The inverting effect of curvature in winter terrain park jump takeoffs - McNeil, J. A. (Skiing Trauma and Safety: 19th Volume, 2012)
Epidemiological studies of injuries at ski resorts have found that terrain parks, and jumps especially, pose a significantly greater head/neck injury risk to resort patrons than normal skiing activities. One especially hazardous situation is when the jumper lands in an inverted position which can lead to catastrophic injury or death from spinal cord trauma. Whereas jumpers can execute inverted maneuvers intentionally, curvature in the takeoff can lead to involuntary inversion. In this work we lay out the basic physics of this phenomenon assuming a rigid body model which simulates a stiff-legged jumper. Included is an estimate of the partially compensating (forward) rotation caused by the ground reaction force. I apply the results to an actual jump having a curved takeoff. For a jump trajectory with a landing just past the "knuckle," the resulting net angle of inverting rotation is found to be about 60°, sufficiently large to pose a potential injury risk. A mitigating takeoff design criterion adopted by the U.S. Terrain Park Council based on human response times is also discussed and compared to the FIS standard for Nordic jumps.