## Directly Down Wind Faster Than The Wind (DDWFTTW)

Over a year ago there was an article in Make magazine by Charles Platt inspired by a YouTube video of a propeller-driven cart that allegedly could go down wind faster than the wind that was pushing it…. Everyone’s first instinct is to think “free energy”, or “perpetual motion machine”.

I was convinced that this was not the case, and that the cart could work. I had seen a similar cart presented by Paul MacReady, founder of Aerovironment. I remember him saying “this is the kind of innovative thinking we need to take the world forward”. The cart he showed was built by Andrew Bauer. There is a paper on it apparently, but I have no been able to find it. As described by MacReady, this cart would be operated in windmill mode, that is, the wind would be used to turn the “impeller” and drive the wheels until sufficient speed was achieved, then the pitch on the propeller suddenly reversed so that it is producing thrust, which would increase the cart’s speed beyond that of the wind speed pushing it.

The cart in the YouTube video, built by Jack Goodman, was a simpler design. Its drag alone would propel it forward, the wheels driving the propeller. At some point the cart would reach a speed at which the thrust would exceed the friction and it would accelerate to a speed faster than the wind that was pushing it. This is not a perpetual motion machine, since once the cart accelerates past wind speed, there is a relative wind vector acting against it (that is, there is drag going the other way) and it would achieve a terminal velocity which is greater than the wind speed.

At the time I was very frustrated by Platt’s treatment of the subject. I did not think his primitive construction methods were nearly enough to prove or disprove anything (although since then a very simple design has emerged). I wrote as such in the magazine’s forum and was challenged by Platt himself to build a cart. With the help of some friends, and guidance from Jack Goodman, I did just that.

Front of the cart. The battery pack and servo are for the steering.

The first test with my version of the cart (shamelessly copied with permission from Jack Goodman) was tested on the treadmill in June of 2008. But the steering was not good enough for it to easily stay on the treadmill for long periods of time. After some modifications and arduous waiting it still wasn’t good enough for several minutes of continuous testing, so we had to retort to some guide plates.

The treadmill test is scientifically sufficient to prove that, once at wind speed, the cart can exceed it. If a cart is going down a road at x miles an hour in x mile-per-hour winds, then the wind speed relative to the cart is zero and the ground speed relative to the cart is x. Thus the cart on the treadmill at x miles per hour is exactly the same situation. If the cart can move up the treadmill, or add tension to an anchor rope, as is the case in our tests, then that means that there is positive net thrust, that is, the thrust exceeds the friction and thus the cart can accelerate. The treadmill cannot simulate what happens after that (the relative wind goes from zero to against the cart) or before (when the wind is going faster than the cart). However, the first point is inconsequential, because we are not looking for the terminal velocity, just knowing that it is greater than wind speed. As for the second point, there are numerous ways to get the cart to wind speed if its own drag is not enough: imagine, for example, a set of hinged sales that open flat like a book when the wind blows from the aft and close into a “double flag” when the wind blows from the front.

One way to analyze this from an energy point of view goes as follows: imagine the cart has just reached wind speed; let’s call this state 1. At some short time later, the cart is at state 2. Between the two states 1 and 2, the cart’s kinetic energy change is
$$1/2m(v_2^2-v_1^2)$$
and this energy change must come from the work done by the cart by any external forces over some distance $$l$$ covered in this time. The two forces acting on the cart are the thrust of the propeller $$T$$ and the overall resistance (friction, propeller turning drag, other losses) $$F_r$$. So our equation reads
$$1/2m(v_2^2-v_1^2) = Tl – F_rl$$
If the speed at station 2 is larger than that at station 1 (meaning the cart has accelerated past wind speed), then the quantity on the right side must be positive. That is,
$$T \geq F_r$$
Part of the resistance comes from the propeller itself. It is essentially a rotating wing, so it has lift and drag, and the two can be related by the lift to drag ratio, which depends on a number of factors, but to some extent can be considered a design choice. If we call the ratio $$a$$ then our expression becomes
$$aD \geq D + F_l$$
where $$D$$ is the propeller drag force, and $$F_l$$ are all the other losses combined. This inequality can be simplified to yield
$$a \geq \frac{F_l}{D} + 1$$
Note that if our losses are small relative to our drag, the lift to drag ratio need only be greater than 1—an easy task. Either the losses must be minimized (good bearings, low rolling friction, etc.) or the drag on the propeller must be increased. As bad as that sounds, what this really says is “or the propeller must be made bigger”, or “the propeller must be made to generate more thrust”, keeping a constant lift to drag ratio, of course.

There is another equally superficial analysis which shows that, if taken to wind speed, the cart immediately decelerates. However, initial short-time treadmill tests showed that the cart definitely moved up the treadmill at some speeds; it just wasn’t obvious whether it would do so continuously, or if it was only releasing stored energy or momentum from being held in place on the treadmill.

So it was essential that, in these tests, the cart be allowed to run on the treadmill “indefinitely”, to show beyond any doubt whether or not the net thrust it produced at certain speeds was constant or not. The answer seems to be a most definite yes.

The videos below are divided into two parts. The first probably shows enough for most people; if you’re a real skeptic, you can watch the second one which shows us changing the treadmill speed several times back and forth.

Part 1 of the test:

Part 2 of the test:

By the way, if you want to see other YouTube videos on the subject, search for DWFTTW and DDWFTTW.

1. JB wrote:

Nice job on the cart.

I’m JB and my partner and I are the ones that entered the Mythbusters video into their challenge.

Platt just doesn’t get the inertial reference frame thing with the treadmill, and he certainly doesn’t get the whole “the belt won’t reverse at the moment we go through 0 apparent wind speed”.

This little brainteaser twists so many people up it’s hilarious.

Again, nice work.

JB

Tuesday, November 25, 2008 at 2:41 pm | Permalink
2. JB wrote:

JB again:

BTW, I have the original Bauer papers in .PDF If you wish to have them let me know and I’ll email them to you.

Tuesday, November 25, 2008 at 3:28 pm | Permalink
3. Donkeypuss wrote:

JB, nice work on your carts, too—and the great compilation video.

I want Platt to flat out tell me what he wants to see to be convinced. Hopefully others from Make have noticed the ruckus this cart has caused on the Internet, and give us all a chance to chime in.

Tuesday, November 25, 2008 at 4:15 pm | Permalink
4. spork wrote:

I guess I wouldn’t count on it, but if Platt has even a basic understanding of physics and any intellectual honesty, this video should resolve his lingering doubts: http://www.youtube.com/watch?v=MCB1Jczysrk

Saturday, February 7, 2009 at 11:46 pm | Permalink
5. Alex wrote:

Hey Mr. Donkey,

is there any chance you have worked out equations to describe the motion before reaching wind speed and at wind speed. I am trying to figure out what to include (and being more specific than your combined resistance for my own understanding.)

here are the sorts of questions I have:
when the cart is going slower than the wind, can the force of the wind on its area be considered a postive drag. Is there any negative sort of drag. How might you think of this in terms of relative velocity?

How do you describe the force of the wind on the propeller that is trying to make it rotate opposite to the direction that the wheels are forcing it to move?

Can I have these bauer.pdfs, or can you refer me to JB please?

Thanks!

Thursday, April 30, 2009 at 7:23 am | Permalink
6. Donkeypuss wrote:

Alex:

All the math I’ve done is on this post. It is very rudimentary; a “back of the envelope” calculation. Honestly, I don’t think it’s sufficient to prove much; actuator disk theory (assuming the rotating propeller is a circular plane that provides thrust) has a lot of limitations: for example, if an airplane is stopped at a runway, actuator disk theory says the energy available to the propeller (from the engine) provides the power to move the airplane (thrust times velocity) and rotate the propeller (propeller drag times RPM, more or less). Since the airplane is not moving (velocity = 0), then the RPM would shoot up, because all you’d have left is engine power = prop drag times RPM. This is obviously not the case, because in reality, the propeller is sucking air past it, and that’s consuming most of the engine’s power (hopefully; otherwise it’s a pretty crappy prop).

The two phases of the cart traveling, that is, phase 1, where it’s accelerating to wind speed, and phase 2, where it’s accelerating past wind speed, must be considered carefully.

In phase 1, the cart has beneficial drag in that the drag from the wind on the cart is helping it go forward. There’s a negative force in the “windmill torque” of the propeller, that is, the force of the wind trying to turn the propeller the wrong way. This is overcome by simple gearing; it is much easier for the wheels to turn the propeller than it is for the propeller to turn the wheels (and move the cart backward). It is from this that the discussions about pulling a spool of wire one way or the other arose, I believe. I also think that having a relatively flat propeller (low angle of attack on the blades) makes for a crappy windmill, which also helps: that is, the windmill drag of the propeller, which helps push the cart forward, is larger than the windmill torque, which would make the propeller turn the wrong way and pull the cart into the wind. Note that Jack (the guy who built the cart that started all this) did test his cart in the “windmill” configuration, and it does go into the wind, though obviously not faster than it.

When you get to phase 2—let’s assume when the cart is going right at wind speed—then there is zero drag (on the body of the cart), because the relative velocity is zero. But there is thrust, since the propeller has been turning this whole time. So obviously the cart will accelerate. As it goes beyond wind speed, drag starts pushing against it, so the limit is when thrust = drag + friction—it’s not a perpetual motion machine. So far, several tests have proven this; the treadmill tests prove this, and so do the rotating platter tests.

The real question remains whether or not the wind and the wind alone could get the cart to wind speed in the first place. If the cart had no prop (let’s say it’s a shopping cart in a parking lot), then the maximum speed in a constant wind will be when the drag on the cart equals the friction in it, and this velocity must be less than that of the wind speed. How do you rationalize this? Well, if the cart were going at wind speed, then there is no drag on it, because the relative velocity is zero. But there is friction pushing it back, so it would decelerate. A balloon floating in the wind, on the other hand, has no friction, thus it will go *at* wind speed, because if it went faster, it would have negative drag, and if it went slower, it would have positive drag.

So from one point of view, you can say the propeller drag can be dumped into overall friction, so you have a shopping cart scenario, but you have a propeller providing thrust, too, so if thrust + drag = friction, the cart will stop accelerating. From this point of view, and without going into more detail, you can’t say whether the drag that satisfies this will be positive (cart going slower than the wind) or negative (cart going faster than the wind).

The problem many people have is with the energy point of view. If the difference between the “speed of the ground” (zero) and the wind speed is providing all the energy, and the propeller’s source of energy is the motion of the cart over the ground, how could the cart possibly end up going faster than the wind, which is providing this energy anyway? I think there are some chunks missing in such an argument. I don’t know what they are. Part of it is that the energy standpoint forces you to put relationships between propeller drag and thrust, and I haven’t done this with too much care.

If you wanted to factor in the windmill torque of the propeller, I’d say the key is to just put a constant in front of that force in your equations, and work through until you are forced to make some sort of conclusion, and see if it comes out realistic or not. You’ll get something in the style of what I did, that is, I arrived at the conclusion that the required lift (thrust) to drag ratio of the propeller is realistic, which was enough to convince myself.

I’d also like to get my hands on the PDFs. I haven’t had any luck yet.

Saturday, May 2, 2009 at 9:07 am | Permalink