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geepers

Skiing the powder
Skier
Joined
May 12, 2018
Posts
4,256
Location
Wanaka, New Zealand
I think this is basically what you guys are looking for, from here.

View attachment 154058

Note that this is a calculated radius. The intent of the paper was to compare a finite element analysis that took into account the groove made by the ski with the radii calculated by Howes law which didn't consider the groove. Howes law breaks down at higher edge angles as the calc-ed radius tends to zero - cos(90Deg)=0.

Unfortunately can't see any definition of hard/medium/soft snow. It links to ref #4 and that's not a downloadable paper without joining up to something or other.

The discussion in the paper is interesting.

Discussion
Dependence of the turn radius on edging angle, load on the binding, and snow properties
The edging angle had – as expected – the most substantial effect on the turn radius.
....
Different speed or different weight of an athlete causes an increase of the forces acting on the binding. For the ski-binding model implemented in our simulation we found a linear decrease of the turn radius with increasing force in the range between 1000 N and 2000 N. A heavier skier or a faster skier is thus able to carve a slightly tighter turn. However, for the ski studied here an increase in force by 100% caused a decrease in the turn radius by only between 1 and 1.5 m which corresponds to a relative change between 8% and 17%.



100% is a lot of Oreos!

Varying snow strength has a more complex impact on the turn radius. For edging angles below 40° softer snow lets the ski penetrate deeper into the snow causing the ski to bend more and therefore causes a smaller turn radius. At edging angles above 40° the groove that forms in the snow starts to substantially affect the turn radius preventing small turn radii. This effect is more pronounced for soft snow when a deep groove is created by the ski. For medium and hard snow types, when the ski’s penetration depth is smaller, the impact of this effect on the turn radius is also smaller.


One thing to think about in soft snow. An aim in carving is deflection across the hill. The more the centripetal force acts in the horizontal plane (from higher edge angle) the better. Bending the ski in the vertical plane, whilst useful for getting the ski out of the snow, isn't that useful for deflection across the hill.
 

whumber

Putting on skis
Skier
Joined
Apr 27, 2017
Posts
72
Location
Killington, VT
Note that this is a calculated radius. The intent of the paper was to compare a finite element analysis that took into account the groove made by the ski with the radii calculated by Howes law which didn't consider the groove. Howes law breaks down at higher edge angles as the calc-ed radius tends to zero - cos(90Deg)=0.
You're correct that it's calculated, but they did also compare the calculations with actual measurements both in the lab as well as on snow measurements.

Unfortunately can't see any definition of hard/medium/soft snow. It links to ref #4 and that's not a downloadable paper without joining up to something or other.

This is what you're looking for regarding the definition for hard/medium/soft.

1641441169421.png

The discussion in the paper is interesting.

Discussion
Dependence of the turn radius on edging angle, load on the binding, and snow properties
The edging angle had – as expected – the most substantial effect on the turn radius.
....
Different speed or different weight of an athlete causes an increase of the forces acting on the binding. For the ski-binding model implemented in our simulation we found a linear decrease of the turn radius with increasing force in the range between 1000 N and 2000 N. A heavier skier or a faster skier is thus able to carve a slightly tighter turn. However, for the ski studied here an increase in force by 100% caused a decrease in the turn radius by only between 1 and 1.5 m which corresponds to a relative change between 8% and 17%.



100% is a lot of Oreos!

Varying snow strength has a more complex impact on the turn radius. For edging angles below 40° softer snow lets the ski penetrate deeper into the snow causing the ski to bend more and therefore causes a smaller turn radius. At edging angles above 40° the groove that forms in the snow starts to substantially affect the turn radius preventing small turn radii. This effect is more pronounced for soft snow when a deep groove is created by the ski. For medium and hard snow types, when the ski’s penetration depth is smaller, the impact of this effect on the turn radius is also smaller.


One thing to think about in soft snow. An aim in carving is deflection across the hill. The more the centripetal force acts in the horizontal plane (from higher edge angle) the better. Bending the ski in the vertical plane, whilst useful for getting the ski out of the snow, isn't that useful for deflection across the hill.
That's true, but they're talking about turn radius which is the projection of the ski arc onto the snow surface rather than the ski arc itself; so the horizontal plane component you're referring to is already accounted for by the projection. Assuming I'm not misinterpreting what you've written.
 

Chris V.

Making fresh tracks
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Joined
Mar 25, 2016
Posts
1,366
Location
Truckee
Different speed or different weight of an athlete causes an increase of the forces acting on the binding. For the ski-binding model implemented in our simulation we found a linear decrease of the turn radius with increasing force in the range between 1000 N and 2000 N. A heavier skier or a faster skier is thus able to carve a slightly tighter turn.
Maybe that's good advice what they tell young kids--put rocks in your pockets!
 

Jamt

Out on the slopes
Skier
Joined
Apr 25, 2017
Posts
334
Location
Jämtland, Sweden
The problem with these theories is that it assumes and "edge locked ski". 99% of people trying to carve just go pretty fast with relatively low edge angles and a static position. They will have a turn radius that is MUCH larger than the theoretical one. These people have a larger radius when the go faster, not tighter as it should be.

The original question in this thread ties in to this a bit. Most people are probably better off playing around and searching for the fun feeling with large forces you get in a high dynamic turn rather than focusing on e.g. edge angle. High edge angle is a natural outcome of good dynamic skiing, but high edge angles do not necessarily lead to good dynamic skiing.
 

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