Tabletop Jumping: Engineering Analysis of Trajectory and Landing Impact

Abstract

Abstract This study is an engineering analysis of skiers and snowboarders jumping what is known as a mid-sized tabletop feature at a ski resort. The analysis specifically looks at the trajectories and landing impacts of individuals while jumping mid-sized tabletop features (deck lengths 20 to 30 ft) at a ski resort. For the trajectory analysis, out of a total of 117 jumps by skiers and snowboarders that were observed, 57 jumps were analyzed using a radar gun to determine actual speed on the ramp, digital photography to document flight paths and landing points as well as jumper body position at the moment of take-off. For the impact analysis, a total of 31 jumps by an instrumented subject were videotaped; the landing impacts for 21 of these jumps were measured with triaxial accelerometers to measure the impact resulting from the landing at the boot top, chest, and head levels. With respect to trajectory analysis, the study concludes that simply knowing the ramp angle and take-off speed is not a sufficient dataset to predict where the jumper will land; alternatively, knowing the ramp angle and the landing point is an insufficient dataset to predict the take-off speed. The specific actions of the jumper with regard to raising or lowering the jumper’s center of mass while on the last part of the take-off ramp can significantly alter the effective take-off angle and subsequent flight trajectory. For the jumps observed in this study, the jumpers were able to routinely add or subtract as much as 15° to the actual take-off ramp angle, resulting in effective take-off angles much larger or smaller than the measured take-off angle. With respect to impact analysis, the study concluded that for jumps similar to the those observed in the trajectory analysis, when the jumper lands in an upright controlled manner, the resulting impact (measured in G units) at the boot level ranged from 50 to 100 Gs, with a mean of 75 Gs, it averaged 4.7 Gs at the chest and only 2.5 Gs at the head.