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Turn trajectories.

post #1 of 3
Thread Starter 
Found this article, and it's fascinating how the mechanics/physics of bullet trajectories relate to the relevant physics involved in the arc to arc retracted ski turn.


So what do you guys think? Do you think they hold true for cannon ball trajectories too,,, or would that be more of a pivoted turn comparison?

post #2 of 3
How do we correlate straight trajectories to curved trajectories? Momentum, accelleration/decceleration? There seems to be a bit more involved in ski turns?

Gravity pulls the bullet down from horizontal. How do we relate this to skiing?

post #3 of 3
Heh, heh, heh - Nice try Rick - Is this an attempt to derail the relevance of ‘Ballistic Path’ ideas in that other thread...? Well, a bullet in flight cannot be ‘Managed’ while in flight by the Shooter and the relevance of ‘Drop over Time' is certainly an element of everyday skiing.

What if your Bullet in Flight were being pushed from the side by a strong side breeze (as mentioned in the link)? It would be minimally be supported against Gravity by the air friction in the vertical direction (as also mentioned in the link) but would be ‘guided’ to the side by the side-wind. Doesn’t this seem very much like where I proposed:
Originally Posted by michaelA
… I get the sense that he’s in Float-Mode (with respect to Gravity) in most of those frames showing a seated posture. Even where his skis are engaging for the next turn I think ski-bending we see comes from his ‘lateral momentum’ against the snow surface far more than from any downward pressure on them.
Like the Bullet in flight, Bob is in ‘Float-Mode’ and may well be managing his upper-body reorientation and position with centripetal force from his skis - very much like the Bullet being re-directed by the side-wind. Bob need not be making any real effort to ‘hold himself up’ against Gravity since it takes Time to actually fall all the way to the snow.

The path Bob’s body would otherwise try to follow is a linear path (in the horizontal plane) which follows the same predictable downward-curve over time as the Bullet in Flight does (though covering much less horizontal distance due to his much slower speed).

Does a Cannonball do something different than a modern Bullet? It sure it does!

Back when Cannon were popular they hadn’t yet figured out rifling - that spiral grooving inside the barrel which imparts a spin on the Bullet. Without that spin those round Cannonballs would often curve or dance like crazy on the way to the target even without a side-wind. This is very much like a baseball pitcher throwing a curve-ball or a knuckle-ball. A pitcher who throws the curve-ball must also develop a ‘ballistic plan’ that accounts for both the ball’s drop and the desired directional change.

I think a discussion of Turn Trajectories while in an un-weighted (or partially weighted) state is highly relevant to skiing - especially at the higher speeds involved with racing. Successful racers going at high speed over a small rise pretty much need to consider the ballistic path (trajectory) they are about to experience: it would after all be nice to land back on the race course.

I suspect they are also very concerned about exactly how much Angular Momentum they have on each of their three axes as they leave the ground since this largely determines the position they will be in when they land. Do they think about it in terms of numbers and math? Heck no - but by feel certainly.

Another good example of ballistic relevance is the skier who goes over a small up-curved jump. The typical novice will jump only a short distance and end up landing on their ski tails, or their butt, or the back of their head - depending on how long they are in the air. This is a direct result of that little up-turned ‘lip’ creating a last-moment backward rotation in the overall skier.

After a few crashes (sometimes quite a few) the novice skier learns to absorb that final rotational up-turn with their ankles, knees and/or hips and waist (“sucking up” the rotational impulse as well as the upward thrust).

A more advanced skier might want more distance and therefore choose not to absorb that last little bit of upward thrust. This skier will likely Extend Up & Forward forcefully - pushing down with extending legs but still absorbing the last second backward rotational-torque with their ankles and hips alone. In this way they’ll avoid most or all of the backward rotation and land further down the slope.

Taking it still further, the advanced jumper might execute an aggressive whole-body rotation ‘forward’ in the last moments before takeoff. They do this in order to take the expected airtime into consideration such that they will be able to land far down the hill with Almost-Flat-to-the-Slope skis (therefore needing at least some overall forward rotation).

These are all examples of a skier executing a preconceived ‘ballistic plan’ - though here we’re only considering rotations in the Fore/Aft (Sagittal) plane.

What of the skier at the Apex of a medium radius turn who suddenly goes over an unexpected drop onto a much steeper slope and drops 6 feet? In what direction will their skis be pointed when they land? In what direction will their overall momentum be? (can we say 'directional divergence' ) And in what position will their body be at ski-touchdown? Do any of the answers depend on the slope angle just prior to airtime?

Rick, I’ve got to admit that I’m really perplexed at your lack of interest and apparent contempt for discussion in these areas. They apply so readily to all racing disciplines and to a huge degree in SL - especially the way Ligety often skis it.

Virtually all threads on this forum deal exclusively with Skis-on-the-Snow technique and mechanics. Flexion-related threads sometimes discuss un-weighting - but they barely ever get off the ground ( ) in the area of 'what happens during the Float, and why'.

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