Extreme Ski Jumping

Our physics expert explains how these skiers launch themselves off cliffs without getting a scratch—and why you shouldn't try

Skiing off of a 245 foot vertical cliff–looks like fun. It also looks like an insurance disaster in the making. And yet the skiers make it to the other side with nary a scratch. As you doubtless intuitively suspect, they end up ok because of the relatively "soft" snowy landing. As long as the acceleration involved in coming to a stop during impact is not beyond a certain threshold they can survive the fall. According to Newton's Second Law (F = ma) if you extend the time of impact you reduce the acceleration (a = Δv/Δt) and therefore the force acting on a crazy extreme sport adrenaline junkie. The snow increases both the time and distance over which the collision occurs giving these guys a reasonable chance of walking away alive and without serious internal injuries. So let's estimate how deep the snow needs to be for a safe landing.

As we see in the video the snow looks to be fresh powder, obviously much preferable to wet snow, or layers of icy crust. These guys weren't taking any (more) chances!

For comparison let's start with the even more extreme (and obviously suicidal) case of jumping off of a 245 foot (75 meter) high building onto a concrete sidewalk. Neglecting significant air resistance we can estimate the velocity just before impact:

v = (2aΔx)1/2 = 2(9.8m/s2)(75m)1/2 = 38 m/s or 86 miles/hr.

Since an impact with a hard object like a concrete sidewalk only last about 0.01 seconds, the impact acceleration will be about 3800 m/s2 or 380 g's. We shouldn't be surprised that this acceleration is about five or six times the threshold for a concussion and over twice that likely to cause death. We can also determine that the forces acting during impact would be more than sufficient to break a lot of bones.

Now these guys are probably willing to risk a mild concussion to achieve hero status in the sport of extreme ski jumping. So let's allow a maximum acceleration of 70 g's or 700 m/s2. Then the time of impact should be at least

Δt = Δv/a = (38 m/s)/(700m/s2) = 0.05 sec

This means the impact has to be spread out over a distance of,

Δx = v0t + ½ at2 = (38m/s)(0.05s) + ½(-700m/s2 )(0.05s)2 ≈ 1 meter

Since the snow is going to compact during the collision, and since we're allowing a rather high acceleration threshold, that gives us a minimum distance estimate. These guys appear to be more or less submerged after their respective jumps indicating deeper snow. Just to be clear, though, unless you are willing to risk severe injury and death I would not suggest extreme ski jumping as a weekend recreation.