# Ski jump: how much does aerodynamics matter?

Watching the Olympic ski jump event, I started to wonder: how much does aerodynamics matter for these guys? If I took a skier’s speed and trajectory just after leaving the ramp and calculated a parabola based on 1 g of downward acceleration due to gravity, where would that parabola intersect the hillside relative to their typical landing zone?

Aerodynamics matter a lot. The introduction of the V-style significantly increased lenghts, wikipedia says 10% (V-style).

But it’s an interesting question whether ski jumpers go further because of the air, compared with the same jump in a vacuum. I suspect they do, but that’s just a WAG.

Speaking of Ski Jump…does anyone else find it a little eerie when they are in parachute? It just looks like they are hovering there…

I speculate they’d go farther in a vacuum.

Granted, they get a lot of lift by assuming an airfoil shape, so they fly higher and therefore farther than they would otherwise. But I’d bet dollars to donuts that the overall effect of resistance outweighs the additional distance due to lift.

If we had sufficient data, it would be fairly easy to calculate the vacuum trajectory and answer this question analytically (given actual data for the ski jumpers, which would be very hard to model accurately.)

The clothing that ski jumpers wear is pretty strictly regulated to prevent them from wearing baggy suits that would carry them further.

I would speculate the opposite. Those skis are broad and long and I would suspect generate a lot of lift.

I would love to see a calculation and comparison.

Note also a head wind leads to bigger jumps. Nowadays you even get a points deduction if you have a head wind and extra points if you have the wind in the back.

That would seem to settle it pretty conclusively.

Yeah, that started back in 2009. One interesting point I could find about it is that while the formula is linear and the points deduction of a headwind is equal to the points addition on a tailwind of equal speed, in computer simulation at least, it doesn’t work out that way, with a tailwind actually hurting the distance much more than the headwind helps. Here’s an article that cites a study finding a 3 m/s headwind adds 17.4 meters to a jump, but the same velocity tailwind deducts 29.1m from the jump.

It could still be the case that a ballistic trajectory in a vacuum exceeds either (especially if the whole jump including the slide down the ramp is in vacuum). We’ll know for sure at the Vacuum Olympics in 2034.

Here’s a research paper (note: PDF) on the aerodynamics of jumping - well worth the read if you want to geek out. It starts simple…

…and then gets a bit more complex.

Regarding the benefit/disadvantage of a headwind or vacuum, look at Figure 7 near the end of the paper. This shows that somewhere around 15 meters from the take-off (at which point the jumper has probably assumed the ideal alignment), the lift force is greater than the drag force. These forces aren’t in the same direction so you can’t simply cancel them out, but maybe someone with more time and skills than I could determine what this means when you factor in landing angle and all that good stuff.

Figure 8 on the last page shows differences in distance and velocity with a headwind.

If the data is available for launch angle, velocity at launch and height between launch point and the landing area, it’s pretty straightforward to calculate distance travelled in a vacuum. Then just compare it to the actual distance traveled by the jumper.

A little googling corroborates your claim, so I stand corrected. I find this argument sufficient to resolve the question. Ignorance fought, thanks!

The L/D > 1 data point tells us that the jumper will be able to sustain a 45 degree or flatter glide until he (or she!) re configures for landing. The parabolic path taken by a jumper in vacua will cross below this at some modest height, so on tall jumps the vacuum would hurt. That of course assumes equal launch speeds. The lack of drag on the approach would lead to higher launch speed, assuming the problem of the snow and ice sublimating could be solved. Actually I would not be surprised if the friction at the ski-snow interface was much higher without air in the mix.

Another factor with wind is that it will be closer to tangent to the landing slope than hirizontal, so the jumper with a headwind is actually jumping into an updraft. This is well known and exploited by glider pilots. Known as slope soaring, it is far more reliable and easier (but more dangerous) to learn than using thermals.