Calculating Actual Ski Speed Made Easy ... sort of

[SkiJay]

There have been a number of discussions over the past few months concerning how fast a skier is going during various segments of a slalom pass. Unfortunately, most accessible GPS recorders have a sample rate that is too slow. Sports radar guns don't work well for measuring speed around corners, and the math needed to model a slalom pass, with all of its constantly changing speeds, loads and angles, is likely more complex than plotting a moon shot.

 

But here is a simple way for you mathematician Ballers to accurately calculate maximum speeds with only a GoPro and a calculator. In its simplest form, it will tell you your lowest and highest speeds achieved. But with a little more effort, maybe you can come up with an algorithm to plot a speed/distance graph for the whole pass.

 

The basic idea is to generate a curve that correlates measured actual speeds with the pitch range of the whistle from your fin/ski. Put more simply, how can we turn this sound:

 

https://dl.dropboxusercontent.com/u/1530989/Waterskiing/BOS/Andy%2032.mp3

 

into a simple version of something like this speed plot from a stock car on an oval:

 

http://www.advantagemotorsports.com/images/tire_temps.jpg

 

The data gathering side is easy. First, mount a GoPro directly to your ski, preferably on the tail, to record the whistle from your fin/ski during a few "calibration" passes. For these calibration passes, run the boat down the lake three times at three known speeds, say 25mph, 35mph and 45mph, while skiing out beside the boat at exactly the same speed as the boat (the ski whistles loudest when it is loaded on edge). Next, the analog pitch needs to be converted into numerical frequency values (Hz). Then the Hz values of these three speeds can be used to extrapolate a pitch/speed curve.

 

Next, record the whistle from your fin/ski during a pass. Plot the highest pitched whistle achieved against the pitch/speed curve and voila, you have your highest speed achieved. Better still, come up with an algorithm that plots speed over time or distance through the length of the course and you'll have an interesting tool like the one shown above for the stock car.

 

Race car and superbike teams use this kind of data extensively and it makes a big difference to performance. A speed over distance plot would tell you where you are accelerating and decelerating, and how effective you are at both. Comparing your plot to a better skier's plot tells you if you are accelerating and decelerating as soon, as hard, and as long as the better skier. Many, if not most, race car drivers have become more competitive by using speed/distance data exactly like this.

 

In any case, we have the tools. We just need a baller with the right background and interest to take up this challenge.

[gator1]

Its much easier than that. @thanbogan has the tools. Just need a potentiometer on the rope where it connects to the pylon. Use that to measure angular velocity, add the vectors to 34 mph and voila, actual speed. Or, have the gopro sighted down on the pylon, check angular change of rope to boat vs frame rate, calculate angular velocity, add to 34 mph vector, voila, actual speed.

 

Don't want to measure fin frequency, since it will correlate to speed thru water, not actual speed. You'd fool yourself with slip rates, not velocity. Although, pretty interesting piece of data, that slip rate. More means more pull being wasted on slowing the boat, not accelerating the skier. Would coorelate to "heavy on the line" instead of "angle". Also to front foot weighting vs rear foot pulling. I'd bet the closer you get to Nate, the less difference between water velocity and absolute velocity during full pull.

 

Also, its after drunk thirty, so this may all be bs.

[SkiJay]

Interesting ideas @gator1. The thought of getting to compare slip rate data between skiers and fin changes makes the race car engineer in me salivate!

 

I think the amount of load and slip would only affect the amplitude of the whistle, not the frequency (pitch). You wouldn't even need actual strain or slip numbers, just any measure of relative amplitude of the whistle as it changes throughout the pass to make meaningful load/slip comparisons between skiers or fin changes. Still no special equipment needed.

[gator1]

@skijay, well, its sober o'clock and upon reflection I think this will work. Make a big protractor, tape it to the engine cover. Sight the gopro down at the engine cover. Ski. Replay video, measure angular deflection of rope vs frame rate. Calculate "rpm" of skier around pylon. Angular velocity of skier at 38 off is 2pi37ftXrpmX60/5280= angular velocity in mph. Add that to 34. That's Vt. Calculate your water velocity from the fin frequency. If you are right, and the angle of attack does not change frequency, that's Vw. We'd want Vw/Vt to go down and approach 1.

 

The hydrofoil guys use gopro frame rate to calculate hang time and therefore determine the winner of big air contests.

[SkiJay]

@gator1 I like your protractor idea, easy, cheap & effective. Are you tempted to try it? It's astounding that in this age of over-analyzing everything, a performance sport exists where everyone is still guessing at what the top speed is, even if it doesn't really matter.

[Edbrazil]

Quite a few years back (15+??) Dave Benzel had a system that set on the pylon and input data into a computer, probably angle and force. Think it was called the Lisa system? Someone out there may be more familiar with it. One interesting statistic was the max. towline force recorded by some skiers, and I think that was in the range of 900 lbs. for a short time.

[disland]

I believe if this could be figured out a calculation of skier efficiency would be extremely valuable. If the skier could have a way to measure efficiency he could work on technique at 32 off which is an easy pass for pro's but allow them feedback that could be used at 39 and 41.

[webbdawg99]

Will ANY of this info make ANY of us better skiers??? My brain hurts

[disland]

Yes absolutely. What if after every pass rather then knowing you ran the pass and can count to six someone in the boat could tell you that you were 76.5% efficient. Then you ski another pass make some timing or form adjustment and achieved 82% efficiency. Efficiency is the measure of the desired outcome essentially your ability to get from one buoy to the next in the shortest period of time that will allow you to run the next line length.

[SkiJay]

Excellent point @disland. I know that my coach is ALL about efficency. Being heavy on the line is probably one of the most common errors in slalom skiing, especially too-heavy too-soon off the ball.

 

So you've identified yet another helpful stat that could be gleaned from whistle amplitude and frequency over time, or data from a strain gage, a protractor and a camera. If you divide amplitude by acceleration, you'd plot an efficiency curve throughout the pass. Divide average amplitude by average water speed, and you'd get an efficiency rating for the pass. That would be an excellent number to chase with technique improvements.

 

I'll bet anything that my coach's efficiency ratio at 32 off is substantially better than mine, and I'd love to compare those two plots to see where and when I'm being less efficient. I could take these plots with me and work on narrowing the gaps as homework between coached sessions. A picture is worth a thousand words. All I'd have to do is make my plot look like my coaches plot, and he would have hard data to point to throughout the process.

[gator1]

@skiJay, I'm not tempted. But I agree its a surprise somebody isn't selling something. But this conversation has helped me put the whole heavy/light on the line thing in the rearview mirror. Always confused the crap out of me. My understanding now is: "heavy" means lots of tension on the rope with not a lot of angular velocity being generated. Somebody posted awhile back a pic of Nate WHALING on the line, along with a Nate quote "when the line goes tight there is nothing light about it". In my mind now, "light" means lots of tension on the rope, but lots of velocity being generated. I think our minds are integrating speed gained with load input and spitting out "light" vs "heavy".

 

Probably wrong, but no longer confused.

 

So the question in my fevered little brain now is: what techniques yield high acceleration at a given line tension?

[Marco]

Moving center of mass in direction of travel comes to mind...

[disland]

Unfortunately I question if the fin frequency idea is very accurate. However maybe using video we can use time given that we know the distance traveled if we pick and arbitrary mark like when the front boot hits the apex of the turn next to the buoy.

[MattP]

Who really cares. Just go ski.

[Klundell]

@gator1 I couldn't agree more about your assessment of light vs. heavy on the line. ""heavy" means lots of tension on the rope with not a lot of angular velocity being generated." Perfect explanation. With that said I will never tell someone that they need to be lighter on the line because what that translates to in decreased intensity behind the boat and to run any short line the intensity behind the boat has to be very high. I will try to use coaching cues that will get a person to be more efficient but the term lighter is not one of them. The beauty of a system you are talking about is it would give instant feedback to the coach of whether or not your cues are working for the skier.

[SkiJay]

I assume you're kidding @MattP. It's perfectly okay to not care. It would be a lot less okay to intentionally invalidate other people's desire to explore, question and learn, especially for a forum moderator.

[gator1]

@skijay, I too hope he was kidding. Particularly since the only (and limited) success I enjoy in this sport is due to some analysis capabilities that compensate for a big lack of athletic ability. AND, if all I wanted to do was "just go skiing" I wouldn't be reading his site.

 

@Klundell, It would be pretty easy to come up with a device that compared angular velocity with line tension. Or, to be more technically accurate, compared change in angular velocity with line tension. For a given skier, it seems all you as a coach would be looking for would be the improvement, rather then needing an absolute. The absolute numbers would be kind of meaningless to compare between skiers, but seems like the comparison to a given skiers benchmark as he tried technique changes would be pretty dam cool.

[Than_Bogan]

"Probably wrong, but no longer confused."

 

That is completely freakin' awesome. I will be putting that line to use.

 

@SkiJay If you manage to get some good time series of rope angles, I have done a lot of math/Excel that will allow me to convert this into some measurements of other parameters (e.g. velocity, acceleration, tension [as a function of skier mass]) and some pictures. I suspect it might be "academically interesting." I seriously doubt it will cause anyone to run more buoys.

 

The burden is on you :). I can't justify much effort (unless the government wants to throw a $1million research grant at me!).

[SkiJay]

Exactly @gator1 Comparing the shapes of the curves and ratios would tell most of the story. The actual numbers themselves are almost irrelevant on their own.

 

Thanks for offering your expertise @Than_Bogan. I agree that just figuring out top speed is kind of useless. Comparing performance traces, however, would quantify how well we are doing vs. how well we could be doing on a micro scale throughout the course. That would be very useful.

 

Data acquisition in other sports has become indispensable. If you are not good at it, you lose. I raced on the same team as James Hinchcliff a few years back and believe me, he didn't get to IndyCars by "just going racing." He, and everyone like him, relies heavily on data feedback. I was driving for a three car team recently, and we spent countless hours comparing our driving data, and despite our 50+ years of winning races combined, we could still find more speed this way.

 

I was also around before there was data, and a LOT of drivers hated data, and belittled it as a waste of time and money, including the likes of superstar Al Unser Sr. I believe "Just drive the damn car," was the catch phrase of the time. They didn't last long against the teams that embraced data acquisition. What felt fast to the driver often wasn't according to the data, and trusting the data won and continues to win championships. Al Unser Jr. didn't make the same mistake. He embraced the data age and went straight to the top. It would certainly be good for a giggle to post something like "who cares about data acquisition" on any racing forum these days.

 

In skiing, of course maximizing your time on the water and working with a good coach will always be top priorities. But in a sport where practice time is so severely limited, how could measuring, comparing and understanding what we are doing on our skis do anything but help us progress?

 

Anyway, this whole discussion is moot, because data acquisition hasn't been applied to water skiing ... yet.

[Moggie]

It appears to me that based on the suggestions here that boat manufacturers are missing a trick. It seems entirely feasible that by only entering the line length for a given pass, a boat equipped with a pylon that measured angular velocity and rope tension and ZO could provide useful and accurate telemetry about your pass. Coupled with a camera you could review your most efficient pulls and look at the footage to see what you did differently. Since ZO effectively knows how far through the course it is you could have your progress through the course plotted showing where you were early/late etc.

 

Given how obsessed some ballers are at analysing their skiing (not to mention the fin-fiddlers) it seems strange such data acquisition hasn’t caught on (if only to give a manufacturer a USP).

[gator1]

So, @moggie, I've been goofing around with this a little bit. My Ipad has an app called foreflight that many pilots use to replace a lot of the charts we used to buy, and as a back up for many of the instruments in the helicopter. With an add on GPS module, also sold for use with the foreflight and Ipad, the GPS is very accurate.

 

With the use of a $20 potentiometer and a $63 strain gage I can measure skier acceleration, velocity and load, and since the Ipad knows where I am, map that against location of the skier in the course, just as the foreflight app uses the data to map velocity, heading, altitude on a moving sectional map. Then the Ipad reports that in a visual chart showing a, v and load, on a map of the course.

 

So, any of you ballers want to, or know how to, write an app? Lets crowd source a little virtual R&D team and do this.

[Moggie]

@gator1 great plan although i'm not sure why you need the GPS if you integrate with ZO (which you need for speed). Would it not be cheaper and more convenient to use the data available? I would have thought it would be more accurate than GPS since ZO is pretty good at timing progress through the course and the line will length and pylon angle will determine where the skier is. The only material variable would be slack in the line which could be compensated for using the load readings.

 

Loving this technical exercise!

[gator1]

@moggie: Don't need the zo. The Ipad knows speed and location of the boat. Don't want to have to talk to the ZO guys and get permission to open up their code. The Ipad can do it all, and is as accurate as ZO. Writing the app, I think, is easier if we don't have to talk to the zo.