Flow Over a Ski Jumper in Flight

Journal of Biomechanics 89 (2019) 78–84 Contents lists available at ScienceDirect Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com Flow over a ski jumper in flight: Prediction of the aerodynamic force and flight posture with higher lift-to-drag ratio ⇑ Woojin Kim a, Hansol Lee b, Jungil Lee c, Daehan Jung d, Haecheon Choi a,b, a Institute of Advanced Machines and Design, Seoul National University, Seoul 08826, Republic of Korea b Department of Mechanical & Aerospace Engineering, Seoul National University, Seoul 08826, Republic of Korea c Department of Mechanical Engineering, Ajou University, Suwon 16499, Republic of Korea d Department of Mechanical Engineering, Korea Air Force Academy, Cheongju 28187, Republic of Korea article info abstract Article history: Large eddy simulations (LESs) are performed to study the flow characteristics around two flight posture Accepted 12 April 2019 models of ski jumping. These models are constructed by three-dimensionally scanning two national- team ski jumpers taking flight postures. The drag and lift forces on each component of a ski jumper and skis (head with helmet and goggle, body, arms, legs and skis) and their lift-to-drag ratios are Keywords: obtained. For the two posture models, the drag forces on the body, legs and skis are larger than those Ski jumping on the arms and head with helmet and goggle, but the lift forces on the body and skis are larger than their Flight posture drag forces, resulting in high lift-to-drag ratios on the body and skis and low lift-to-drag ratio on the legs. Lift-to-drag ratio We construct simple geometric models, such as the circular cylinder, sphere and thin rectangular plate, Large eddy simulation Simple geometric model predicting the drag and lift forces on each component of a ski jumper and skis, and validate them with those obtained from LES. Using these geometric models, we perform a parametric study on the position angles of flight posture for higher total lift-to-drag ratio. The flight postures obtained increase the total lift-to-drag ratios by 35% and 21% from those of two base postures, respectively. Finally, LESs are performed for the postures obtained and show the increases in the total lift-to-drag ratios by 21% and 16%, respectively, indicating the adequacy of using the simple geometric models for finding a flight posture of ski jumping having a higher lift-to-drag ratio at low cost. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction the ski-opening angle. The V style, pioneered by Jan Boklöv (Swe- den) in 1985, replaced the parallel style because it improved the Ski jumping is a winter sport and composed of in-run, take-off, aerodynamic performance and increased the flight distance by flight, and landing phases. The score of ski jumping is evaluated by allowing a ski jumper to lean forward (Müller, 2009). On the other the distance jumped and style score given by five judges. The flight hand, the H style with very small ski opening angle and wide spac- distance is determined by the weight of a ski jumper and skis, aero- ing between skis becomes popular. However, the effect of these dynamic forces during flight, and initial flight velocity, where the different styles on the aerodynamic performance has not been fully initial flight velocity is determined from the approach and take- understood. off jump velocities and posture transition from in-run to flight Flow around a ski jumper during flight has been studied exper- (body extension and raising ski head) (Schmölzer and Müller, imentally and numerically. Müller et al. (1995) investigated the 2005; Schwameder, 2008; Yamamoto et al., 2016). The aerody- effect of the V-style flight posture for the first time and analyzed namic force is affected by the flight posture of a ski jumper. There- the first jump in history (over more than 200 m) achieved during fore, ski jumpers put significant amounts of efforts to find their the 1994 Ski Flying World Championships in Plancia, Slovenia. own optimal flight postures. However, it is not straightforward to Müller et al. (1996) conducted large-scale wind tunnel experi- find optimal postures during the flight phase by ski jumpers them- ments to measure the drag and lift areas on ski jumpers for three selves because of many factors determining the flight posture and attack angles, calculated the flight trajectory, and investigated very short flight time. For example, one of the important factors is the effects of body mass, approach and take-off jump velocities, and wind direction. They found that a light ski jumper moved far- ther with a noticeably lower velocity, high approach and take-off ⇑ Corresponding author. jump velocities increased the flight distance, and the wind angle E-mail address: [email protected] (H. Choi). https://doi.org/10.1016/j.jbiomech.2019.04.022 0021-9290/Ó 2019 Elsevier Ltd. All rights reserved. W. Kim et al. / Journal of Biomechanics 89 (2019) 78–84 79 relative to the horizontal direction in the range of 36–216° investigated the effects of the attack angle and position angles on increased the flight distance with a relatively lower landing veloc- the aerodynamic performance and flight distance. However, ski ity. They also showed that the drag and lift areas were decreased jumpers have different flight postures and may have different by about 54% and 56%, respectively, with an almost same lift-to- effects from those angles. Therefore, the objectives of the present drag ratio, as the ski-opening angle decreased from 35° to 0°. study are to obtain the aerodynamic forces on typical flight pos- Schmölzer and Müller (2002) recorded a series of flight postures tures by conducting large eddy simulations (LESs), and to develop of the best ski jumpers during 1999/2000 World Cup competitions simple geometric models of predicting them on the components of in Villach through field studies, measured the attack angle and the postures for suggesting better flight postures. position angles (body-ski angle, hip angle, and ski-opening angle), performed the least-square fits for the attack angle, body-ski angle, 2. Methods and hip angle as a function of flight time, and conducted large- scale wind tunnel experiments for two flight posture models with Two flight postures of ski jumping are constructed by three- different height and ski length at the measured angles (derived dimensionally scanning those of two national-team ski jumpers, from field studies during the competitions) to obtain their drag as shown in Fig. 1. The center lines of body, arms, legs, and skis and lift areas. They obtained increases of lift-to-drag ratio and lift, are used to determine their attack angles (a), roll angles (/) and and a decrease of drag with decreasing hip angle from 180° to 170°. yaw angles (k), and these flight posture parameters for jumpers 1 As the angle of attack decreased from 40° to 30° or the body-ski and 2 are given in Table 1. The attack angle of skis, a ,is angle decreased from 15° to 1°, the lift-to-drag ratio increased Ski body known to be an important parameter to determine the flight dis- but both the drag and lift decreased. Seo et al. (2004) optimized tance and it has been observed to increase continuously from 26° the flight distance by controlling the ski-opening and body-ski to 39° during the flight (measured for the best ten jumpers in angles during flight for a simple flight posture model, and the 19th Winter Olympic Games by Schmölzer and Müller, 2005). increased the flight distance from 131 m to 139 m at the body- Since we could not measure this angle of attack for the present ski angle of 7° by changing the ski-opening angle from 25° to posture models, we fix the attack angle of skis at a =30° around 26°. They found that the control of the ski-opening angle Ski body for jumpers 1 and 2 which is near the time-averaged angle of was more important for increasing the flight distance than that attack of 28.5° during the flight (Schmölzer and Müller, 2005). of the body-ski angle. Meile et al. (2006) obtained the drag and lift The ski length (l), minimum ski spacing (s/l), and frontal (A ) and areas and pitching moment on a flight posture model through f planform (A ) areas are 2.43 m, 0.08, 0.622 m2 and 1.020 m2 for wind-tunnel experiments for various attack, body-ski, hip, head, p jumper 1, and 2.54 m, 0.10, 0.755 m2 and 1.183 m2 for jumper 2, shoulder abduction, and ski-opening angles. They found that the respectively. drag area continuously increased with the attack and body-ski We perform LESs of flows over two flight postures, respectively. angles, while many local maxima of the lift area existed and the lift The numerical details are given in the Supplementary materials. area maintained a maximum near the sum of the attack and body- The Reynolds numbers considered are Re = qUl/l = 540,000 for ski angles of about 50°. Jung et al. (2014) performed an optimiza- jumper 1 and 564,000 for jumper 2 due to slightly different ski tion study for the flight distance by controlling the attack and lengths of jumpers 1 and 2, where q and l are the fluid density body-ski angles during flight with constraints on the upper and and viscosity, respectively, and U is the flight speed. The present lower limits of the attack and body-ski angles, respectively, and Reynolds numbers are much lower than those in field studies, increased the flight distance from 113.8 m (Schmölzer and but still provide meaningful interpretation on the force coefficients Müller, 2002) to 125.9 m.

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