Physics — Acceleration Down the Ski Hill

the father of modern Physics
Sir Isaac Newton
First off, let us understand one thing, when talking of the physics we are here we need to honor Sir Isaac Newton and not Albert Einstein. NO one skis so fast that we need to consider relativity when discussing the physics of skiing!

Physics — Rehashing Previous Material

It has been a long times now but I have been introducing a bit of physics into our conversations on skiing. In this installment I link to I calculate the gravitational force pushing me down the ski hill.

Just a refresher, I am claiming I weigh 100 Kg (actually I am less than that and actually it does not matter). and am on a slope that is 30° above horizontal, which is a 58% grade. This means there is a force of 490 newtons pushing me down the ski hill. Remember, this is the force parallel to the slope and that is what counts here.

Physics — Calculating The Speed of a Schushing Skier

Again, F=ma and that gives us 490/100 = 4.9 meters per second2 of acceleration. Let us further assume I am skiing down the hill and it takes me 30 seconds to get from top to the bottom. At the end of the 30 seconds I would be traveling 4.9*30 = 147 meters/second

However, what does that mean, after all most of us (US resident folks that is) think in imperial units.

So, to convert from meters per second we will do this:

  • METERS/HOUR * 1 KM/1000 METERS gives us KM/HOUR
  • KM/HOUR * 1 MILE/1.6 KM gives us MILES/HOUR

Now we will run the numbers:

  • 529,200 METERS/HOUR * 1 KM/1000 METERS = 529 KM/HOUR

  • 529 km/HOUR * 1MILE/1.6 KM) = 331 MPH

Physics — Questioning the Results

Seems fast, no? In fact, I have run through this calculation a number of times, but there is a good explanation. What are we leaving out? A few things:

  • Friction
  • There is friction between the snow and the surface of our skis.

  • Air Resistance
  • Again, this is a force that makes a huge difference especially as the speeds pick up. We know this is an important factor because racers work hard to minimize the air resistance.

  • While, a 30° slope does not seem so steep, in reality it is.
  • Most recreational skiers do not ski 30° slopes.

The big limiter is wind resistance as the faster we go the stronger the wind resistance force becomes and we all know that there is a limit to the speeds at which objects can achieve solely via gravitational forces, for a sky-diver that limit is around 122 mph and one can assume skiers are not radically different one way or the other.

Physics — Theory Must Match Reality

We may conclude the laws we are working with are incorrect, but they are not, we simply fail to include all the forces at play. In fact we can limit the condition and come to a conclusion the laws are correct and then revisit our assumptions and add in the additional forces. Those additional forces (especially the air resistance) complicate the mathematics and a second or third consideration may take on that math. In fact, I find it much like skiing in that we work to master the gentle slopes first and then when we master those we move to bigger ski challenges.

Good Stuff!

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