Interesting technique to apply - pick an arbitrary ‘wrong’ answer; then systematically work thru error-reduction iterations until finding a correct solution. ...Might be a strictly ‘Guy’ thing though. It’s sorta like how Guys drive to unknown destinations while refusing to ask for directions. We might ‘miss’ a whole bunch of times - but each ‘miss’ gets smaller until we can go, “Hey, Look - there it is!”
I like the exercise proposed in post 134 - making medium turns at a given ‘ski-speed’ and then trying to make short turns of the same shape and using the same ski-speed across the surface of the snow. This would demonstrate definite differences and also reveal a fly in the ointment.
In particular we'd notice that our ski speed along its surface path
would not match our upper-body speed through the air above
. With short radius turns our upper-body will travel a much shorter path (relatively speaking) than our skis will travel and more slowly along that path as well.
Tracing the circular ski-path in the snow for short turns we might see a radius of 4’ but our upper-body (perhaps our CM) might trace out an elliptical path with a side-to-side radius of 2’ with a crossover-to-crossover radius of 4’. ( a 2-1 ratio per turn )
This alternate path for the upper-body directly affects Ghost’s G-Force evaluation above since only the bottoms of our skis
actually get close to "the speed in a given radius" that his G-Force evaluation looks into. The actual G-Force at the ski as calculated for a given ski-speed and radius is always less than expected since most of our mass is well inside that radius and not traveling as fast, nor on as small a radius (elliptical path, remember?). This impacts our ski-pressure against the snow surface and therefore friction, compression and displacement of snow under our ski.
Looking at JASP’s lateral
acceleration vs. forward
acceleration … this certainly fits in there somewhere but exactly how
is a matter that needs further investigation due to the varied pressure(s) and varied amounts of friction as just described.
In a pure sense the increase (or decrease) of directly-sideways acceleration does not impact our current forward speed in any way. In nerd-speak only that portion of the ‘sideways force’ not perfectly perpendicular to the instantaneous tangent <cough> of our current path affects our forward speed. Skew that directly-sideways force just a bit forward and some portion of it slows us down. Skew it back a bit and we speed up slightly.
Centripetal force from the bent ski certainly turns the skier but in a perfectly frictionless world that sideways force would not detract from our speed. Without friction it would be a lossless (and progressive) conversion
of our down-the-slope speed into across-the-slope speed. Think about a perfect SuperBall hitting a frictionless wall at a 45-degree angle. It would just bounce off at the same speed… where does the force that redirects the ball away from the wall actually come from?
(WHY do I keep ignoring Friction? Well, I like to simplify things as much as possible and figure out what's happening at that level first. Once I know what happens without friction, I can work out what impact friction has on each component of the turn and develop the solution further ... sort of like Ghost's "Start somewhere wong, then make it progressively 'righter" thing above.)
Let’s stay away from muscular/biomechanical involvement for a while longer and first try to figure out the purely mechanical
foundations of what’s really going on with turning & speed-control.
If we know exactly
what’s going on (mechanically) with the slope, snow, skis, gravity, ski-path, (etc) in isolation - then we can pin down exactly what is required of the skier (biomechanically) to reduce or perpetuate speed. The Bio stuff is essential - but it is
on top of the fundamental mechanical situation. Some of this can be figured out with Rigid-Body dynamics but I think we’re going to need another look at Non-Rigid (segmented) Bodies to pin it down properly.
But hey… it’s Summer
. Not like we got anything better to do right now.