A few weeks ago, one of my roommates took me ice boating. I had never been before, and it turned out to be an unexpectedly thrilling and somewhat horrifying experience.
Ice boats are very fast. Even the simplest ones can move at over ten times the speed of the wind, which means that in our tame 6-10 mph breeze, I was flying over the ice at highway speeds. When I wasn’t too preoccupied by my white knuckle steering grip, the physics nerd inside of me couldn’t help but wonder how these crazy speeds are possible.
A standard ice boat consists of three blades which keep it moving in a straight line along the ice, a wooden body big enough for one person to sit on, and a small sail. A sail works a little bit like a vertical airplane wing, converting wind into lift perpendicular to the sail. Even if an ice boat is pointing close to into the wind, the aerodynamic force can have a component in the direction of the boats travel. Since the blades keep the boat on a straight line, the net result of this is a forward acceleration.
What really allows ice boats to go so fast is their “relative wind”. Someone on an ice boat doesn’t actually feel air moving past them at the real wind speed. Since the boat is moving, the wind speed they feel, or the “relative wind” is a vector sum of the wind velocity and their velocity. Image an ice boat moving at a 90 degree angle to the wind. If the boat is moving 10 mph in a 10 mph wind, the sail will feel a 14 mph coming from a 45 degree angle. If the boat accelerates to 20 mph, the sail will then feel a 22 mph relative wind.
This means the force on the sail actually increases as an ice boat goes faster and faster. The boat will continue to accelerate until its relative wind angle becomes too small, and the force on the sail is perpendicular to the boat’s motion. For a standard ice boat, this is a relative wind angle of about 10 degrees. This is how, even with a small sail, an ice boat can out race the wind which powers it.