# How does mass affect the distance a ski jumper travels

I did an experiment to explore this. My results found that their is an optimum mass of a ski jumper. I am unsure about the maths behind this. Can anyone help.

• Considering a frictionless slope, mass should not affect the distance travelled by the skier during a jump. Jan 24, 2016 at 12:13
• Hi, welcome to Physics.SE. PLease read the posting guidelines. in particular, show all the work you did so we can identify right and wrong parts thereof. Jan 24, 2016 at 13:06
• @N.S.John and no air resistance as well. Jan 24, 2016 at 15:15
• Related: physics.stackexchange.com/q/56276 , physics.stackexchange.com/q/22080 and links therein. Apr 3, 2016 at 19:48
• I would measure the jumper's speed when it just about leaves the ground to see if that correlates to the mass. Your question may be misleading. May 26, 2017 at 3:20

Most interestingly it is the opposite of what I find when riding a bike down a hill and what was hinted at above.

Long distance ski jumpers benefit from maximizing their surface area while simultaneously decreasing their weight. The less they weigh and the more drag they can produce, the farther they go. Their bodies are the primary source of weight and, as a result, there is incredible pressure for competing ski jumpers to be as thin as possible.

http://thesocietypages.org/socimages/2015/07/10/ski-jumpings-weight-problem/

Again anorexia rears its ugly head.

• this is true but not quite the full story i think. if you get too light you would not get enough speed on the start run, which is also a factor to get far. i guess the weight where that happens is a lot lighter than any human though. in addition there is the jump strength requirement. so i think you are right in a practical context, but if we look at it from a purely academic point of view there is probably an optimal mass. May 7, 2016 at 8:53
• There are mow restriction on how light a ski jumper can be. nytimes.com/2010/02/12/sports/olympics/12skijump.html?_r=0 May 7, 2016 at 11:36

Increasing mass means that wind resistance has less effect. Consider the extreme example of a ski jumper who only weighed 1 gram, in still air. How fast would the jumper be moving by the time they left the slope?

• Well, increasing the mass -to-cross-sectional-area ratio helps, not just the mass. Jan 24, 2016 at 13:05
• The ski jumper also has to worry about lift. This means that the ski jumper simulation should involve something dealing with the maximum ski length and width (e.g., ski area), the drag of the ski jumper and skis, the weight of the ski jumper, his cross-sectional area in the air, etc. This would NOT be a simple simulation, as there probably isn't a simple function that relates mass to maximum ski area. Sep 3, 2017 at 0:49

The downward acceleration in addition to g is also due to air resistance....

For speeds such as those of the ski jumper the air resistance in Newton's is taken to be proportional to velocity. ie -KVy hence the total downward acceleration is...

-(KVy/m + g)

So we see higher the mass m the lesser the downward acceleration and fitting this in the trajectory equation we get a higher range.

Interestingly air resistance offers a force opposite to direction of motion in horizontal direction as well...even here for the same force the negative acceleration decreases with mass.(-KVx/m)

In other words: Increasing the mass makes air resistance have less effect ( as @DirkBruere points out ) ...other factors remaining constant.

See Trajectory of a projectile' Wikipedia.

Note that const K will increase with the cross sectional area of the jumper...so what we are looking at is higher mass for same cross sectional area ( As @CarlWitthoft observes)

But is it really projectile motion?

Wikipedia page on ski jumping suggests that gliding is also at play here...so much so that a variation of ski jumping is called ski flying. In view of this @Farcher s remark may be correct ie having a greater x section area and less mass may be advantageous ...at least that's what appears to be the case.