the time I do have just evaluating if the DDWFTTW claim is genuine or not, and not how efficient it is or what any other technical details of performance might be (I‘m not trying to win a race). The thing is the carts as they are currently designed appear to work fine so why fix something that isn’t broken? I have read what you said and think I understand it.

I'm just trying to address your earlier problem with the concept of the ground as a headwind. You're quite right in asserting that, as a headwind, the ground will never have more force to apply to the cart than is represented by the cart's own momentum. Acknowledging that, we can proceed to subtract the lesser headwind speed from the greater to determine what power we now have available.

 

[schroder]

I’m very pleased that you haven’t completely abandoned the thread and if I understand you correctly you are happy to continue with a step by step analysis? As I pretty much now totally (but not quite 100%) think DDWFTTW is possible I prefer it that you don’t believe it is so. I want it vigorously tested not confirmed.

I can’t agree with you when you say “there is no equivalency in the reference frame of the cart on the turntable” and then say that the test you got me to conduct was equivalency.

I don’t think I said the test with the fan was equivalency. I do believe it indicates a lack of equivalency, however. This is very similar, if not exactly the same point that zoobyshoe is making about a HH and TH environment. On the turntable, the direction of the cart is opposite to the direction of the running table, and it is also opposite to the direction of the wind. It is a Headwind-Headwind environment. This simulates the environment of a cart which has already achieved DDWFTTW. In an outdoor test, the cart will be going at least initially, in the same direction as the wind, but relatively opposite to the stationary ground. This is clearly a Tailwind-Headwind situation. The problem is, there is no evidence at all that a cart which is in a T-H situation can ever make the transition to a H-H situation. No evidence at all that such a transition can ever take place, or has ever taken place. By interpreting what is happening in the H-H situation, we cannot justifiably make predictions about what will happen in a T-H situation. That is why the reference frames are NOT equivocal! No predictive relationship exists between the simulation on the turntable and a real run downwind. IF the turntable or treadmill simulation is the only “evidence” of DDWFTTW, then there really is no evidence, since there is no equivalency. Think about that for a while. An analogy, I have thought up, may help clarify your thinking. Suppose I say I have invented a balance scale which works in the opposite way to other scales. The side which has the heavier weight will go up, instead of down. In order to demonstrate this I place a weight on one side, but I point to the other side to show it is going up! I have inverted the outcome and from that I claim that when you place a weight on the scale it will go up. But in the real world test, which is not inverted, it of course goes down! No equivalency because the original demonstration was a simulation of what really happens! That is exactly what is happening with the turntable and the treadmill. If you really want to show that the cart is going faster than the treadmill, you need to remove the inversion. You need to have the cart running in the same direction the table is going and show that the cart is going faster than the table. That would show that it could also go faster than the wind. As long as the artificial inversion exists, by virtue of the cart and the table going in opposite directions, nothing has been proved, only simulated.


Give that some thought. It is a lot to digest!

 

[rcgldr]

no evidence at all that a cart which is in a T-H situation can ever make the transition to a H-H situation.

In spork's treadmill videos, he pushes the cart so it's moving backwards, a T-H situation, and once free, the cart responds by accelerating forwards back into a H-H situation. In swerdna's 2nd video, the cart is moving at the same speed as the turntable because of the block held by the fishing line. When the block is realeasd, the cart is in a T-0 situation (no relative ground movement), it transitions into a T-H situation, then continues on into a H-H situation. Why don't you consider these videos as "evidence"

advance ratio versus propeller diameter, we need a new term?

After more thought on this, the prop diameter does play a big part in what I've been calling advance ratio. The purpose of advance ratio is to multiply the force while dividing the speed. Most of the carts use a 1:1 gearing between wheels and props, so there's no effective gearing in the transfer of torque. The prop diameter multiplies the force for a given prop pitch, and the prop pitch divides the speed. Unlike gearing with a mechanical device the prop diameter is independent of the prop pitch, so the increase in force is independent of the decrease in speed.

Increasing the prop diameter increases the thrust, and increase the required torque from the wheels, which increases the opposing force from the ground. More force at the prop means more opposing force from the ground, but since the rest of the speed related drag forces are unaffected, higher overall forces at prop and wheels would be more efficient until some efficiency limit at the prop or traction limit at the wheels is reached.

As zoobyshoe mentioned, I'd also like to see the math for the prop worked out, but I haven't found a source that details both thrust and speed output in zero or low headwind situations. Many of the sources I've found state that prop pitch doesn't matter in a static (zero headwind) situation, because they are dealing with relatively high pitch factors where there are diminishing effects. At the relatively low pitch factors in these slow flyer props, the pitch makes a significant difference.

The current DDWFTTW cart models are already functional, so prop research would only optimize the carts if they weren't already near some limit of their designs already. Also the choice of props is limited to what is available for purchase for these small models.

Is anyone here aware of a good formula for torque and angular speed input versus thrust and speed output for a propeller of given pitch and diameter?

 

[atyy]

As zoobyshoe mentioned, I'd also like to see the math for the prop worked out, but I haven't found a source that details both thrust and speed output in zero or low headwind situations. Many of the sources I've found state that prop pitch doesn't matter in a static (zero headwind) situation, because they are dealing with relatively high pitch factors where there are diminishing effects. At the relatively low pitch factors in these slow flyer props, the pitch makes a significant difference.

The current DDWFTTW cart models are already functional, so prop research would only optimize the carts if they weren't already near some limit of their designs already. Also the choice of props is limited to what is available for purchase for these small models.

One of the things that puzzles me is that vanesch rough calculation (#214) with forces at steady state seems to say that DDFTTW is delicate needing A=B+C, and that it won't perform as required if A greater or less than B+C. But other arguments by you about some ratio being greater or less than 1 seem to indicate it's not so delicate, and the models themselves seem pretty robust. I wonder if there are steady state turntable velocities that show the three regimes that vanesch's calculation indicate exist?

 

[zoobyshoe]

As zoobyshoe mentioned, I'd also like to see the math for the prop worked out, but I haven't found a source that details both thrust and speed output in zero or low headwind situations. Many of the sources I've found state that prop pitch doesn't matter in a static (zero headwind) situation, because they are dealing with relatively high pitch factors where there are diminishing effects. At the relatively low pitch factors in these slow flyer props, the pitch makes a significant difference.

I am not sure that the figures for an engine driven propeller are going to be directly applicable to a wind driven windmill rotor. We are wondering how much power a rotor of given dimensons can extract from a headwind of given speed and then we must determine how much power would be required to drive that windmill, (which is on a cart on wheels) into that head wind.

A book I have says:

"It can be shown mathematically that no windmill can ever extract more than 59.2 percent of the power from the air column. Windmills are therefore rated on the basis of a power coefficient (Pc) which is the fraction of the available power extracted. "

-How to make Home Electricity from Wind, Water & Sun
by John A. Kuecken
Tab Books 1979

I am very sure the formulas we need to work this out exist somewhere.

 

[atyy]

One of the things that puzzles me is that vanesch rough calculation (#214) with forces at steady state seems to say that DDFTTW is delicate needing A=B+C, and that it won't perform as required if A greater or less than B+C. But other arguments by you about some ratio being greater or less than 1 seem to indicate it's not so delicate, and the models themselves seem pretty robust. I wonder if there are steady state turntable velocities that show the three regimes that vanesch's calculation indicate exist?

Ooop, that's not right. I should have had (I think):

B/(B+C-A)>1
B>B+C-A
A>C

which I hope is equivalent to Jeff Reid's two regimes.

 

[swerdna]

I don’t think I said the test with the fan was equivalency. I do believe it indicates a lack of equivalency, however.

Seems to me you are testing for equivalency using non-equivalency. Sorry but that doesn’t make any sense to me.

This is very similar, if not exactly the same point that zoobyshoe is making about a HH and TH environment. On the turntable, the direction of the cart is opposite to the direction of the running table,

Exactly as it would be in relation to the ground in an outside test.

and it is also opposite to the direction of the wind.

Don’t you mean the same direction only faster? The tailwind becomes a headwind but the direction of that the cart and wind are traveling are both the same. Don't forget the important part of the equation that never travels faster than the wind - the thrust of the propeller.

It is a Headwind-Headwind environment. This simulates the environment of a cart which has already achieved DDWFTTW. In an outdoor test, the cart will be going at least initially, in the same direction as the wind, but relatively opposite to the stationary ground. This is clearly a Tailwind-Headwind situation. The problem is, there is no evidence at all that a cart which is in a T-H situation can ever make the transition to a H-H situation. No evidence at all that such a transition can ever take place, or has ever taken place.

I think there has been. But here’s a different and totally conclusive form the evidence for you - I could tow the cart up to the speed of the wind using a motorised vehicle. The claim is NOT that a cart can go from a stationary position up to the speed of the wind and beyond. The claim (as I understand it) is that a cart can sustain ably travel directly downwind faster than the wind only using the immediate force of the wind. I don’t see that what happens at below wind speed is of any relevance to that claim.

By interpreting what is happening in the H-H situation, we cannot justifiably make predictions about what will happen in a T-H situation. That is why the reference frames are NOT equivocal! No predictive relationship exists between the simulation on the turntable and a real run downwind. IF the turntable or treadmill simulation is the only “evidence” of DDWFTTW, then there really is no evidence, since there is no equivalency. Think about that for a while. An analogy, I have thought up, may help clarify your thinking. Suppose I say I have invented a balance scale which works in the opposite way to other scales. The side which has the heavier weight will go up, instead of down. In order to demonstrate this I place a weight on one side, but I point to the other side to show it is going up! I have inverted the outcome and from that I claim that when you place a weight on the scale it will go up. But in the real world test, which is not inverted, it of course goes down! No equivalency because the original demonstration was a simulation of what really happens! That is exactly what is happening with the turntable and the treadmill. If you really want to show that the cart is going faster than the treadmill, you need to remove the inversion. You need to have the cart running in the same direction the table is going and show that the cart is going faster than the table. That would show that it could also go faster than the wind. As long as the artificial inversion exists, by virtue of the cart and the table going in opposite directions, nothing has been proved, only simulated.

In my tests I have clearly observed the cart moving faster than the moving surface that gave it it’s energy and that it sustains this speed. It doesn’t matter to me that it was in the opposite direction. As The wind is totally created by the speed of the moving surface it follows that the cart was also moving faster than the wind. If all this is equivalent to what would actually occur in an outside wind test I don’t fully know. At the moment I can’t see any reason why it’s not however. If I’m going to pursue this matter further I think my next step is to build and test carts in actual wind or wind tunnel conditions (preferably wind). If I were to do this and provided a video of a cart beating bubbles downwind consistently, would you accept this as fairly conclusive proof? I won’t say complete proof because I could be cheating.

 

[rcgldr]

I'd also like to see the math for the prop worked out, but I haven't found a source that details both thrust and speed output in zero or low headwind situations. Is anyone here aware of a good formula for torque and angular speed input versus thrust and speed output for a propeller of given pitch and diameter?

I am not sure that the figures for an engine driven propeller are going to be directly applicable to a wind driven windmill rotor.

When the apparent headwind is zero or positive, then convention propeller equations should apply. The fixed positive pitch propellers being used in these carts don't act as a windmill rotor, unless the wheels are sliding. A windmill rotor requires a prop with negative pitch, the equivalent of an advance ratio < 0 (negative), the torque reaction from a negative pitch prop would result in a backwards force by the wheels against the ground which would respond with a forwards force on the cart. Negative pitch would be good for startup, providing faster acceleration but to a lower than tailwind terminal speed, it wouldn't achieve DDWFTTW. You need a prop with a limited amount of positive pitch (effective advance ratio < 1) for DDWFTTW.

 

[rcgldr]

Let us model this crudely. With a velocity (wrt ground) v_cart corresponds:

a force by the air on the cart: F_air = A x v_cart + B x (v_wind-v_cart)
a force on the wheels: F_wheel = - C x v_cart

Positive signs are "downwind". A, B and C are model constants. The term with A is the propeller acting as a propeller and it is driven by the speed of the cart. The term with B is the drag of the wind, and also the effect of the difference between wind velocity and propeller. The term with C is the force excerted through the gearing mechanism of the propeller (reaction from the fact that the wheels drive the propeller).

crude model

This isn't a good model of the DDWFTTW cart. The force from the prop is a function of v_wind as well as v_cart.

If A is very large compared to B and C, which means a high gearing ratio, the cart will move upwind

Except that large A doesn't mean high gearing ratio, but instead high force, such as a larger diameter. A is defined to be a force here, so it would have to be negative to create an upwind cart.

A>C
which I hope is equivalent to Jeff Reid's two regimes.

Sort of, this "crude model" doesn't quite describe the DDWFTTW cart as I just mentioned.

Forward force from the prop is a function of prop diameter, prop pitch, prop angular speed, and apparent wind. Prop angular speed = wheel angular speed x gear reduction factor (currently the two gear reduction ratios are 1/1 or 13/16). Prop geometric forward speed = prop angular speed x prop pitch. Actual speed of air through the prop is a function of prop geometric forward speed and apparent wind (slip ratio).

It mostly boils down to two requirements:

One requirement for a DDWFTTW cart is that the forward force from the prop + air interface is larger than the opposing backwards force from the wheel + ground interface that powers the propeller, so that the net forward force (prop force - wheel force) accelerates the cart or maintains a DDWFTTW speed against the opposing drag related forces. The other requirement is that the forward force > opposing force is achieved while the power output is less than the power input.

Since power = force times speed, the DDWFTTW cart can take advantage of the fact that apparent headwind speed is < ground headwind speed, because advancing the air through the prop at a lower speed than ground speed allows the force from the prop to be greater than the opposing force from the ground, without consuming more power than is generated by the ground + wheel interface.

It's my guess that the prop parameters aren't that critical if maximum speed isn't the goal, just any speed DDWFTTW, as long at the prop pitch and any gearing reduce the advance rate of the prop versus the wheels sufficiently. Once some miminal prop diameter is reached, the prop will generate enough force for the cart to operate. If the diameter is increased beyond the minimum, then the forward force increases due to the larger diameter, and the opposing force increases due to the increase in torque required to drive the larger diameter propeller. Generally a larger diameter prop is more efficient than a smaller diameter prop, so it's my guess again that a larger diameter prop will result in better forward force versus torque ratio (for a given prop pitch), so increasing the diameter of the prop beyond minimum will probably improve the cart's speed. There's some point of diminishing returns, but I don't know what that limit is.

 

[zoobyshoe]

Since power = force times speed, the DDWFTTW cart can take advantage of the fact that apparent headwind speed is < ground headwind speed, because advancing the air through the prop at a lower speed than ground speed allows the force from the prop to be greater than the opposing force from the ground, without consuming more power than is generated by the ground + wheel interface.

The power available to the cart at this point from the ground as headwind is directly proportional to the cart's total momentum: its mass x its velocity, plus whatever momentum is stored in the prop and tires as flywheels. From this point forward it's all consumption: there's no more energy input into the cart system.

 

[vanesch]

This isn't a good model of the DDWFTTW cart. The force from the prop is a function of v_wind as well as v_cart.

That's why there is the second term in the first equation, which depends on the "seen" wind velocity. It includes not only passive drag, but also whatever effect it has on the prop.

Except that large A doesn't mean high gearing ratio, but instead high force, such as a larger diameter. A is defined to be a force here, so it would have to be negative to create an upwind cart.

For a downwind cart, it is a positive number (after all, for a downwind cart, the propeller acts as a propeller which is driven by the wheels: there is power flowing from the wheels to the propeller). For an upwind cart, I guess indeed that it works as a turbine, so A should be negative.

One requirement for a DDWFTTW cart is that the forward force from the prop + air interface is larger than the opposing backwards force from the wheel + ground interface that powers the propeller, so that the net forward force (prop force - wheel force) accelerates the cart or maintains a DDWFTTW speed against the opposing drag related forces. The other requirement is that the forward force > opposing force is achieved while the power output is less than the power input.

Since power = force times speed, the DDWFTTW cart can take advantage of the fact that apparent headwind speed is < ground headwind speed, because advancing the air through the prop at a lower speed than ground speed allows the force from the prop to be greater than the opposing force from the ground, without consuming more power than is generated by the ground + wheel interface.

Indeed. That's why this thing is not an over-unity device: the same force *taking* power from the ground (which moves faster than the wind) takes in more power than it costs power applying that same force (in the other direction) to the air (which moves slower). I already started writing two posts on this power balance, but each time I got distracted, and wasn't happy with what I wrote, so I deleted them.

 

[schroder]

In spork's treadmill videos, he pushes the cart so it's moving backwards, a T-H situation, and once free, the cart responds by accelerating forwards back into a H-H situation. In swerdna's 2nd video, the cart is moving at the same speed as the turntable because of the block held by the fishing line. When the block is realeasd, the cart is in a T-0 situation (no relative ground movement), it transitions into a T-H situation, then continues on into a H-H situation. Why don't you consider these videos as "evidence"

I do not accept these as evidence of a transition because the transition is into a simulated H-H situation, and not an actual example of a H-H situation. It is simulated because the ground is moving and being powered by a Motor! In the true H-H situation, the ground is stationary, the cart is moving but it does not have a motor to drive it! Let’s assume the cart is somehow pushed into a true transition to H-H. What exactly is supposed to keep it there? The ground is stationary, the wind is a headwind against the cart. Just exactly what is supposed to keep the cart moving forwards? You absolutely cannot say that because it is happening on the treadmill, it will happen in the real world situation because there is NO MOTOR! Why is that so difficult to comprehend? I stress that the treadmill/turntable situation is a simulation only and NOT an actual example of DDWFTTW. Give it some thought, please.

 

[rcgldr]

The power available to the cart at this point from the ground as headwind is directly proportional to the cart's total momentum.

I'm using the cart itself as a frame of reference here. Power equals force time speed. The power output is the thrust from the prop times the speed of the air through the prop. The torque required to produce the power at the prop is transferred to the driving wheels which apply a forwards force to the ground which reacts with an equal and opposing backwards force (Newton 3rd law pair). The power input to drive the prop is this backwards force from the ground times the speed of the ground.

 

[schroder]

My Final Analysis:
The treadmill/turntable demonstrations are exactly equivocal to a motorized cart running into a headwind. They have nothing at all to do with a wind-powered cart going downwind faster than the wind.

 

[rcgldr]

I do not accept these as evidence of a transition because the transition is into a simulated H-H situation, and not an actual example of a H-H situation. It is simulated because the ground is moving.

Ok, so let put a cart outdoors facing west at about latitude 89.44 of the Earth. Relative to the north pole, the ground is moving eastward at 10 mph. Say the wind is moving at 0 mph relative to the north pole. Initially the cart experiences an apparent tailwind of 10 mph and accelerates west. As the cart speeds up, the apparent wind transitions to 0, and then into a headwind. Say the cart reaches terminal velocity at 4 mph west, relative to the north pole. At this point the westward facing cart experiences an apparent wind of -4 mph, and an apparent ground speed of -14 mph. How is this significantly different than the turntable?

 

[zoobyshoe]

I'm using the cart itself as a frame of reference here. Power equals force time speed. The power output is the thrust from the prop times the speed of the air through the prop. The torque required to produce the power at the prop is transferred to the driving wheels which apply a forwards force to the ground which reacts with an equal and opposing backwards force (Newton 3rd law pair). The power input to drive the prop is this backwards force from the ground times the speed of the ground.

I am also using the cart as the frame of reference. Since the wind is 0 the only power source is now the ground. The only energy available from the ground happens to be equal to the energy represented by the cart's momentum, which is limited. The cart can use some of it to accelerate some air. It doesn't gain energy from this as it does when encountering fast air and leaving slowed down air in its wake.

Slowing the wind down is how any wind powered device extracts energy from the wind.

Now the cart is encountering slow air and leaving it faster in its wake. The whole cart system is losing energy.

 

[atyy]

The closest I can come to making sense of schroder's objection is: have the forces been correctly transformed in switching frames?

 

[rcgldr]

Since the wind is 0 the only power source is now the ground.

There's a spinning prop producing thrust when the apparent wind is 0. The prop rate of rotation is related to ground speed, not apparent wind speed.

Slowing the wind down is how any wind powered device extracts energy from the wind.

Now the cart is encountering slow air and leaving it faster in its wake. The whole cart system is losing energy.

The prop is slowing the air down to a speed less than that of the cart's forward speed. For example, a 10 mph taiwind, a cart moving at 14 mph, and the prop generating upwind thrust at 6 mph. The thrust from the prop slows the 10 mph tailwind down to 8 mph, and this is the source of energy that propels the cart DDWFTTW.

 

[Subductionzon]

zoobyshoe, the air still has a different speed than the ground in your frame of reference. The air is still and the ground is moving backwards at 10 mph (for a ten mph tailwind and the cart matching windspeed). So if the cart changes the speed of the wind so it is closer to the ground speed then is has taken some of the potential energy out of that wind and it can be used to raise the speed of the cart, enabling it to go downwind faster than the wind. The carts energy comes from the difference between air speed and ground speed, something that will exist regardless of the cart's speed. This cart is just an elegant way of harvesting that potential energy.