Available online at www.sciencedirect.com
Procedia Engineering 60 (2013) 378 – 384
6th Asia-Pacific Congress on Sports Technology (APCST)
Evaluation of aerodynamic drag utilizing a viscoelastic model Keisuke Hataa*, Akira Shionoyaa, Hazim Moriab, Harun Chowdhuryc, Firoz Alamc a
Department of Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka-machi, Nagaoka, Niigata, 940-2188 b Department of Mechanical Engineering, Yanbu Industrial College, Yanbu Al-Sinaiyah, Kingdom of Saudi Arabia c School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Bundoora, Melbourne, VIC 3083, Australia Received 20 March 2013; revised 16 May 2013; accepted 2 June 2013
Abstract The purposes of this study are construction of viscoelastic model to evaluate the aerodynamics drag and evaluation of textile of suits for sprinter. In previous studies, evaluations by computer simulation for the aerodynamics are almost CFD (Computational Fluid Dynamics). However, the evaluation by CFD is complex and when we evaluate products for sports, the parameter for evaluating should be simple form as possible. Therefore, we constructed the viscoelastic model to evaluate the aerodynamics drag. This viscoelastic model is constructed from mass, elastic element and viscosity element. In this result, we confirmed the variation of viscosity element in textile part. Moreover this parameter represented transition from laminar flow to turbulent flow. These results could give the important suggestion to design of the suit by laminar-turbulent transition, would be the new method to evaluate and create the new concept of the suit for sprinter. © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license. © 2013 Published by Elsevier Ltd. Selection andSchool peer-review under Mechanical responsibility RMIT University Selection and peer-review under responsibility of the of Aerospace, andof Manufacturing Engineering, RMIT University Keywords: Aerodynamics drag; fabrics; viscoelastic model
1. Introduction Sprint race is a kind of the event in Track and Field competition. Especially, 100 meter race is the shortest event, reaches the fastest speed (44.72 km/h at World Record) in sprint events. Therefore, sprint performance is affected by the wind. A sprinter experiences an aerodynamics drag force resist motion. In the race, accelerating 80% of maximal speed until 20 meter from starting [1], a sprinter has to maintain top speed as long as possible. Therefore, aerodynamics is crucial factor in sprint race.
* Corresponding author. E-mail address:
[email protected].
1877-7058 © 2013 The Authors. Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of the School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University doi:10.1016/j.proeng.2013.07.021
Keisuke Hata et al. / Procedia Engineering 60 (2013) 378 – 384
In the previously study about the relationship between sprint and aerodynamics, Linthorne [2] has also explained about improvement of running speed by assistance of tailwind and altitude, using the past data as basis. Utilizing mathematical model based on energy release, Ward-Smith [3] has shown that adjustment to running time consequent upon wind effects are mainly determined by the parameter relating the project frontal area of athletes and air density. Quinn [4-5] has shown difference of the effect of wind by lane allocation and wind direction in 200 meter and 400 meter race, utilizing another mathematical model. On the other hand, Pugh[6] has investigated the relation between the oxygen intake and the air resistance, he has estimated that the contribution of air resistance which is about 8% of the total energy for a 5000 meter race and about 16 % for a 100 meter sprint. In the study about the actual measurement of aerodynamics, Hirata et al. [7] have developed a movingbelt system for fundamental and accurate wind-tunnel experiments, and have shown its basic performance such as the distribution of flow velocity and turbulence intensity above the moving-belt. Moreover, Chowdhury et al. [8] have conducted wind-tunnel experiment for comparison of rough surface textiles of sport wear. They have shown that wind the wind velocity to transit to turbulent boundary layer depend on roughness of surface. However, there is little that the study measuring actual aerodynamics parameters from view point of sprint performance. On the other hand, there are several studies about the computing simulation for the aerodynamics of sports suits. For example, Defraeye et al. [9] have analyzed about cyclist aerodynamics, utilizing turbulent-model by Computational Fluid Dynamics (CFD). In this matter, although CFD has been used as a kind of analyzing method of aerodynamics for many kinds of studies and its effective method, CFD needs complex process and its result is complex too. Moreover, Navier-Stokes Equation that is the main algorithm of CFD has not been solved yet. For that reason, it s not necessarily accuracy without huge processor. Therefore, the purpose of this study is to measure the aerodynamics parameters of fabric for the sprint wear and to evaluate the sprint wear by wind-tunnel experiment. Furthermore, we suggest a simulation model to evaluate the fabric and show the possibility to evaluate by the mathematical model except Navier-Stokes equation. The model is based on the vibration model by mass, viscosity element and elastic element, and that is to represent the aerodynamic drag force and identify the parameter of aerodynamic property of fabrics. 2. Method 2.1. Fabrics for testing and cylindrical object Three types of sprint fabric were selected for this study. These fabrics are two loose type singlet (different manufacture each other) and one compression type suit. Each fabric is named as Fabric1, Fabric2 and Fabric3. The parameters of these fabrics are following: The coefficients of kinetic friction are 0.14, 0.15 and 0.13, the surface roughness are 0.8 mm, 1.5 mm and 0.5 mm respectively. And then the surface roughness is defined as the distance of peak point and peak point of the structural roughness on surface. Each fabric was wrapped on the plastic cylinder fixed on the ground completely as illustrated in Figure1 with appropriate tension. Then fabrics were cut to wrap, length of width is 260 mm in Fabric1 and Fabric2, and 250 mm in Fabric3. Therefore, Fabric3 was stretched tightly comparing Fabric1 and Fabric2. These compressive loads are 95.75 N/m2, 104.5 N/m2 and 126.31 N/m2 respectively, and the tension was not controlled. This cylinder is same one to Moria et al. [10]. As a simple way to represent the body configuration of human, these body parts can be represented as multiple cylinders. Comparing to actual body arrangement, this cylindrical object represents the aerodynamics phenomenon simply, especially this configuration gives the least interference to force measurements for the simultaneous study
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of aerodynamic drag and lift [11]. However, the edge of top and bottom of the cylinder was not secured. Therefore, this result would be affected by these edges. The effects of body parts being in close proximity to each other using simplified cylinders were studied by Chowdhury et al. [8]. 2.2. Wind tunnel The RMIT Wind Tunnel was used for testing. This wind tunnel was used for experimental evaluation. This is a closed return circuit with a maximum air speed of approximately 100 km/h with a rectangular test section (3 m wide x 2 m high x 9 m long). The test section has a turntable to yaw suitably sized objects. The tunnel was calibrated before conducting experiments. The air speeds were measured via a modified NPL ellipsoidal head Pitotstatic tube (located at the entry of the test section) connected to a MKS Baratron pressure sensor through flexible tubing. The cylindrical body geometry is used to evaluate textile features as fibre orientation and surface roughness [8]. The fabric of each sprint suit was wrapped on the cylinder with appropriate tensions. The cylinder had a diameter of 90 mm and length of 220 mm, while the 6-axis force transducer (type JR-3) had a sensitivity of 0.05% over a range of 0 to 200 N. 2.3. Experimental procedure With a view to measure the aerodynamics drag, the cylindrical object was exposed to wind at various speeds. Speeds of wind started from 10 km/h to 100 km/h with increment of 5 km/h up to 50 km/h and 10 km/h from 50 km/h. Then, the cylindrical object was fixed to 90 degree. The measured aerodynamic forces were converted to non-dimensional drag coefficient (CD). 2.4. The evaluation model In order to evaluate each fabric, we suggested the evaluation model constructed by mass, viscosity element and elastic element as shown in Figure 1. This model is to represent the aerodynamics drag force. In this study, the aerodynamics drag force is regarded as one of the collusion phenomenon from view point of that all materials have mass, elasticity and viscosity even air. This model consists of the part of cylinder and the part of fabric, the part of cylinder is connected the ground through an elastic element. Mass of fabrics and cylinder is substituted for m1 and m 2 respectively. In the case of simulating just smooth cylinder, the part of fabrics was got out on the Model. Then, the wind speed is regarded as a kind of force field, it is put on the equation of fabric part that is the surface of cylindrical object as the value that timed to the converting constant( Cwwf ) . These differential equations are as shown in Equations 1 3.
Cylinder Wind
Wrapped fabric Cylinder
Fabric
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Keisuke Hata et al. / Procedia Engineering 60 (2013) 378 – 384
Fig. 1(a) Cylindrical object; (b) Simulation model for aerodynamics drag force.
(1) (2) (3)
m1 , m2
: Mass
x1 , x2 , x3 k1 , k 2 , k 3 , pf , pc, p
: Displacement : Elastic Element
c1 , c2 , qf , qc C wf
: Converting Const
va
: Wind Speed
: Viscosity Element
The aerodynamics drag force is represented as shown in Equation 4.
DragForce
k3 x p
(4)
This simultaneous differential equation is solved by Runge-Kutta method numerically. And the represented drag force is optimized on the experimental drag force each wind speed utilizing the NelderMead method, then all parameters (elastic element and viscosity element) are calculated and identified. Then, the aerodynamics drag force was supposed that it is constant value continuously. 3. Result 3.1. Experimental result The drag forces and the drag coefficients for four series (a smooth cylinder and all three fabrics) are plotted against the speeds from horizontal which are shown in Figures 2(a)-(b). The range of transition laminar boundary layer to turbulent boundary layer was from 15 m/sec to 25. However, the range of running speed is up to 12 m/s from only view point of transition. 8
Drag force [N]
7
Drag Coefficient , CD
Smooth cylinder
6
Fabric1
5
Fabric2
4
Fabric3
3 2 1
Wind speed [m/sec]
0 0
20
40
60
80
100
120
0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3
Smooth cylinder Fabric1 Fabric2 Fabric3
0
20
40
Wind speed [km/h]
60
80
100
120
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Keisuke Hata et al. / Procedia Engineering 60 (2013) 378 – 384
Fig. 2(a) Aerodynamic drag force; (b) Aerodynamic drag coefficient.
3.2. Identified parameters In order to suggest the new evaluation method, the parameter of the evaluation model was identified by fitting to the experimental value. These are the viscosity parameters on the part of fabric. These parameters showed different tendency and have different regression line obviously. 8
Drag force [N]
7 6 5 4 3
y = 0.0885x - 7.0938 r=0.98 p
