How to sail downwind faster than the wind?

Recently a group set a record for sailing a wind-powered land vehicle directly down wind, and a speed faster than wind speed. Wikipedia has a page talking about it, but it doesn't explain exactly how it works.

I can imagine some configurations, but I don't get how a system could be set up to push forward with a tailwind (when the cart is moving slower than the wind) and push forward with a head wind (when the cart is moving faster than the wind).

Could someone help explain how this is possible?

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This problem has been beaten to a bloody pulp across the web over the last year or so. google.com/… I personally wrote about it in the comments on blog posts in two places scienceblogs.com/dotphysics/2008/12/… [comment 1] scienceblogs.com/dotphysics/2008/12/… [comment 2]. Or see scienceblogs.com/goodmath/2008/12/… or en.wikipedia.org/wiki/Sailing_faster_than_the_wind – Mark Eichenlaub Nov 17 '10 at 6:29
Sailing faster than the wind is possible.For good explanations read the physics of sailing and Terry Tao's blog post. – Pratik Deoghare Jun 7 '12 at 17:23
Sorry to nitpick, but I'm asking specifically about sailing faster than the wind directly down wind. I'm not sure if that's what you're referring to or not. – Steve Armstrong Jun 8 '12 at 23:06

It does sound counterintuitive. The actual device used gears attached to a wind turbine. Even though the turbine was moving faster than the wind, the thrust (IIRC) was such as to slow down the wind field. So energy was being extracted from the wind field to turn wheels via the right gear ratio. In any case energy is removed from the wind field so no laws of physics were violated. Traveling at angles to the wind is easier to visualize. In fact wind turbine blades travel at right angles to the wind at multiples of the wind speed. But that is different. This was a really clever device, and unless shown how it works (I don't remember the details) most physicists think "no way". I suspect it might have to be pushed to faster than wind speed to get it going. Without wheels attached to the solid ground it wouldn't work, its basically increasing the wind field coupling to the solid earth.

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From what I understood of en.wikipedia.org/wiki/… , your suspicion about it needing to be initially faster than wind seems false. But the rest of your answer seems good :-) – Frédéric Grosshans Nov 17 '10 at 13:53
The initial report I read (supposedly from one of the guys judging the attempt) said that for some of the runs, the cart started from rest and the wind did everything: kimballlivingston.com/?p=3971 – Steve Armstrong Nov 17 '10 at 14:52
+1 There is a strong tendency to over-think this problem. Once you "get it" it's trivial. There's another way to demonstrate it that I'd like to try: Take a bicycle wheel and mount anemometer cups on it at about 1/2 of the radius of the wheel, and set it rolling. It should ideally be able to get up to 2V (V=wind speed), because the cups at the bottom of the wheel are travelling at 1V. – Mike Dunlavey May 21 '12 at 14:14
I'm not sure any "extra" energy needs to be delivered to kick the vehicle over the wind-speed limit. Certainly for a device like the Blackbird you'd need some sort of gear shifting at the limit; one could certainly arrange to store some wind energy, probably in the form of a flywheel, which could be used at the limit to give the vehicle the needed kick. – Emilio Pisanty May 23 '12 at 1:01
@Emilio: The mistake is in thinking of this as an energy problem. It's not. It's just a transmission problem. The variable pitch angle of the propeller creates a variable "gear-ratio" between the speed of the vehicle and the speed of the wind. There's no limit to that ratio, but as the speed goes up, the force goes down by the same proportion, so the speed of the vehicle is limited by its air resistance. – Mike Dunlavey May 23 '12 at 14:04

Another explanation.

This has also been explained in terms of a wheel on a treadmill, if you consider the air to be relatively thick and rigid.

Of course, in order to make this work with real air, some of the air will be pushed backward, and since the top of the wheel is traveling forward at a relatively high velocity, air resistance has to be minimized by streamlining, etc. That's why these things don't work if they are casually made.

But basically it's a simple matter of leverage, and exploiting the difference in velocity between the surface and the air.

AND Yet another explanation. Think of the wind as something that pushes, and think of the surface of the propeller as a sliding wedge.

As the wind pushes that surface forward a certain distance, the wedge itself travels forward a greater distance.

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This came up recently on the Skeptics stack exchange.

I was intrigued, so I puzzled over it until I think I understood how it worked, and put the explanation here.

I was a little enthusiastic and got clobbered there for insufficient references. C'est la vie. Even so, it's a nifty counterintuitive technique.

EDIT: Here's another little diagram that illustrates the geometry.

At the bottom is a wheel in contact with the ground, and it is linked by a chain or something to a surface that is being pushed against by a pusher, representing the wind. The initial position is shown in black, and the final position is shown in gray. The surface being pushed against has an angle, or pitch ratio, which ranges from 0 for absolutely vertical, to 1 for 45 degrees. As the vehicle moves forward 1 distance unit, the pushing surface rises vertically 1 unit, so it is following a 45 degree path up and to the right. Depending on the pitch of the pushing surface, the pusher moves forward anywhere from 1 unit to 0 units. So the pitch ratio determines the speed ratio between the wheels and the pusher, just as if it were a transmission.

So, for instance, if the pitch ratio were 2/3, the ratio of wheels-to-pusher distance travelled would be 3. Of course, to get higher speed ratios depends on things like friction, efficiency, etc.

FURTHER EDIT: Possibly this image illustrates it better:

There is an airfoil which is following a helical path because it is geared to the wheels. It has a pitch angle, and thus an angle of attack with respect to the helical path. In a given dt of time, the airfoil travels a distance dX in the X direction. In that same amount of time a parcel of air is deflected a distance dx in the X direction. There is a ratio dx/dX and its inverse dX/dx. Thus the angle of attack determines whether the wind drives the vehicle forward or backward, at any "gear ratio", or not at all.

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The wheels use regenerative braking drive a propeller/turbine to provide thrust not the other way around.

In a typical sailboat or other wind powered craft the wind provides thrust and the resistance given by the conveying mechanism (water or wheels) is typically minimized.

In this scenario however, the wheels have a little bit of regenerative braking applied to them and the power collected is used to power what is effectively a rearward facing fan.

Without powering the fan the speed of the vehicle would top out just a little below the speed of the wind, when the thrust from the stationary propeller equaled the drag on the wheels. Adding the regenerative braking would increase the braking force, but this is more than made up for by the increase in thrust from the propeller. Through gearing we can apply whatever ratios we want but we have to expend less power than we generate.

Available Power

$$P_{braking}=V\,F_{braking}$$

Propeller Power

Propellers are complicated, but as a first (very bad) approximation we could use the same formula

$$P_{thrust}=V_r\,F_{thrust}$$

But here we have to use the velocity of the propeller relative to the wind:

$$P_{thrust}=(V - V_w)\,F_{thrust}$$

Since the wind is blowing forward we'll use less power than we generate if we apply enough thrust to balance the braking force, which means we'll have extra power to apply more thrust and accelerate.

Better approximation of the thrust-power-windspeed relationship to come...

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The reason is in the mechanism of the force that drives the sailboat. The mechanism is not the pressure that the wind excerpts on the sail, but the lift that is created by the wind flow around the sail. So it is the Bernoulli principle that is powering the sailboats.

edit: Sorry, I didn't notice that you said downwind...

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LOL... nice vote. – Vagelford Nov 24 '10 at 21:51