Saturday, August 28, 2010

Racing the Wind!

Blog Entry the Third.  This time, rather than weighty matters, I'm going to tackle a light and airy science topic.  The question before us is this:

Is is possible for an object solely powered by the wind to move downwind faster than the wind itself?

Sounds preposterous right?  Turns out it is much easier than you might think, as proven by Rick Cavallaro and John Borton, as recounted in the Wired magazine article.

EDIT:  (Disclaimer) For the record, while I am qualified to talk about physics, I am not by any means an aerodynamics or sailing expert and not conversant with the jargon of either, so I have used some loose terminology below.  For example, where I say "real" or "actual" wind below, I mean "true wind".  I also may not be using the term "tacking" entirely correctly -- or at least it has multiple meanings only one of which is applicable here.  The cartoon vector diagrams do not account for every subtlety, but do describe the "jist" of what happens with the air flow and forces involved.

I just saw that article yesterday, and this is the first I have heard of a great controversy that has raged across the internet among profession and amateur sailors, aerodynamics engineers, and even, apparently Nobel Prize winning physicist advisors-to-the-president.  See the article to learn more.

Simply moving faster than the wind is nothing new to sailors, and is not controversial.  They do it with a technique called "tacking", which has to do with the angle of the boat and the angle of the sail relative to the direction of the prevailing wind.  A sail boat moving across the wind can easily move faster than the wind.

In the diagram above, you can see how it is possible to move faster than the wind.  To understand the basics of a force provided by a sail, wing, or propeller, you don't really have to understand fancy aerodynamics such as the "Bernoulli effect".  What it boils down to is the sail (or propeller, or wing) deflects the flow of air -- it pushes on the air which results in an equal and opposite force on the sail (or wing, or propeller).  Here we end up with a force at an angle to the direction in which we want the boat to go, but the keel of the boat prevents sideways motion.  As long as there is enough force in the forward direction to overcome the drag at a particular speed (the drag increases with speed), the boat can accelerate.  When the forward component of force equals the drag, the boat will move at constant speed.  If you have a big enough sail to generate lots of force, and your boat has a small enough drag coefficient, it can easily move across the wind faster than the wind itself is blowing.

To understand the rest of what I am about to explain, take note of the yellow and red arrows in the diagram.  They show the induced wind and apparent wind felt by the boat.  Induced wind is just the wind you feel because you are moving.  If the air is still and you run at 10 miles per hour, then you will feel a 10 mph wind blowing on you.  The apparent wind is the combination of the real wind and the induced wind.  If the wind is already blowing at 10 mph and you run 10 mph with the wind, then you won't feel any wind, because you are keeping pace with the actual wind -- or you can think of it as your induced wind exactly cancels out the real wind.  If you run at 10 mph, against a 10 mph wind, then you will feel a 20 mph headwind.  If the real wind is a crosswind, then your induced wind will combine with the real wind to change both the speed and angle of the apparent wind.  This is what we see in the above diagram.

Notice the position of the sail and the direction of the force in the diagram above.  This example already has the boat going quite fast, so the apparent wind is coming in at an angle getting somewhat close to a straight on headwind, even though the real wind is coming in from the side.  The angle of the sail is necessary to catch the wind at this angle.  Notice that the force is almost sideways to the boat, but still a little bit forward.  This means that most of the force is wasted against the keel (which prevents the sideways motion), but there is still some force pushing the boat forward against the drag.  It is the forward component of the force that matters -- as long as that is enough to overcome drag, the boat can go even faster.  But the faster you go, the more the induced wind looks like a full-on headwind.  To catch that wind with the sail,  you have to anlge the sail so that you end up with almost all the force going sideways.  This reduces your forward force and eventually the drag (which gets bigger as you get faster) will exactly cancel your forward force (which is getting smaller as you get faster).

Now you know the basics of how a sail boat can go faster than the wind, but this example was for a boat going across the wind.  You can't outrace the wind by gong sideways!  What if we want to go in the direction of the wind?  Intuition will tell you that once you match the speed of the wind, you won't feel any more wind at your back -- your force will have dropped to zero and that means the drag will actually start slowing you down.  In other words you won't even be able to match the wind speed -- you have to go a little slower so the sail catches just enough wind to give you a forward force that matches the drag, and then you coast along at your maximum downwind cruising speed.

Interesting, isn't it, that  you can go faster by crossing the wind than by going with the wind.

How can we outrace the wind if gong with the wind means we cannot go faster than the wind?  The answer lies in tacking.  The above diagram is for a boat going exactly perpendicular to the wind.  But what if we go at an angle, partially with the wind, and partially across it?  Take a look at the next diagram.

Now the boat is going partially with the wind and partially across the wind.  The black, yellow, red triangle in the bottom right shows how the real and induced winds combine to form the apparent wind.  Another thing to look at is the velocity.  Here the velocity is not only faster than the wind, but if you look at the upper left of the diagram, you see that the portion of the velocity in the direction of the wind is faster than the wind itself.  In other words this cartoon boat is moving downwind faster than the wind.  But can this be done in real life?  The answer is yes.  It is just a matter of having enough sail, and a sufficiently streamlined, low-drag ship, so that the forward part of the force in this configuration is greater than the drag.  Real sailors on real yachts do this sort of thing all the time.  It is not controversial, though it may be surprising to anyone who does not already know about it.

EDIT:  I have learned from someone with expertize in aerodynamics and sailing that, in fact, this is not quite common knowledge and not quite non-controversial, even though it has been proven in both theory and practice.  A lack of awareness of this basic fact no doubt contributes to the controversy.

But how can we race the wind directly?  Suppose there is a balloon or wisp of smoke and we want to beat it to a particular point directly downwind?  If we go at an angle, as in the diagram above, then we won't reach our destination.  The answer is to make a zig-zag pattern using the mirror image of the above diagram.  Then we can beat the wind at its own game:

Above we see our boat zig-zag its way to beat a wind-blown balloon across the finish line.  Maybe the balloon should be frowning.

The Controversy

Everything I have explained so far is well known to sailors and to experts in aerodynamics (Edit: or perhaps not so non-controversial).  But it gives you just enough knowledge to understand the "controversy".  If you followed the link to the article and read it, then you already get what the fuss was about.  What I have shown you is how a boat can tack or zig-zag to beat the wind.  The big controversy is whether you can beat the wind in a straight line.  An ordinary sailboat cannot do this for reasons explained a few paragraphs up.  Once you match the speed of the wind, you no longer have a wind to provide any force, so you cannot get any faster, right?

Certainly appears to make sense.  And this is central to the thinking of everyone including respected experts who scoff (or scoffed) at the idea of beating the wind at its own game.

The first way to think about it is to imagine using shorter and shorter zigs and zags (but a lot more of them).  If you make  your zig-zags small enough, you are for all practical purposes just going in the straight line downwind.  But of course a boat can only turn so sharply, and it loses speed on the turns, so this is not a practical approach.  But it is on the right track.

What if we somehow let the sail and the mast move laterally in the zig-zag pattern, while the boat moves staight?  This is in principle the solution.  But the forces involved make it effectively impossible to engineer.

The ultimate solution, then, is to let the sail rotate instead of moving side-to-side.  In other words the sail becomes a propeller blade -- and for balance we'll have at least two blades.  This is the solution used by Rick Cavallaro and John Borton.  But there still is a little more to it.

If the propeller is simply free to turn, it is like a ship without a keel.  Remember all that sideways force acting on the boat?  If there was no keel, the boat would rapidly lose speed and change direction (if it did not just tip over).  And for the propellers, that force would just end up slowing down the propeller and the ship (or wind-car) will slow down as well.

Borton & Cavallaro deal with this problem in their wind-car by connecting the propeller to the wheels with a transmission.  This locks their motion together in a way that is mathematically equivalent to the effect of a keel on the tacking ship.  The equivalent for a straight-downwind-sailing ship would be a kind of "rotating keel" (one for each blade on the propeller all on the same axle).  The rotating keels would need to to be angle to correspond to the equivalent angle of a tacking ship.  A keel is just large flat blade, and angled blades on a rotating axle is just a propeller.  Basically the "rotating keel" would be another propeller, this one underwater, linked to the "sail" propeller with a locked transmission so they rotate at the same rate.  The pitch angle of the "keel propeller" will have a steeper pitch than the "sail propeller".

Edit:  Technically, the rotating keel will act as a 'turbine' not a 'propeller' -- propellers push the medium (air or water) and provide thrust to whatever they are attached to.  Turbines are pushed by the medium, which cause the turbine to rotate.

One last thing.  Some will insist that Borton & Cavallaro's sail car worked by storing up energy in the rotating propeller like a flywheel, and then releasing that energy all at once for a burst of speed faster than the wind.  You can imagine that the transmission from propeller to wheel has a clutch, then they could let the wind spin up the propeller, pop the clutch and have the car rush forward realy fast for a short burst.  If this were the case it would obviously be cheating.  But the way the propeller is locked to the wheels, no appreciable energy is can be stored and released in this way.  If the tail wind stops, the car will slow and stop almost immediately.  The same would be true of my proposed "rotating keel" -- it would not be used to propel the ship forward.  The rotating keel serves the same purpose as the keel in the tacking ship -- it forces the sail-propeller to move in a specific helical pattern which is equivalent to the keel forcing the normal tacking sailboat to move in the desired straight line (at an angle to the wind direction).

Counter-intuitive though it may be, the Borton & Cavallaro car really does beat the wind at it's own game!


Anonymous said...

Nice article. I emailed you some comments.

Rick Cavallaro

Anonymous said...

So when the boat travels perpendicular to the wind this all makes sense since the boat will always feel the force of the wind no matter how fast it is going.

But when it is moving at an angle (on a tack) and has a component of its velocity in the direction of the wind, when eventually it is travelling faster than the wind (that is the boat has a velocity component in the direction of the wind that is faster/same speed as the wind), then the Real Wind vector you have will no longer be a contributing force, correct? If so then the only contributing force is the induced wind, and it's not obvious how that propels the boat forward.

Can you provide a diagram showing the forces when the Real Wind vector doesn't contribute, or explain why the Real Wind vector always contributes? - I'm not a naysayer, I just don't get it :(

Scott Graham said...

That's a good question which reflects exactly why this is so counter-intuitive. The true wind is always a contributor to the apparent wind. The apparent wind is what the sail "feels". Take a look at the second diagram, where the downwind component of velocity of the boat is already faster than the wind. In the lower right of that diagram you see how the induced wind vector (always directly opposite and equal to the boat's velocity) adds to the true wind vector to product the apparent wind vector. Notice that the apparent wind is going in a roughly west-by-southwest direction -- that is the apparent wind is not gong at all n a northerly direction. I think this is what you mean by the real wind no longer contributing (as opposed the first diagram, where the apparent wind will always be going at least a little bit to the north). But the true wind is still contributing -- if the true wind was not contributing, then the apparent wind would just be equal to the induced wind (opposite and equal to the motion of the boat).
The red vectors show what the sail does to the apparent wind -- it deflects the apparent wind and the reaction force on the sail is in a direction almost completely sideways. This is why sailboats need a keel (basically a big "fin" -- think of an upside down shark). Most of that almost sideways force is wasted trying (and mostly failing) to push the keel sideways through the water. Because the force is also a little bit forward, that part of the force is still available to overcome drag and accelerate the boat. The boat will reach maximum speed when the force that can be generated this way (with optimum alignment of the sail) exactly matches the drag.

Anonymous said...

In the second diagram, where the boat is tacking downwind, isnt the 'deflected real wind' shown deflected in the wrong direction?
Logically i'd expect that the 'real wind' must still be deflected opposite to the direction of travel of the boat, which would be left, not right, in your digram?


Scott Graham said...

Hi Steve. Good question.

Take a look at the vector diagram in the lower right that shows how the true wind and induced wind (negative boat velocity) add to give you the incoming apparent wind. Now, assuming you agree that the diagram accurately reflects what happens to the apparent deflected wind, with your minds eye or on paper, draw that same diagram, but also put in another red arrow, anchored at the same point as the existing red arrow -- but this arrow is in the direction of the deflected apparent wind. The deflected apparent wind should also be slightly slower (shorter arrow). To get the deflected real wind, you must subtract the induced wind (or equivalently, add the boat velocity) -- from the tip of your new arrow, draw an arrow exactly parallel and in the opposition direction as the yellow arrow. Now draw an arrow from the anchor point to the tip of this arrow, and that is your deflected real wind. If you have done this carefully, then it will be forward and to the east of the (incoming) real wind.

Actually, having looked at this, I do realize there is a visible mistake. While I have the direction of the real deflected wind correct, it should be slower -- the arrow for the deflected real wind should be significantly shorter.

eyytee said...

As you already noted: The deflected real wind should be slower, than the real wind. This is where the energy comes from in the ground frame: the air is slowed down.

This is an animation that shows the air movement in different frames of reference:

Focus on the red dots. They trace an air particle in equal time steps. In the surface frame you can see that the direction of deflected true wind is the same as in your diagrams, but the dots are denser (slower movement) than before defection.

Scott Graham said...

eyytee, That is a good video. I recall seeing that and related videos when I first began looking into the 'puzzle'.

But I think those videos are a little confusing. Despite already knowing how it works, it took me some time sorting out what was what in that video. Someone coming to this who does not already 'get' it, may be not really be convinced by that video.

In retrospect, I think my wind diagrams are not any better.

What I think is needed is a carefully constructed series of videos that build up a person's intuition about the problem so in the end it becomes obvious. I'm working on such a series of videos.

Stay tuned.

eyytee said...

Scott Graham said: "What I think is needed is a carefully constructed series of videos that build up a person's intuition about the problem so in the end it becomes obvious. I'm working on such a series of videos."

On my youtube channel you will find several animations with different levels of complexity.

This is the simplest one (a lever):

Then you make it continuous (gears):

Or you start with a sail boat as a squeezed wedge:

And then make sure only the airfoil has lateral movement:

This is the most complex one with forces, energy for both directions (up & downwind):