GUT 104

In slalom, the skier maintains a constant connection to the handle.  This physical constraint ultimately defines the skier’s path through the slalom course.  In other words, the skier can only go where the handle goes.  Specific elements within the system dictate how the handle moves, and therefore how the skier moves, through the course.  Understanding the relationship between these elements will help build the foundation for more detailed GUT chapters.

Chapter 104 will explain how only three variable elements combine to dictate the handle path.  This discussion is broken into two parts.  The first part looks at the motion of the handle relative to the boat.  The second part looks at the motion of the handle relative to the slalom course.  

Part 1: Motion of the Handle Relative to the Boat

To get started, let’s investigate the motion of the handle with respect to the boat while ignoring its down-course travel.  There are only three variables that define the motion of the handle.  They are:

1. Length of the rope

2. Swing height

3. Swing speed

Rope Length

Like a pendulum, the handle swings on a fixed circular path around the pylon.  This path is always a semi-circle (assuming no slack) with its curvature defined by the rope length.  As the rope gets shorter, the radius of this curvature becomes tighter.  Also, since the width of the course is constant, the overall length of the path traced by the handle, called the Arc Length, will increase as the rope gets shorter.  This is graphically shown in Figure 1, below.

Figure 1 : Handle Motion 23m & 10.25m

Swing Height

Figure 1 also illustrates something about swing-height.  The swing-height, or how high the handle must travel on the boat for the skier to reach the buoy line, increases as the rope gets shorter.  The point when the handle reaches its maximum height is called the “handle apex.”  It should be noted that the handle apex is not the same as the ski apex – more on that in a later section of GUT.  The greater the swing-height at the handle apex, the wider the handle will be in the course.  Since the total width of the course is a fixed distance of 23 meters, a minimum swing-height for each line length is needed to reach the buoy and run the pass successfully.

Swing Speed

Like a pendulum, there is a symbiotic relationship between swing-speed, how fast the rope swings around the pylon, and swing-height.  Greater swing-speeds can help the skier carry the handle to a higher point on the boat.    Similarly, starting with a high handle apex can improve the skier’s ability to generate speed.  The faster and higher the handle reaches its apex, the earlier in the course that apex will be, and the wider in the course the skier can travel during the reach and extension.  Figure 2 below highlights the link between swing speed and height.

Figure 2 : Handle Motion Relative to the Boat

Part 2: Motion of the Handle Relative to the Slalom Course

Part one established that for a given line length, the motion of the handle relative to the boat is defined by only swing-speed and swing-height.  How, then, does the handle’s motion relate to the slalom course?

Imagine that we are observing the system from Part 1 as it moves down the lake, the same way it does when we are skiing.  Watching the handle swing back and forth, we are able to trace its zig-zag pattern on the water.  Relative to the slalom course, the handle path traced on the water is based ONLY on the swing-speed and swing-height of the handle!

Slow and Low vs. Fast and High 

If we think about the absolute minimum swing-speed required to get from one buoy to the next and successfully run the course, the handle path could theoretically become a straight line from buoy to buoy (the shortest distance between two points).  In terms of geometry, this path will cross the CL equidistant between the buoys in the down-course direction.  Additionally, the handle will not apex until it arrives at the turn buoy.  This kind of handle path creates the sensation that most people describe as being “late, fast, and narrow” to the buoy, when in reality the skier swung “slow and low.”  The handle path for a minimum theoretical swing-speed and swing-height is shown below in Figure 3: A.

Conversely, a handle path created by a high swing-speed and swing-height is shown below in Figure 3: B.  If the skier is able to generate a great deal of speed into the base of the swing, the handle will cross the CL much earlier.  In addition, if the skier is able to sustain a high swing-speed as he swings up on the boat, the handle will reach its maximum height on the boat more quickly, and the handle apex will occur well before the next buoy.  This is what most people would describe as being “wide and early”, when in reality the skier swung “fast and high.”