What's essential for carving on hard snow?

[markojp]

I don't know about you, but I feel like if I am "carving" that straight line traverse it is only because I am subtly steering the tips down the hill the whole time to keep the line straight. If I just stood there and let the ski do it's thing it would curve.

If I tipped it up more, it would arc.

 

[mdf]

One complication that may invalidate the turning radius "theorem" is that different parts of the ski dig deeper into the snow. The theorem is based on the intersection of a cylinder (perpendicular to the ski, representing the possible 3-d locations of points along a circular sidecut when the ski bends) with a flat plane (representing the snow surface). I'm sure the mathematics is correct. I'm not sure the assumptions represent a real ski exactly enough to explain the situation for very small and very large deflections.

 

[François Pugh]

Soft snow has a lot of give to it.
It's not that you can't carve ice; it's that you can't carve and ice proves it.
Edit:
OP said hard snow. Maybe that means something different in different regions.

 

[karlo]

Has it been mentioned? Be highly attuned to where the fall line is and will be

 

[CalG]

Has it been mentioned? Be highly attuned to where the fall line is and will be

The fall line relates to gravitational forces.

Gravity is a 'weak force' on the spectrum. Inertial forces dominate the physical world.
Gravity is a LAW however, and we humans are puny and weak ourselves ;-)

 

[markojp]

Soft snow has a lot of give to it.
It's not that you can't carve ice; it's that you can't carve and ice proves it.
Edit:
OP said hard snow. Maybe that means something different in different regions.

FWIW, I've encountered hard snow in every region in the world I've lived. The notion that it only exists in the eastern US and Canada is silly.

 

[Superbman]

FWIW, I've encountered hard snow in every region in the world I've lived. The notion that it only exists in the eastern US and Canada is silly.

True words. Hardest snow I've ever skied is in High Alpine resorts that have had two weeks of adverse weather.... My knees and feet still hurt from one long run at Snowbird a few years ago. I actually think East coast hard snow skis better that big mountain uber firm. YMMV.

 

[Mark-172]

Great list of items. I could add that the "4-edge" method is better than the "2-edge" method. I couldn't begin to explain, but there is an excellent guide available at www.thesportloft.com (see attached). Click on "high performance skiing" link. BTW, I highly recommend them for ski boot fitting when in SLC, Utah...

 

[Chris V.]

Hard snow technique unnecessary. There is no hard snow at Squaw Valley. Bwahahahahaha!

 

[Seldomski]

I've skimmed most of this -- apologies if this has been already mentioned...

Some of the disagreement in this thread (earlier) seems to hinge on rotary input and/or steering of the skis in carving. When the skis are flat, you are not actually carving anymore. The ski is not on edge. At this moment, there is nothing to keep the ski traveling the same direction other than the inertia of the ski/boot and possibly some snow that is pushed up around the ski (hero snow). There is a finite period of time you are in this 'in between' or transition state where carving is not possible (ski is flat on surface). You must actively point/assist the skis so they continue to travel the appropriate direction as your body crosses over the skis (or the skis cross under you). You must actively rotate your legs so that the ski continues in the correct path to set up the next edge engagement.

Carving skis are designed to make transition easier in a few ways, including (not limited to):
1) Mass/rotational inertia. By being heavy/and or having high rotation inertial vs. steering, they will tend to keep traveling the same direction and resist rotations at transition.
2) Width. By being narrow, the time the ski is flat is reduced. Edge to edge is quicker. There is less time for the ski to rotate to an unfavorable position during transition. Favorable is being exactly the same path it was on when the prior edge was released.

For me, the trickiest part of carving is this transition period, especially on hardpack. On hardpack, the ski will rotate more easily at transition since there is likely to be no snow around your ski to help keep the ski tracking straight. You need to align the edge precisely with the ski direction to get it to bite early in the turn. Misalignment is not tolerated by the snow and will result in a skid.

Rotary input at transition is crucial in getting a carved entry to the next turn. The rotary input is not to twist the ski on the snow while it is flat. It is to keep the ski traveling straight while it is flat. The rotary is necessary because the skier's body is moving relative to the skis at transition. So if the skier does nothing, they will drag the skis away from the ideal line.

Exactly which joints are rotating to achieve this is beyond my abilities to describe.

So to get back to @LiquidFeet 's original post, I think this transition is the trickiest bit to do on hardpack. (turn entry from the prior turn finish) And good sense of ski rotation is crucial.

 

[Marker]

As a technically-trained intermediate skier, this inclines me to make observations that I may not have the skiing background to fully understand. I noticed in the photos above of railroad tracks that the distance between the different set of tracks at the transition for a given ski was noticeable (nearly pure arc-to-arc tipping?). However, I'd swear I saw nearly coincident tracks for each ski at transition when watching an excellent skier from the lift at Killington (this was over Christmas, so recent). I don't see how this is possible without subtle rotation. Thoughts? Be kind, I take lessons, not give them...

 

[James]

Anything useful in here?:

http://sport1.uibk.ac.at/mm/publ/18...of_the_Ski_Snow_Contact_for_a_Carved_Turn.pdf

 

[Dakine]

That reference is new to me but builds on some that I have.
Data speaks louder than words.....

 

[skier]

I think I can link all the concepts together now to make sense of things I've seen in posts, experiences, and physics. The critical platform angle does make a difference in being able to carve the top of the turn. Here's why.

When you have centrifugal force balancing with gravity while going around a circle, the maximum lean that you can have is a straight body 90 degrees to the surface of the ski. If you lean more than that you'll exceed the critical platform angle and there will be a component of the centrifugal force that pushes the ski up and out the groove. When the body is balanced with a 90 degree angle to the base of the ski, the centrifugal force counteracts gravity to keep from falling. For a given edge angle and turning radius, this dictates the speed, if you go faster, the CF increases, and it would topple the body out the circle unless we increase the lean. But, for a fixed edge angle if you increase the lean, you'll exceed the critical platform angle and you will slip. So, by equating the CF with gravity we can calculate the maximum speed for a particular edge angle.

CF=m*v^2/r*cos(theta)

Fg=mg*sin(theta)

where theta is the edge angle

set CF equal to Fg:

mv^2/r*cos(theta)=mg*sin(theta)

v=sqrt(g*r*tan(theta))

With an edge angle of 70 degrees and a turning radius of 16 meters, the maximum velocity is 20.76 m/s or 46 mph. This is pretty fast and probably something else would go wrong first, but now let's consider a low edge angle. Let's say we're at 5 degrees with a turning radius of 16 meters. Now the maximum speed is 3.7 m/s or 8.3 mph. It's impossible to carve any faster than that. The logical response is that we don't make sharp 16 m turns at 5 degrees. But, the answer is that you're supposed to. The turning radius of a ski is Rsc*cos(theta). For very small theta the turning radius is essentially Rsc which ranges from something like 10-35 meters. In order to carve, the ski must follow that arc given by the sidecut radius. Even if that arc is an ellipse, and we say it's just an approximation, it should still follow that approximate arc to approximately carve. So, worst case scenario, let's say we want to carve a 35 meter circle at 5 degrees. The maximum velocity is 5.5 m/s or 12 mph.

So, you see that even at modest speeds it's impossible to carve even the approximate circle given by the sidecut of the ski, and the only way for the equations to work is to dramatically increase the turning radius. This is done by the ski skidding. That's what we do when we arc to arc carve just by tipping and gradually increasing the edge angle. Not only that, but the faster you go the larger this skidding region will be at the top of the turn. At fast speeds you might not hit edge lock until very large edge angles.

 

[geepers]

As a technically-trained intermediate skier, this inclines me to make observations that I may not have the skiing background to fully understand. I noticed in the photos above of railroad tracks that the distance between the different set of tracks at the transition for a given ski was noticeable (nearly pure arc-to-arc tipping?). However, I'd swear I saw nearly coincident tracks for each ski at transition when watching an excellent skier from the lift at Killington (this was over Christmas, so recent). I don't see how this is possible without subtle rotation. Thoughts? Be kind, I take lessons, not give them...

Guessing.... the snow was soft enough to make a continuous track if it could be seen from the chair.

 

[geepers]

I think I can link all the concepts together now to make sense of things I've seen in posts, experiences, and physics. The critical platform angle does make a difference in being able to carve the top of the turn. Here's why.

When you have centrifugal force balancing with gravity while going around a circle, the maximum lean that you can have is a straight body 90 degrees to the surface of the ski. If you lean more than that you'll exceed the critical platform angle and there will be a component of the centrifugal force that pushes the ski up and out the groove. When the body is balanced with a 90 degree angle to the base of the ski, the centrifugal force counteracts gravity to keep from falling. For a given edge angle and turning radius, this dictates the speed, if you go faster, the CF increases, and it would topple the body out the circle unless we increase the lean. But, for a fixed edge angle if you increase the lean, you'll exceed the critical platform angle and you will slip. So, by equating the CF with gravity we can calculate the maximum speed for a particular edge angle.

CF=m*v^2/r*cos(theta)

Fg=mg*sin(theta)

where theta is the edge angle

set CF equal to Fg:

mv^2/r*cos(theta)=mg*sin(theta)

v=sqrt(g*r*tan(theta))

With an edge angle of 70 degrees and a turning radius of 16 meters, the maximum velocity is 20.76 m/s or 46 mph. This is pretty fast and probably something else would go wrong first, but now let's consider a low edge angle. Let's say we're at 5 degrees with a turning radius of 16 meters. Now the maximum speed is 3.7 m/s or 8.3 mph. It's impossible to carve any faster than that. The logical response is that we don't make sharp 16 m turns at 5 degrees. But, the answer is that you're supposed to. The turning radius of a ski is Rsc*cos(theta). For very small theta the turning radius is essentially Rsc which ranges from something like 10-35 meters. In order to carve, the ski must follow that arc given by the sidecut radius. Even if that arc is an ellipse, and we say it's just an approximation, it should still follow that approximate arc to approximately carve. So, worst case scenario, let's say we want to carve a 35 meter circle at 5 degrees. The maximum velocity is 5.5 m/s or 12 mph.

So, you see that even at modest speeds it's impossible to carve even the approximate circle given by the sidecut of the ski, and the only way for the equations to work is to dramatically increase the turning radius. This is done by the ski skidding. That's what we do when we arc to arc carve just by tipping and gradually increasing the edge angle. Not only that, but the faster you go the larger this skidding region will be at the top of the turn. At fast speeds you might not hit edge lock until very large edge angles.

There's something not right about that analysis.

Let's take really small values of theta (approaching zero) such that Fg approaches zero. Then cos(theta) would approach 1 and now speed has to approach zero unless radius approaches infinity.

Don't know about anyone else but that is contrary to my experience in making rail road track turns.

There's probably a few things to add to the model:
1. Skis do not have infinite torsional rigidity
2. Snow (or ice) has to be deformed to create a platform to turn the skier. That groove in the surface has to have some width so not all the edge of the ski has to reside on a perfectly flat plain.
3. The pitch of snow won't be perfectly flat
4. Tip behaviour https://www.sciencedirect.com/science/article/pii/S1877705810003395
5. Our weight is distributed over 2 skis. Even in high performance turns (unless the inside ski is in the air) we have some component of our mass inside the turn that allows angulation over and above that of a point mass rigidly attached at 90 degrees to the ski.
6. The ankle also controls platform angle.

There's probably a lot more...

I have a feeling that if the whole answer was a couple of trig equations and some linear algebra the industry may have solved it by now.

 

[Josh Matta]

I wanted to do that drill, looks so fun.

 

[skier]

There's something not right about that analysis.

Let's take really small values of theta (approaching zero) such that Fg approaches zero. Then cos(theta) would approach 1 and now speed has to approach zero unless radius approaches infinity.

Nothing wrong with the analysis. Ok, let's take really small values of theta. The maximum carving velocity goes to zero. Is that a problem? Emphatically, no. What that means is with a flat ski, it's impossible to carve at any speed, and I wholeheartedly agree that matches all of our experiences. When the ski is flat, there is no carving. It's only skidding along the length of the ski. So, we go from skidding to carving through a finite transition region.

 

[Marker]

Guessing.... the snow was soft enough to make a continuous track if it could be seen from the chair.

Well, from Australia you would need soft snow to see it, but anyone familiar with the North Ridge Triple at Killington over the last few weeks would know that it is easy to see railroad tracks in eastern hardpack.

 

[geepers]

Nothing wrong with the analysis. Ok, let's take really small values of theta. The maximum carving velocity goes to zero. Is that a problem? Emphatically, no. What that means is with a flat ski, it's impossible to carve at any speed, and I wholeheartedly agree that matches all of our experiences. When the ski is flat, there is no carving. It's only skidding along the length of the ski. So, we go from skidding to carving through a finite transition region.

Your analysis has nothing to do with the side cut of the ski - the object going around the turn could have any side cut (including a straight edge) and your calc would pop out the same number. Here's an example where the same calc is used to determine the speed a vehicle can go around a banked track without relying on tyre friction.

The zero angle should give it away. Replace ski with ice skate. Are you saying an upright ice skate can't carve a straight line regardless of speed?


You've imposed three limitations that aren't real:
1. Platform angle of 90 degree. We're not stuck at 90 degrees to the ski base. We can counter balance so that (using Ron Lemaster's definition) the platform angle is less than 90 degrees. That means the groove in the snow (the banked track our ski is going around) is steeper than the inclination angle of our CoM so there's some Fg keeping the ski in the track.
2. We have 2 skis and we can actively distribute weight between them so we can control our balance when Fg does not equal CF.
3. Every single part of a ski has to fit a precise geometric shape to the manometer for the ski to carve. We are not skiing on uniformly smooth pitches of infinite hardness. (It only feels like it at times...)

Long and short is we can and do make a variety of radius turns on fixed side cut skis without skidding.