单车空气动力学aerodynamicsofcycling
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Lines tangent to the velocity vector throughout the flow field
Figure from Fundamentals of Fluid Mechanics pg. 97
Fluid Mechanics & Dynamics
Stagnation Point
Due to the fluidity of air. Composed of normal (Pressure) force and tangential
(frictional) force. Extremely geometry dependent.
Fluid Mechanics & Dynamics
Dynamic pressure = ρV2/2gc gc = 32.174 lbm-ft/lbf-s2
Drag
The force in the direction of relative f low.
Propulsion power to overcome drag:
Ŵ = drag force x relative vehicle velocity
Position Velocity & Power Output Reducing Drag Drafting Crosswind effects
Introduction
Aerodynamics, or wind resistance is an everyday experience to bicyclists. At average speeds aerodynamic drag is the largest resistive force aside from the gravity of a large hill
pico1.e.ft.fontys.nl/aot/newton.jpg
Fluid Mechanics & Dynamຫໍສະໝຸດ Baiducs
Continuity equation
Mass is conserved
V1
V1A1=V2A2
A1
V2 A2
Bernoulli equation
P1+1/2 ρV12 +γz1 = P2+1/2 ρV22 +γz2 Relationship between Pressure, Velocity, and Elevation
Shear Force
Velocity Gradient
Viscosity (μ)
Velocity of fluid is zero along surface due to friction . (No slip condition)
Fluid Mechanics & Dynamics
Streamline
Based on conservation of linear momentum (Kinetic Energy)
Aerodynamics
Two effective forces
Pressure
Friction
For cyclists, pressure effect is much larger than friction due to nonstreamlined body.
Fluid – a material that deforms continuously and permanently under the application of a shearing stress.
Important properties
Density (ρ) Specific weight (γ) Specific Gravity (SG)
Figure from Bicycle Science pg. 174
Aerodynamics
Drag Coefficient
CD = drag/(area x dynamic pressure)
Dynamic Pressure can be approximated for speeds under 100 mi/h as:
Streamlined bodies incorporate gradual tapering to minimize pressure effect and separation of fluid
(a) Normal pressure and friction forces (b) Attached and separated flow around a cylinder (c) Attached flow and pressure recovery along a streamlined body
Aerodynamics
Drag coefficients of various geometries
Figure from Bicycling Science pg. 191
Largest pressure obtainable along a streamline Velocity is zero
Figure from Fundamentals of Fluid Mechanics pg. 108
Fluid Mechanics & Dynamics
Air as a fluid
Aerodynamics of Cycling
Stephen Kulju
mira.co.uk/Services/images/bike.jpg
Outline
Introduction Basic Fluid Mechanics Drag and Friction Bicycle Aerodynamics
When studying aerodynamics air is treated as a fluid. Follows all laws of motion and all laws of fluid
mechanics
•ΣF = mâ •Conservation of Energy •Conservation of Mass
Figure from Fundamentals of Fluid Mechanics pg. 97
Fluid Mechanics & Dynamics
Stagnation Point
Due to the fluidity of air. Composed of normal (Pressure) force and tangential
(frictional) force. Extremely geometry dependent.
Fluid Mechanics & Dynamics
Dynamic pressure = ρV2/2gc gc = 32.174 lbm-ft/lbf-s2
Drag
The force in the direction of relative f low.
Propulsion power to overcome drag:
Ŵ = drag force x relative vehicle velocity
Position Velocity & Power Output Reducing Drag Drafting Crosswind effects
Introduction
Aerodynamics, or wind resistance is an everyday experience to bicyclists. At average speeds aerodynamic drag is the largest resistive force aside from the gravity of a large hill
pico1.e.ft.fontys.nl/aot/newton.jpg
Fluid Mechanics & Dynamຫໍສະໝຸດ Baiducs
Continuity equation
Mass is conserved
V1
V1A1=V2A2
A1
V2 A2
Bernoulli equation
P1+1/2 ρV12 +γz1 = P2+1/2 ρV22 +γz2 Relationship between Pressure, Velocity, and Elevation
Shear Force
Velocity Gradient
Viscosity (μ)
Velocity of fluid is zero along surface due to friction . (No slip condition)
Fluid Mechanics & Dynamics
Streamline
Based on conservation of linear momentum (Kinetic Energy)
Aerodynamics
Two effective forces
Pressure
Friction
For cyclists, pressure effect is much larger than friction due to nonstreamlined body.
Fluid – a material that deforms continuously and permanently under the application of a shearing stress.
Important properties
Density (ρ) Specific weight (γ) Specific Gravity (SG)
Figure from Bicycle Science pg. 174
Aerodynamics
Drag Coefficient
CD = drag/(area x dynamic pressure)
Dynamic Pressure can be approximated for speeds under 100 mi/h as:
Streamlined bodies incorporate gradual tapering to minimize pressure effect and separation of fluid
(a) Normal pressure and friction forces (b) Attached and separated flow around a cylinder (c) Attached flow and pressure recovery along a streamlined body
Aerodynamics
Drag coefficients of various geometries
Figure from Bicycling Science pg. 191
Largest pressure obtainable along a streamline Velocity is zero
Figure from Fundamentals of Fluid Mechanics pg. 108
Fluid Mechanics & Dynamics
Air as a fluid
Aerodynamics of Cycling
Stephen Kulju
mira.co.uk/Services/images/bike.jpg
Outline
Introduction Basic Fluid Mechanics Drag and Friction Bicycle Aerodynamics
When studying aerodynamics air is treated as a fluid. Follows all laws of motion and all laws of fluid
mechanics
•ΣF = mâ •Conservation of Energy •Conservation of Mass