This photo caught my eye
http://www.epicski.com/content/type/61/id/190789/width/1000/height/1000/flags/LL
What might be the inherent turn radius of a ski when engaged with the snow surface at 80+ degrees?
This photo caught my eye
http://www.epicski.com/content/type/61/id/190789/width/1000/height/1000/flags/LL
What might be the inherent turn radius of a ski when engaged with the snow surface at 80+ degrees?
This photo caught my eye
http://www.epicski.com/content/type/61/id/190789/width/1000/height/1000/flags/LL
What might be the inherent turn radius of a ski when engaged with the snow surface at 80+ degrees?
Looks like a 35 m GS ski. 35 * cosine (80)= 6. 6 m when it hooks up, a bit more when it's bouncing.
Would that calculation account for camber? ;-)
(the 6m number has to be incorrect, if you take a moment to consider)
I haven't worked out if that's the correct equation (but I'd guess Ghost knows what he's talking about)... but why must 6m be wrong if you think about it?
That's a carved turn along the arc of a 12m diameter circle, if I understand it correctly - which is fairly large.
http://www.epicski.com/a/the-complete-encyclopedia-of-skiing-epicski-skiing-glossary
It's the correct formula al lright, but it gives the curve that would ensue if you were able to press the ski firmly down to a flat surface while tipped (intersection of plane and cylinder at an angle, IIRC). In reality, judging from my experience, the equation works quite well (allowing for flex and snow surface irregularities= not perfect) on hard flat surfaces up to about 60 degrees, then if the ski is stiff it progressively diverges from the equation.
Might be easier to calculate the actual skied radius if you know the speed and g force (from a=V^2/R). e.g. 4.5 g s at 40 mph yields 7.2 m radius skied at 77.5 tipping angle with a dialed up radius from the formula of 7.6 m.
One more thing I forgot to mention, The intersection of the circular cylinder defined by the ski sidecut and the plane defined by the snow surface is, of course, an ellipse. The turn radius is the "radius of curvature" -- the radius of the best matching circle. The cosine formula gives the radiuse of curvature at the furthest out point (the axis of the ellipse) which typically would be under your center of mass, or approximately the center of the ski. The value at other points on the ski will be very slightly different. One project I have so far resisted is figuring out the how the curvature varies along the ski, and how extreme an edge angle is needed before the effect becomes non-negligible.
Looking carefully, at the extreme condition of a ski base at 90 degrees to the snow surface, the natural turn arc radius due to ski "side cut" goes to ZERO.
For in that condition, the ski's widest points become the points of contact with the resisting surface. vis. a length of ski edge wire shaped as a "moustache" running over the snow surface "~"
The ski would run straight, give or take any difference in "angle of attack" between the shovel and the tail (ski camber)
The ski side cut could only influence the depth of snow surface contact or penetration.
All other attitudes are caught between the conditions of the extremes.
I'd think in actual usage if you got it to 90 degrees there would be loading on the ski and it would be flexed, creating rocker, or negative camber, with just the tip and tail in contact with the snow. That would still turn the ski on an arc I think.
http://www.epicski.com/a/the-complete-encyclopedia-of-skiing-epicski-skiing-glossary
It's the correct formula al lright, but it gives the curve that would ensue if you were able to press the ski firmly down to a flat surface while tipped (intersection of plane and cylinder at an angle, IIRC). In reality, judging from my experience, the equation works quite well (allowing for flex and snow surface irregularities= not perfect) on hard flat surfaces up to about 60 degrees, then if the ski is stiff it progressively diverges from the equation.
Might be easier to calculate the actual skied radius if you know the speed and g force (from a=V^2/R). e.g. 4.5 g s at 40 mph yields 7.2 m radius skied at 77.5 tipping angle with a dialed up radius from the formula of 7.6 m.
The line of reasoning consistent with g forces would be very useful to define the turn radius attributed to any combination of ski side cut and ski reverse camber due to loading. Instrumentation would not be complex, but not many are so invested.
ETA Using the "correct formula", how does the natural turn radius of skis such as the "Spatula" work out? I know they turn the same way as more traditionally side cut skis.
Certainly! Just not a turn arc attributed to or calculated from "Ski Side cut". ;-)
of us