The mechanics of takeoffs in the aerials event of freestyle skiing

The aerials event of freestyle skiing is a relatively new discipline having only been introduced into the Olympic Games as a medal event in 1994. The purpose of this study was to develop a simulation model for the takeoff phase of aerials, with the intention of learning more about how the requisite linear and angular velocities at takeoff are generated. Experimental data was collected for six triple somersaulting aerial jumps. The jumps were filmed with four high-speed video cameras and a total of 17 points were manually digitised for each camera view of each jump. The digitised coordinates were reconstructed using a three dimensional direct linear transformation (3D-DLT) and processed using a film program written in FORTRAN. The program produced kinematic data for the takeoff phase of the six jumps. A simulation model for takeoff was developed, comprising of a rod (body) and a ski. At the connection between the rod and the ski is a passive torque, governed by the stiffness coefficient K. Experimental values for the height of the centre of mass (CoM), moment of inertia (MoI), initial linear velocity (VG) and initial angular velocity (ωpg) were used as model inputs. A combined drag and air resistance coefficient (D) was varied with K to match the experimental VG and ωpg at takeoff, resulting in an average difference of -0.07% for VG, and -16.10% for ωpg. A straight body simulation was run, eliminating the effect of joint angle changes on CoM height and MoI, it was found that a straight body matches the experimental data just as well as a simulation using joint angles. This result suggests that joint angles changes play a different role, other than to generate angular and linear velocity. Further alterations were made to the model parameters; K was varied, which increased the angle of the CoM behind the normal to the skis (ψ) as K increased. Initial angular velocity was varied with results suggesting that a forwards leaning motion at the start of the kicker generated a larger angular velocity at takeoff. An additional ankle torque was implemented for the final 0.1s of takeoff, this increased ωpg and reduced the difference to just -3.01%. Conclusions were drawn that the passive torque of the skis and an additional ankle torque prior to takeoff play a large role in governing takeoff conditions.