aerodynamics
TRANSCRIPT
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Stephen Kulju
http://www.mira.co.uk/Services/images/bike.jpg
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OutlineIntroductionBasic Fluid MechanicsDrag and FrictionBicycle Aerodynamics
PositionVelocity & Power OutputReducing DragDraftingCrosswind effects
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IntroductionAerodynamics, 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 hillDue to the fluidity of air.Composed of normal (Pressure) force and
tangential (frictional) force.Extremely geometry dependent.
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Fluid Mechanics & DynamicsFluid – a material that deforms continuously
and permanently under the application of a shearing stress.
Important propertiesDensity (ρ)Specific weight (γ)Specific Gravity (SG)Viscosity (μ)
Shear Force
Velocity Gradient
Velocity of fluid is zero along surface due to friction . (No slip condition)
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Fluid Mechanics & DynamicsStreamline
Lines tangent to the velocity vector throughout the flow field
Figure from Fundamentals of Fluid Mechanics pg. 97
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Fluid Mechanics & DynamicsStagnation Point
Largest pressure obtainable along a streamlineVelocity is zero
Figure from Fundamentals of Fluid Mechanics pg. 108
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Fluid Mechanics & DynamicsAir as a fluid
When studying aerodynamics air is treated as a fluid.
Follows all laws of motion and all laws of fluid mechanics
http://pico1.e.ft.fontys.nl/aot/newton.jpg
•ΣF = mâ•Conservation of Energy•Conservation of Mass
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Fluid Mechanics & DynamicsContinuity equation
Mass is conservedV1A1=V2A2
Bernoulli equationP1+1/2 ρV1
2 +γz1 = P2+1/2 ρV22 +γz2
Relationship between Pressure, Velocity, and Elevation
Based on conservation of linear momentum (Kinetic Energy)
A1 A2V1 V2
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AerodynamicsTwo effective forces
PressureFrictionFor cyclists, pressure
effect is much larger than friction due to non-streamlined body.
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
Figure from Bicycle Science pg. 174
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AerodynamicsDrag Coefficient
CD = drag/(area x dynamic pressure)Dynamic Pressure can be
approximated for speeds under 100 mi/h as:Dynamic pressure = ρV2/2gcgc = 32.174 lbm-ft/lbf-s2
DragThe force in the direction of relative
flow.Propulsion power to overcome drag:
Ŵ = drag force x relative vehicle velocity
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Aerodynamics
Drag coefficients of various geometriesFigure from Bicycling Science pg. 191
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AerodynamicsLaminar Flow
Layers of fluid flow slide smoothly over one anotherTurbulent Flow
Boundary layer is composed of vortices that increase surface friction.
Common at rear end of non-streamlined vehicle
Turbulent
Laminar
http://www.cheng.cam.ac.uk/research/groups/electrochem/JAVA/electrochemistry/ELEC/l2fig/laminar.gif
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Bicycle AerodynamicsBicycle is responsible for 20-35% of drag.Loose Clothing increases drag by up to 30%.
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Bicycle Aerodynamics - PositionPositions
Goals: reduce frontal area & reduce drag coefficient
CD Frontal Area
CDA Power to Overcome Drag
Tops 1.15 .55 m2 .632 m2
345 W
Hoods 1.0 .40 m2 .40 m2 220 WDrops .88 .36 m2 .32 m2 176 W
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Bicycle Aerodynamics - PositionDrag Coefficients Figure from Bicycling Science
pg. 188
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Bicycle Aerodynamics - PositionRearward vs. Forward position (23.57 – 22.28
N drag)•Forward seat position decreases drag at the expense of comfort and pedaling mechanics.•Union Cycliste Internationale limits the fore-aft position of the saddle requiring it be at least 5 cm behind the bottom bracket spindle•Injury preventive measure
Image and caption from Road Cycling Handbook
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Bicycle AerodynamicsFairings
Reduce Drag Coefficient up to 50 %http://www.lightningbikes.com/sf40blu.jpg
Image from Bicycling Science pg. 191
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Bicycle Aerodynamics - DraftingDrafting
http://pro.corbis.com/images/AX933548.jpg?size=67&uid={51D3B79C-B5D0-4A72-B318-B002D5C78EBC}
Traveling close behind another rider
Broken up air vortices propel second rider
Offers advantage to both front and rear rider
Riders in group expend 40% less energy than solo riders
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Bicycle Aerodynamics - DraftingDrafting
Negative drag propels object forward at close distances(~ 1 diameter and under)
Image from Bicycling Science pg. 199
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Bicycle Aerodynamics - DraftingDrafting
No advantageto side by sidedrafting.
Aerodynamic interference of two side by side struts.Image from Bicycling Science pg. 201
Higher CD occurs at distances less than the of the width of the strut (or rider)
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Bicycle Aerodynamics -CrosswindsAerodynamic drag is usually calculated
assuming calm weatherCrosswinds create aerodynamic moments and
instability.
CP (point of action of aerodynamic forces) should be behind the CG for maximum stability.
Fcrosswind
FcrosswindCG
CGCP
CP
stable instable
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References"Efluids bicycle aerodynamics." EFluids. 04 Apr. 09
<http://www.efluids.com/efluids/pages/bicycle.htm>. Gregor, Robert J. Road Cycling - Handbook of Sports
Medicine and Science. Malden: Oxford, 2000. Munson, Bruce R., Donald F. Young, and Theodore
H. Okiishi. Fundamentals of Fluid Mechanics. 5th ed. Jon Wiley & Sons, 2006.
Tamai, Goro. The Leading Edge - Aerodynamic Design of Ultra-streamlined Land Vehicles. Cambridge: Robert Bentley Publihsers, 1999.
Wilson, David G., and Jim Papadopoulos. Bicycling Science. 3rd ed. MIT P, 2004.