Some useful descriptions of the learning process:
[Fitts & Posner 1967]
| Awareness (Cognitive) | 1 | Early | I think I understand, but … |
| 2 | Late | Aha! I get it | |
| Practice (Associative) | 3 | Early | I can’t feel it – is this OK? |
| 4 | Late | It works if I think about it | |
| Acquired (Autonomous) | 5 | Early | I don’t have to think about it |
| 6 | Late | I can trust it when the going gets tough |
[Whitmore 1984]
| 1 | Unconscious incompetence |
| 2 | Conscious incompetence |
| 3 | Conscious competence |
| 4 | Unconscious competence |
If we consider a skier of mass m sliding straight down a uniform slope of angle θ degrees, then the magnitude of the total force on the skier (measured down the slope) is:
F = Fg – Ff – Fd
where
Fg = mg sinθ is the force from gravity
Ff = μmg cosθ is the frictional force from the snow for some constant μ
Fd = ½ρv2CA is the drag from air resistance
Now for 2 different skiers sliding at the same speed, v is constant and ρ is the density of the air, so is a constant. We further assume that both skiers have the same shape (not size) and are wearing similar clothes, so we can assume C, the drag coefficient, is approximately constant, and hence
Fd = kA
for some constant k, where A is the area of the skier’s body presented to the air in the direction of travel (the cross-section).
Then
ma = mg sinθ – μmg cosθ – kA
so
a = g sinθ -μg cosθ -kA/m
Hence the acceleration of the skier down the slope depends on the ratio A/m. If we assume that the skiers’ bodies have the same constant density ρ, then the acceleration is dependent on A/ρV, where V is the skier’s volume. For a linear increase L in dimension, A goes as the square of L, and V goes as the cube, so in fact, with the assumptions stated, the “bigger” skier will accelerate more, hence go faster, because the retarding force due to drag will be less.
So there you have it – bigger skiers go faster – maybe!
This is a fairly common question from intermediate to advanced skiers who have graduated on to skiing steeper, icier slopes at higher speeds.
The physical cause is too much pressure on a ski which is moving sideways, making it alternately grip then release in an oscillatory fashion, especially towards the end of the turn, when the pressure increases due to combined centrifugal force and gravity. The effect depends on the ski’s stiffness and damping, but it can be quite spectacular!
From a technique point of view the problem is caused by over-rotation resulting in the ski moving sideways, plus too high an edge angle for the applied pressure. The solution is to make rounder turns, especially in the all-important control phase (initiation through to fall line), so that the ski is moving forward rather than sideways, and to use the turn shape, rather than skidding, to control speed. It also helps to flex and relax the legs towards the end of the turn to absorb some of the pressure. If you need to skid the turn a bit more, try less edge angle so that the ski doesn’t try to grip as aggressively.
What radius turns can I carve on a ski with a given sidecut?
Let S be the sidecut radius of the ski. Then, assuming that the ski is bent fully into reverse camber, the turn radius R is, to a reasonable approximation:
R ≈ S cos θ
where θ is the edge angle between the base of the ski and the snow. [The gory details of this calculation will appear <here> at some point.]
Here are some calculated values for a 17m sidecut ski:
| θ (degrees) | turn radius (metres) |
|---|---|
| 1 | 17 |
| 10 | 16.7 |
| 20 | 16 |
| 30 | 14.7 |
| 40 | 13 |
| 50 | 10.9 |
| 60 | 8.5 |
| 70 | 5.8 |
If you are making turns with a radius less than the table suggests, then you must be:
Ask a beginner (especially a child) how they think they might turn on skis and they will usually crank both knees to one side, imitating what they see on TV. Ask them how they might turn in a snowplough and they will crank one knee inwards. Ask them if they can think of any other ways to turn in a plough and they might say “press on one ski more than the other”, or, if prompted, “turn the skis”. It’s always seemed to me that, of the three mechanical ways to cause a ski to turn (edge, pressure, rotation), rotation is the least intuitive to the early stage learner. And yet it is the method of choice for introducing plough turning in most ski teaching systems.
Watch a skilled instructor demonstrating rotation and you will likely find it difficult to see what movements they are actually making, involving as it does a subtle rotation of the femur head in the hip socket on both legs. Perhaps this is partly the reason why the Snowsport England system recommends rotating the outside ski more than the inside ski. The rotation of both skis in a plough at the same time is also difficult to achieve at low speeds on a dry slope due to the amount of friction, which is another reason to push the outside ski round more. The disadvantage of this is that it widens the plough and reduces glide.
A further problem with teaching rotation first is that it can lead to skiers who prefer it over the other techniques of pressure and edging, and end up as “twist and skid” intermediates.
Lately I’ve been experimenting with teaching pressure as the first plough turning technique. The advantage is that it is intuitive, uses simple, obvious movements, and promotes a nice turn shape, particularly in the crucial control phase (CSIA phase 2) of the turn, from initiation through to fall line. Turn shape is something I explore in other articles, and it is proving to be one of the most important focuses in my teaching. Get a good turn shape and everything else follows more easily.
As long as you ensure that the skier doesn’t make a hip movement out over the ski to press on it (thus losing edge angle), pressure is a very effective way to introduce turning and avoid storing up problems for later.
All teaching systems incorporate a model for assessing the performance of a skier who is carrying out a task. In BASI, there is the TIED model. CSIA has skier assessment and development. Most systems do not give too much detail about the actual fault analysis process. Below is a method I learned during a CSIA level 2 course (my thanks to Steve Young, CSIA examiner, for sharing this).