Orf.at – News: Orf.at – News: Derzeit muss der ÖSV neben Franz auch auf Abfahrtsolympiasieger Matthias Mayer (sechster und siebenter Brustwirbel gebrochen), Joachim Puchner Patellasehnenverletzung), Thomas Mayrpeter (Kreuzbandriss), Markus Dürager (Schien- und Wadenbeinbruch) und Daniel Danklmaier (Kreuzbandriss, Meniskusverletzungen) verzichten.

Abstract The influence of important parameters on the flight trajectory for jumps in downhill World Cup races was investigated. To quantify the impact injury risk at landing the parameter equivalent landing height (ELH) was introduced, which considered a variable slope inclination during the landing movement. Altogether 145 runs at 4 different jumps in World Cup races and trainings were recorded and analyzed. A simulation model was developed to predict the flight phase of the skier. Drag and lift areas were selected by parameter identification to fit the simulation trajectory to the 2-dimensional data from the video analysis.

Safety assessment of jumps Abstract The maximum values of the ELH which can be absorbed with muscle force was taken from the study of Minetti et. al (1998) for elite female and male ski racers. A sensitivity analysis based on the 4 jumps showed that ELH is mainly influenced by takeoff angle, takeoff speed, and the steepness of the landing surface. With the help of the developed simulation software it should be possible to predict the ELH for jumps in advance. In case of an excessive ELH, improvements can be made by changing the takeoff inclination or the approach speed.

Safety assessment of jumps Introduction In Böhm et al. (2008), Hubbard (2008), and McNeil et al. (2009, 2012) jumps in snow parks were investigated. They solved the equation of motion for the skier for specified takeoff speeds and inclinations of the takeoff to assess the impact velocity normal to the hill, which is related to the impact energy at the landing. As a practical measure Hubbard (2008) introduced the equivalent fall height (EFH), which equals the height a point mass falls down, if it is released with zero speed and its final speed equals the normal impact velocity. Thus, the equivalent fall height is a measure to assess possible impact hazards.

Safety assessment of jumps Introduction In a series of simulations the dependency of the equivalent fall height on the parameters that describe the jump, including hill geometry, were shown. Böhm (2008) and Shealy et al. (2010) measured the takeoff speed and the hill geometry for real jumps. However, an exact determination of the aerodynamic forces was not carried out in these works. Studies having determined the most important parameters for calculating the flight trajectory in downhill races under realistic circumstances could not be found.

Method: field measurement 4 Locations, 145 jumps analyzed Himmelreich (SH), Panorama (PS), Mausefalle (MF), Kamelbuckel (KB) Video recording 3 fix cameras, 20 Hz, 6 MP (Casio Exilim EX_F1) Additonally landing: 300 Hz, 0.2 MP Passpoints: gates, nets … Theodolite (CTS-2B) 2d reconstruction: DLT method Terrain Inclinometer slope inclination (inclinometer, Pieps 30° Plus)

Method: Digitizing

Method: data analysis Video analysis: Trajectory, take off speed, take off angle, EFH and ELH Solution of the equation of motion is fitted to the measured trajectory (least square fit) Drag and lift determined by parameter identification Variation of take off speed and angle  effect on EFH and ELH

Demo Video Landung

Method: simulation model α…velocity direction of center of mass β…slope inclination t 0 … take-off t 1 … first snow contact (landing point) t 2 … end of the lowering movement t1 t2 v1 v2

Method: simulation model Equivalent fall height (Hubbard, 2008) 𝐸𝐹𝐻= 𝑣 𝑛 2 2𝑔 applicable for landing area with const. inclination Equivalent landing height 𝐸𝐿𝐻= 𝑣 2 − 𝑣 1 ² 2𝑔 𝑣 2 − 𝑣 1 = 𝑣 1 𝑡𝑎𝑛 𝛼 2 − 𝛼 1 v1 v2 v2-1 𝛼1…velocity direction of center of mass 𝛼2…slope inclination 1 … first snow contact (landing point) 2 … end of the lowering movement t1 t2 v1 v2

Results: reconstruction accuracy max. difference between cameras: 11.8 cm for center of mass RMS error for the ski lenght: 2.2 cm

Results: 4 jumps γ0 3 -3

Results: slope inclination

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

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

ELH (m) Sprung ins Himmelreich (female) Panoramasprung Mausefalle Kamelbuckel

Diskussion: * EFH measure for necessary energy absorption, Simulation model * Take-off angle, take-off velocity and steepness of landing area - dominant factors for ELH * L and D only minor influence * Prediction of injury hazard of individual jumps EFH versus ELH * EFH measure for necessary energy absorption, if inclination of landing area is constant * ELH needed, if inclination of landing area is NOT constant * Critical ELH (?) male 1.5 m, female 1.2 m

Perspectives With the help of this simulation software, it should be possible to predict the ELH of a jump in the future, so that in case of an excessive ELH changes can be made in the takeoff inclination or the course tracking. The required input parameters for the simulation may be estimated as follows. The slope inclination of the jump can be measured with an inclinometer. The approach speed could be measured with a speed measuring device of the forerunners, or estimated by persons with longtime experience, in order to give a prediction as precise as possible.

CASE STUDY OF A SEVERE INJURY OF A TERRAIN PARK JUMP INTO AN AIRBAG Kurt Schindelwig, Hans-Peter Platzer, and Werner Nachbauer

Introduction On December 2010, a skier started about 25 to 30 m above the predetermined starting point bypassing the side of the entry barrier. He landed after 1½ rotations on his neck at the very end of the airbag and suffered a severe injury.

Goal Identify parameters causing the landing at the end of the airbag Suggest preventive measures

Literature: Simulation of approach and flight phase of a jump by solving the equation of motion at terrain park jumps (Hubbard,, 2009; McNeil et al., 2012; Levy et al., 2015) at downhill races (Schindelwig et al., 2015) Important measure for impact risk: impact velocity normal to the slope Important measure for impact risk with airbag: horizontal flight distance (land into or behind the airbag)

Method: Measurement 5 jumps into a airbag (dimensioned and shaped similar to the kicker at the accident) Pictures 60 fps: Camera EXILIM PRO EX-F1, Casio Slope inclination: Inclinometer Pieps 30° Plus, Pieps Control points 3d-data: Theodolite CTS-2B, Topcon Digitizing control points and eight landmarks of the skier Calculation of 3d-data of skier’s center of mass Eight landmarks

Method Solving the equations of motion of approach and flight trajectory for skier’s center of mass (Schindelwig et al., Scand J Med Sci Sports, 2015) Comparison measured – simulated data  verify the approach and flight simulation

Method: Definition of terms takeoff speed tangential takeoff speed normal takeoff speed horizontal flight distance Crucial value 8.5 m 16 m

Method: Sensitivity analysis Approach inclination: 8, 16, 32° 1. Determine approach length  middle airbag 𝜇=0.04; 𝐷=0.8 m²; 𝑣𝑤=0 m/s; m=90 kg; vn= 1.2 m/s; kicker height 2.5 m; kicker inclination takeoff 31° 2. Variation: friction coefficient; drag are; wind velocity  behind airbag

Results: Max. difference measurement - simulation: tangential takeoff speed: 0.4 m/s flight position CoM: 0.12 m Measured range: tangential takeoff speed: 7.6 to 9.3 m/s normal takeoff speed: 0.9 to 2.0 m/s

Results: Reconstruction accident case Simulation approach phase (𝜇=0.04, 𝐷=0.8 m²): 25-30 m more approach  tangential speed >12.0 m/s Simulation flight phase  tangential speed = 11.4 m/s Reduction tangential speed 2.4 m/s  Landing: middle airbag

Results: Sensitivity analyses Approach inclination 8° Landing point 𝜇=0.04, 𝑫=0.8 m², 𝑣𝑤=0 m s middle of the airbag Approach length 134 m Approach inclination 8° 𝜇=0.04, 𝑫=0.5 m², 𝑣𝑤=0 m s behind the airbag Bent position tuck position

Results: Sensitivity analyses Approach inclination (°) Approach length (m) Friction coefficient () Drag area (m²) Wind velocity (m/s) Horizontal flight distance (m) 8 169 0.04 0.8 8.5 0.02 13.2 0.5 >16 2.6 16 46 11.1 0.3 12.1 7.3 32 18 10.5 10.7 15.4 Bent position tuck position

Discussion Reconstruction the accident case: lengthening the approach by lateral passing the fences  increase of the tangential takeoff speed  landing at the end of the airbag Main problem at the accident case: No fences on the side of the approach Skier underestimated the influence of tangential takeoff speed on horizontal flight distance By lateral positioned fences and not only

Discussion By lateral positioned fences and not only

High: approach inclination < 8° Discussion Approach parameters on horizontal flight distance at given start position: High: approach inclination < 8° snow conditions change  adjusting start position But the risk to land behind airbag remains Low: approach inclination > 16° No risk to land behind airbag But too demanding for beginner or intermediate jumper’s

Discussion Safety improvement: airbag with a raised edge at the end http://www.katalinnovations.com

Safety analysis of winter terrain park jumps into airbags (2017) Zielsetzung Simulating the jumper’s approach and flight phase provides the possibility of analyzing the horizontal flight distance by parameter variation, which is crucial for the safety analysis of terrain park jumps into airbags. For this aim, the equation of motion was solved for the jumper’s approach and flight phase to predict the horizontal flight distance. Further aims of this study were to analyze the two accident cases and to develop preventive measures to improve safety of jumps into airbags.

Safety analysis of winter terrain park jumps into airbags (2017)

Method In a first step, field measurements were conducted to obtain data in a similar situation as in the second injury case. In a second step, approach and flight phase of the measured jumps were simulated by solving the equation of motion. In a third step, this simulation was used to study influence factors for the horizontal flight distance of the jumper. In a final step the two injury cases were reconstructed.

Five jumps (J1…J5) – Camera EXILIM PRO EX-F1 - 6 megapixels / 30 fps. The camera was rigidly mounted, and the focal length was kept constant. Position control points and camera were surveyed using a theodolite.

Tang. takeoff speed (m/s) 7.7 8.3 7.6 7.9 9.1 Table 2: Approach and jump parameters of the five recorded jumps J1 to J5.   J1 J2 J3 J4 J5 Skier S1 S2 Approach length (m) 46 55 49 62 Approach speed (m/s) 10.9 11.5 10.8 11.1 12.2 Tang. takeoff speed (m/s) 7.7 8.3 7.6 7.9 9.1 Normal takeoff speed (m/s) 1.0 0.9 1.9 2 Horizontal flight distance (m) 6.4 8.1 7.2 9.7

Parameter variations “Standard situation”: m=85 kg, v n =1.2 m/s, ρ= 0.93 kg/m3, D=0.8 m2, v w =0 m/s, and μ=0.06 The kicker was implemented as a circular arc followed by a straight line (kicker’s height h t =2.5 m, kicker’s inclination at takeoff α t =31°, length of straight section l t =1.5 m). The radius of the circular arc r k was 12 m calculated with r k = h t − l t sin α t 1− cos α t .

Variation 1: Using the values of the “standard situation” the approach length was varied until the jumper landed in the middle of the airbag ( l f =8.5 m) for the approach inclinations 10°, 20°, and 30°. Then the required variation of ski-snow friction coefficient was determined to move the landing point from the middle to the end of the airbag (M2E) ( l f >16 m). By analogy the required variations of drag area and tail wind speed were conducted.

Variation 2: Using the values of the “standard situation” and different kicker geometries the tangential takeoff speed was varied until the jumper landed in the middle of the airbag. Then the required increase of the tangential takeoff speed ∆𝑣 𝑡 to M2E was calculated as a function of kicker’s takeoff inclination 𝛼 𝑡 (15° to 55°) for the kicker heights ℎ 𝑡 (2.5, 3.0, 3.5, and 4.0 m).

Variation 3: Similar steps as in Variation 2 were conducted for the normal takeoff speed 𝑣 𝑛 . With 𝑣 𝑛 =0 m/s the tangential takeoff speed was varied until the jumper landed in the middle of the airbag. With that 𝑣 𝑡 the required normal takeoff speed 𝑣 𝑛,𝑏𝑒ℎ𝑖𝑛𝑑 to M2E was calculated as a function of 𝛼 𝑡 for the four kicker heights. 4.0 m).

Variation 1: Approach inclination (°) Approach length (m) Friction coefficient () Drag area (m²) Wind velocity (m/s) Landing point 10 150 0.040 0.8 MA 0.035 BA 0.5 2.7 20 39.4 0.016 - 7.5 30 22.4 0.009 11.9 - indicates that no solution exists and the cursive numbers indicate unrealistic values.

Variation 2: Figure 4: Required increase of the tangential takeoff speed ∆ v t to move the landing point from the middle to the end of the airbag versus the kicker’s takeoff inclination α t . The four lines from bottom to top refer to the kicker table heights of 2.5, 3.0, 3.5, and 4.0

Variation 3: Figure 5: Required increase of the normal takeoff speed ∆ 𝐯 𝐧 to move the landing point from the middle to the end of the airbag versus the kicker takeoff inclination 𝛂 𝐭 . The four lines from bottom to top refer to the kicker table heights of 2.5, 3.0, 3.5, and 4.0 m.

Reconstruction of case report one The flight trajectory simulation revealed for landing at the end of the airbag minimal tangential takeoff speeds of 13.4 and 12.5 m/s for the normal takeoff speeds 0.0 and 1.2 m/s, respectively. A decrease of these two tangential takeoff speeds of about 1.2 and 1.8 m/s would have led to a landing at the middle of the airbag.   Reconstruction of case report two The flight trajectory simulation revealed a tangential takeoff speed of 11.4 m/s for the landing at the end of the airbag. A decrease of the tangential takeoff speed from 11.4 to 8.9 m/s would have led to a landing at the middle of the airbag.