The Great Wind Cart Controversy

I recently came across the long standing discussion on whether you can make a wind powered cart that can travel directly downwind faster than the wind itself.  If you want a poster-child for contentious online discussion, you need look no farther than the DWFTTW (Downwind Faster Than The Wind) brouhaha.  It comes complete with home experimenters, free energy enthusiasts, quotes of the laws of thermodynamics, questions about the equivalence of experimental conditions, and accusations of chicanery.  If you want to come up to date on the whole thing, check out Mark Frauenfelder's post (http://blog.makezine.com/archive/2010/11/what_ive_learned_about_wind_carts.html)at the makezine blog for a comprehensive review and analysis.      

Against my better judgement, I'm going to put in my 2 cents.  Thinking about this problem has lead me down a pretty circuitous path to a conclusion that I never would have expected.  Sometimes reality has a way of smacking you down, then giving you candy. 

I definitely started on the nay-sayer side of things.  To my mind, the wind was turning the propeller, which was then turning the wheels.  Sure, I thought, when you first let the cart go, the wind is turning the prop, which is driving the wheels, but as the cart's speed increases, its apparent wind would decrease.  By the time it reached the absolute speed of the wind, it would be seeing no apparent wind, and so no driving force to keep it moving.  You certainly wouldn't see it continue to accelerate.  That's patently ridiculous, I thought to myself.  In fact, if you could get it going faster than the wind, it would be seeing wind from the front, and the driving force would be trying to slow it down.

"Aha!  That's where you've got it backward!" the supporters would say.  The propeller is geared so that as the cart moves forward, the wheels turn the propeller, which pushes the air back and drives the cart forward like a swamp boat.  So there!

Now wait a minute!  You're telling me that the cart moves forward, which turns the wheels, which drives the propeller, which pushes air back, which, thanks to Newton's first law, pushes the cart forward even faster?  My father once told me about this great invention he thought of as a child.  Make a car where the front wheels are coupled to the back wheels using a 2:1 gear ratio.  Push it forward, and as the front wheels travel a centimeter, the back wheels will want to travel two.  The car will accelerate forever!  Of course, once he thought about it a bit more, he realized what he really invented was a car that you could only move it you were dragging at least two of the wheels.  This "wheels driving the propeller" explanation sounded a lot like a not terribly efficient variation of my father's illusory "faster forever" car. 

So then I thought about how one really would make a DWFTTW cart, assuming it were possible.  The obvious thing was to start with something that was at least close.  Here's a thought experiment.  Like many thought experiments, this will require AEAEEA (Arbitrarily Excellent and Exceptional Engineering Abilities) along with a small dab of unobtanium to grease the wheels, but bare with me.  It's no secret in the sailing community that you can, in fact, travel faster than the wind.  It comes from the fact that you can also travel upwind.  Not directly upwind, mind you, but at some angle to the wind.  If you're familiar with the sailing theory, you can skip this review and go straight to the thought experiment.
 
Let's take a look at this picture of a boat on a close haul.  The wind is coming in and filling the sail, which is forming a nice, curved airfoil shape.  As airfoils will do, the sail is generating lift in the direction of the black arrow.  The boat would simply move sideways, except for the keel, which has lots of drag from side to side, but only a little moving forward.  The sideways force is counteracted by the keel (that other black arrow) and the net effect is that the boat moves forward, even though it's moving partially upwind. 

Now a boat will only experience the actual wind speed and direction when it's at rest.  As soon as it starts moving, there is also the apparent wind created by that motion (think sticking you hand out the car on the highway).  Imagine a boat starting out on a beam reach: that's traveling at 90 degrees to the wind.  If is has low drag, it could easily get as fast as the wind speed.  The wind that you'd actually feel on the boat is going to be the vector sum of those two speeds.  Its going to be coming from closer to the bow, and it's going to be FASTER than the actual wind speed.  If you can sail that close to the apparent wind, then you can probably go even faster.  If you can really reduce drag and sail close to the wind (like in an ice boat) you can travel at as much as ten times the wind speed. 



Now boats have a lot of drag to contend with as the plow through the water.  By comparison, carts on land have almost none.  So imagine now that you're in a land yacht, traveling at 90 degrees to the wind, nice and fast, and you start to turn downwind.  You could find yourself in a situation like this.  You're going almost with the wind, and just as fast, or even faster.  You're speed is partially canceling out the windspeed, but because you're not going directly downwind, you still experiencing some wind.  For a cart that's more than enough to keep moving, and even accelerate.  It's not the fastest direction to sail (that's the beam reach), but you can still outrun the wind. 

Like I said, it's no secret that a boat can go downwind, and do so even faster than the wind (it's called a broad reach), but that wasn't the question.  The question was can you go DIRECTLY downwind, and keep going faster than the wind.  You clearly can't do it this way, because there is one thing that any sort of sailing vessel can never do, and that's sail straight into the wind.  Once you turn you're speeding yacht straight downwind, you're apparent wind will be coming from dead ahead, and you'll lose power. 

THE THOUGHT EXPERIMENT

Ok, this will work better on land yachts or ice boats, but I'm going to go back to my dinghy graphic because that's what I can draw.  We've established that one boat can go almost downwind faster than the wind, so let's make a catamaran out of two dinghies with a Rube Goldberg accordion arm between them.  You start out running the two boats away from each other on a broad reach.  When the arm is about to reach it's limit, you jibe and start bringing the boats closer together.  Repeat as needed. 



"Now wait just a darn minute!" you say.  (Yes, dear reader.  I'm imagining you just turned you into Jimmy Stewart.  I don't know why)  "It's a cheat.  You have two boats, and neither one is going directly downwind."

Ah.  That's where you're wrong, Jimmy.  I don't have two boats.  I have a double rigged stretchy catamaran thingy.  If you stand in the center of the accordion arm, you are always at the center of mass of the vessel, and you are always going straight downwind.  I admit it's a bit complicated, but maybe we can simplify things.  I'd be afraid of pinching a foot in the accordion as is closes anyway.  Instead of that, let's put a rigid bridge between the two boat hulls.  And instead of having the hulls move back and forth, let's just mount the rigging on sleds that slide back and forth on a track we'll place along the bridge.  Tilt them one way relative ot the wind and bring them together, then jibe them the other way and move them apart.  The only cost to us that now we're actively driving the rigging back and forth, but we could drop a water wheel or what-not over the side to trade a little of our forward momentum for the power.  We'll also want to control the speed the rigs move to best emulate the lateral movement you got from the boats before. 



All this jibing back and forth is getting tiresome.  If we could somehow make the sails pass through each other, they could travel the whole length of the bridge and we'd have to jibe them half as often.  What if we made a double decker bridge?  Then the each sail could be on a different level.  They will simply pass one over the other in the middle. 

Ok.  So far so good.  Now what if at the ends we... 

Wait. 

Hold on. 

Do you see what we have here?  Think of what's going on at the center of our double decker bridge as the two sails pass each other.  The sails are behaving like airfoils, yes?  That's what sails do afterall.  They are canted in opposite directions to each other, and moving in opposite directions.  Where else have we seen something like that?  Answer: the top and bottom of a spinning propeller. 

While both sides of the argument talked about the importance of wheels and propellars, there was an implicite assumption about the rod/chain/belt/gears that connected them.  We all assumed that the linkage was supposed to be carrying the torque that ultimately propelled the cart.  In fact, it's more of an encoder, ensuring that the "sails" are moving laterally at an appropriate speed.  The cart may be going directly downwind, but the propeller blades aren't.  That's where the "cheat" is.  This isn't a wind turbine powered car, or a fan boat on wheels, but instead a sailboat that moves its sails around to cheat about which way the wind is actually blowing. 

Pretty neat huh?  I've managed to talk myself into DWFTTW without having to resort to Clerk-Maxwell's demon, over unity, or the healing power of crystals.  Phew!  Now I'm going  to put on my asbestos underwear and hit "post."