The physical forces of slalom skiing

[Hersh]

Does anyone know the general forces experienced in slalom skiing? G's pulled in the apex. Lb's of pressure taken when the boat hits. Top speed crossing the wake. Etc. I apoligize if this thread is reduntant to some of you, but I just haven't been able to find any centralized reliable information. Thanks.

[Horton]

The better the skier the lower the Gs & load?

[Than_Bogan]

I've tried to do some math to answer these questions, and it gets nasty real fast. If you make all sorts of simplifying assumptions, then you can come up with something. Said assumptions are patently false, but *may* be close enough that these values are at least in the ballpark.

 

I don't have everything in front of me, but I do recall that while the top speed doesn't change all that much as the line shortens, the accelerations and the line tensions increase a lot.

 

If memory serves, I came up with a bit under 2g's as the peak acceleration at 36/-38, and that occurs at the apex of the turn -- i.e. is mostly deceleration. The acceleration exiting the turn is a bit less (but feels like more because it's accompanied by a dramatic rise in line tension).

 

The peak line tension for the same case is very roughly 3x the skier's body weight, although it should be noted this is extremely brief. So brief that it's arguable the skier's task is to "absorb" this more than it is to "hold" it.

 

It's been rare that good measurements have been taken, but when I have seen them they seem to be at least in the general vicinity of what my very primitive analysis has suggested.

[Than_Bogan]

@OB 9 g's! DAMN.

 

I just remember the 117th reason that I wouldn't last 20 seconds in the Marines.

[Brady]

@Hersh I have been told numerous times that going thru the ball, speeds are at approximately 30 mph, and then behind the boat your speed approaches 70mph. In a span of 38 feet, the acceleration, or G-force is:

 

Final Velocity (V) = Initial Velocity (U) + Acceleration (A) times Distance Traveled (S)

 

If my numbers are correct, the total G force sustained--Acceleration (A)--from the turn through the wake is 1.54 G's, which pales in comparison to other activities, such as what @OB and @SkiJay participated in. And those numbers are for the elite of the field; not for your average weekend warrior.

 

These G's are very similar to the Force that @ShaneH exerts on his body fleeing the scene when a woman is trying to tie him down to get him to commit.

[Than_Bogan]

Oh, also top skier speed is in the general vicinity of 1.5x boat speed, but this one is extra-sensitive to the exact path that the skier takes. It can be relatively low (although always must be greater than the boat speed because even the average speed must be greater than that since more distance is traveled in the same amount of time). And my vague guess is that a skier who is running late and pulling long into the buoy may well end up at 2x boat speed or more.

[ktm300]

I have ridden in the boat with one of the smoothest 34 guys around. Runs 39. Had a strain gauge hooked up to a laptop that would plot the load through the course. Within a ski length inside the buoy line, the peak load was about 650lbs (varied some with onside being a bit higher). Load right behind the boat was 400 or so. If you watch the West Coast Slalom video, it shows that TW peaks at around 750 right off the ball and drops down to about 400-450 at the centerline behind the boat. Glad I got to see this because it answered, for me, how to put into perspective all of the light on the line talk. "light on the line", to me, means good movement not light load. The load in motion feels lighter. I have heard but, do not know, that Mapple spikes(ed) to 1000lbs. Better get strong or stacked or both.

[Than_Bogan]

@ktm300 Yep, those numbers seem reasonable. 4-5x body weight is totally possible at -39/-41. Note that, to minimize the load, one loads a bit later, such that the peak is roughly behind the boat. But to maximize the chances of running it (which is the actual goal!!), it doesn't surprise me that loading harder and earlier is the way to go.

[Brady]

@Than_Bogan. Load does not convert to G's however. Just wanted to make that point, because if someone assumes that "4-5x body weight is totally possible at -39/-41" converts to G's they would make a bad assumption. I would make the supposition that it would be impossible for the human body to be able to hang onto the line while pulling even 2 g's. (even with Clinchers!! LOL)

 

@ktm300. I would love to get a hold of that program and to figure out the the acceleration rates throughout the turn in relation to line length. That would keep me occupied all day long.

 

BTW, My wife says I am addicted to BoS too much and that she would prefer if I would start looking at porn more because my behavior is "Becoming Weird."

[MattP]

Ahhh math y'all do way you want. From the pros and others in the industry I hear it's 4Gs.

[Than_Bogan]

@Brady Completely true, and a common mistake. It's theoretically possible to continuously hold a force of many times your body weight while remaining dead stationary, and thus experiencing no g's at all.

 

@MattP Assumption-laden math and mediocre measurements are still more trustworthy than "I hear from pros." That doesn't mean 4g's is wrong, it just means I eye it with great skepticism until it is backed by measurements and/or other evidence.

[MattP]

@Than_Bogan well said pros have researched and been in the sport long enough to know what they are doing in their sport.. Take it how you want it. Do your math. I believe what I believe for now until proven otherwise.

[Than_Bogan]

@MattP Fair enough. I think we're in the same boat there, as far as your last sentence.

[A_B]

The original Dave Benzel article (thinking it was Spray magazine) tested and plotted Mapple, and his peak was almost identical on both sides, but almost dead center behind the boat. That may be changing now, in particular with Nate, but someone like Jeff Rodgers is probably still peaking behind the boat... Mortyski made a run at putting a similar test unit together with new technology, but ran into some IT issues.. I tried to track down the original LISA unit, as it was called. Talked to Benzel, who gave me the guy's name who designed it. I called him and he said he basically threw it away, as there wasn't any commercial interest in it. This was years ago.

A unit like this would clear up a lot of misconceptions as where skiers load and I also think would debunk the "light on the line" stuff, that is just my personal opinion. I wanted to use it as a training tool to see where I was peaking and if my offside was really as bad as I thought, as people told me I was pretty symmetrical, but I always felt my offside was weaker.. The Spray article tracked Mapple against 2 regular guys skiing into 35 or 38 off, and their offside peak was quite a bit less than their onside, and not anywhere near the consistency of Mapple. He was like a machine (proven on paper).

[ktm300]

I think the higher load just inside the buoy line v. behind the boat is based upon speed and movement. The slower the ski, the higher the load on the line; hence, behind the boat the load is lighter as the skier has accelerated to a higher speed. The acceleration was created between the buoy line and the center line. Skimming v sinking.

 

@Brady Just get two monitors. porn and bos needn't be an either or proposition

[BraceMaker]

@KTM300 - perhaps he just needs the soundtrack to make BOS just normal enough.

[ScaredOfCorbets]

'Lb's of pressure taken when the boat hits.' It seems that that can be very high, depending on skier weight, amount of rope slack, boat speed, etc.

 

For Gs, it depends on are you talking about average sustaining or peak. Both are relative short duration, and of course peak is very short. So from observations, it seems 1.5 to 2 for sustaining and 3 to 4 for peak are reasonable.

[PatM]

I stopped reading when @Than_Bogan started with that math stuff. Let me know when you come up with a final figure.

[Waternut]

@Brady your equation is wrong. It's Vfinal^2=Vinitial^2+2*A*D.

 

70mph=31.3m/s (estimated max speed of a pro)

30mph=13.4m/s (estimated speed at the ball)

38ft=11.6m (distance between the ball and the center of the wake)

 

Doing the math, you end up with an acceleration of 34.5m/s^2. The force of gravity is 9.81m/s^2 which gives you a continuous acceleration rate of about 3.5G's. However, we all know that the acceleration out of the ball is greater than the acceleration at the wake so to say a pro feels G forces around 4G's is by no means unrealistic. Just keep in mind that instantaneous G forces and sustained G forces are entirely different. A good fighter/aerobatic pilot can pass out at 6G's if he holds that turn long enough but 9-11G's for a split second may not make an average person pass out.

[Than_Bogan]

I haven't double-checked anybody's equations or arithmetic, but the inputs are wrong. A minor note is that 70mph is much too high. A critical note is that the distance the skier covers is waay more than 11.6m. That would assume he goes directly back toward the wake, thus crossing the center essentially at the "previous" boat gate buoys. In fact, he travels significantly downcourse during this time in addition to covering the small distance back to the centerline. A better guess would be about 18m, but it's gonna be different for each skier.

[Than_Bogan]

@Pat M I should slap you a Dislike for that, but you're just too darned likable!

 

I need a new nemesis who is easier to hate! :) At least I can call you "The Undertaker" and have it be sort of true...

 

I wonder if I can "Off Topic" my own posts... nope.

[Waternut]

Ok if we're gonna get technical let's geek out and go for the gold. I do know that you can't accelerate until you're hooked up with the rope which happens inside the ball and I do agree with you @than_bogan that the angle the skier creates going into the wake plays a huge role in this. Let me see what I can come up with and I'll come back...

[doonez]

When they say "be light on the line" aren't they just trying to put it in a way that you can understand? I believe the goal is to FEEL like your being light on the line which can be accomplished by a good body position ie stacked etc and therefore you are not using so much energy because the load is being transferred straight through your body to the ski rather than your muscles having to transfer it and therefore you are using less of your own bodies energy (when you activate your muscles). So you are in fact putting the same load on the line but using less energy and it FEELS lighter. This is skiing more efficiently because you are using less energy if you are stacked. It is the same concept behind the Goode Powervest. It makes it easier because it helps transition the load of the boat to your lower back automatically and into your ski meaning that you can handle the load better and get to the next ball with max speed and having used less energy. That's just my understanding of it anyway (I hope its easy to understand)

[Waternut]

Ok here is my over analyzed epic geek results. For the record, I felt challenged and was bored because it's too dark for me to do anything I really want to do. Nothing was assumed. Everything was measured or calculated to the best of my ability with kinematic equations and geometry. I primarily used two videos. First was Greg Badal slow motion.avi to get times between rope hookup and wake crossing. I used a stopwatch and averaged the results to 0.75 seconds between rope hookup and wake crossing. I then used the video Thomas Degasperi water ski champion 2011 to get wake crossing angles because there are great shots from a helicopter traveling right behind the boat. I averaged the angle measurements to a 60° angle at the wake. Lastly, I looked at the kinks in the ski's path (where the skier hooks up with the boat) and found that on average, the skier gets 25% of the way to the wake before he starts accelerating.

 

Using the numbers above, the skier travels 43ft at a 60° angle between rope hookup and the wake crossing. If a skier travels across the wake at 60° angle, he must go 67mph to keep up with a boat moving at 36mph. Using that information, we can get the initial speed at rope hookup which was found to be 11mph. Now we have, initial speed, final speed, and the time it takes to get there so we can calculate acceleration which averages out to be 3.38G's over the 0.75 seconds.

 

The only other way I know beyond this is to slap an accelerometer on someone and go do some high tech measuring.

[Than_Bogan]

Very interesting. And much different from what I expected. I'll have to think about it a bit.

[ForrestGump]

60 degree isn't correct. It's been well established to be in the 47-50 degree range.

[Brady]

@jfw432. I concede. I was using my math skills from many years back, and it is obvious you are smarter in this area....or you are a much better bull shiter.....whatever the case. Now I am going to start telling people that my passion exerts as many g's as @OB 's wash outs! Maybe this explains many OTF's---skiers are G-LOC ing coming thru the ball.

 

One last question, is there going to be a test on this?

[Waternut]

Ha I win! I am so smart...S-M-R-T smart! I still suck at skiing though.....

 

I'm gonna go pretend like I have a life now. lol

[A_B]

 

All of our short line brain farts explained - Temporary G Force Blackouts!

[wilecoyote]

The measurements have been taken. (sort of)

 

http://www.soe.uoguelph.ca/webfiles/jruncima/Waterskiing%20top_files/Water%20Skiing%20Biomechanics-%20a%20study%20of%20intermediate%20skiers,%20non-publisher%20release.pdf

 

Unfortunately with less than ideal skiers, and with an eye toward lightening load for recreational skiiers. None the less, these are solid numbers and we can assume better skiers would generate more than the peak numbers achieved by these skiers.

 

Max recorded speed was 1.51Xboat speed. Max rope load not including deep water start, was less than 1.5X weight.

 

The author of the subject is a prof at the University where I work. I've been meaning to introduce myself to him. Maybe we could use his gear and measure some short line guys in the course.

[A_B]

All they need is an arm hooked up to rope to sense angle where the skier is at and plot over the set course length and it would show data like LISA. Where the load happening..

[Bruce_Butterfield]

The g force will be highest for a very short duration at the peak of the turn. Think of it more like the g load you get when landing from jumping off a 3' high table rather than a roller coaster (maybe 2g) or a fighter.

 

There are several ways to calculate, but are highly dependent on guesstimates of speeds and time.

 

Method #1: Reduction of speed in turn in very short time (0.1-0.3 sec) (a=delta v/delta t).

Assume speed into turn is 40mph, speed out is 10-30mph. (yellow is my best guess)

Note that bad technique will result in higher g.

 

G calculated from change in speed

Delta V mph Delta V ft/s t (s) A (ft/s2) g (ft/s2) G

30 44 0.3 147 32.2 4.6

20 29 0.3 98 32.2 3.0

10 15 0.3 49 32.2 1.5

30 44 0.2 220 32.2 6.8

20 29 0.2 147 32.2 4.6

10 15 0.2 73 32.2 2.3

30 44 0.1 440 32.2 13.7

20 29 0.1 293 32.2 9.1

10 15 0.1 147 32.2 4.6

 

 

Method #2: Constant speed through a turn of a given radius (a=v^2/r).

Assume speed between 20 and 40mph, radius between 10-30ft (5 ft means its turn & stop and method #1 would be more applicable)

 

G calculated from constant velocity turn

V (mph) V (ft/s) r (ft) A (ft/s2) g (ft/s2) G

40 59 30 115 32.2 3.6

40 59 25 138 32.2 4.3

40 59 20 172 32.2 5.3

40 59 10 344 32.2 10.7

40 59 5 688 32.2 21.4

30 44 30 65 32.2 2.0

30 44 25 77 32.2 2.4

30 44 20 97 32.2 3.0

30 44 10 194 32.2 6.0

30 44 5 387 32.2 12.0

20 29 30 29 32.2 0.9

20 29 25 34 32.2 1.1

20 29 20 43 32.2 1.3

20 29 10 86 32.2 2.7

20 29 5 172 32.2 5.3

 

 

So peak G in the turn is probably somewhere between 2-6g, but again for a very short period of time.

 

For the longer sustained G, the acceleration from the buoy to the wake can be calculated with similar assumptions:

 

G calculated from min speed at buoy to max speed at wake

Assume max speed 55 mph

Assume time from buoy to wake is 1/3 of buoy to bouy time of 2.68 s at 34mph

 

Min speed at buoy Delta V mph Delta V ft/s t (s) A (ft/s2) g (ft/s2) G

10 45 66 0.89 74 32.2 2.3

20 35 51 0.89 57 32.2 1.8

25 30 44 0.89 49 32.2 1.5

 

 

 

So max sustained G is in the ballpark of 2g, but again for less than 1 second.

 

This is all interesting discussion for bored off-season skiers, but largely irrelevant to progressing in the course. The real take away is that if you are pulling g's, you are skiing inefficiently.

 

Sorry the formatting seems to be hosed up, but I'm sure Than will check my math!

[Onside135]

Wow...That is all!

[Brady]

@jfw432 I recant my conceding to you the argument!!!! @Bruce_Butterfield just proved beyond a shadow of a doubt that the maximum G's you can pull is 2!!!!! If you don't believe, just try and read through all his mumbo jumbo. The key thing to look at is his final sentence......2 G's.

 

@OB. Yes, I know, get my ass on the water.....taking care of that tomorrow. Conditions are looking perfect. Highs of 45 degrees with water temp of 35 degrees. Going to be a great day pulling 2 G's in Salt Lake whilst relishing the fact that @Than_Bogan and I were correct!!!!

[Than_Bogan]

@All Turns out I don't have the time or energy to verify/refute any of this. I continue to believe the numbers I originally posted are pretty solid. In particular, I'm confident it's possible to ski around those numbers -- i.e. without experiencing any substantial g's. An actual skier may vary considerably, of course.

[MattP]

Thats 2Gs at old man speed. @Bruce_Butterfield care to do the math for us 36 guys?

[SkiJay]

A Moto GP bike generating ~1.8 G's is leaned over ~60 degrees. This further supports a maximum of 2g's for a skier leaned over ~70 degrees in a screemer of a turn.

[BraceMaker]

@skijay - you would have to account for slip as well though.

 

I assume the motobike leaned 60 degrees has a fairly good grip on the ground, if the tires lost traction and slid the G's would reduce and the turn would be larger.

 

The ski gets to slip, which has to compound the numbers.

[SkiJay]

Actually @BraceMaker, while you are correct in saying a loss of grip will increase the turn radius, slip is irrelevant with regard to the generation of maximum g's. The amount of lateral support necessary to maintain a 60 degree lean angle is the same whether there is a lot of slip or none. That lateral support is measured in g's.

 

As an unrelated matter of interest, there is a sideways sliding component to a race bike while it is cornering too. The angle of attack of a race tire at the limit is quite similar to the angle of attack of a fin during the pre-turn ... useless trivia.

[Horton]

Bob Corson emailed this to me. His is one of the god fathers of ski tech...

 

I saw your thread on the issue of physics of the slalom course, acceleration, etc. In years past, I did a lot of modeling etc. on jump and slalom physics. There were articles in the Water Skier about it but maybe 20 years ago now. One of the interesting facts/questions about slalom is why is it harder when the rope is shorter? The answer is that the path traveled is actually longer, the shorter the rope. To go a longer distance in the same amount of time obviously requires a higher average speed, thus a higher peak speed and a lower minimum speed.

 

[PatM]

I think my head just exploded

[Brady]

What I got out of that post is that 1. Mr Corson is brilliant and, 2. He absolutely agrees that the g's experienced are less than 2.

 

Pretty black and white!!

[Murrski]

@Hersh - I was watching some waterski videos on Vimeo and stumbled on this one of Jeff Rodgers. It's a segmented video but overlays real time skier speed and G-force. No idea if these are actual measurements or just swags but just thought I'd share. https://vimeo.com/20243735

[A_B]

I got in touch with Will Keown, who produced the video. He said there was no g forces measured or speed. He just inlaid WAG's based on what he has read in magazines or other training videos.

 

Myth busted.

[ToddF]

This is literally a shoestring guess but, someone skiing at 38 off has to travel 9-10% further than someone skiing at 15 off. which could mean anywhere from 15-20 feet further from buoy to buoy. and total course distance could be 120 more feet skied

 

Does that sound about right or completely off?