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Slalom Rope Angles


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  • Baller

So, I was curious and had a little fun with Excel. I decided to calculate the rope angles from center-line for all the line lengths. I had to add a little for skier reach. So, my assumption is that as the line gets shorter, the reach increases. I arbitrarily put in 1 meter of reach at -15 and added 0.1 meter of additional reach for each shortening. For -43 off, the skier reach factor has risen to 1.8 M (nearly 6 ft total skier reach). This seems about right given that a 6 foot person's arm length is approx 1/3 of their total height (2 ft).


Anyway, here are the results:

Line Angle

-15 36.68 degrees

-22 42.26 degrees

-28 48.10 degrees

-32 53.53 degrees

-35 59.12 degrees

-38 64.42 degrees

-39 68.62 degrees

-41 74.23 degrees

-43 84.67 degrees




These numbers kind of support the concept that something different happens at -28 and again at about -35. At -28, the angle rises above 45 degrees. It is the first time that the skier is no longer simply behind the boat and must move up to a neutral, or "free of the boat" position. At -35, the angle is nearly 60 degrees which is just that next geometric threshold.


I'm sure some of my assumptions about skier reach are worthy of challenge. Also, the rope is not fully taunt at the apex of the skier's reach/turn. Still, these numbers are fun to look at and think about.


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  • Baller

Wow! thread resurrection!


So, I have been thinking about your question, @MichaelGoodman. I do not have a scientific answer. Maybe, @Than_Bogan can help me out.


Here's my thoughts, though:

Regardless of the rope length or boat speed, the course itself is a constant. If a skier were capable of skiing directly at each buoy from gates to 1 to 2 and so on, then the path which the ski travels would be identical in total distance. This type of path would resemble a triangle wave. http://www.till.com/articles/QuadTrapVCO/images/disc-plot-tri.gif


Some people think of slalom as more symmetrical, linked turns or arcs, or a sine wave. sine-plot.gif


Still, if that is the path, it would be consistent because the course is a constant.



So, the question is does the path vary due to line length changes?


We can all agree that the path of the ski varies greatly when we compare it to the boat's pylon. We all agree that the skier gets closer to the back of the boat as the rope shortens, and that the skier must move up alongside of the boat further to reach the width necessary to round the buoys as the rope shortens. So, it is easy to dismiss the idea that the ski's path relative to the course is the same at -38 vs. -15. But it is really different?


When, I watch skiers from a vantage point on the shore in line with their path from 1 buoy to 2 buoy, I see each skier take a very similar trajectory across the boat's path. Think about the old slalom theory of "coordinates" which suggested that there is an ideal path all skiers should strive to ski, and that both too aggressive and to easy of a path cause problems. Hmmm...


What does appear to change is the speed of that path.


Again, assuming we are comparing -15 @ 34 MPH to -38 @ 34 MPH, the time the skier is between the entrance and exit gates is the same. So, how can the skier appear to be going faster at -38? Well, this is because the range of speeds the ski is traveling from buoy to buoy is greater at shorter lines. I think that the -38 pass requires the ski to accelerate more and then decelerate more than the -15 pass.


So, does the greater variation of speed affect the ski's actual path through the course? Maybe, maybe not.


The more I think about this, I am starting to wonder if the skier's comfort/confidence is the primary variable which affects the ski's path. By this, I mean that if a skier's hardest pass is -32, then that pass will look more like a triangle wave than a sine wave. Same could be said of -39 for the skier who calls that his hardest pass. Further, I would expect that a extreme short-line skier could ski -22 so early that their ski path might start to look more like a square wave with all of the space before the buoy. Clearly the shortest distance between two points is a straight line, so early with space means the ski is traveling a longer distance from buoy to buoy. And if the time the skier is spending between gates to gates is constant, and the total distance traveled is longer, then the ski's average speed must be... faster. (Recall, the current popular adages: Speed in the right direction is a good thing. Maintain a higher average speed. These ideas are the result and enablers of skiing a path with early space.)


So, I think the more skilled the skier and the easier the line length, the more distance is traveled. The harder the pass, the more the ski's path loses the extra space and approaches a buoy-to-buoy, straight line. This happens at the skier's hardest pass regardless of the line length. However, I do think that skiers who can successfully get into -39 are more likely to ski an earlier path due to their skills. Thus, they likely ski a greater distance due to their skill.


Now my head hurts. Hope my ramblings gave you something to think about.

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  • Baller

Fellers the Adams at Denali have all of this stuff worked out. You don't have to buy their skis...but they have it worked out as explained in the GUT threads--check 'em out. Their skis happened to be mighty good, too.

You need lots of speed and need to be high on the boat at short line. It becomes more and more dramatic at short lines.

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