Is 'critical angle' even a thing?

[geepers]

One of the instructors on our CSIA L3 prep course back in Feb had this interesting way of challenging our thinking. After listening to replies on some question or assess some-one's skiing he'd ask: "Are you sure?" Generally time to think again.

So it's in that spirit I make this case.

In another thread there was much discussion on this thing called critical angle, defined as the contact angle between the ski base and the surface.0 degrees for a ski sitting flat on the surface and progressively larger angle as we start flashing the ski bases to the scenery. Supposedly there's a critical angle such that a ski carrying weight will slip prior to this critical angle being reached when tipping the skis, the exact angle depending on the surface.

Others drew attention to a different angle - platform angle. This is the angle between the ski base and the force vector of the skier's center of mass due to gravity and turning.

This reference https://www.real-world-physics-problems.com/physics-of-skiing.html (thank you @skier) indicates why the platform angle is key and the angle between the ski base and the snow is not at all critical - see the section Preventing Ski From Slipping On Snow.

As long as the angle ψ is greater than 90 degree then there will be a component of that force vector Fr that will be pressing the ski into the snow and there will be no force to make the ski slip. This will happen even from a ski flat on the snow as long as we angulate our CoM and stay over the ski.

Note for those familiar with the Ron Lemaster diagram of platform angle. The angle Ron uses is the other angle of the ski base force and force vector (180 degrees - ψ). So that angle must be kept less than 90 degrees. Same result.

 

[Dakine]

That's a very static picture of a dynamic problem.
There is such a thing as critical angle but that angle is constantly changing during the turning process as the platform builds under the ski as it carves into the snow.
The angle is a function of all that went before plus the type of snow.
I would guess that the critical angle is higher early in the turn before the ski has built a platform than later when the ski can ride the berm without blowing out.

 

[skier]

I created the confusion about the critical edge angle in the other thread. I hunted down some posts where I originally heard about it, and I think the term just wasn't used correctly which led to my confusion about it's significance in our other discussion. If there's one radius where a ski will carve "perfectly", then there's only one platform angle for perfect carving. So, it appears that the "critical platform angle" was being substituted for the perfect carving angle in those posts which is why they were saying you can't have perfect carving until you reach the "critical platform angle". But, I don't think that's a good use of that term, obviously because it confused me, and then I'm using that term that way and wasn't able to communicate with anyone else. So, I think the more common way of looking at the critical platform angle that was pointed out to me in the other thread is the best way.

That being said, I don't think there's anything magical about the critical platform angle. It's just a way of pointing out how you'll get the maximum lateral reaction force from the snow (friction?). So, it's not necessary to slip with larger angles, but the maximum reaction force drops off rapidly as the angle is increased such that you will slip in many circumstances. For example, if you stand on a slope with skis flat you've exceeded the critical platform angle as you pointed out, but you won't slip on every slope. On some gentle slopes if the snow is deep and heavy you can still stand without sliding. So, I think it's a thing, it just points out where the maximum lateral reaction force from the snow drops off very rapidly as a function of platform angle.

 

[geepers]

That's a very static picture of a dynamic problem.
There is such a thing as critical angle but that angle is constantly changing during the turning process as the platform builds under the ski as it carves into the snow.
The angle is a function of all that went before plus the type of snow.
I would guess that the critical angle is higher early in the turn before the ski has built a platform than later when the ski can ride the berm without blowing out.

[french accent]Are you sure?[/french accent]

 

[markojp]

Are you guys talking about 'platform angle'?

 

[geepers]

I created the confusion about the critical edge angle in the other thread. I hunted down some posts where I originally heard about it, and I think the term just wasn't used correctly which led to my confusion about it's significance in our other discussion. If there's one radius where a ski will carve "perfectly", then there's only one platform angle for perfect carving. So, it appears that the "critical platform angle" was being substituted for the perfect carving angle in those posts which is why they were saying you can't have perfect carving until you reach the "critical platform angle". But, I don't think that's a good use of that term, obviously because it confused me, and then I'm using that term that way and wasn't able to communicate with anyone else. So, I think the more common way of looking at the critical platform angle that was pointed out to me in the other thread is the best way.

That being said, I don't think there's anything magical about the critical platform angle. It's just a way of pointing out how you'll get the maximum lateral reaction force from the snow (friction?). So, it's not necessary to slip with larger angles, but the maximum reaction force drops off rapidly as the angle is increased such that you will slip in many circumstances. For example, if you stand on a slope with skis flat you've exceeded the critical platform angle as you pointed out, but you won't slip on every slope. On some gentle slopes if the snow is deep and heavy you can still stand without sliding. So, I think it's a thing, it just points out where the maximum lateral reaction force from the snow drops off very rapidly as a function of platform angle.

Well, not magical, just physics. As long as there's no force to propel the ski 'up' the groove then we're in grip city. (Of course a ski has only so much torsional rigidity so not all the ski may be at the same platform angle.)

Interesting to consider the ways to stay away from a slipping platform angle.

 

[geepers]

Are you guys talking about 'platform angle'?

Well, the possible clue is in the words "platform angle" in my OP.

I did put a note in there for those familiar with Ron Lemaster's diagram if you are wondering why one's >90 and Ron's version is <90 degrees.

 

[Fuller]

If I were to buckle down and read everything I could concerning the physics of skiing, to the point of really understanding it, would it make me a better skier? Or should I spend my energy in some other fashion?

 

[skier]

If I were to buckle down and read everything I could concerning the physics of skiing, to the point of really understanding it, would it make me a better skier? Or should I spend my energy in some other fashion?

Honestly, I think it depends on the person. I don't think you'll go out the next day and be better, but it can help create a lesson plan to practice the right stuff to get better. If you have a coach, then just do what they say, but if you are self learning .... Also, it's extremely helpful with picking the right equipment, after all, lots of physics has gone into the tech.

 

[Chris V.]

If I were to buckle down and read everything I could concerning the physics of skiing, to the point of really understanding it, would it make me a better skier? Or should I spend my energy in some other fashion?

I think just reading a lot on this site is a great start. It's helped me. Honestly, a lot of instructors don't understand this stuff. Clearly knowing the why will assist focus.

 

[skier]

I've got another thought about the critical platform angle. It seems it makes lots of sense standing on a slope sideways. However, in a turn if you reverse angulate with your hips, so that you exceed the platform angle, won't you fall over? Let's just say for kicks and giggles that even though the critical platform angle is exceeded you still don't slip. Well then your edge angles are less, so the turn gets wider, and CF gets less, but yet with the opposite angulation your mass is more inside, so I think you fall over. If that's true, then there might not be any information of any use given by the critical platform angle. By the time you balance with CF and gravity in a turn, you might always meet the critical platform requirement, so there's no use worrying about it at all. ??

 

[markojp]

Well, the possible clue is in the words "platform angle" in my OP.

I did put a note in there for those familiar with Ron Lemaster's diagram if you are wondering why one's >90 and Ron's version is <90 degrees.

Yeah... having trouble focusing... While it isn't magic, it is simple physics. Platform angle per R. LeM is important if you (third person) want to ski effectively on harder snow.

 

[Doug Briggs]

Isn't the critical angle simply the platform angle that is required to keep the ski carving vs skidding?

 

[Rod9301]

I think the relevance of the critical angle is that angulation, and getting your shoulders over the ski keeps you from skidding, while simply increasing the edge angle will not.

 

[geepers]

If I were to buckle down and read everything I could concerning the physics of skiing, to the point of really understanding it, would it make me a better skier? Or should I spend my energy in some other fashion?

Depends what your objectives are and what issues are getting in the way. Understanding more of the physics of skiing may at worst be harmless and then again it may provide some insight.

I've got another thought about the critical platform angle. It seems it makes lots of sense standing on a slope sideways. However, in a turn if you reverse angulate with your hips, so that you exceed the platform angle, won't you fall over? Let's just say for kicks and giggles that even though the critical platform angle is exceeded you still don't slip. Well then your edge angles are less, so the turn gets wider, and CF gets less, but yet with the opposite angulation your mass is more inside, so I think you fall over. If that's true, then there might not be any information of any use given by the critical platform angle. By the time you balance with CF and gravity in a turn, you might always meet the critical platform requirement, so there's no use worrying about it at all. ??

If that was the case then we wouldn't see a huge number of skiers slip, sliding their way down the hill. Most of them have no trouble balancing a push bike around corners. Nor would we hear self-critique from even the world class skiers who say "And I move to the inside too quickly."

The challenge is we have two legs and are able to spread our weight between two skis so we don't always optimize our balance laterally.

And then there's this which affects the angle our ski bases makes with our legs. We can gain (or lose) angles by the way we torque our feet.