### Olympic Snowboard Physics - the 1440 Triple Cork

Slopestyle snowboarding will make it's first appearance in winter Olympic competition this year. It'll be a thrill to see some of the world's top competitors going at it in one of the most entertaining forms of the sport.

Without a doubt, whoever takes home gold (and probably silver and bronze) will have to land a stunning and relatively new maneuver known as the 1440 Triple Cork.

Check out this video of Billy Morgan, one of the first people to master the confusing maneuver.

It can be tough to follow, but basically the move consists of four complete rotations (4 x 360 degrees = 1440 degrees) and three instances where Billy appears to be roughly upside down (i.e. inverted in snowboarding lingo).

The maneuver looks complicated, and is certainly one of the most difficult moves in the sport. You have to wonder how anyone could manage to put all the pieces together to land it consistently in competition. Fortunately, snowboarders have physics on their side, which makes this trick (a tiny bit) easier than it looks.

In order to get a handle on what's happening during the 1440 Triple Cork, first consider my snowboarder sketch.

 For those who care, I modified this sketch so it uses a right-hand coordinate system, not that it matters for the post - 2-7-14
Each of the dotted lines is called an axis. They are natural ways to talk about direction relative to a snowboarder. The z-axis is a line running from the center of the board up through the rider's head. The x-axis runs parallel to the direction from the back tip of the snowboard to the front tip (i.e. the forward direction), and the y-axis points into the page, going in the snowboarder's stomach and out his back.

Rotations around any one of these directions are much easier to grasp than a 1440 Triple Cork. Take a look at these three examples to see what I mean.

First, a 1440 spin around the z-axis.

A triple rodeo (i.e. a barrel roll) demonstrates rotation along the x-axis. See Billy Morgan pull one at about 1:35 in this video.

And a triple front flip consists of rotations around the y-axis. Here's the first triple front flip ever landed in competition.

As hard as those three moves may be, they're at least visually and conceptually simple. That's because things tend to rotate well around the sorts of axis I've sketched above. For this reason, they are called axes of symmetry.

If you try to spin something around a line that's not an axis of symmetry, you end up with complicated motion, as is the case for a 1440 Triple Cork -  or this rectangular block.

The orange lines labeled 1, 2,and 3 in this video are the three axes of symmetry, but this block is rotating around a purple line labeled H. That mixes things up a lot. Essentially, the block appears to be tumbling, but its really just spinning around its z-axis and swinging around H. This swinging is technically known as precessing. The farther H is from all the symmetry axes, the more pronounced the precessing would be.

This is exactly the motion that a snowboarder goes through during a Triple Cork. If you imagine that the left end represents the snowboarder's head, you can see how he would be inverted at various times in flight.

The trick begins with the snowboarder throwing himself into a spin around his z-axis while leaping to one side. This knocks his axis of rotation off of the natural z-axis, leading to the precessing spin that causes him to turn nearly upside down three times for every four spins.

Because Morgan is in the air for a relatively short time when doing a Tiple Cork and has done a great job of choosing a rotation axis very far from any of his axes of symmetry, it's difficult to recognize the precession even if you know what's happening. It's easier to see in this animated gif of a poorly thrown football in flight (which I lifted from a great site that explains the same sort of motion I've been talking about, except for footballs.)

Of course, this ball would have to be much more poorly thrown to get anywhere near the precession magnitude that Morgan is able to achieve.

One final puzzle is how Morgan can consistently spin four times and precess three times. In other words, why does he always do a 1440 Triple Cork, instead of a 1440 Double Cork sometimes or 1440 Quadruple Cork? It turns out that the relative rates of spinning and precession depend on how the mass is distributed in the spinning football, or block, or snowboarder. (Wobbling footballs, for example always precess four times for even three spins, regardless of how big the wobble is.) Provided Morgan crouches and grabs the board the same way every time, he will always precess three times for every four spins.

All he needs to do is hit the jump with enough speed, launch with a motion that puts him into a wobbly, precessing flight, and hold the correct body position. If he can do all that he will perform a perfect 1440 Triple Cork every time.

There is a little room for adjustment, however. If he finds he's rotating to slowly, Morgan can speed thing up by compressing himself into a tighter crouch. If he's rotating too much, he can slow things down by loosening his crouch or extending an arm. But those things usually come near the end of the move and don't affect most of the flight.

So what's next? An 1800 Quadruple Cork? Possibly - but it's probably going to require a much bigger jump to achieve the hang time that spinning 5 times would require.

What might be easier, believe it or not, is a 1440 Quadruple Cork. All that would require is the snowboarder crouching much less that Morgan and others do during cork tricks. By stretching out more along the z-axis, they would dramatically increase their precession to spin ratio. It wouldn't look as cool, in my opinion, as the grab that most snowboarders perform during cork tricks, but it should be possible. Then again, some things are much easier said than done.

1. this is the most boring stuff ever

2. Shaun white just won the gold with back to back 1440's. I had no frickin idea what it was. It's amazing!!

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