by SkiNerd 

April 22, 2022

loading deflection and angular acceleration In skiing

Loading & Deflection 

Loading of a ski could simply refer to the snow pushing against it. Maximum forces typically build towards the bottom of an arc when the ski grips and steers out of the fall line.

A deflection, in physics, refers to the change in a object’s velocity when it collides with a surface (or force). A turn in skiing is more like a million tiny deflections otherwise known as centripetal force.

Centripetal Force

Centripetal force pushes the skier on a circular path. When the centripetal force is released the skier will travel at the same velocity along the tangent to that circle from the point of release.

Loading the Ski

Snow pushing skier in a arc

Release the ski and Float

Skier released from arc travels along a tangent

Load Up & Release

For the most part, gravity is responsible for creating a skiers momentum as they point their skis down the hill. The skier can only travel perpendicular to the fall line for a short period before friction from the snow and air resistance slows them down. 

With this in mind, expert skiers will often do the everything in their power to keep this momentum (or possibly even increase it) as they redirect their mass across the slope.

This tactic of preserving momentum across the slope comes in handy in a race course where the skier can save precious milliseconds getting over to the next gate.

Have you ever felt that sensation of getting catapulted out of a turn? Some folks refer to this effect as rebound

I equate it to a skateboarder in a halfpipe, a cyclist on a pump track… or a child pumping on a swing.

To be clear, it’s difficult, if not impossible, to do this with the same sort of efficiency in a ski turn. The effect is very short lived, and still requires the potential energy from gravity so you won’t be able to wiggle your way indefinitely across the flats. 

But I do think we can use the concept to help send our mass a little further across the slope. In skiing, you just have to carve out your own halfpipe with your skis in the snow.

Skateboard Pump - Centripetal Acceleration- Conservation of Angular Momentum

A skateboarder pumps through the arc of this bowl by extending at just the right time. This brings his C.O.M. closer to the axis of rotation and he accelerates out of the curve.

How does it work?

The law of conservation of angular momentum says that in the absence of any applied torque, (L) angular momentum remains constant. So if you can decrease the objects (I) moment of inertia, then (w) angular velocity has to increase to compensate.

Conservation of Angular Momentum Equation

The angular momentum of an object, L, is defined as the product of the object’s moment of inertia, I, and it’s angular velocity, ω:

Think about ‘moment of inertia’ as a measure of how difficult it is to get something to rotate. 

It takes a considerably larger effort to swing a golf club with a 10 foot long handle than it does to swing a golf club with a 10 inch long handle, because the (r) radius of rotation of the club head is much larger.

Essentially you can reduce an objects moment of inertia by reducing its radius of rotation.

As a simple ski instructor, these kinds of equations melt my brain, so let’s look at some more visual examples.

Consider my daughter and I on this merry go round. While hanging off the end, we’re traveling around the arc at a constant velocity. As we move in towards the middle (closer to the axis of rotation) the whole merry go round spins faster. 

Merry Go Round - Conservation of Angular Momentum
figure skater - angular momentum

As this figure skater pulls her arms in towards herself (the axis of rotation) she spins faster.

Let’s Apply These Principals To Skiing

Provided the skier can minimize any slowing effects from the snow, when they move their mass inside the arc, they are effectively moving their mass closer to the axis of rotation. A skier does this through inclination and/or angulation rather than the vertical move of the skateboarder.

Conveniently this move inside also rolls the skis further on edge, which bends them so the arc tightens. Now we have more centripetal force pushing on our skis and this allows us to move inside even further, and so on, and so on. Resisting this additional force adds energy back into the system, and poof… we’re ejected out of the turn.

Reducing radius of rotation

But There’s A Problem

This sounds great in theory, but sadly there are plenty of forces trying to negate this effect in a ski turn, and most of the time they succeed.

A skateboard ramp has a pretty tight curve and very little friction. Tightening the arc on skis often requires more twisting or pivoting of the skis to create a larger steering angle, which slows us down.

Plus, you can only add as much additional force as your muscles are strong enough to resist.

But if we can minimize slowing forces, while tightening the arc and/or moving our mass further inside the arc, it’s plausible our skis could accelerate (or at least reduce the amount we decelerate) out of a turn, just like a skateboarder boosts out of a halfpipe.

Skiing Symptoms - Windshield Wiper Turns
Skiing Symptom - Skidding
Skiing Symptoms - Chatter

So Let‘s Set Ourselves A Challenge! 

Next time you’re on the slopes, see if you can:

  •  Widen the corridor without increasing vertical distance down the hill
  •  Preserve as much momentum as possible from one arc to the next 
Turn Shape - Corridor
Turn Shape - Vertical Distance

Find The Blend To Maximize Performance

The key to maximize this effect is exquisite timing of lateral (and perhaps fore/aft, vertical & rotational) moves, and having enough strength to resist the additional forces.

My biggest piece of advice is to load the working ski progressively. Anything that happens with too much or too little intensity will surely have a negative effect. Timing the maximum load strategically, and tightening arc at the bottom of a turn just prior to the release, should harness this extra energy to fling us further across the run.

Things that should increase the halfpipe effect:

  • Going Faster - More speed means there’s more force to work with.
  • Tighten the radius using ski design - To tighten the arc we need to create a larger steering angle. We can do this by twisting the ski, however this usually corresponds with more slowing forces. Alternatively, we can roll the ski further on edge and use the skis’ design properties to create a steering angle that tightens the arc with fewer slowing forces.
  • Move your COM further inside - In skiing we do this through inclination. The inside leg bends and/or the outside leg to extends allowing gravity to pull the mass down and inside the arc. Conveniently this also tightens the arc, and when the arc tightens you can move the mass further inside:) As you continue tipping into the he turn, you’ll likely need to supplement with angulation to keep pressure on the working ski.
  • Tip to tail through the arc - Pressure shifted slightly towards the forebody of the working ski will create more torque (or turning force) on the skier as the snow pushes the tips into the arc. This can be useful when there isn‘t much pressure on the ski at the top of the arc. Once the ski is weighted, pressure through the middle of the side cut will allow the whole length of the edge to penetrate the snow. And finally, pressure slightly towards the tail can put a stop to this tip torque, helping the skis exit the direction change and accelerate out of the turn. Overdoing this will cause problems, but when done just right, it can simulate that halfpipe as the curve transitions to the straightaway.

Things that will decrease the halfpipe effect:

  • Going Slow - Gravity still works when you’re going slow, but the turning forces that allow you to move laterally are kinda lame.
  • Lengthening the Arc - Elongating the turn may allow the skis to accelerate more down the hill (by way of gravity), but will reduce angular acceleration. A turn shape that elongates towards the bottom (like a comma) won’t produce much of the halfpipe effect.
  • Drifting & Oversteering - Twisting the skis too quickly or too much tends to slow them.
  • Poor Pressure - If you drop the mass inside too quickly you’ll lose pressure on the outside ski just when you want to increase it (and your halfpipe will be gone). On the other hand, too much pressure too quickly and you may not have the strength to resist it, the skis will chatter, or the pressure may fling you in undesired directions.

Some Additional Resources

Science Friction - Ski Technique Diagnostics

Outsmart your ski instructor and troubleshoot your own ski technique

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I like skiing, outdoorsy stuff, artsy stuff... and hanging with my family;)

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Science Friction - Ski Technique Diagnostics

Outsmart your ski instructor and troubleshoot your own ski technique

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