Aerodynamics of Sports Balls - Penn Engineering(空气动力学运动球-佩恩工程).pdf
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Aerodynamics of Sports Balls
Bruce D. Kothmann
January 2007
Unless Otherwise Specified, All Data From
Mehta, R.D., “Aerodynamics of Sports Balls”
Annual Review of Fluid Mechanics, 1985.17:15
Spherical Sports Balls
• Complex Aerodynamics : Rotation Non-Uniform Surface
• Begin with Non-Rotating Uniform SphereSpherical
Symmetry Implies Aerodynamic Force Must be Opposite
to Direction of Flight (Drag)
• Then Consider Seams SpinAsymmetryLift
2
Drag on Non-Rotating Uniform Sphere
Dimensional Analysis
• Drag (F ) Depends on:
D
– Speed, V F f V ,D ,ρ ,μ ,k
– Diameter, D D ( )
– Density, ρ
– Viscosity, μ F
D
– Roughness Length, k C
D 2
• 6 Parameters Minus 3 0.5ρ V A
Dimensions (Mass, Length,
Time) = 3 Dimensionless k
Parameters Re ρ VD ε
– Significantly Reduce Experimental D
Testing Required μ
– Match Re and ε to Find CD and Then
Compute Drag
ˆ
CD f (Re, ε )
3
Experimental Data for Drag on
Non-Rotat
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