Yep, I got it now.

As far as the speeding up or slowing down, I was saying the stored momentum could be maintaining the speed basically constant, and any variation ie, moving forwards, would be as a result of a slight wind or change in the treadmill velocity. likewise a headwind could "wind" it up, moving it backwards then releasing it and moving forwards.

With a measure of the incline and the treadmill velocity this is less likely. The point of equilibrium is much higher than I would expect if it were stored momentum alone.

Now I'm curious what the effect of less friction between the tires and treadmill would have? What is the down force on the tires as the velocity increases?

Lastly, what happens when I put this on a bicycle? I've got 4 spare bicycles, two pulleys, a v-belt... looks like a busy weekend.

As far as the turntable goes, I'm not big on that. Linear to angular to linear all about a fixed axis hurts my head when I get thinking about it. There's a lot more going on there than just the cart and the wind. I know, I know, rotating frame of reference. Still, the arm to attach it to the table and even the wind is all a little bit different.

I never thought it was a fraud, just needs explaining. The prop generates more thrust than one would expect.

quote:

Originally posted by debunkthejunk:
Now I'm curious what the effect of less friction between the tires and treadmill would have?

If the tires slide, the prop can spin backwards. In one of sporks outdoor videos, a gust of wind does just this, send the cart downwind with the prop turning the wrong way and the tires spinning until the prop gets close to wind speed and recovers.

quote:

What is the down force on the tires as the velocity increases?

This is why the driving wheels are in front. The forward force on the prop also generates some dowforce at the wheels.

I'm not sure about cart speeds well below wind speed, but as the cart speed approaches and exceeds wind speed, the thrust from the prop diminishes, the downforce on the wheels diminishes, but so does the torque from the prop.

Some of us have taken the term "advance ratio" to mean the ratio between effective prop pitch versus wheel circumference (times any gearing factor). For sporks cart, the gearing is 13:16, the wheel diameter is 3 inches, and the prop pitch is 7.5 inches (per revolution) (the prop diameter is 15 inches, which determines the force but not the speed of the thrust).

The wheels advance 3 x pi or 9.4 inches per revolution. The prop advances 13/16 x 7.5 inches = 6.1 inches per revolution. The advance ratio = 6.1 / 9.4 = .647 (this is mentioned in an earlier post).

Zero thrust occurs when the prop pitch speed = the apparent headwind speed. This occurs when (cart speed) = (wind speed) / (1 - advance ratio), when cart speed = 2.83 times wind speed. This is the theoretical maximum speed for this cart. Due to prop inefficiencies, gearbox losses, rolling resistance, aerodynamic drag, actual maximum cart speed is probably around 1.5 times wind speed.

quote:

Originally posted by jeffareid:
The wheels advance 3 x pi or 9.4 inches per revolution. The prop advances 13/16 x 7.5 inches = 6.1 inches per revolution. The advance ratio = 6.1 / 9.4 = .647 (this is mentioned in an earlier post).

I'm not following how this ratio can be tranlated to a velocity? I don't remember thrust being a function of the radius swept out by the tip of the prop? Certainly this is a very complex mechanics problem. Wind relative to the prop, wind relative to the cart, wind relative to the road,thrust,drag,linear and angular momentum. This is a fourth year physics students worst nightmare come true.

Debunk, it isn't as bad as it sounds but it is a bit of a brain teaser.

The idea is to change the momentum of the wind to harness the energy in it, very much like what a wind turbine does but doing it on the run (that's the tricky part). The propeller slows the air down with respect to the ground to harness the energy of the air moving over the ground. That's the essence. The rest is a balance between the rolling resistance of the cart at any given speed vs the energy in the wind, given by the standard wind power graphs.

If the energy in the wind is high enough to overcome the total drag of the cart, the cart will go faster than the wind. The advance ratio is the gearing system that allows the prop to keep pushing the air back even though the cart is above the speed of the wind along the ground. Sort of an overdrive.

The advance ratio has to be between 0 and 1 for the cart to work as witnessed in the various videos.

If the prop is geared to push the air back at the same speed that the air is moving over the ground (an advance ratio of 0), the cart won't work because the prop can't slow the air down as the cart passes through it. The prop is essentially freewheeling.

If the prop is geared to push the air back faster than the air is moving over the ground (an advance ratio greater than 1), the cart won't work because the prop will be using more energy than it can get from the wind (speed difference between the air and the ground). It will be trying to stop the air completely, then add momentum to the air in the opposite direction. If it could do that, it would be a perpetual motion machine!

quote:

Originally posted by jeffareid:
The wheels advance 3 x pi or 9.4 inches per revolution. The prop advances 13/16 x 7.5 inches = 6.1 inches per revolution. The advance ratio = 6.1 / 9.4 = .647 (this is mentioned in an earlier post). Zero thrust occurs when the prop pitch speed = the apparent headwind speed. This occurs when (cart speed) = (wind speed) / (1 - advance ratio), when cart speed = 2.83 times wind speed. This is the theoretical maximum speed for this cart. Due to prop inefficiencies, gearbox losses, rolling resistance, aerodynamic drag, actual maximum cart speed is probably around 1.5 times wind speed.

quote:

Originally posted by debunkthejunk:
I don't remember thrust being a function of the radius swept out by the tip of the prop?

Thrust is a combination of prop diameter, prop pitch, prop speed, and apparent headwind. The prop pitch is how far the prop "geometrically" advances per revolution. This is accomplished by decreasing AOA as the radius increases on each rotor blade. The prop pitch speed is how fast the prop is trying to move the air, the actual speed the air moves / geometric speed is called slip ratio. However if the apparent headwind equals the prop speed thrust is zero because the prop doesn't linearly accelerate the air.

quote:

I'm not following how this ratio can be tranlated to a velocity?

The advance ratio along with wind speed can be used to determine when the apparent headwind = prop pitch speed and zero thrust, and this is the theoretical maximum speed of the cart. The real maximum is much less because of prop parameters. The acutal apparent headwind speed needs to be significantly less than prop pitch speed in order for the prop to generate sufficient thrust (at a low speed) to achieve DDWFTTW.

quote:

Wind relative to the prop, wind relative to the cart,...

Downwind is considered to be postive.

Wind relative to cart = wind speed - cart speed. An apparent headwind is considered to be negative.

Wind at the prop ~= 1/2 (apparent headwind + exit velocity), due to induced wash The pressure aft of the prop is higher than ambient, and continues to accelerate as it's pressure decreases to ambient. "Exit velocity" is the point where the afffected air's pressure returns to ambient.

prop analysis.htm

Thanks guys. The principle makes perfect sense now. I'm wondering what the actual theoretical maximum speed is now. I'm just curious if anyone has a more advanced analysis of the cart motion yet? I'm back in school and really should brush up on my physics. Obviously.

The theoretical downwind speed of the cart is determined by the advance ratio (i.e. the theoretical distance the prop would advance in a single revolution divided by the distance the wheels would roll in that same single revolution of the prop). As the advance ratio approaches 1.0 the theoretical speed of the cart approaches an infinite multiple of the wind speed. For any given advance ratio, the cart's theoretical speed is a given multiple of the wind-speed. However... as we get closer and closer to an advance ratio of 1.0 we can tolerate less and less frictional loss.

The curve showing the acceptable losses for a given advance ratio takes a pretty steep slope in the neighborhood of 2.5X wind-speed. To do better than that requires extremely efficient transmission, and prop, and very low rolling resistance. Also, at higher multiples of wind speed, the aerodynamic drag of the cart's frame or body becomes a bigger issue.

So it's impossible to simply say the theoretical maximum speed of the cart is X. Because the theoretical maximum speed is actually unlimited. What you can do is predict the actual speed given the performance parameters of the transmission, prop, and rolling resistance.

Interesting update on this "Myth"...

JB and I have now given a seminar on these "downwind faster than the wind" vehicles at San Jose State University and Stanford. There is a Berkeley student that is trying to get us an invite to speak there as well. She approached Berkeley professor, Nobel Prize winner, and advisor to Obama - Dan Kammen about that invite. She gave him links to our video.

Kammen told her it can't work. So it gets interesting again (at least to me).

Another update: spork et al are presently working on a much larger manned cart that should be finished next spring. The goal is to reach 2X the windspeed.

You can also follow his progress on the build at this site.

Congratulations on your progress.