Sunday, October 28, 2007

Anatomy of a Monster Aerial

When snowboarding's living legend Terje Haakonsen launched off of the big quarterpipe at The Arctic Challenge last March, he sailed 9.8 mind-blowing meters (32 feet) in the air. He set the world record for big air on a snowboard and gave us some wicked footage to boot. Transworld's video is my favorite clip of Terje's air, but the YouTube video below is pretty entertaining too.

I thought it might be interesting to run some of the numbers to see what sort of physics was involved when Terje shattered the record. Here's what I've come up with so far . . .

-Terje's top speed as he approached the bottom of the giant quarterpipe was at least 70.92 kilometers per hour (44.1 mph).

-The g-forces he experienced as he rode up the ramp peaked out at around 4 to 5 times the force of gravity, which means his legs were briefly supporting the equivalent of about 337 kilograms (743 pounds) or more.

-Terje's trip above the top of the ramp lasted just about 2.8 seconds, although I'm sure it seemed a lot longer to him.

-As you may recall from my post about the FMX backflip limit, it takes energy to rotate as well as catch air. Terje set the record with a massive 360 aerial. If he hadn't been spinning he could have gone just a little higher. But it turns out that doing an air-to-fakie instead of a 360 would have only boosted him another centimeter or so. It looks like the Arctic Challenge judges couldn't have measured such a slight difference, so he still would have ended up with the same 9.8 meter record.

What if Terje had approached the hill at world record downhill snowboarding speeds instead?

-At an approach speed of 201 kilometers per hour (124 mph), the current world record for snowboarding, Terje would have sailed about 79 meters (259 feet)in the air.

-He would have experienced a crushing g-force 32 times gravity, the equivalent of about 2400 kilograms (5291 pounds), as he rode up the ramp.

-His total hang time would have been about 8 seconds.

In case you want to check the numbers yourself, I've listed the equations and other information I used to make these estimates below.

The Mathy Bits

Some of the things you need to know to analyze Terje's monster air are

Terje's mass - roughly 75 kilograms

The radius of the Arctic Challenge quarterpipe's transition - about 10 meters

Terje's moment of inertia when he reaches down to grab the board is about 5 kilogram meters^2. (I got that number from page 313 of a book called "The Physics of Sports", edited by Angelo Armenti, Jr.)

The equation for gravitational potential energy, E = m g h


E = energy

m = mass

h = height

The kinetic energy equation, E = (1/2) m v^2

where v is velocity, and v^2 means velocity squared

The centripetal force equation F = (m v^2)/r

where r is the radius of the quarterpipe's transition.

The equation for motion of an object under constant acceleration x = x0 + v0 t + (1/2)g t^2

where g is the acceleration due to gravity

t is time and t^2 is time squared

The equation for rotational energy is E = (1/2) I w^2

where I is moment of inertia

w is angular velocity