# Windicated!

One the first posts here at complementary slackness was on the apparent phenomenon of a machine that can go downwind faster than the wind (DWFTTW). Now it’s been convincingly demonstrated by Rick Cavallaro and co at fasterthanthewind.org and verified by the North American Land Sailing Association that DWFTTW is possible; their cart traveled directly downwind at 2.8 times the wind speed.

Does anyone know of scientific articles on this phenomenon?

[Edit: after further thought, my earlier arguments on how it might work don’t seem to have been “windicated”. So I updated the post DWFTTW accordingly.]

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### One response to “Windicated!”

1. Here’s an alternative argument, which concludes that it should even be possible to go upwind:

Propellers are a bit slippery to reason about, because you get sidetracked into worrying where the excess air ends up when you slow it down in order to extract work from it, and so forth. Instead, imagine that we let the density of the air go towards infinity and that the propeller is “ideal” in the sense that it always rotates at a rate proportional to the (positive or negative) airspeed of the vehicle. Any torque that attempts to force the propeller to rotate at a different rate will become (with 100% efficiency) a forces that accelerates or decelerates the car accordingly.

Now, with this idealization the propeller simply works like a slip-less wheel that rolls on the airstream. So instead of an air propeller, we can equally validly consider a car that rolls on two parallel conveyor belts that move with different speeds. The left conveyor belt represents the ground and the right one represents the wind. Let the conveyor-belt car have four wheels, and put a differential in the front axle and an inverse differential in the rear axle.

No matter how the car itself moves, the output shaft of the front differential will always rotate at a rate that is directly linked to the difference in speed between the left and the right conveyor belt. This is a constant, and provides an energy source we can use for any mechanical work we’d like. The rotation of the output of the rear differential will be proportional to the car’s velocity relative to the average velocity of the two conveyor belts. Connect the two differentials with an appropriate adjustable gearing, and you can in principle make the car travel at any desired velocity with respect to the average-of-the-belts system.

(It’s now a simple matter of algebra to show that the two differentials can be replaced by a single simple gear).

In reality the propeller is not ideally equivalent to a wheel. However, a difference between the actual rotation of the propeller and the ideal rotation that matches the current airspeed will always lead to a force pair that tries to minimize that difference, so a real car will tend to accelerate as close to the ideal state as the various internal losses (such as air drag on the non-propeller components) will allow.