Geometry / Phsyics of Slalom

[JAS]

Ok guys, after watching some Youtube of Karina's 1@41 and being totally amazedwith her smoothness, I stumbled on a short clip of Wade Cox from Edged in Water.

 I bet I've watched the overhead footage 50 times, focusing on the Wade's angle cross course, rope angulation relative to ski angle, Upper body rotation relative to ski angle. edge change locations. I'm kind of a visual learner and this vantage of a great skier brings many of the concepts together. A few thoughts

Importance of keeping handle tight to hips at edge change may have more to do with changing direction of skier. After all it is the swing of the skier that brings him up on the boat and ultimately maximum width in the course. Reduce swing up on boat, reduce width. The skier as a ball of mass going cross course would continue going cross course without imput from ski and/or rope. Rope tension directed to skier center of mass swings skier into arc matching handle path and allow ski to take independent wider path. Since less load on the ski ( rope is doing some of work to change path of skier mass) less load/drag and more speed at the ball.

Conversely if arms are let out then the force on the rope is at the shoulders, considerably above skier center of mass, edge change is forced, harsher, cutting short its cast, creating more drag. With narrower path the skier slows sooner, doesn't advance as much on the boat, and finishes turn with less velocity.

Also check out (1) Upper Body rotation behind the boat to allowing the ski to cast wide, (2) actual skier cross course angle (3)Upper body counter rotationand forward reach at the ball,  (4) Quickness of turn and hookup (5) Skier path vs Line  angle (can see zone where line tension in critical and where it is not.)

Just good stuff, what do you guys see?

[miski]

JAS - I think you are right on in terms of the physics of arms in and using the rope for the swing up to the side of the boat. I also think what you mention here is one of a number of cases where physics makes it easier to understand as opposed to harder. For a moving mass to changed direction, a force component perpendicular to the path is required. For the ski to do this, it has to have a slip angle relative to the path - if you zoom in on this video or look at many still images from overhead it is easy to see this slip angle. The higher the slip angle, the higher the force... But, with slip angle comes induced drag because the force the ski generates is perpendicular to the ski and not purely perpendicular to the path, so there is a drag component from the turning force.

The rope alternatively is free force perpendicular to the path (until the ski path diverges from the handle path which occurs mostly through the reach). So, keeping the handle fixed relative the mass center uses the rope as opposed to the ski to change path and reduces induced drag from turning with the ski.

There are two other angles combined with slip angle that seem to define the state of the ski - roll and plane angles. These don't get talked about much, but for me anyway make things easier to understand. The slower you go, the more plane angle is required to generate the force to keep the skier on the water and not in it. With planing angle, you get the same induced drag component as with slip angle, so the slower you go, the more drag on the ski. So for our pre-turn, this means the more you slow down, the faster you slow down...   Also, it seems that you get more tip up if you finish a turn slow as opposed to fast.

Slip angle has the same speed influence, the slower the ski, the more slip angle required to generate a given lateral force. During the cut, slip angle is required to generate lateral force to resist the line load and accelerate. Limiting the line load when slow and trying to delay the max load until later when ski speed is higher results in less drag getting across the wakes and is why it feels so much easier when you can ski this way.Last case for now: when you combine a slow turn finish and an early pull, giant slip and planing angles make the force requirement very high to "get out of the hole".

Roll is much more complicated and it's effects are determined by rocker, flex, etc...  but roll certainly varies the orientation of the working surface(s) that influence Fy/slip and Fz/planing; for instance I think the more roll you have, the more lateral force you will get for a given amount of slip angle.

This is all similar to aircraft, tires, boat hulls etc... the story of Col John Boyd and his Energy-Maneuverability-Theorum is a fun one with a lot of analogies.http://www.jjraymond.com/books/nonfiction/boyd.html 

Sorry to bombard this new thread...   also, this doesn't mean I can do any of this on the water J 

[miski]

No comments? Is this the virtual cold shoulder?  JAS ???

I never thought about any of this until reading all of the great posts on here... since you ruined all of my happy day-dream time, the least you could do is provide a little feedback :)

[Thomas Wayne]

Jack Horton, et al (at Horton Lakes) used to have an instructional phrase they would chant: "Bend your knees, look up at the trees, give me a hundred dollars please."

Of course they said that in jest (and probably not to the people paying the "hundred dollars"), but the idea exemplifies what most skiers need in order to learn new techniques: simplicity. Give us a conceptual tool, a neumonic device or even just a simple rule - such as "Consciously read the logo on the back of the boat until your edge change", or "look down the buoy line until you hook up to the handle", or "Counter, crank, load!".  You know, something the average fifth grader can sink his/her teeth into.

When you start talking "roll angles" and "Fy/slip... Fz/ planing" I think you lose a lot of your target audience. As they say in sales and in show business, "Presentation is everything".

That said, I find it interesting; but then, I've always been a bit geeky about practical applied physics. Which reminds me, have you got an extra pocket protector I could borrow?

 

TW

[miski]

I know - just couldn't stop w/ it...   JAS had already put it relatively simply.

What about tip-up and speed though - I was considering changing fin from stock and did move my bindings forward for awhile, but I figured out that if I had high enough speed leaving the turns, my tip was down ok. Does that make sense? 

No slide rule, but how about a Ti-30...

http://www.vintage-technology.info/pages/calculators/t/calctexas.htm

 

[JAS]

Growing up skiing on a river behind an outboard with a stretchy rope I was a yanker and puller for years.  It seemed ridiculous for the amount of time that I put into the sport that I couldn't get past 22@34. 3 years ago had the chance to ski with Rossi and Williams and realized that I was putting way too much effort into my skiing and that mimimizing load was the ticket. Delaying load, holding low as possible, and turning all the way back to the wake has helped tremendously with cross course speed, but I noticed that I was still narrow. This summer I read Bruce Butterfield's comments on handle control at the edge change and added that to my skiing. Suddenly I started to feel like a weight at the end of a string. With this tension in the line after the edge change I immediately started getting farther up on the boat and wider. Schnitz comments on Karina minimal time off the handle provide another improvement with a quicker turn and back to the  handle with more speed.  

But why have these things worked for me? I think MISKI has provided an amazing explaination of the forces that we all struggle against. In reality we are not fighting the balls, but rather we are fighting physical laws. 
Acceleration of mass, drag, change in direction, it that simple. In waterskiing, more than any other sport than I've been involved, what seems obvious is not. For me understanding why something happens helps me understand why something is not happening. I'm 53 and hopefully skiing better each year. Got to love this sport! Thanks MISKI for your insight.

JAS

[WadeWilliams]

Tips and tricks are great but the greater understanding you can have of the physics involved leads to a greater understanding of the movements you need to make behind the boat to give yourself an opportunity to succeed. Waterskiing is easy. Physically strenuous? Yea. Mentally challenging? Ya. Frustrating as ****? Ya, got that too. I would go so far to say there's nothing as hard as waterskiing is when you look at it that way. But technique? ... Technique? Techique is something that is difficult to master but the more you can simplify what you are trying to do the more that you will be in harmony with the physicis involved. The more you struggle to "fight" against phsycial laws, the greater that... it will be a fight! It is not a fight, nor is it supposed to be.

More at  Pro Ski Coach

[JAS]

Wade is right and fighting physical laws is a poor choice of words and not what I actually meant to describe. Why, without physical laws we would have no sport of waterskiing.  For a given skier, at a given pass length, there is a minimum amount of work that must be done to negotiate the ski course. The skier's body movements is the variable that creates movement back and forth, otherwise he/she would simply drag behind the boat. The challenge is to maximize use of positve energy and mimimize creation of negative energy. This was the basis of my thoughts at the beginning of this thread of how handle control contributes to an efficient technique.

 JAS

[Thomas Wayne]

Incidentally, converting Cox's boat path and ski path [from the overhead] to vectors and analyzing those vectors in CAD reveals that his angle to the boat path, mid-wake, is between 60 and 62 degrees.  BTW, based on the skiing, I assume a rope length of -35', but the accuracy of that assumption does not affect the angular analysis.

 TW

[miski]

TW - overhead video is pretty cool - lot's of info there if you analyze it. Could do a NFL type zip-line overhead camera that follows the boat/skier (just would need to figure out how to keep it at same height above the water), then line frames up by the buoys to get the entire path. Also, could scale ski length and frame to frame get speed based on frame rate.

At 36mph, I get 62-67mph for 60-62deg... wonder what the highest minimum speed you -38 guys turn at.

Also, never intended slip angle stuff for on-water mental process...  Lord knows, I can go out w/ something specific to work on, and finish the set and realize I never thought of it once. I just spent the last two days outside the course w/ coach hollering at me: one position through the wakes!, don't squat!, handle down until past spray!...    I think slip is interesting though - for me, it backs up the techniques all of you experts on here talk about. For ceratain it doesn't contradict the comments in the old posts Horton re-posted like Point of Hookup or Cast Out - those are what got the thought process going more in terms of proving them. BTW - really appreciate these posts alot - wish this info was available when I was 18.