Sport aerodynamics: A case study of ski-jumping

• Prof. Dr. Wolfram Müller, Department of Medical Physics and Biophysics, Karl-Franzens-University, Graz
• Dr. Walter Meile, Institute of Fluid Mechanics and Heat Transfer, Graz University of Technology

• Dipl.-Ing. Ewald Reisenberger, Institute of Fluid Mechanics and Heat Transfer, Graz University of Technology

Funded by the Austrian Scientific Research Fund (FWF) - P14388-TEC

In competitive ski-jumping, not only the athletes'''' motoric abilities are important. Their body weight plays a major role in achieving appropriate jump lengths. This has lead to alarmingly underweight athletes with high risk in health, and several cases of anorexia have been reported. Questions of safety, health and fairness are often closely associated with competition regularities. As a main goal, the development of future regulations focusing on health and safety of the athletes seems urgently necessary. Important biomechanical factors are investigated by the cooperation partner. At the institute, the aim of the project is to achieve a better understanding of aerodynamical fundamentals. Detailed knowledge of lift and drag production as well as their interaction during different flight phases is acquired. Therefore, we compose a jumper model from geometrically simple objects, like rectangular bodies, cylinders, cones etc. Starting from a simple model of the upper part of the body, legs, arms, head and skis are added modularly for separate and combined wind-tunnel measurements. From this, the individual influence of all parts on aerodynamic forces and their interaction may be deduced. Furthermore, numerical simulations applying various turbulence models are performed with a commercial CFD code (Computational Fluid Dynamics) for comparison. This should yield conclusions on the reliability of CFD simulations in sports.

Accurate simulation models for flight paths, as developed by our cooperation partner W. Müller (see above) require precise aerodynamic data as input values taking the positional changes during the flight phase into account. Most of the required data could be collected only during field studies and full-scale measurements in large wind tunnels. Because of the enormous effort necessary for such studies it would be desirable to provide suitable data subject to changes (flight style, positions, equipment, regulations) via simulation. This has led to the idea of performing very basic studies on the aerodynamics of ski jumping starting from simple geometrical configurations. Thereby it should be evaluated if human bodies may be represented by suitable combinations of simple geometries in Computational Fluid Dynamics (CFD). Furthermore, a way to estimate the interaction of individual parts should be developed. Both tasks require suitable data about the aerodynamic characteristics of the objects within a wide range of the orientation relative to the flow. While a lot of data is available for cylindrical and similar geometries as well as for flat and cambered plates, practically nothing could be found on slender prismatic bodies with either sharp or cylindrically shaped edges. On the other hand, bodies of comparably simple geometries and varying thickness are widely used in technical applications exposed to aerodynamic loads from natural wind or other flow fields.

During the first stage of the project the following bodies were investigated: a flat plate (aspect ration 5:1) for comparison and prismatic bodies of varying thickness and with either sharp or rounded edges (aspect ratio 2:1). The exact dimensions are sketched in the following figure and specified in the accompanying table.

 

The results of drag and lift measurements for all profiles with cylindrically shaped edges are depicted in the following diagram. The notation prxx means profile/rounded edges/thickness in mm. Frm the individual polars the crucial influence of thickness becomes evident. In the case of rounded edges this influence can be mainly ascribed to the curvature of the appropriate body surfaces. The flow along the curved parts in fact behaves like the flow around circular cylinders.