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eleeski
Posts: **3,989** Infinite Pandas

## Comments

315Baller1,128Mega BallerJust approximations, down course slide not considered.

What about VRope?

If:

VRope = Rope Vector Velocity

Ω0= Rope angle (to boat)

VBoat = Boat Velocity

Then:

VRope = Cosine Ω0 × VBoat

Ω0 = 900, Cosine Ω0 = 0 × 34 mph = VRope = 0 mph (rope speed at the buoy 41 off)

Ω0 = 760, Cosine Ω0 = .242 × 34 mph = VRope = 8 mph (rope speed at the buoy 39.5 off)

Ω0 = 690, Cosine Ω0 = .358 × 34 mph = VRope = 12 mph (rope speed at the buoy 38 off)

Ω0 = 600, Cosine Ω0 = .500 × 34 mph = VRope = 17 mph (rope speed at the buoy 35 off)

Ω0 = 00, Cosine Ω0 = 1.00 × 34 mph = VRope = 34 mph (rope speed behind the boat)

What about VMax?

Assume:

VMax = VHandle = VSki

(for the most part skier speed is equivalent to handle speed)

Ψ0= Skier path angle

Ω0= Rope angle (to boat)

VHandle =VRope × 1/Cosine Ψ0

or

VHandle = [Cosine Ω0 x VBoat] × 1/Cosine Ψ0

Assume Ψ = 530 behind boat (1/Cosine 530 = 1.701)

Then:

Vmax= 34 × 1.701 = 57 mph

A 15 off skier probably doesn’t generate a 530 angle behind the boat, but for the sake of illustration if one assumes a skier path angle generated somewhere in that range, think about the ΔV required as the line shortens; 0 to 57 to 0 mph in 2.68 seconds at 41off, 34mph!! For that matter the ΔV’s at 35off are quite impressive!

8,335★★★Triple Panda Award Recipient ★★★5,310Mega Baller3,261★★★Triple Panda Award Recipient ★★★6,952Mega BallerThis is indeed right up my alley, but it turns out this problem is Really Freakin' Hard. I've been trying for some time to develop the ability to compute optimal paths based on a given criteria and the math gets real ugly, real fast. The best case is usually a nasty differential equation that can only be "solved" by numeric simulation, and the worse case is so ugly that we can't even get it down to a differential equation.

On the other hand, the problem of determining the maximum and minimum speeds, at least to a good approximation, of agivenpath, is pretty doable.One surprise (although now that I see it, it feels obvious) is that the maximum speed generally does not occur directly behind the boat, especially at short lines. It actually occurs a bit after that, and the reason is that the skier is now still going fast in the "accross" direction, but is *also* "catching up to the boat" in the "forward direction." So the net speed continues to increase on the other side of the wake -- you can almost think of it as the swing of the rope is pulling the skier ahead faster. Naturally, this doesn't continue very long, so the peak speed is generally just outside the wakes.

Similarly, the minimum speed doesn't occur out at the apex, but slightly after that, and for the same reason: The "swing" of the rope is now in the backward direction, so it continues to reduce your speed for a few moments until the whole acceleration patterns begins anew.

What I can do is report the min and max of the rope handle (which is a pretty good approximation of the skier's minimum and maximum since they happen to occur when the skier's c.o.m. is fairly near the rope handle) for a variety of rope lengths, and assuming a path that I have reason to believe is *near* to optimal, although I can't yet prove it. I'll try to put this together when I can, but I'm really not too sure when that will be.

As far as the suboptimal paths, there is no obvious bound. If you make things bad enough for yourself, you may have to achieve Ludicrous Speed if you want to actually make it. So the worst case is limited by the speed you CAN achieve, not the speed needed to complete the slalom course efficiently.

1,596Mega Baller3,989Infinite PandasEric

1,128Mega BallerThe skiers VMax is inextricably linked to the velocity of the rope along its vector and the tangential vector along which the handle travels at any given point. So VMax can certainly be at the 2nd wake if good technique is executed (handle control); if the tangential vector of the handle path to that of the rope is at an angle greater than when directly behind the boat such that the VHandle = [Cosine (rope angle) x VBoat] × 1/Cosine (ski direction angle)] product is relatively greater.

Due to poor technique I’m quite certain that as the line shortens my VMax is before the 1st wake and my (ski angle direction) diminishes approaching the 2nd spray = bad = something upon which to focus for correction this Spring. Rather than “locking & loading” (static technique); creating the “velocity swing” (dynamic technique through the spray to spray work zone).

6,952Mega BallerWell, maybe. My first instinct is that the real-world variations of the boat actually have a very slight *dampening* effect. I strongly suspect that the boat's minimum speed is happening right around the same time as the skier's maximum, and vice versa. This is because the maximum load on the boat occurs directly behind the boat (true of nearly any "sane" path as far as I can tell), so unless ZO

over-compensates for that load (which I think skiers would absolutely hate), that's going to be about where the boat speed is slowest.Of course, I've noted that the skier's maximum speed occurs a little after that. So if ZO were set to "gun it" at that particular point, it is conceivable that ZO could slightly increase the skier's maximum speed.

But, even if that's the case, it doesn't necessarily tell us much! Speed isn't necessarily a bad thing! In fact, a long time ago I discarded "minimize the maximum speed" as a good criteria for an optimal path, because a lot of that speed just comes and goes "for free" due the geometry. What's important is the effort that the skier has to put in, and sometimes carrying more speed at certain spots ultimately leads to less effort.

I really would like to be able to model details like boat speed variation and comment "intelligently" about such details, but the math is border-line intractible even with a lot of simplifying assumptions. So I'm not optimistic.

163Baller3,989Infinite PandasGloerson's analysis based on angle out of the buoy is interesting but the turn angle is way too variable (at least if I'm skiing). Maybe speeds do react primarily to angle. The overhead view of a top skier in the course would be enlightening.

The radar guns of Andy and Deena are suspect on two fronts. One, does a radar gun get an instantaneous speed or a dampened out average? Two, Andy and Deena are smooth skiers. I wonder what happens when they scramble? I would suspect that the speed swings are much higher when not following the smoothest passes or skiers.

I know I personally have come ripping into the buoy at warp speeds (time slows down giving me time for my life to flash before my eyes). I won't comment on whether I made the next buoy.

The feel from the boat does have significant effect on how I ski. Maybe the magnification of the skier speed is not where the boat speed variability manifests itself. But the nature of the boat's speed variations do matter to my skiing.

Than's claim that maximum speed occurs at the second wake has ramifications on training technique. I'm intrigued!

Eric

6,952Mega BallerCertainly true! Hard to quantify.

Eric: "Than's claim that maximum speed occurs at the second wake has ramifications on training technique. I'm intrigued!"

Hm, it does? I think this is just more a consequence of the geometry. Even if you are already starting to ease up your pull, the fact that the rope changes from swinging you opposite to the direction of the boat's travel to the same direction as the boat's travel causes your net speed to increase. Theoretically you could force the maximum speed to occur in a very different spot, but I believe any such path would be extremely suboptimal.

Btw, it's actually beyond the second wake at extremely short lines on most "sane" paths that I've considered.

1,596Mega BallerNot done with radar, done with LISA (I believe that was the name anyway, a device for measuring a number of skier parameters).

569Solid Baller1,596Mega Baller1,097Mega BallerHorton is my hero

2,314Mega BallerI bagged a GPS and skied with it under my vest. It said my chest clocked a 57mph top speed. Oddly enough, it showed my lowest speed in the course to be zero!

www.FinWhispering.com... Your ski should be your dance partner, not a wrestling opponent569Solid Baller315Baller197Ballerover 43 mph the top speeds would have to be much higher than 43 even with a pefect skier path.

438Solid Baller784Solid Baller438Solid Baller367BallerWe plan to.

Plenty of apps out there that do acceleration logging.

Just need to find a nice compact waterproof case to put it in under your vest.

Hopefully one that floats.

Other thing that would be fun to jump for is one of these:

http://www.gcdataconcepts.com/products.html

1,036Crazy Baller