DDWFTTW Turntable Test

OmCheeto

Yes.

But what you said was:

"exceeds the speed" is the phrase that troubled me. Can you elaborate?

swerdna

If a cart travels faster than the wind it exceeds the speed of the wind. Travelling Directly Downwind Faster Than The Wind is exceeding the speed of the wind. But as Jeff has just correctly pointed out upwind is not the same as headwind. The cart is going downwind faster than the wind in to an apparent headwind.

OmCheeto

Yes.
Yes.
I didn't interpret that from his post. (see below)
???????????????
It may be that I still have the original FTTW device stuck in my head.
What are we trying to prove again?

rcgldr

No, the ground is also part of the power source. If the ground were frictionless, then the cart would just slide along at the same speed as the wind.

All wind powered devices have to "slow" down the wind in order to extract power from it. The DDWFTTW cart is designed to be able to slow down the wind with it's propeller, even when the cart itself is traveling somewhat faster than the wind.

Requirements: The thrust speed from the propeller must be greater than the apparent headwind experienced by the cart in order to overcome the overall drag and go DDWFTTW. The power output at the air + propeller interface must be less than the power input from the ground + wheel interface (otherwise the excess power consumption could only occur from deceleration of the cart).

"Advance ratio" as used for DDWFTTW carts is ultimately the speed of the air through the prop divided by the speed of the ground at the wheels. It can be approximated by noting the prop pitch (advance distance per revolution), gear ratio, and driving wheel diameter. The advance ratio has to be < 1 for a DDWFTTW cart. The advance ratio is also an effective force multiplier, after losses.

With an advance ratio of .5, prop speed is .5 of the wheel speed, and perhaps prop force is 1.4 times that of wheel force (70% efficiency). With a 10 mph tailwind, and with the cart traveling at 10 mph, the prop speed is 5 mph, and the cart is operating with zero apparent wind. The prop thrust is 1.4 times greater than the opposing force from the driving wheels, enough in excess of the overall drag, that the cart acclerates into an apparent headwind condition. At 12 mph, the prop speed is 6 mph, but the apparent headwind is 2 mph, so the prop only acclerates the air by 4 mph (idealized situation here). The thrust and corresponding opposing force from the driving wheels will be reduced, but the overall drag will increase, and eventually the cart reaches a terminal speed when forces cancel (total thrust = total drag).

With 100% efficiency, the maximum speed of a DDWFTTW cart would be wind speed / (1 - (advance ratio)). An advance ratio of .5 would allow double the wind speed, an advance ratio of .75 would allow quadruple the speed. However 100% efficiency isn't possible. Prop efficiency is 85% to 90%, and there are loss factors due to drivetrain efficiency, rolling resistance, and aerodynamic drag. The actual maximum speed of a real DDWFTTW cart will be faster than the wind, as seen by the videos, but I doubt it's possible to achieve double the speed of the wind, mostly because of prop efficiency issues.

Note that iceboats are a type of sailcraft that when heading at an offset to the wind, can achieve speeds where the net downwind speed is more than double the wind speed. The sail is able to divert the apparent wind so that the upwind component of the diverted flow is faster than the iceboats net downwind component of speed. Note that the primary (non-drag related) force from the ground is perpendicular to the direction of travel of the iceboat, but directly opposes forward motion of a DDWFTTW cart (unless you pair up 2 constantly tacking iceboats via a long connector and call that a DDWFTTW cart), which is why I believe that a iceboat or landsail will outperform a typical DDWFTTW cart.

OmCheeto

And to think I just edited myself a few minutes ago saying we needed a new section at the forum: Scientific Semantics.

Was DWFTTW first posted on the net on or about April 1st, along with cold fusion? I noticed it had around 8000 matches on google.

zoobyshoe

You're saying the force of friction represents a power source?

vanesch

I don't see why DDWFTTW is a problem in this case. DDWFTTW is only not possible if you don't have any "reference" other than the wind. But if you have a ground, I don't see why this is a problem - I mean, why should it be impossible to go downwind faster than the wind ?

After all, the velocity difference between wind and ground allow you to extract some energy, and that energy can be used to drive something. If friction and all that are low enough, you can drive that something faster than the wind speed. Hey, you could have a stationary windmill which sends out microwaves, which are captured by an antenna and power an electrical motor of a car which can then drive as fast as it can.

Nice demonstration, BTW.

atyy

Is there any restriction on the speed of the centre of mass of the windmill and the car? (Sorry, I should be able to work this out myself, but I'm too lazy to think.)

rcgldr

Yes, without friction the maximum speed of any sailcraft or DDWFTTW cart is limited to the wind speed. With friction and a non-parallel heading, a sailcraft can outrun the wind as mentioned before. The DDWFTTW cart uses the force from the ground friction to drive the wheels which in turn drive the propeller. The force from the ground is backwards and opposes the force from the downwind air and the air acclerated through the propeller, but effective gearing divides the speed from gear to prop while multiplying the force. This is useless without a tailwind, since the prop speed would be less than the apparent wind. However with a tailwind, if the cart is moving at near the same speed as the tailwind, the apparent wind is near zero, so even a large reduction of ground speed at the wheels to thrust speed at the prop will be greater than the apparent wind, and the overall effect results in the wind being slowed down, a requirement for a wind powered device.

It's not quite that simple since propellers generate their own induced wash and require their own "advance ratio" in order to generate thrust, but even the effective prop speed is halved (real world losses are much less than this), with a an effective advance ratio of a puny .25, it's still enough to allow the cart to go DWFTTW. For example, if advance ratio is .5 and prop speed loss is another .5, the prop thrust speed is .25 that of the ground speed. In a 10 mph tailwind, the cart could be moving at 12 mph, with an apparent headwind of 2 mph, but the prop speed is 3 mph, generating 1 mph of thrust, and slowing down the wind (by 1 mph), the key principle of any wind powered device, even though the cart is moving faster than the wind, and this (1 mph) reduction in wind speed could be enough overcome all the drag factors and allow the cart to maintain it's speed.

My guestimate is that a efficient DDWFTTW carts should be able to go around 1.5 times the wind speed. I don't know how to determine the actual limit, which depends on how thrust is generated (is there anything more efficient than a propeller for relatively low apparent winds?).

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).

vanesch

No, of course not. The windmill could almost be massless (made out of neutrinonium ?) and the car could go as fast as it goes (call it "lightbullet").

You could consider having two extremely light windmills, planting one down (connected with a rope to your car) that will generate electricity for a few seconds, then fold it up and take it in (with the rope, almost no effort as it is essentially massless), and plant at the same time the second windmill, having it produce electricity for a few seconds, fold it up and take it in while planting the first one again, etc...

A kind of "walking on windmills". Very clumsy, but as a proof of principle, I don't see what stops it.

Of course, there is conservation of momentum, and hence what must remain at the same velocity is the center of gravity of the air (consider a big, but limited amount) and the car, which should move at a velocity slightly smaller than the wind speed (as the car is initially at rest). So we have to "slow down" enough wind to compensate for the increase in speed of the car ; but as there is no limit as to the amount of wind we slow down (or even reverse direction), this doesn't put a hard limit on the speed of the car. This will come out of the energy balance of the whole thing I guess.

Phrak

Jeff, your definition of the 'cart to propeller advancement ratio' greatly simplified the mental picture. None of this has been obvious--witness a locked thread and, so far, the lack of a mathematically formulated proof.

There is an equivalent mechanical arrangment, to good approximation, where the propeller and wind is replaced by a second wheel on a moving surface. In swerdna's case, this surface is stationary with the room. The second wheel is smaller in diameter to obtain an avancement ratio of less than one, as you say. This arrangment should be more intuitive to grasp, without the complications of variable angle of attack.

Just as with swerdna's direct drive wheel and propeller system, there are two mechanical force couplings. These are 1) the rotating shaft, and 2) the rigid member that connects the two wheel hubs. The coupling concept seems to be the useful thing to do to generate vector diagrams.

schroder

Amazing statement! You admit that without a wheel touching down, the cart can go a Maximum velocity equal to the wind speed. Now, you touch down a wheel, introducing friction with the ground, and you claim the cart goes faster! The wheel requires friction with the ground to turn. The force to turn it and overcome that friction, comes from the cart, and ultimately from the wind. That would have to slow the cart down, not speed it up! Unless you truly believe that a wheel can be both pushed and pulled at the same time! Imagine that, an over unity wheel! Simply amazing.

Phrak

Whoa guys! Your definitions are simply different. Jeff means the wheel doesn't slide on the surface. You are talking about rolling friction. Jeff is talking about sliding friction that ensures the wheel spins as it moves over the ground.

schroder

What is the difference?

zoobyshoe

If the cart is traveling faster than the wind, how can the wind catch up to it so the propeller can slow that wind down?

rcgldr

It was mentioned before, but perhaps more in the wiki thread than the previous ones here. The advance ratio has to be < 1 for downwind carts, and > 1 (with prop pitch reversed) for upwind carts.

A similar analogy has been made using a yo-yo and string. The string is wound around the axis exiting forwards at the bottom, while the "wheels" of the yo-yo rest on the ground. If you pull on the string, and there's no slippage, the yo-yo will move forwards faster than the string, by the rate of the speed that the string is wound around the axis of the yo-yo. The string could be replaced by a thin rod that moved along the bottom of the axis of the yo-yo with the same result if there was no slippage. Note that the larger the axis, the faster the yo-yo moves with respect to the string with a similar advance ratio formula, yo-yo speed = string speed / (1 - (axle diameter / wheel diameter)). The speed increases as the ratio approaches 1 (at > 1, such as a thick axis with smaller hubs resting on a pair of rails, the yo-yo goes in the opposite direction, similar to an upwind cart requiring and advance ratio > 1.

I think the issue here is that using the air as a power source is more "lossy" than using a solid.

schroder

Which is an example of gearing and pulleys and has nothing to do with the present topic.