# If DDWFTTW is possible, would this be a viable application?

1. Feb 5, 2009

### DyslexicHobo

Since it appears that this is a recently discovered phenomena, it seems like there should be a lot of new applications that utilize it. Obviously the carts that use the wind to travel can move faster, but it seems like this idea can be used in other areas.

I have a project for my engineering class this semester to design and build a vertical-axis wind turbine and mathematically represent it in Matlab. The test is going to be conducted by putting our turbine in front of a 3-ft wide fan blowing at 3m/s and 5m/s. The grade will be determined by its average power output.

Would DWFTTW be able to be implemented by using the vertical-axis turbine as my turntable with a propeller apparatus on top as my device that would travel faster than the wind? This turntable would be out of the 3-ft wide radius of the fan, so the device on the turntable's motion wouldn't be effected by the wind.

I'm very confused as how how exactly conservation equations are applied to DWFTTW (mostly due to the fact that the prop is driven by the wheels, I think), so it's really hard for me to visualize how this would all work as far as power output. I'm guessing that it would cause more unneeded drag than it would do good, but I'm just checking.

Thanks
-jz

2. Feb 5, 2009

### Beaujolais

Sounds really goood:P

3. Feb 5, 2009

### swerdna

It’s hardly a “recently discovered phenomena”. The Brennan torpedo (invented 1877) used essentially the same principle only in water. http://en.wikipedia.org/wiki/Brennan_Torpedo . This is the only practicle use I’ve ever seen for the principle.

4. Feb 5, 2009

### DyslexicHobo

The way I see it, after a certain amount of time, the turbine will be spinning at a constant speed (given that the wind speed is constant). The turntable on the top of the turbine would be spinning at that same rotational velocity. A device such as the one in http://www.youtube.com/watch?v=VgaXpHOxtQg" video, is placed on top of the turbine. It creates no opposing force on the turntable, therefore does not stop the main turbine apparatus from harvesting the maximum amount of energy. The device mounted on the turntable can then turn in the other direction with some rotational acceleration. Because it is creating an acceleration with its propeller, can that energy not be harvested somehow?

Am I missing some energy loss somewhere? Thanks!

Last edited by a moderator: Apr 24, 2017
5. Feb 5, 2009

### rcgldr

The DDWFTTW carts try to maximize speed, not power, from a wind. The power output by a DDWFTTW cart is less than the power input. If the power output is measured at the turntable as torque time angualr velocity, then the cart might be an interesting way to create an opposing torque on the TT, but the issue would be a fixed speed. You'd be better off with some type of load, like a brake, that would allow the same opposing torque across a broad range of speeds.

The limit for power output from a wind powered device is related to Betz law:

http://en.wikipedia.org/wiki/Betz'_law

I'm not sure of the optimal parameters for a vertical wind turbine for a given diameter of wind flow from a fan.

6. Feb 5, 2009

### DyslexicHobo

I'm sorry, but I'm not sure if you answered my question or not. You seem to agree that the cart would create some torque about the turntable which could be offset by a brake. Instead of a brake we could have a load (like a generator!). Doesn't this mean we're getting extra power? :/ I'm extremely confused.

7. Feb 5, 2009

### Staff: Mentor

It would work - just not as well as a wind turbine. A turbine already uses the key property of DWFTTW: relative wind. So all you're doing is adding complexity without adding any benefit.
What's the "extra"? If there is no brake (no generator), there is no power output. Adding a generator doesn't give you extra power output, it just gives you power output. If you use one of these devices, an awful lot of power is wasted in friction in the various drivetrains. A wind turbine uses a much simpler drivetrain (potentially direct-drive for your purpose) and therefore loses much less to friction, leaving much more for output.

You're coming close to the misunderstanding of this that causes people to think it is a perpetual motion machine.

8. Mar 13, 2009

### spork

There are still some significant misconceptions about the DDWFTTW vehicle. In reality the vehicle CAN be used to harvest wind energy. Interestingly, in this configuration the Betz limit does not apply because the prop is acting as a propeller and not a turbine (even though the vehicle itself can be said to be a turbine - depending on your definition). Because the cart "processes" more wind, it can in fact be more effective than a windmill which is affixed to the ground.

And just as there is no theoretical limit to the maximum speed of the cart relative to the wind, there is also no theoretical limit to the amount of power that can be harvested by such a cart. In practice the internal losses are very critical, and will make it difficult to produce a cart that goes downwind at much more than 2.5X to 3X wind speed. Similarly, it would be challenging to make a cart that harvest more than about 30% greater power than a fixed turbine.

9. Mar 13, 2009

### rcgldr

Speed isn't limited, but power is, and I assume that it's in compliance with Betz law. The theoretical limit of power generated by these carts ("wind powered" device) is related to the cross sectional area of the affected air and by how much that speed of that air (wind) is slowed down (with respect to the ground).

10. Mar 13, 2009

### spork

The power that can be harvested from these carts is NOT limited. Because the cart is moving through the air, rather than simply waiting for the air to flow over it, it can harvest the energy from more air. I'm sure you can understand that if I slow twice the overall air-mass I will harvest twice the energy. This cart is theoretically capable of moving at any multiple of wind-speed and can thus theoretically harvest an unlimited amount of energy. As mentioned above, the practical limitations are not as impressive, but there's no question it can "produce" more energy than a stationary windmill of the same size.

This is true for both the direct downwind cart AND the direct upwind cart. In the case of the downwind cart the Betz limit simply doesn't apply as the prop is acting as a propeller. The Betz limit does apply to the upwind cart because the prop actually acts as a turbine.

11. Mar 13, 2009

### Staff: Mentor

I'd like to see a mathematical proof of that, spork. These devices move parallel to the wind, which implies to me that they harvest exactly the same wind energy as a stationary wind turbine.

Remember, a wind turbine can be made to accelerate to an arbitrarily high speed too, but that doesn't change the amount of power it can harvest.

12. Mar 13, 2009

### spork

The mathematical proof will appear in a peer reviewed paper. I therefore can't present it here. I think what I've presented should be sufficient, but I'll go a step further...

Consider the total energy available to a stationary turbine. It would be equal to the energy in the wind that passes over the disk in a given period of time. Ignoring the Betz limit for now (which only makes things worse for the stationary turbine) that would be equal to the incoming wind velocity times the disk area of the turbine, times the time interval in question.

For the cart, the amount of energy available to it is also equal to the energy in the wind it encounters in that same period of time (we'll assume for now that either device can remove ALL the energy from the wind it processes - though this is more nearly true for the DDWFTTW cart because it isn't limited by Betz - and for other slightly more sublte reasons). The wind processed by the cart is equal to the (cart_speed - wind_speed) times disk area, times time interval. When the cart speed is greater than 2X wind speed this number clearly becomes greater than for the stationary turbine. Because the downwind cart is not subject to Betz, we see the advantage well before 2X wind speed.

For the upwind cart, the advantage is available at any upwind speed, but this cart is subject to Betz.

The fact that it's planted into the ground is what limits the amount of energy it can harvest.

If I place a stationary net in a river, there's a limited rate at which it will catch fish. If I move it upstream at a constant rate it can catch more fish. If I move it downstream at greater than 2X the current it will also catch more fish.

13. Mar 13, 2009

### Staff: Mentor

I agree with your explanation, so I guess then my issue is with the utility of this statement (besides making that little red warning light in the back of my head flash):
While it is true, similar statements can be made about regular wind turbines, since all you are really saying is that given an infinite amount of input power (a finite wind speed over an infinite land area), you can generate an infinite amount of output power. How is that a useful thing to say?

14. Mar 13, 2009

### spork

Well, I'm not quite sure what you're asking. I'm describing the physical principles of the cart vs. a traditional wind turbine. The wind turbine has a theoretical maximum power output for any given wind. It is given by the turbine diameter and wind speed (and further reduced by the Betz limit). The cart does not have such a theoretical limit. Because the cart can move through the wind (in addition to the wind moving over the cart) the theoretical amount of power it can harness is without limit.

If you're asking whether I think this is a useful or practical thing to actually do, I make no such claim. I was simply responding to incorrect statements made about the cart's operation and limitations.

15. Mar 14, 2009

### rcgldr

Using Betz's law as a basis, maximum power is achieved when the speed of the air (wrt ground) after interaction of the cart is about 1/3rd the speed of the wind (wrt ground). It doesn't matter how fast the cart is moving or which direction the cart is moving. The air flow through the prop doesn't matter, it's the how much the wind is slowed down by the prop wash. The prop doesn't interact directly with the wind, instead it's the prop wash (the only component going upwind when a cart is going DDWFTTW), that slows down the wind.

16. Mar 14, 2009

### spork

Thanks for that. I'm sure the reviewers will correct my work before allowing me to publish. Then again, they'll probably realize that no wind powered vehicle can ever achieve greater than wind speed directly downwind.

How would one possibly even respond to that!!?

I guess that's why airplanes don't have wings. Afterall the flow over the wing doesn't matter; the downwash is the important thing.

This can't be helped on an internet forum. You'll need some hands on assistance at a whiteboard at the very least.

17. Mar 14, 2009

### rcgldr

What I meant was when a cart is going DDWFTTW, then the prop operates in an apparent headwind, and is going DDWFTTW also. It accelerates the apparent headwind suffieciently faster than the carts downwind speed that the prop wash is effectively upwind, and it's that prop wash that slows down the wind. The prop wash is the only thing related to the cart that isn't going DDWFTTW.

What I meant by this is that the air flow through the prop will vary depending on the cart speed, but it's the prop wash that slows down the air. The air flow through the prop has to be greater when the carts downwind speed is faster. The net affect on the wind is relative to the prop wash versus ground speed, not prop wash versus cart speed.

18. Mar 14, 2009

### spork

One of the common misconceptions is that the prop produces a buffer of high pressure air behind itself, and that this is how it's able to be "pushed on" by wind it's outrunning. This is not the case. Tufting the flow behind the prop would show there is no convergence of air masses. The prop is fully submersed in the medium (air) that just happens to be moving relative to the ground. Nothing about the flow relative to the prop or cart is any different than what would be seen by an airplane taking off. It's better to imagine a screw advancing through a block of wood while that block of wood is moving along the ground. There's no worry of the screw "outrunning" that which is pushing it along.

Additionally, the prop does in fact produce an aft thrust - but it cannot produce a thrust that results in an airstream that's upstream. It can only slow the air in its wake relative to the ground. If the prop had sufficient pitch to produce upwind flow - ironically it would cease to behave as a propeller, and would then act as a turbine. The cart would no longer go DDWFTTW, but instead would go directly upwind. You could achieve the same results by simply putting smaller wheels on the cart.

The prop wash IS the air. It is acted upon by the prop in precisely the same way that air is acted upon by a wing.

19. Mar 14, 2009

### rcgldr

Flow at the prop is slower and at higher pressure than aft of the prop, as the air continues to accelerate and decrease in pressure (back to ambient) aft of the prop. This zone of accelerating speed and decreasing pressure aft of a prop could be interpreted as a "buffer of high pressure air".

http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

Airplane taking off or flying in a tailwind situation.

Agreed. Upstream relative to cart, downstream relative to ground.

This still doesn't cover the case for no limit on power. Imagine that the driving wheels on a cart also drive a generator as well as the propeller. What's the optimal situation for generating maximum power to the generator? Seems to me that the faster the cart goes, the less power left over to drive the generator.

20. Mar 15, 2009

### spork

Yes, that is basic actuator disc theory. This dynamic is no different than it is behind the prop of an airplane in flight (or on the ground). What it is not, is an explanation for how the tailwind can push on the cart that is outrunning it. For that theory to have any meaning, the "buffer of high pressure air" would have to be increasing in length at a rate equal to the cart's velocity minus the wind velocity. This is clearly not the case. The pressure and velocity profile you're describing is constant at steady-state.

A tailwind doesn't figure into the aerodynamics of a plane in flight. Everything about the velocity and pressure profiles around a plane flying upwind is identical to those profiles for a plane flying downwind.

I thought we were onto a whole new topic. I thought I explained that satisfactorily above.