angular momentum and handle control: Lets get our geek on

[gator1]

So, I'm coaching on Saturday, trying to get the skier to keep the handle close to her core. Got me thinking about why this is a good thing.

 

Laws of physics say that angular momentum is conserved. When an ice skater does her spin, she rotates faster as she tucks her arms in. This is because she is decreasing the distance her mass is from the center of her rotation.

 

The formula for angular momentum H=rxmv. r is radius, m is mass, v is velocity. So, assume you've got about a 2 foot reach between handle at core and arms outstretched, butt dragging. The r at 35 off is 40 ft (roughly). So a 2/40 = 5%. This means that as you reach out and drag your butt, you immediately slow down by 5%. BUT, as the rope gets shorter, it matters more.

 

At 41 off, you have a radius of 34ft. 2foot reach/34 =6% slow down, just when you want to be maintaining speed. Cool

[MarcusBrown]

not to mention the "reach" is usually always accompanied by an "edge change"....which means, that as you reduce your angular momentum (by allowing your body to travel further from the pylon), you also start edging or carving towards the buoy.

 

AKA....you gain most of your width by staying as close to the handle as possible, for as long as possible....not by casting the ski out towards the shore.

 

that make sense, @gator1?

[Than_Bogan]

Yeah -- I like that way of thinking!

 

Not only is it geeky, but it seems like it's a useful observation in general: On both ends:

 

1) When you want to maintain speed, you need to keep your mass close to the handle.

2) When it's time to slow down, you can do so rather quickly by releasing and skiing away from the handle.

 

These are things that many pros seem to suggest. Jamie B was having me work on both of these. But for whatever reason I never put it in the context of conservation of angular momentum. Obviously there's more going on, but that's a good starting point to model it, and leads to some "actionable" conclusions.

 

Nice thinking.

[Jordan]

Not a geek-like observation but what I think it really does is allow you to remain in a controllable position.

 

When your hands and arms get too far away from your body, it is very easy for the boat to pull the top of your body forward and cause you to break at the waist. When you break at the waist not only is that bad for balance, it transfers the load from your skeleton to your muscles - and they don't stand much of a chance against the pull of the boat.

 

When your elbows are tucked in and handle is near your hips, it is very difficult to get pulled forward or to break at the waist.

 

I know, I know, not physics equation was even mentioned....sorry guys :-)

 

 

 

[Skoot1123]

@gator1 - great point! In addition as you cast the ski outbound you will loose more speed since the reach would then be 2 feet (length of arm) plus the distance from your shoulder to the bottom of the ski (though at my level I don't get near that far layed out). As the effective reach is increased, the decrease in % slow down is exponential.

 

Couldn't this also be used to our advantage - say in a scramble mode?

[ForrestGump]

Damn, you guys make my head hurt sometimes. What happend to turn and lean?!?!?! ;)

[gator1]

@marcusbrown, Um, to be truthful, if you told me anything I'd say "yessir, that makes a ton of sense" even if it didn't, then I'd spend the next 24x7 madly trying to figure out what you said.

 

But, in this case, yes, it make sense as the skiers center of gravity does move even farther away from the pylon as they switch edges. So probably doubling the effect to a 10% decrease in speed right when you want it most.

 

@shaneH, when you are a 98 lb weakling, turn and lean doesn't work. I grew up with a natural athlete (uncle) as coach and mentor. "get in the zone", "just pull harder" "cut later", "don't think about it, its gotta feel right" never worked for me. Had to get a headache to get in the game.

[gator1]

And, this is just another example of the extreme counterintuitive nature of this sport I love to hate. "get wide by staying tight" "get angle by being light on the rope" "turn with the front foot" "pretty girls in swim suits shouldn't be in ski ads".

 

Sometimes it seems like if you are stuck, think about what it seems like you should do, and do the opposite. You'll probably be right more than wrong.

[gregy]

This also explains why some skier seem to accelerate coming around to the handle. Given angular momentum is conserved and you minimize frictional loses by making a smooth turn then if the radius decrease by handle coming back in, velocity must increase.

[Than_Bogan]

angular momentum is conserved relative to an axis moving at constant speed. A frisbee or the solar system are examples.

 

That said, it's only conserved when there is no net torque operating on the system. Marcus showed one example of the skier adding torque to the system. And the water's drag does, too. But I still feel conservation is an interesting starting point to model some of what we want to happen in the slalom course.

 

If it doesn't help you, move along! If it might, take some time to think about it.

[Than_Bogan]

@gregy I don't think that part is going to work. Angular momentum is directional, so the net effect of a turn is to add a ton of torque to the system so as to reverse your angular momentum.

[gregy]

yep definitely a lot going on. It seems to me like two different radii. First the radius of the rope. Then the radius of the skier rotating around his center of mass.

[Than_Bogan]

OH! Gotcha. That may make sense; would have to give it more thought.

[ral]

IMHO, skiing is not that counterintuitive. Altough I can follow all the physics here (lately, I work on doing 3D mineral stockpile modeling based in different types of stacking and reclaiming for accurately predicting feed into SAG mills to be able to have optimal automated predictive control by the DCS over the mill parameters and thus reducing energy consumption and maintenance of the mentioned mills... Or whatever that means...), I do not think that anyone is intentionally avoiding having the elbows against the vest until reaching, and that anyone being able to have great handle control as per the Godfather of the subject (B.B.) by keeping elbows against the vest thru the wakes and after edge change is having too much trouble in their reach process, although probably most of the ones that can do that at 38 off or more have not been on a 7xx level physics course...

[ral]

By the way, for anyone interested (i.e. nobody...), we are talking about 40'+ diameter mills, with 35,000+ HP gearless drives...

[Waternut]

I politely disagree but I may have trouble explaining it in text. I feel like you conserve momentum by keeping the handle close but not in the same way that a figure skater does. A skater has their center point on their body allowing their body to spin about itself.

 

In skiing we are working with a pendulum about the center point of the boat. With a pendulum, the longer the line and the heavier the weight, the more momentum the pendulum carries in the downswing but unless the line length or weight changes, it can't go any higher than it's starting point. If you increase the line length on a pendulum's upswing, you decrease it's acceleration which kills it's momentum which translates into it not going as high and a skier not getting as wide as they originally had hoped.

 

So in my mind, you keep the line length as short as possible to get as far up on the boat as possible and then increase your line length at the last second to slow your momentum and give yourself more time in the turn before getting back on the "shorter" line and accelerating again.

[gator1]

Heyyyyyy, so that was fun! Thanks to all for the thoughtful comments

 

@ral, I accept the challenge: you use a computer to figure out what shape to make the pile of stuff to feed into a VERY BIG mill. Right?

 

@thanbogan I was watching the AM/CP side by side video. They aren't just keeping their arms at their core. They are actively pulling the rope in, and bending their elbows to do that. Although Andy doesn't do it equally on his weak and strong side. (I should probably call him up and let him know I've diagnosed a fault in his technique) So I was thinking WTF are they doing that for? @rico, you are right, they are pulling the handle somewhat higher to keep it as close as possible.

 

@waternut, I don't think you disagree. What you said in your last two paragraphs is exactly the point. Just replace your phrase "as far up on the boat as possible" with "don't lose your speed when you need it most" and we just wrote the same thing. And you are correct, calculating actual gnat's ass correct angular momentum requires two components, the speed with which the skier is rotating about their center of gravity, added to the speed the skier is rotating about a point fixed in space (in this case the "space" is the control volume drawn around the boat and skier, moving at a constant speed with the boat). I left out the speed with which we rotate around our own axis because the angular momentum corresponding to that component is insignificant compared to that resulting from swinging around the pylon.

 

@gregy, you also talk about the two components of momentum, same answer, the spin about our cg is minimal compared to swing at end of rope. The cool thing is as we go from laid out, and ski back to the handle, then lean away from the boat, our CG is moving ever closer to the pylon. The max water velocity we can attain is a factor of strength, form, which result in the ski's minimizing its slip. So if we can keep our cg close to the boat as long as we want velocity, we get to keep the velocity we worked so hard to earn. Where does the reverse C edge change keep our CG? Yep, right up close to the boat. Hmmmmmmm. That sneaky Nate guy....and if we can maximize the effective radius change from full lean to laid out, and do it at the right spot, we can get the maximum effect of this momentum conservation.

 

Sooooo, since it is well past drunkthirty yet again, and in proofing the above it strikes me that I am sounding increasingly pendantic and pompous, I'll sign out now. Thanks to all.