Faster than the Wind

31
August
2010

I have always loved learning about seemingly simple puzzles that smart people vehemently disagree on. The solutions to these puzzles are often very counter-intuitive, and the moment of clarity that comes from seeing that the solution must be true can be an intensely satisfying experience.

Probably the most famous of these puzzles is the Monty Hall problem, named after a game show host and involving three closed doors behind which are two goats and a car. It has a very simple setup, but reveals a very subtle truth about probability and selection that escapes most people when they are first given the problem. When the solution was published in a magazine, thousands of readers wrote in to say that it was nonsense, though it has been proved countless times both practically and theoretically. I won't describe it in detail, but you should read about it on Wikipedia and try the New York Times' simulation.

Another problem that caused a lot of heated debate on the internet involved an airplane on a treadmill which is set to go at the same speed as the airplane's wheels and whether or not it would be able to take off. This has all the trademarks of a problem with a very simple setup but non-obvious solution. Unfortunately, however, the answer is just that the question is formulated in a way that doesn't make any sense. I need only refer you to Randal Munroe of xkcd's beautiful explanation.

I recently learned of yet another problem which has caused many people on the internet to become enraged over other people's belief in a machine that seems to break the laws of physics. (Spoiler alert: This machine can be and has been built.) That machine is one that can travel directly downwind, faster than the wind, and is only powered by the wind.

I gave that description to one of the professors I work with and he was quick to think of a wind-blown vehicle that keeps going from momentum after the wind slows down and of a car that stores energy from a wind turbine and uses it later to accelerate to faster than wind speed. This made me realize that the setup needs to be framed more exactly. Can a car be built that uses only wind power and could be released from resting point in a steady wind and beat a free floating balloon to a point further downwind?

The intuitive answer seems to be no. If you can only use wind power (gravity is also out), then there is no available extra force after you make it to wind speed.

My professor was on the right track when he was thinking of storing wind energy, but it turns out that the wind energy doesn't actually need to be stored to be useful. Rather, it just needs to be kept in the vehicle's mechanical system and used to push back against the wind.

This can be achieved by simply linking a propeller with the wheels of the car, assuming of course that you have a relatively efficient propeller and transmission. The wind energy that turns the prop is also used to turn the wheels, but it doesn't dissipate there. The turning of the wheels in turn helps keep the prop in motion, so that it isn't just turned by the wind, it is turned by the wheels and pushes back on the wind. The propeller and wheels form a feedback loop to ensure that energy that is normally lost to friction is used to accelerate the car.

It might sound like I'm describing a perpetual motion machine, but I assure you that I am not. The beauty of this solution is that is can lose a lot of energy to friction and still be able to break wind speed. I find it most useful to conceptualize the propeller as what is driving the car rather than being the thing that is gathering energy from the wind. If you started the car off with a little push, you'd be accelerated both by the wind at your back and by the propeller pushing back on the wind. As the wheels started to turn faster, the propeller would push back on the wind harder, and increase your acceleration. This would continue until the drag on the car canceled out the wind's force on you plus the propeller's force on the wind.

I had watched this video of some folks who had built a manned cart of this design and struggled through this explanation which uses much more physics than I am used to dealing with, and I was ready to believe that this was possible, but I still hadn't seen why it must be possible. My own moment of clarity came to me when I started trying to explain how the car worked to one of my friends. He too, was ready to accept that it was possible but had to think a bit before he really "got it". His way of viewing it, which I found very satisfying, was to not think about the car as the thing that the wind is pushing on. Rather, you can think about the car and the air that the propeller is pushing behind it as being a single unit. It is the frontier of air between the propeller and wind that gets up to the same speed as the wind, but because the propeller is still pushing the car away from that frontier, the car can end up going several times the speed of the wind.

It is a source of comfort to me that reason can conquer intuition in these situations.

Blackbird can travel faster than the wind.



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