Nachbauer, W.1 , Mössner, M.2 and Schindelwig, K.1 SAFETY ASSESSMENT OF JUMPS IN SKI RACING Nachbauer, W.1 , Mössner, M.2 and Schindelwig, K.1 1) Department of Sport Science, University of Innsbruck, Austria 2) Centre of Technology of Ski- and Alpine Sport

Introduction Statistic world cup ski racing From 1605 athletes of the Austrian Ski Federation winter seasons of 1995/96 to 2012/13 595 injuries - from these 237 severe (Nachbauer et al., 2013) Landing back-weighted after jumps second most common skiing situation of an ACL injury Accurate prediction only with wind tunnel experiments (drawback - high costs) (Brownlie et al., 2010, Chowdhury et al., 2010) 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 2

Goal Develop a simulation model to predict the injury hazard of jumps in downhill ski races Hazard measure - equivalent fall height (EFH) Variable inclination landing area – concept of effective landing height (ELH) 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 3

Method: field measurement 4 jumps – 145 jumps analysed Sprung ins Himmelreich (SH), Panorama Sprung (PS), Mausefalle (MF), Kamelbuckel (KB) 3 Cameras 20 Hz, 6 MP (Casio Exilim EX_F1) 300 HZ, 0.2 MP (Casio Exilim EX_F1) Theodolite (CTS-2B) position of cameras, gates, … Inclinometer (Pieps 30° Plus) slope inclination 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 6

Method: 3d reconstruction 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 5

Method: 3d reconstruction skier’s plane π ε image coordinates 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 5

Method: simulation model Forces Equation of motion – point mass 𝑥 𝑦 = 𝜌 2𝑚 𝑥 2 + 𝑦 2 −𝐷 𝑥 −𝐿 𝑦 −𝐷 𝑦 +𝐿 𝑥 − 0 𝑔 𝐹 𝐺 =𝑚𝑔 𝑢 𝑦 𝐹 𝐷 =− 1 2 𝜌𝐷 𝑣 𝑣 𝐹 𝐿 = 1 2 𝜌𝐿 𝑣 𝑣 ⊥ 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 7

Method: simulation model Integration of the equation of motion Runge-Kutta scheme Δt of 0.01 s Drag and Lift determined by parameter identification Least squares fit the solution of the equation of motion is fitted to the measured trajectory 𝛼…velocity direction of center of mass 𝛽…slope inclination index 0 … take-off index 1 … first snow contact (landing point) index 2 … end of the lowering movement 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 7

Method: simulation model 𝛼…velocity direction of center of mass 𝛽…slope inclination index 0 … take-off index 1 … first snow contact (landing point) index 2 … end of the lowering movement t1 t2 v1 v2 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 7

Method: simulation model Equivalent fall height (Hubbard (2008) 𝐸𝐹𝐻= 𝑣 𝑛 2 2𝑔 (valid for landing area with const. inclination) Equivalent landing height 𝐸𝐿𝐻= 𝑣 2 − 𝑣 1 ² 2𝑔 𝑣 2 − 𝑣 1 = 𝑣 1 𝑡𝑎𝑛 𝛼 1 – 𝛽 2 v1 v2 v2-1 t1 t2 v1 v2 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 7

Results: reconstruction accuracy max. difference between cameras: 11.8 cm for center of mass rms deviation for the ski lenght: 2.2 cm 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 10

Results: high speed video of landing movement 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 10

Results: slope inclination

Method: jump parameter α0- β0 3 -3 Jump v0 (km/h) α0- β0 (°) D (m2) L (m2) EFH (m) SH 86 (77-91) 2.3 (0.6-3.6) 0.32 (0.23-0.61) 0.06 (-0.06-0.16) 0.78 (0.45- 1.04) PS 92 (85-99) 0.5 (-0.1-1.2) 0.43 (0.33-0.52) 0.07 (-0.01-0.12) 0.62 (0.35- 1.01) MF 93 (86-97) 2.1 (0.7-4.7) 0.46 (0.35-0.58) 0.02 (-0.05-0.06) 0.89 (0.62- 1.37) KB 109 (103-116) -0.1 (-2.7 - 2.4) 0.42 (0.27-0.65) 0.01 1.98 (0.92 - 3.22) 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 7

Results: EFH versus ELH jump „Mausefalle“ EFH (m) ELH (m)

Results: EFH versus ELH jump „Kamelbuckel“ EFH (m) ELH (m)

ELH (m) SH (female) PS MF KB

Diskussion: summary Accurracy greatest difference of vertikal position: 118 mm  error of determination of drag and lift area +/- 0.3 m² EFH versus ELH equivalent fall height (EFH) assess the energy absorbed upon landing, if inclination of landing area is constant equivalent landing height (ELH) is needed, if inclination of landing area is NOT constant Simulation model a prediction of the injury hazard of a jump is possible 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 10

Conclusion Simulation model was developed to predict the equivalent fall height for jumps Necessary parameters were measured for four jumps during world cup races. Take-off angle, velocity and steepness of landing area are the most dominant factors for the equivalent fall height. The equivalent fall height is an important measure to assess the effect of possible impact hazards and, thus, the given simulation model can be used to improve the safety for jumps in ski racing. 18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June 2013 10