Building a Safer Ski Jump

In Italy some researchers at the University of Padova have built a "safety-first" ski jump. This feature uses the profile of the jump itself to reduce the likelihood of injury. Normally equipment such as helmets and skier training is used to reduce injury, but the jumps themselves are not built by engineers. This jump uses two techniques related to concepts learned earlier in the semester, to reduce the likelihood of injuries. The first is that the jump is fairly flat. When a jump is curved upwards it gives the skier an angular velocity. This is great if you are trying to do a flip, but if you are not it can cause unintended inversions which have a serious risk of head or neck injury or even death. The second technique is that the contour of the jump reduces the effective fall height of the jump. This is the fall height that a person would have to fall vertically from to have the same impulse. Reducing the impulse is done by reducing the component of the skier's velocity perpendicular to the snow by making the jump steeper as it is further away from the takeoff point. This means that the skier will experience less of an acceleration, and so less force upon impact. The force of impact, especially if one does not land in an ideal position on their feet, can have significant concern for injury. By building a jump as shown below the researchers were able to reduce EFH to about 0.5 m which was achieved 0.25s after impact.

Using this data we can calculate the force on the skier. First we must calculate the speed at impact using the kinematic equation vf^2 = vi^2 + 2a(xf-xi).  vi is 0, a is 9.8 m/s^2 and xf-xi is just our EFH. This gives vf = 3.13 m/s. We can then use F = (p2-p1)/t to find force as p is mv we just found our v and we can assume a 70kg person. t is 0.25s. This gives F = 876 N. We can also find acceleration by doing vf/t. Which gives a value of 12.52 m/s^2 or 1.28 g's which is a very gentle acceleration due to the impact which is the goal of these researchers.

http://www.digitaltrends.com/outdoors/italian-safer-ski-jump/
https://www.researchgate.net/publication/310235588_Designing_Building_Measuring_and_Testing_a_Constant_Equivalent_Fall_Height_Terrain_Park_Jump