Physics of Skiing! | FPM Podcast #13

[ROBOT]

This week is a fun call MB had with an FPM Member, Alex Montagu, who was doing a school project on the Physics of Water skiing.  So, we figured we'd share.  Thank you Alex, for reaching out!!

We apologize for the Audio...MB's head set sucks....now we know!

0:00 - Intro - High School Physics Project!
0:50 - Why Physics
1:22 - If you care about skiing better, you want to Understand physics
1:47 - EVERYONE is a Physicist!!
3:45 - Center of Mass of an Object
4:57 - A Skiing example of Center of Mass
6:44 - TRIM THEORY: a Skateboard vs Water Ski example
7:26 - Drag and Trim
9:08 - Handle Path and Physics:
9:40 - 15 Off
10:45 - 41 Off
16:15 - To Turn Sharper, you NEED more LOAD!!
18:00 - G FORCES!! - Why We LOVE Skiing!
19:25 - Skiing the MIDDLE Path
22:20 - WHY skiing the Middle Path works
23:18 - 15 Off creates higher Average Speed than 41 Off.
25:50 - Vectors in Water Skiing
30:20 - Force Vector Components
35:18 - Free Body Diagram:  Why Vectors Matter
37:45 - 2 Things that Accelerate Skier to CENTERLINE
41:30 - Body Position is everything
42:20 - Human Performance: completely dependent on our ability to find Flow while skiing (stop thinking)
43:55 - 2 Brains simultaneously…
44:30 - ZeroOFF Settings and How Critical is it Really??
46:58 - Roll Angle of Ski
49:20 - Water Skiing is a great way to waste some time and learn about Life!
49:50 - Has become an Elite Sport: Too Expensive
50:40 - There are always ways to make it affordable!
52:20 - Who’s Going to MOOMBA?

This podcast is Available on Apple Podcasts, Google Podcasts and Spotify! - Search "FPM Podcast"

This podcast is Available on Apple Podcasts, Google Podcasts and Spotify! - Search "FPM Podcast"

Apple Podcasts: https://podcasts.apple.com/us/podcast...

Spotify: https://open.spotify.com/show/7hPWjzP..

[bko]

@MarcusBrown

The shortline-skier has to "cover more ground" - he has to get higher up on the boat (when going around a buoy) AND back behind the boat each time.

So isn't his path longer than the path of someone on a 15off rope?

And doesn't this conclude that the average speed of a short line skier must be higher than at 15off?

 

[MarcusBrown]

@bko its a bit tricky, so I'll try to keep it simple.

Relative to the boat, a shoreline skier DOES have to "cover more ground" in the sense that to run 38 off, they have to get maybe 65 degrees up beside the boat, (instead of ~40-45 degrees at 15 off) to get around buoy 1, THEN do the same thing but on the other side of the boat, before buoy 2.  So relative to the pylon, the skier is traveling a larger Arc, and getting higher on the boat on each side (higher than a 15 off skier would), which is what the Adams have covered at length, by talking about moving the handle as high as possible on the side of the boat, as fast as possible.

BUT, if you actually traced the path of a 15 off skier from a drone, vs a 41 off skier, the 15 off skier is actually traveling a longer path.  They have more rope, and ultimately are able to break the buoy line sooner, AND apex much further up course.  All of this points to a longer skier path through the course, at longer rope lengths, as a general rule.

[Horton]

@MarcusBrownthe 15 off skier is going MUCH slower at centerline and no matter the line length the skiers must be going slower than the boat at apex. So how is the 15 off path longer?

 

( shit - I think I just answered my own question but you tell us anyway )

[Drago]

@bko the average speed of all line lengths is the same. 
 

[switchbackr]

Just now, Drago said:

@bko the average speed of all line lengths is the same. 
 

At the same boat speed.

Then, as line length reduces, the acceleration and deceleration rates increase.

[bko]

@Drago @switchbackr All paths of skiers at any line length have the same length?

Maybe.

Someone needs to plot skiers' paths in drone videos to really find out.

[dchristman]

The boat is traveling straight down the course at (15.28 m/s) 55kph for 259m.

Skiing precisely ball to ball would be a distance of  293.75m, so an average speed of 17.33 m/s.

If you could ski a perfect square wave ball to ball you would cover 397m, and would be going 23.42 m/s.

The further you ski outside the balls the further you travel, and therefore the faster you go.

As the line gets shorter, the distance you can travel beyond the ball line gets smaller and you are getting closer to skiing ball to ball.

Conclusion- believe what @MarcusBrownis telling you!

Edited March 29, 2023 by dchristman

[MarcusBrown]

Now you guys have me overthinking this simple statement I made...I'll have to do some drone analysis at some point, to definitively get answers.

But remember years ago, when David Nelson compared "New School, Traditional and Coordinates Style of Skiing"?

He stated in one of his conclusions "As far as our actual speed is concerned: If you follow an efficient line, it should not seem strange that your speed at 32 off will be higher than your speed at 39 off – your momentum swinging on a longer rope naturally results in a more S shaped path, and allows more distortion than you can get with a short rope. If you ski a longer distance in the same amount of time, you’re going faster."

He did do his analysis with video from the boat, and he was making assumptions....but I still maintain that for a given skier ( @twhisper , lets say), there is a high likelihood that he'll travel a further distance through the course running 15 off, compared to running 39 off.....and therefore, have a higher average speed.

[Than_Bogan]

I strongly disagree with Marcus on this point.  At some point, I'll communicate with him privately and see if he is persuaded by any of arguments.

[Drago]

@bko not what I said

if I run a 28 off pass @ 36 

Will Asher runs a 41 @ 36 

it's a tie: 36 mph average, 16.08 seconds 

One could deduce that Will would be going way faster, followed by way slower, to get the average. Or we can hook a bunch of stuff up and prove it.

The only thing I can do just like Will Asher 😉

[Horton]

What occurs to me is that as the rope gets shorter the skier gets from the ball to the wakes faster and faster. At 15 off it takes forever to get back to center. If it takes more time to get from A to B & the line is tight then the path must be longer.

From the second wake to the ball is another story. IDK.

@Than_Bogan The post of this forum is these conversations. If you disagree with MB lets hear it.

[Rednucleus]

A 15 off skier does not create the angle across course that a short line skier creates - so distance ball to ball is longer at 15 off since I ski more of a diagonal ball to ball vs a more perpendicular path, and I go slower.

[Horton]

@Drago yes if we are only measuring the speed exactly parallel to the boat.  

[Drago]

 

3 minutes ago, Horton said:

@Drago yes if we are only measuring the speed exactly parallel to the boat.  

Average speed. It take 16.08 seconds for every skier to run a pass at 36 mph. Gate to gate. (Unless you have slack through the exit gate)

I am not talking about path 

[Than_Bogan]

@Horton I understand why you'd prefer that, but discussing math and physics in a crowded room is very, very painful.  I'm not up for it.  I simply wanted to make people aware that there is a different view, and perhaps later Marcus or I will convince the other.

[dchristman]

@Than_Bogan  show your work!

[Horton]

@Drago well then yes 

[Horton]

@Than_BoganIt is water skiing. Of course it is painful.

[Drago]

Talking about Coordinates is Real Pain

[MarcusBrown]

@Than_Bogan I have not put much thought into this in some years, but now that I think about it, something occurs to me that is quite clear:

The smooth "Sine Wave" of the skier path at 15 off (between any two buoys) might just be the shorter path, when compared to the necessarily more "Square Wave" of a skiers path at 39 off.  

With that quick thot experiment, and realizing the Square Wave path will probably be longer than the Sine Wave path, I can easily see how average speed could be higher for the Square Wave path through the course (39 off skier)

Still quite a few thoughts brewing...

[buoyboy1]

@lundberg....Matlab Model Guy really needs to weigh in on this.....

 

[Bruce_Butterfield]

I remember reading David Nelson’s stuff a few years back and he was most definitely wrong in his conclusions.  Skiing a shorter line absolutely requires a longer distance travelled.

I will try to explain without making Horton’s head hurt too much (although that is a nice benefit)

For simplicity, lets assume we are on a river with a 36mph current and the slalom course is floating by and the “pylon” is a bridge abutment.  This lets us consider only the path of the handle from 1 to 2 ball.  The path of the boat is separate and the same for all line lengths, so it is “cancelled out”.  The distance from buoy to buoy is simply the arc length the handle travels.  Yeah, the handle is not the “exact” path, but for comparison between line lengths its perfectly valid.  The change in the skier’s “reach” between line lengths is in the noise.  i.e. the line length change between 35 and 38 is 3 feet, while the change in skier’s reach may be a few inches.  

The length of handle path is simply the radius of the arc times the angle moved (in radians), or L=Rho x Theta for anyone who remembers 10^th grade geometry.  Even though the rope (radius) gets shorter, the angle traveled gets much greater. 

line off	r (m)	theta (deg)	theta (rad)	R theta buoy to wake (m)	buoy to buoy arc length (m)	handle avg speed @36 (m/s)	handle avg speed (mph)
15	18.25	39	0.7	12.4	24.9	9.8	22.0
22	16	46	0.8	12.8	25.7	10.1	22.7
28	14.25	54	0.9	13.4	26.8	10.6	23.7
32	13	62	1.1	14.1	28.2	11.2	25.0
35	12	73	1.3	15.4	30.7	12.2	27.2
38	11.25	90	1.6	17.7	35.3	14.0	31.2

 

The arc length at 38 off is 40% more than the arc length at 15 off.  The skier has 2.53 sec to get from 1 buoy to the next.  Longer distance traveled in the same time requires a higher average speed.

QED

Other comments:

This a comparison of the minimum distance traveled for each line length.  The “square wave” effect of the shorter lines will increase the distance travelled even more.

The “average speed” in the chart above is ONLY the radial speed.  To get total speed requires vectorially adding the boat speed back in. (now I get to make Horton’s head hurt!)

For anyone questioning the validity of using a stationary pylon and fast current in the river, ask yourself if you are at the drag races, does anyone factor in that the earth is moving thousands of mph through space when determining the faster car?  The movement of the earth is the same for both cars, so it “cancels out” the same as boat speed when only considering differences between line lengths.  For the geeks, this is relative motion.

While is certainly possible to measure path lengths from a drone, I suspect it would be very difficult and have a high margin of error.

[DW]

Sine Wave v Square wave path description is a good one, that helps visualize the pendulum path of the bottom of the pendulum (the handle) which is longer for a short rope v long rope considering the handle needs to be at the same distance (width) from center (not quite due to required lean angle but close).  Hence, skier average speed will be higher for the skier that travels farther between the end gates as will acceleration forces.  Edit - was adding lengths and BB posted those.

@Than_Bogan - agree with Horton & others, once you threw it out please demonstrate your theory and if we are not worthy of your math description simply provide a concise summary of your opposing viewpoint.

Edited March 28, 2023 by DW

[Horton]

[03RLXi]

I suspect @lundbergwill be able to produce a plot that shows the different distances 

 

[ALPJr]

Hmm… seems to me that @Dragois right on the avg speed and @Rednucleusis right on the variability of speed between the peak highs and the lowest lows. Everything else sounds like it’s still to cold to ski in a bunch of places 😊

[Menzelskier]

As a math and physics teacher, I agree with Bruce. And as a math and science teacher I will try to simplify the principle he states.

In Bruce's table are two easily comparable arcs. A 16m radius (22 0ff) would generate a circle with a circumference of 2(16m)(3.14) = 100.5m (rounded). An 11.25m radius (38 off) would give us a circle of 2(11.25)(3.14) = 70.7m (rounded).

Now the nice thing about 22 off is that we get about a 45 degree angle from wake to ball, giving us 90 degrees total travel, which is one-quarter a circle. One quarter of 100.5m is about 25m.

Using the same principle, 38 off gives us 90 + 90 = 180 degrees, which is half a circle. Half of 70.7 meters is about 35m. And 35m is a significantly longer distance that 25m!

Just for fun, what if you skied 22 off but went out to 90 degrees? Then you would be skiing an arc of 50m. Try doing that in 2.53 seconds!

[Rodwishart1]

The new skiing Bible might be taking shape... 

Matlab guy posted here... 

[503Kento]

Seems like the guys in this thread should be able to validate the various theories.

)

[Drago]

My recollection of coordinates (Schnitz gave Nelson's theory that name), is Dave was basically telling shortline skiers they were working too hard. That we (I guess I was one back then) just needed to lighten up and go ball-to-ball ("the key is you have to backside the buoy"-Schnitz). I suppose, mathematically, that might work. But in reality it's impossible. I don't think a robot could do it. Shortline skiers are athletic humans, not math theories, we (well, not me anymore) use our tools to their optimum.

Just thinking out loud here. If you consider what we all agree on with the 1/2 buoy rule at short lines (if the skier has the handle, it is pretty much impossible to stay outside the buoy line for any amount of time), my guess is the shortline skier travels a shorter distance. If you could plot two drone shots, I bet it's not a huge difference.

guys, you cannot increase average speed. The boat goes 36, you are attached to it, and you start and stop at the same place

[AdamCord]

I tried my best to avoid this thread because I knew I'd get sucked in....and alas....here I am. I apologize in advance for what comes next:

 

It would appear that this all started when @bko asked a seemingly simple question...does a shortline skier need to cover more ground than a long line skier?

 

I read through all of the responses and I think I can confidently say that everyone here is right ! Hooray! Also everyone here is wrong. Boo. The reason is that because the original question seems straight forward, there's actually a lot of nuance in the question:  "does a shortline skier cover more ground than a long line skier?"

 

The answer is YES! ABSOLUTELY! Except for the times when they definitely do NOT. 

 

Let me explain. At a longer line length, the options for where a skier can ski and which path they can take are many. They can ski wide and early, and they can ski outside the buoy by a wide margin, making what could be considered a version of a square wave. Conversely they can take a path that is straight from buoy to buoy, drawing Zs all the way down the lake.

 

As the rope gets shorter, however, our options for where we can ski are reduced. By the time we get to 41off, the path is probably not just "as wide as a garden hose", but man it's close. Also as the rope gets shorter we MUST take a path that's more buoy to buoy. When you're approaching 90 degrees to the boat there isn't enough kinetic energy to keep the skier out there for long, and when the rope is crazy short it may be just enough to slip your ankles outside the buoy.

 

Having said that, let me address some of the excellent points made above. @Bruce_Butterfieldand @Menzelskier I like where your heads are at, but I think you are ignoring the fact that the speed of a 15 off skier (relative to the boat) is vastly different from a 39 off skier. So just because the 39 off skier covers more ground relative to the boat, they are moving much slower (relative to the earth) at the start of that swing and much faster at the end. What results when looking from above may actually be a pretty straight line. So if we're asking if the skier covers more ground relative to the boat, you're spot on. If you're talking relative to the world...maybe not.

 

I think @MarcusBrownhad it right from the beginning...IF you're talking about the same skier. Will Asher at 15 off could get to the next buoy line 50 feet early AND 8 feet outside the buoy line. That is obviously going to be a longer path than what he can run at 41 off. But compare him to someone like @Horton who can barely run 15? Then their paths may be pretty close.

 

I also want to address David Nelson and Schnitz with coordinates since it was brought up and also since I'm on a work trip in a hotel and have nothing better to do....I don't think those guys were totally wrong. I also don't think they were totally right, but if I understand coordinates correctly they were talking about moving the apex of the turn closer to the buoys instead of trying to apex way up course...? If that's what they were preaching then as I have said above, you can only be 90 degrees to the boat for a moment, so at super shortline that better be right when you're at the buoy and not a moment too soon. As we have also tried to preach with GUT the handle path going to swing up and past the platform of the boat when the rope gets short...trying to take that handle to the shoreline will get you nowhere. So again I don't know that I fully understand what those guys were talking about, but in general it doesn't sound too crazy to me.

 

end of dissertation 😅

Edited March 29, 2023 by AdamCord

[Menzelskier]

1 hour ago, AdamCord said:

Having said that, let me address some of the excellent points made above. @Bruce_Butterfieldand @Menzelskier I like where your heads are at, but I think you are ignoring the fact that the speed of a 15 off skier (relative to the boat) is vastly different from a 39 off skier. So just because the 39 off skier covers more ground relative to the boat, they are moving much slower (relative to the earth) at the start of that swing and much faster at the end. What results when looking from above may actually be a pretty straight line. So if we're asking if the skier covers more ground relative to the boat, you're spot on. If you're talking relative to the world...maybe not.

You have listed multiple frames of reference. To me, the basic frame of reference is the boat, for unless there is slack all paths travel along the arc of a circle, as the radius of the line never changes for any given line length. A skier at 15 off can certainly choose a longer arc, but it is not necessary. All calculations can be performed using the boat as a stationary frame of reference (which it is for the drivers, passenger, and skier). If we change the frame of reference to be the lake itself, then we will have a zig-zag graph. If we change it to a point above the Earth's rotation, then the skier could be traveling backward in such a frame. The frame of reference from the boat is the simplest in my mind. But it may not be that for everybody!

Jumpers take advantage of long line lengths to get way out on the boat so they can generate acceleration for the longest period of time.

[Drago]

@Gloersen uh, you're right. I’m not thinking straight I have a bad fever

[ALPJr]

Yes @Gloersen makes sense. Imagine two football players standing at the goal line. One runs straight down the right hash marks and the other player runs a zig zag between the right and left hashes, and both get to the opposite goal line in the same amount of time. Who travelled faster?

Edited March 29, 2023 by ALPJr

[skibrain]

Lots of competition here for Baller of the Month. 

[lundberg]

@AdamCord

I agree with Adam, there a ton of caveats / nuances when comparing different line lengths.  You have a lot more options when the rope is long.  That said, I'm convinced that if you assume a tight line all you need to know about the handle path is the angle of the rope in relationship to the boat path over time.  The plots that I made in the thread "Slalom Ski Path Physics (Matlab Model)" show the handle path and other dynamics for different rope lengths assuming you only go as wide and you need to go around the buoy and have a particular swing velocity profile over the arc that is traveled (angle of rope over time).  With those things constant you can see from the plots that a short rope has a longer path and thus a faster average speed over the water (different the than the average speed down the lake).  If the swing profile is different it changes your path.   You could show that a different swing profile with a wider apex and/or higher cross course peak speed could make a long line path longer than a shortline path.

This year I'm going to see if I can make my camera mount track tight with the rope (bad for video but good for collecting angle data).  With a little offline filtering I bet I can make handle path plots plus all the speed and acceleration data too. (assuming constant boat speed)

@03RLXi

I just changed jobs and don't have access to Matlab right now (hopefully soon) but it should be straight forward to show average directional speed and distance from the model data that I have already.  Stand by....

 

@MarcusBrown pointed out to me that the title of my previous tread was wrong and should have been "Slalom Handle Path Physics"  (not Ski Path) and I agree.  I've been thinking about how to parametrize the ski location in relationship to the handle.  

Here is what I'm thinking:

Define the ski location as the point between your front and back foot.

From the top view (drone perspective)

1) at the apex of the swing the ski is at the reach length away from the handle and inline with the handle to the pylon.

2) as the turn starts the handle stops moving up on the boat and starts falling back down the arc, but the ski keeps gaining and rotates around the handle.  At the end of the turn it is closer to the boat than the handle and in line with rope (or maybe a little behind) 

3) at some point in the swing as you start to stand up the handle and the ski will be at the same spot.

4) as you approach apex the ski starts to move away from the handle until the turn starts

 

So I think all I need are locations in the swing where

1) the ski is starting to take load (after turn, maybe where down course speed starts increasing) and how far in front of the handle it is

2) ski is under the handle

I should be able to interpolate between the full reach and point 1, point 1 and point 2, and point 2 to apex. 

 

I'm open to input!

 

[dchristman]

I would like to put forth two more thought experiments.

Let's assume the length of the line is approaching infinity, thus theta approaching 0deg.  @Bruce_Butterfield you can still keep it tied to the bridge abutment if you want.
What is the length of the skiers path?  The potential path approaches infinity, but what path would a skier take through the course? Take 41 feet off that line. Now what would the skiers path be?

Now assume the the length of the line is approaching 0. Closer to 0 would yield a skier path closer to the boat path, approaching 259m.  

My new conclusion is - I  don't think the answer to this question is going to help anyone add balls, but I am grateful that slalom gives us this stuff to think about during the off season @Hortonprovides us the place to talk about it.

 

Edited March 29, 2023 by dchristman

[coach3]

The intent of this thread, may be why 39 off is more difficult than 15 off; i.e., is it distance traveled? @AdamCord bottom lined it to skier path has to be more correct at 39 than 15, (higher on the boat). The average speed and distance traveled may be similar between long line and short line. The increased difficulty might be: more acceleration and deceleration is required at 39 than 15. Simple as that?

[dchristman]

It doesn't take much to see that this little problem don't amount to a hill of beans in this crazy sport. Someday you'll understand that.

[dchristman]

Maybe I'll have to revive this project

[MarcusBrown]

Here’s a quick and dirty overlay of 15 off vs 39 off

skiers are @twhisper (39) and Lucas Acondo (15) 

very interesting. 
 

Definitely going to do an overlay of the SAME skier, at long and short lines, at some point in the near future. 

 

 

View this post on Instagram

A post shared by Marcus Brown (@marcus_brown_)

[lundberg]

@MarcusBrownthat is an awesome clip!

Here is what my model looks like for 18.25m vs 10.25m  (remember this is handle path not ski path so the rope does not get to full width)

58 kph / 36 mph with peak swing speed at center-line

Average speed from buoy to buoy is 

18.25m (15' off) = 67.7 kph (42.1 mph) / distance travelled = 47.9m

vs

10.25m (41' off)  = 68.4kph (42.5 mph) / distance travelled = 48.4m

(shortest possible path with no reach would be 47m)

 

[dchristman]

@lundberg Could you vary the width for 15 off to the point where the path length equals the 41 off... what is that width?

[Bruce_Butterfield]

@dchristman my slide rule doesn't have those fancy graphing capabilities, but if we make it easier and just look at the handle, at 38 off the handle is 90 deg with the boat and the buoy to buoy arc is 35.3m.  Solving the other direction for the same arc length at 15 off yields an angle of 55 deg and the handle being 3.5m (11.6ft) outside the buoy line.  In other words if you ski 15 off and get the handle 11.6ft outside each buoy, you will be traveling the same distance as you would at 38.

[MarcusBrown]

@Bruce_Butterfield I hear you on arc length, and completely agree that at 38, the arc length traveled around the boat is much greater than at 15 off (for a given desired width).

However, arc length traveled around the boat (between any two buoys) doesn't necessarily correlate to a longer ski path.

In your river analogy, yes, the skier tied to the bridge at 38 off travels a further distance, relative to the bridge, than a skier at 15 off.

BUT, we don't care just about distance traveled relative to the connection point....we care about distance traveled over the water, or relative to the water, as was mentioned by @AdamCord

Again, not discounting your analysis, just trying to make sure we are on the same page.

[Bruce_Butterfield]

@MarcusBrownyes, mostly agreement.  My arc length is a simplification because the actual path of the skier/ski/COM gets insanely complicated and I don't think there is a reasonable way to model and get close.  Overhead drone video may provide some cool insights, BUT the path will vary from skier to skier, AND buoy to buoy for the same skier.

The river analogy is still valid - the boat (current) speed is the same, so that frame of reference is constant and can be ignored if we are only looking at variations between line lengths.  The "distance" changes since the handle is not the classic pendulum and will accelerate/decelerate with the skier and be more of the square wave path discussed before.  Yes the square wave path will be longer than the simple arc.

My point is the math/physics dictate that the minimum path is longer with a shorter rope.  Longer path in the same time requires higher average speed.  IMO, that's the fundamental reason shorter lines are more difficult.  I think we are in agreement that minimum path is not the same as optimum path.  

Edited March 30, 2023 by Bruce_Butterfield

[Horton]

I am going to review this today 

 

 

[lundberg]

@Bruce_Butterfield @MarcusBrown @dchristman

I think the interesting question is not "is one path longer or is the average speed higher", but instead what are the dynamics of the skier's speed from buoy to buoy as the rope length changes.

The average speed / path length in my model is very close between 15 off and 41 off (0.4 mph and 0.5m)  

To make the path lengths the same at 15 off and 41 off in my model I can just tweak the reach length which changes the rope angle from 37.2 to 38.9 degrees  (vs 78 degrees for 41 off with a much greater reach)

[Menzelskier]

Marcus Brown -- I wonder if your video could be re-edited. When I look at the ropes, it is clear that the skiers have been superimposed, but their actual runs have not. The 15-off run's boat is well ahead of the 38-off boat. You can tell this by the still shot of the first frame, and since the 15-off skier should be 23 feet back of the 38-off skier at the wake crossing, this tells us just how far ahead the first boat is. Could these videos be re-superimposed to the same time frame? I think this would be better at showing the actual relative positions of the two runs and might prove further instructive.