1. 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

2. 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

3. 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

4. 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

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

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

7. Method: simulation model
Forces
Equation of motion – point mass
𝑥 𝑦 = 𝜌 2𝑚 𝑥 𝑦 −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

8. 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

9. 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

10. 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

11. 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

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

13. Results: slope inclination

14. 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
( )
0.32
( )
0.06
( )
0.78
( ) PS 92
(85-99)
0.5
( )
0.43
( )
0.07
( )
0.62
( ) MF 93
(86-97)
2.1
( )
0.46
( )
0.02
( )
0.89
( ) KB
109
( )
-0.1
( )
0.42
( )
0.01
1.98
( )
18th annual Congress of the EUROPEAN COLLEGE OF SPORT SCIENCE, 26th – 29th June

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

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

17. ELH (m)
SH (female) PS
MF KB

18. 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

19. 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