Last night, the Mythbusters tested the myth of propelling a sailboat with an on-board fan. At first, the myth seemed busted when the scale model sat still thanks to Newton's Third Law. But, as is usual Mythbuster style, the team decided to ramp up the test to show that it didn't matter how big the fan was, the boat would remain still - but it didn't. Using a model plane engine followed by a model plane ducted fan jet, the Mythbusters were able to get their scaled contraptions moving (albeit inefficiently). This test was finally confirmed using a swamp boat with the fan turned backwards. On a windless day, blowing the 60+mph wind into their sail resulted in forward motion of about 3mph.

Naturally, this was something to talk about at the Nerd Facility I work at with all our whiteboards and geeks. Discussions abounded about why the myth worked from recycled force vectors and sail design, air compression and expansion collisions to air escaping the sail imparting an additional force (like a rocket nozzle). But in the end, we kept negating all of our explanations by falling back on Newton's Third Law with a twist of Conservation of Momentum (of the thrusting gas). So what's the math behind how it worked?