Wim has great technique – makes it look so effortless! (see plots showing ski path and speed) • Earlier apex than several pro’s I’ve analyzed – apex several meters before buoy at 28, apex just a meter before buoy at 39 • 28 and 32 runs look very typical of most skiers, with max speed at 1st wake – meaning he’s pulling all the way to that point, and that he’s crossing center only 17-18 meters past the buoy. At this line length, I don’t think this is bad, but this is not a good strategy at extreme shortline, as you’ll see exemplified with Wim and pro’s I’ve analyzed. • Beginning at 35, speed max’s several meters before 1st wake, meaning his pulls are shorter than at 32, and his max speed is lower too, staying nearly constant from that point till just past the 2nd wake. Consequently he’s crossing centerline about 3 meters later, at 20 meters, or halfway between the buoys – establishing a path closer to a sine wave than I’ve seen with any other skier. It looks like at the point the speed maxes, Wim is already starting his transition to an inside edge – a very gradual transition that comes to a rapid conclusion just past the 2nd wake. Very nice examples of sine wave or “swing” as Schnitz has named it. • Beginning at 35, on most buoys, his apex is just barely before the buoy, but midway thru the turn his shortline path crosses his 28 and 32 paths. He initiates a faster turn at shortline by dropping into his turn more agressively, creating less angle between lake and legs, resulting in a quicker, lower radius turn. Notice the angle out of turn is decreasing as line shortens. • During his pull, his shoulders rotate gradually toward boat, causing his ski to counter-rotate away from boat – maximizing angle and setting up his transition to the inside edge • After centerline, back arm is kept close to body, reducing the torque that rope pull would otherwise exert and cause rotation and loss of angle. When the back arm releases the handle, the inside arm reaches in line with the rope, which again minimizes torque, keeping ski on trajectory of max width. • Upper body counter rotation starts about 6 meters before buoy, simultaneous with increased lean toward boat, causing rotation of the lower body and ski, bringing more of the front of the ski into the water, which initiates the turn. • Turn is further accelerated as inside arm reaches forward just prior to buoy to create rotational torque around the center of mass.
So, that does it for my analysis & comments of Wim’s skiing, and the things I think he’s doing right. Now I’d like to talk about what goes wrong, for most skiers, in my opinion. I suspect maybe Wim starts to get into trouble at 41, but I don’t have any video of that to examine – so I’ll confine myself to three sets of observations I have made: 1st of my own skiing (35 off), 2nd of a few video clips I have of several pros as they fail at 39 or 41 or 43 off, and 3rd of my observations of skiers at all levels at my local ski club. In all these cases, problems begin when at our shortest pass, we take the pull from the boat too soon, generate too much angle, pull too long, and get too much speed. Usually, the excess speed results in a delayed edge change, and we end up narrow and fast – end of pass. In the best case, if you’re very athletic, you can still manage a not-too-late edge change and turn that speed into wide & early – but then you have to repeat the whole thing again, and usually your pass comes to an end not too many buoys later – or maybe you complete the pass one time in ten, and think you’re on the right track, but you notice after many years you haven’t improved. That should be a clue - you’re not on the right track if you’re not improving – and even if you do improve, there may still be a better way. You may know somebody who ski’s 39 off with ease telling you to do something else – but you could probably find yet another 39 off skier who’d tell you something different!
Let me draw an analogy to make my point. During the hottest part of the day, a group of hunters on safari in Africa retired to their tents for siesta. Upon waking, one of the hunters noticed a hungry looking lion coming toward his tent, between them and their guns. He woke the others and started putting on his tennis shoes. A friend asked if he thought he could outrun a lion – he said, “no, I’m just going to outrun you!” Just because someone can ski better than you doesn’t mean they know what they are doing, or that they can even accurately describe what they are doing themselves. And who should you listen to? My high school track coach couldn’t run as fast as me, but because he had a scientific understanding of the physics of running, he could tell me what I was doing wrong and what I needed to change. I’m looking at this from a point of view of physics, and I know I don’t completely understand it yet, but I think I’m on the right track. I can test my theories against data I can extract from video, as well as against my sometimes misleading perceptions in the course. When those two disagree, I choose data over perception.
So, here’s my two cents worth: 1. As the line shortens, progressively delay your pull: Like Wim, the guys who can consistently run 38 or 39 have less angle across course than they did at 28, and they cross centerline later too. This isn’t an accident – Chris Rossi wrote me last year that he and other pros are trying to delay the pull from the boat more as the line gets shorter. If you load the line when the rope is still nearly perpendicular to the boat, you’ll get a very hard pull, lots of speed, and lots of angle – but you’ll pay for it later in various ways. If you delay the pull till you’re behind the boat, you’ll have given up some angle and be a little further downcourse, but you’ll get the speed you need, and more importantly, you’ll continue on with the control you need. It’s the first piece of getting efficient – a word I associate with Wim’s effortless passes. And delaying your pull will make it easier on your driver to stay on center – that has big benefits for your skiing! 2. As the line shortens, end your pull progressively sooner: The conventional advice I’d heard until a year ago was “your hardest pull should be at the 2nd wake”. If you followed that advice you’d always have a late edge change – so most good skiers weren’t following that rule, even if they gave lip service to it. The funny thing is, about the only time skiers do follow that rule is on their hardest pass. I notice pretty much all skiers pull harder as the line shortens, their edge change is progressively delayed, and then they wonder why they are having problems at that pass. Of the skiers I’ve seen, Wim ends the pull and begins the edge change sooner than anyone. I haven’t seen any other skier whose speed stays constant from just prior to the first wake to just after the 2nd wake – but looking at Wim’s effortless passes makes me think he’s on to something important. Schnitz noticed this first – his Swing style is all about this. It’s a more efficient way to ski. 3. Make your gate more efficient too: The ideal place to cross the centerline in the course is half way between buoys – as proof I cite the 39 off passes of any skier I’ve ever analyzed who can consistently run 39 – this has several ramifications: There are 41 meters between buoys, so half way is just over 20m. The gate is 27 meters from the 1st buoy, so you have two options to ski the gate like you ski the rest of the course. The common approach is to “ski up high on the boat prior to the gate”, meaning really wide and nearly perpendicular to the boat, then delay turn-in to the last possible moment, and come hot through the gate for a wide and early 1 ball. If you think of this as coming in around “0” ball 14 meters before the gate – then you have the same strategy. But can you cross centerline 14 meters past the next 6 buoys? I can at 15 off. I almost can’t at 22 off. Wim and Rossi and Parrish don’t at 28 off – they cross 17-18 meters down course. Maybe they could pull hard and cross at 14, but I doubt you could convince them that would be a smart thing to do! At 39 off they cross 20 meters downcourse. I bet they think that is the right place to cross. Regardless – there is no way anyone can ski the gate like the rest of the course at shortline – we should all stop trying! Coming in too hot through the gate sets you up for failure at your shorter passes. You can handle a hot gate on an easy pass, but then you can recover from all sorts of mistakes on your longer passes, right? – that doesn’t mean your mistakes are beneficial! The other approach is to ski the gate efficiently too. That way you don’t have to have one style for the gate and another for the course. Refer back to my original article below for more on that.
WHICH SKIING STYLE IS BEST?
By David Nelson BS Physics, BYU 1975 MS Electrical Engineering, UCLA 1977 AS (Avid Skier) on snow since 1965, on water since 2000
David, July 6, 2006
Using the coordinates of turning in when the left hand gate lines up with #1 and skiing to the exact same place before #1, my speed should decrease as I shorten the line as I am starting from a narrower point. Therefore I am covering less distance in the same time. At 15 off I will travel 24 feet further than at 39 off if I am at a position 24 feet wider. Yes or NO?
This is a difficult thing to explain, and to understand - but that is exactly why this point is so crucial! Something very important is going on and few realize it!
First take the case of an 18.25m rope. When the skier is at the gate, the boat pylon is 18.25m into the course. When the skier rounds ball1, the rope will be at a 35degree angle from the boat, so the pylon will be 42.5m into the course. So the boat has traveled 42.5-18.25= 24.25m. It has traveled at a constant speed of 34mph or 15.28m/s. Dividing 24.25m/15.28m/s=1.58 seconds. That is how much time the skier has had to ski from the gate to ball 1.
Now with a 10.75m rope: When the skier is at the gate, the boat pylon is 10.75 into the course. When the skier rounds ball1, the rope will be at a 65degree angle from the boat, so the pylon will be 31.8m into the course. So the boat has traveled 31.8-10.75= 21.05m. It has traveled at a constant speed of 34mph or 15.28m/s. Dividing 21.05m/15.28m/s=1.37 seconds. That is how much time the skier has had to ski from the gate to ball 1.
Assume in both cases the skier follows the same path between the gate and ball1. The straightline distance would be about 29.4m (hypotenuse of a right triangle with sides 27m and 11.6m). A typical path, allowing for some curvature might be 10-20% longer than that. Assume 15%, which gives a path of 33.8m. Then the average speed of the 15off skier is 33.8/1.58=21.4m/s or 47.6mph. The average speed of the 39off skier is 33.8/1.37=24.67m/s or 54.9mph.
So the difference in time and therefore speed is based on the shortline skier having to ski up higher on the boat. And remember these are average speeds. Refering back to my article, the speed at the gate will be much higher than the average, and the speed at ball1 will be very close to the boat speed to avoid getting slack or pulled narrow. And my diagrams always showed this was the case. Now, with this argument, I have explained why that occurs.
Also keep in mind that after ball1, the speeds of longline and shortline skiers is very similar if an efficient path is followed. Also, after ball1, the average speed is quite a bit lower for shortline. This, I'm sure, is one of the reasons making the shortline gate so much more critical and difficult to master. The gate speed you need at shortline sets you up for failure beyond ball1. The perception of very high speed thru the gate at shortline is accurate! But if you try to maintain that speed thru the rest of the course you'll be in trouble - going back to what I wrote in my first article. I think most people do try to maintain that speed, keeping them in the mindset of wide & early rather than efficient. I think this helps explain why shortline gets so much more difficult.
If you've found my original writing on this hard to understand, I'm sure you're not alone. If this makes sense now, it might be a good idea to post this as clarification to what I wrote. And it might be a good idea to post the newest info first on your page, rather than making people scroll down to the bottom of the page.
(note: there are a few refinements of this argument in what is published on your web site, which I omitted to simplify the examples. For example, when the skier's ski is at the gate, 0m into the course, the handle is probably at about -0.5m and so the boat pylon would also be about 0.5m less far into the course. I also assumed, based on watching videos of skiers, that a 15off skier's lean at ball1 may only be 60degrees, whereas a 39off skier's lean is more like 30degress to the lake. I also took into account skier height and handle position at the ball. Not all skiers are the same in height or technique - so there is some room for variation, but the logic of my argument holds. For example, the angle the rope makes at 39off may actually be 70 or 75 degrees, not 65 - which I said was a minimum.)
Understanding Slalom by David Nelson
Waterskiing is a great sport! Still, there is one thing that really bugs me: it’s all the debate over different styles of skiing. I don’t know of any other sport where there is so little agreement on the right way to do things. For every question there are at least three different answers. In an effort to improve, I’ve been caught up in the debates over Traditional, the multiple New School ideas, and Coordinates styles of skiing. I’ve been frustrated that the advantages claimed by each style seem to be based more on opinion or anecdotal evidence than on anything that can be proved or compared directly. Since no one has enough time or incentive to learn all three styles and make a direct comparison - that is not likely to change. So like everybody else I’ve been forced to choose one style and disregard the others, unsure I’ve made the right choice, and doomed to continue getting involved in debates that can’t be won or lost!
So for years I’ve thought about how one could analyze these styles and come up with solid comparisons. At first, the problem seemed too complex to handle without having access to advanced hydrodynamic modeling tools like the ones used to design aircraft or America’s Cup yachts, and a super-computer to run the simulations. But the more I thought about it, the more I realized complexity usually results not from the sheer difficulty of the problem as much as from the tangled interaction of a few fundamentally simple issues, and that the with the right approach, these simple issues could be identified. Remembering that Isaac Newton said, "If you can’t measure it, you can’t understand it", I began to focus on what could easily be measured. I made some measurements of various skiers, applied some math and physics, ran reality checks, refined it, and committed the whole scheme to software on my computer. So now I can take a video of a skier’s pass, run it through my laptop, and get accurate information on the skier’s path, speed, acceleration, and angle. And I can see how my skiing is different from a pro like Andy Mapple. What’s more, I think I have solid answers to questions like:
What makes a shortline pass so much harder to run?
Do I need to pull harder, or ski faster to run a shorter pass?
Which ski style will help me improve the fastest?
So, if these questions interest you, click on the following link.
That's what I decided to call it: "The lessons of Nelson". What a great body of work this paper holds. It must have taken David a hell of a while to compile all that stuff, translate it to something meaningful and explain it in understandable terms.
I'm elated by the content of his paper. One, because he finally gives meaning to stuff you and I have been brewing up for so long but could'nt put together as well as he did. Two, is that it gives us the data to stop the "bitching" on what style is the best, as long as everyone is able to accept the facts and let go of the sacred cows (territorial boundaries of style).
Many will argue with M. Nelson's findings. But they better be prepared to live up to the proof and build as strong an argument as he did. Shooting down a theory is easy with critical verbal blasting. I can hear it already: "Who's this guy ?", "Can't even ski 39 off !" and yati yati yati... One of the most vocal critic, student of engineering, will have to bow to the reality of hard numbers, won't he ?
Kingdoms are threatened. Let's see what the reactions will be. Will the preachers shout to beware of the cry of the infidel ?
Stir the brain cells, blast open the gates of ignorance. Let the truth be known.
I love this.
I have removed the problematic post that was here!
David Nelson's Rebuttals Below;
Re: longer is shorter? *PIC*
Posted By: Glen
Date: Wednesday, 1 March 2006, at 7:53 a.m.
In Response To: longer is shorter? (Bill Gladding)
I did some calculations a while back (slow at work). This is probably beating a dead horse but it helped me understand what makes shortline so difficult. We know the boat travels the same distance for all rope lengths. Imagine the skier as a pendulum swinging from ball to ball disregarding the movement of the boat as depicted in the illustration. (If it works I've never tried uploading an image before)
Length of arc = (Degrees/180) x (rope length) x (3.14) Distance through arc for 15 off : 81.7 feet x 6 crosses = 490 feet For 38 off : 116.2 feet x 6 crosses = 697 feet
This means the shortline skier travels 207 feet more over the length of the course. The average speed of the skier through the arc @ 15 off is 19.7 mph. The average speed for the 38 off skier is 28 mph. The speed of the skier relative to the water is a combination of the boat speed and the arc speed.
This doesn’t take into consideration reach but the 35 ft difference for the 2 line lengths obvioulsy won’t be offset by reach.
David Nelson’s Reply:
It is interesting to think of the skier swinging like a pendulum back and forth thru the course. For an ideal pendulum swinging, plotting the position of the pendulum versus time gives a sine wave path, regardless of the length of the rope between the anchor point and the pendulum. A pendulum takes an efficient path too! Even though I’m tempted to use this result to prove my argument, there are reasons why pendulums can’t explain a skier’s path. The first is that the period of a pendulum, or time it takes to swing back and forth once, is a function of the square root of the length of the pendulum. Comparing the two different rope lengths, the square root of (75-15)/(75-39.5) is 1.3. So if the skier were swinging like a pendulum, a 15 off skier would take 1.3 times as much time to get between buoys as a 39.5off skier. But in the case of the skier behind a boat going 36mph, the skier, regardless of line length spends about 2.55 seconds between buoys. This is why pendulum analogies always falsely proclaim the shortline skier to be faster than the longline skier - it assumes a condition that is not true. The second reason the pendulum is not a good analogy partly explains the discrepancy in the period, namely, an ideal pendulum starts with a fixed amount of potential energy and zero kinetic energy, and converts back and forth between them with no net increase or decrease in energy. A skier, however, is constantly expending energy, as is the boat, and the water is constantly absorbing energy as the skier moves thru the course. Bottom line is this: the pendulum analogy gives the wrong answer on speed - it's like comparing apples and oranges.
Posted By: Wade Williams / Date: Saturday, 25 February 2006, at 2:03 p.m.
In Response To: longer is shorter? (Bill Gladding)
Yes, the course does stay the same dimension. However, the line you have to ski with gets shorter. The shortest distance between two points is a straight line. When you are at 15 off, you can run all 6 buoys by skiing close to a straight line between the buoys. However, as the line gets shorter (especially at 35+) it is no longer feasible to ski a straight line between the buoys. You have to ski with more cross-course direction, and from the wakes to the buoy, you must maintain this direction outbound so that you will be able to ski around the buoy. Think of a racecar driver. If you're approaching a hard left turn at 200MPH, you're not going to take the left side of the track into the corner and then spin the wheel -- you'd just spin out. Instead, drivers apex their turns -- by going wide to the right and then turning; in effect making that corner into as straight of a line as possible (so they can carry as much speed through it and win the race). If you were to measure the left hand side of the track from the beginning to the end of the turn, it would be a shorter distance than the apex line that swings right and then left.
Enter diagram time...
In this diagram, the Yellow represents all the possible lines one could take at 15. While all of these lines are possible, most skiers when they are learning ski a line similar to the Blue. As you can see, this line is close to a straight line, and represents one of the shortest lines to successfully ski the course with. Contrastly, the Red represents a successful line at, say, 38 off. As you can see, this line is longer than the blue.
As the line gets shorter, it becomes more and more important to take this apexed line, rather than skiing directly from buoy to buoy. Hence, as the line gets shorter, you must ski a line that uses this apex theory more efficently... or, as the line gets shorter, you must cover a greater distance = you must ski faster. Skiing faster will not only allow you to ski this line, but it will also create more stability for you to get your center of mass moving laterally. You also need to ski further up on the side of the boat (so you can use all of the line, as 38 off is 6 inches short of the buoy) so this extra speed will help you achieve this as well.
Shorter = Longer while the time stays the same = You must ski faster. This is why proponets of "New School Slalom" or "Efficiency" talk about maintaining speed, rather than pushing on your ski to make it turn (loosing lots of speed)
David Nelson’s Reply: I definitely agree with Wade’s first points that you can’t ski a straight line between the buoys or make really sharp turns around them. I know I used to think I turned pretty sharp, and so do most people I’ve talked to – it just feels that way when you ski. A few years ago I drew the shape of the line I thought I was skiing. I got it out recently, and it showed me turning around the buoy on a radius of 2 meters. The G force from turning that sharply at a speed of 34mph is 6G’s! That seems unrealistic to me for several reasons: the limits of my strength, the ability of the water to hold up against such a force, and lastly, the comparison with Rossi’s and Parrish’s measured turn radius, which is sharper than mine, only producing 4G’s of acceleration. I’ve seen a plot of a skier path that was supposed to be measured where the turning radius was 1 meter – which works out to 24G’s of acceleration! A 175 pound skier would be placing over two tons of pressure on his ankles, and on the ski, and the ski on the water. It’s interesting to speculate which one will break first. This is another example proving our perceptions are often not reality.
Getting back to Wade’s email: I also like his illustration of the possible and likely paths at various line lengths. In particular, the apexed red path for 38 off, with the gradual turns around the buoys, is pretty close to the measured paths in my analysis. Wade shows the path crossing the centerline about 17 meters down course, close to what I measured from shortline video. His first segment in the preturn of that red apexed path is a straight line, which I take issue with – but generally I think his path is close to reality.
I also agree that skiing this apexed path will generate higher speeds than skiing a straight line – because you cover a greater distance in the same amount of time. But what Wade doesn’t say, and what seems to confuse a lot of people by it not being said, is that if you skied one of the possible yellow paths at longer line, you’d be skiing a still greater distance in the same amount of time, so the longline skier would be going faster than the skier on the red apexed path. So, the red apexed path is more efficient, and it is slower, whether our brain says so or not, and there is no reason why you can’t ski that path at longline as well as at shortline.
David Nelson’s Reply; to several other threads on Nicholl’s message board: Some argue we should not ski an efficient path because we’re better off being early and having time to recover from mistakes. True, being early gives you more time to recover from mistakes. But I bet you don’t make many mistakes at longline, and I bet you’re not skiing early on your hardest pass. The pro skiers I looked at were not as early at shortline as at longline. If we were to ski a more efficient path at long line, I believe it would improve our ability to ski more buoys at shortline, by making us more consistent, and by making the physical sensations at longline more like that at shortline. Wouldn’t we be better off avoiding mistakes at shortline than having the time to recover from them? It goes back to what I said in my article about how much time it takes to develop new neural pathways in a completely new situation: the more different we ski long/short, the more we have to adapt, and the longer it takes to become successful.
More David Nelson, June 20, 2006
Here's a couple more thoughts on skier speed and the preturn position.
There is a simple reason for keeping the handle close to the body in the preturn to stay wide. To explain, consider two cases:
1. Imagine what would happen if you put your arms straight out in front of you immediately after your edge change. Your arms and the rope would form a roughly 90 degree angle. Your arms would act like a lever, and the boat's pull would create torque that would turn your body and ski toward the boat. You wouldn’t stop rotating until your arms and ski were pointing at the boat. You'd ski very narrow as a result. This is of course a very poor position which no one would use, but it highlights the consequence of generating torque.
2. Now imagine you rotate your arms to your side, so that the pull from the boat, your arms, and your body (center of mass) are in line. Now the pull from the boat won't create any torque, so you won’t be turned by the boat’s pull to a narrow path. With your arms to your side, and close to the body, you come close to this zero torque position. The elbow closest to the boat should be tucked in close to your side and back a little, and your reaching arm should come straight across your chest. Since our body anatomy won’t allow our arms to be exactly to the side in a zero torque position, there is always a little torque turning us narrow. So keeping our arms in close at least minimizes the length of the lever, thus minimizing the torque.
Of course – this position will keep the line tight, because you’d ski as wide as your speed and the boat’s position will allow.
A related question is why counter rotation helps widen your path. Again, torque matters:
Imagine you reach with your arm in line with the rope, as most pro’s advise. This keeps the torque from the boat near zero. Then, as you counter rotate, starting with your shoulders, you generate a counter torque – away from the boat. When you turn your shoulders, your whole lower body and ski will rotate too, so the ski turns away from the boat. This widens your path. It also creates lean because your ski has to move away from the handle as your path widens. Then, as you round the buoy, you rotate your reaching arm back to your opposite hip – generating torque that aids in the turn and gets you pointed across course prior to the pull.
This raises another question: if instead of reaching in the direction of the rope, what if you reached a little behind the rope – would this make you ski even wider. I’ve tried this – it does result in a wider path, because it creates more counter torque. I was a little less stable in this position, however, crashing a few times from being too wide. I find that reaching in the direction of the rope, and counter rotating the shoulders will result in as much width, without overdoing it, and leaves you in a better position to start your pull, because your shoulders will be facing down course (down the fall line in the snow skiing analogy) rather than across course.
More Info: Why shortline passes seem faster, and may BE faster
I think most people do ski their hardest pass at a higher speed – it comes from trying to ski with the same technique you used successfully on longer passes. If you do that, here’s what happens: you’ll start the pull too early, when you’re still too wide. This will give the boat more leverage on you, and you will generate much more speed than one of the pros will generate on the same pass even though you’ll already be going faster, your instinctive response on your hardest pass is to pull harder, because you’re expecting to be late. So you pull hard and generate even more speed into the wake.
the consequence is a delayed edge change. This happens because we don’t even start to transition to the opposite edge till we’re at the wake. With the higher than normal speed, and a body that still takes just as long to transition to the new position, our edge change is later. This is true of every skier, novice or pro, I’ve ever seen. And to make matters worse, the harder you were pulling, and the longer you held the pull, the later the edge change will be, and the more likely you’ll be to ski flat for a while. All of these factors tend to make us fast and late to the next ball – and a very common side effect is slack around the turn. This sets you up for an even worse next ball.
So, I have no argument with those that say they are going much faster on their shorter passes than they did on their longer passes. My point, however, is that this is part of the problem – the reason they are not running their shorter passes. You need a slightly different technique for each shorter pass, to avoid excessive speed.
Here are some other observations on why I don’t think higher speed is desirable or inevitable at shortline.
Why is it harder to run a tailwind pass than a windless pass? The extra speed we pick up from the wind speed does not help us. One key to a successful tailwind pass is pulling less, to bring our speed back to normal. Why are we more likely to run a headwind pass than a windless pass? Slowing down helps.When you finally conquer that hardest pass, does it still seem like you are screaming down the course? Most skiers I’ve talked to, myself included, feel like it’s a walk in the park – no hurry, no rush – the result of skiing slower. I think most of it has to do with our perception, but the data shows the reality of lower speed as well. Or when you watch a 41 off skier run a 38 off pass – doesn’t it look almost effortless? It is – it’s efficient.
More David Nelson- Added JULY 6 2006
In my article, in conclusion 2, I wondered whether skiing faster thru the gate was necessary or good. Now I know: the speed must increase as the line shortens, but because it’s hard to deal with, we shouldn’t try and increase the speed more than necessary.
The reason the speed must increase is the skier has to ski up higher on the boat at shortline to get around ball1. So at 15 off, during the time the skier has to ski 27 meters downcourse from the gate to ball 1 and 11.5 meters wide, the boat has to travel from 18.25 meters to 42.5 meters downcourse, or about 24 meters. And the angle the rope makes to the course centerline is only about 35 degrees (note: the angle to the ski is slightly higher). A 39off skier travels the same distance, while the boat moves from 10.75 to 31.8 meters, or about 21 meters. Here the angle is about 75 degrees. At 43 off, the angle is 80 degrees! (based on a skier 6’ tall with typical lean angle and reach at the buoy) This gives the 15 off skier 1.62 seconds to reach the ball, whereas the 39 off skier has 1.41 seconds, and at 43 off you have 1.28 seconds. So for each line length, assuming an efficient path from the gate to ball 1, the gate speeds are 44.7mph (15 off), 45.6mph (22 off), 46.7mph (28 off), 47.7mph (32 off), 48.9mph (35 off), 50.2mph (38 off), 51.3mph (39 off), 52.9mph (41 off), and 56.5mph (43 off). (these speeds are for a 34mph skier – multiply by 36/34 for 36mph) Between ball 1 and ball 2, however, you have the same amount of time at any line length, so the need to ski faster goes away – and in fact you can ski faster between the balls only by taking a longer path, as mentioned in my article.
This mismatch in speed between the required gate speed and the optimal speed after ball 1 points out part of the difficulty in shorter lines. It explains why slack at ball 1 is so common when first moving to a shorter line – it takes a while to learn how to deal with the extra speed and get into a rhythm and path that will work after ball 1. The mismatch between gate speed and course speed starts to increase dramatically after 35 off, so making the transition becomes much harder. This helps explains why so many people can ski 32 or 35 off, but so few can ski 39 off. I believe that by knowing that this mismatch does and must exist, a skier ought to be able to do a better job dealing with it.
Keep in mind the speeds I just presented were for an efficient path, and other paths are possible. If your gate speed is faster, you’ll be able to turn that additional speed into being earlier/wider, but then you’ll have an even bigger mismatch in speed after ball one, unless you can maintain the earlier/wider path throughout the course. At longer lines, most of us tend to do this. As the line shortens, we all seem to reach a point where that strategy fails – where like the pros I looked at, we either ski an efficient path or fail to run the pass.
One other related difficulty factor as the line shortens: at 15 off with the skier at a 35 degree angle behind the boat, the boat is still exerting a considerable downcourse pull on the skier as he rounds the buoy. At 43 off, with an 80 degree angle, the pull from the boat is only 1/5 as strong. So the shortline skier has to rely much more on momentum to keep their speed matched to the boat. If he skis faster, he gets slack. If he skis slower, the boat pulls him narrow. Shortline is really a delicate balancing act of many different forces!
These speeds were computed for 34mph. At 36mph, you can increase them all by a factor of 1.059