Aerodynamics of Cycling_Kulju

Stephen Kulju

http://www.mira.co.uk/Services/images/bike.jpg

OutlineIntroductionBasic Fluid MechanicsDrag and FrictionBicycle Aerodynamics

PositionVelocity & Power OutputReducing DragDraftingCrosswind effects

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.

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)

Fluid Mechanics & DynamicsStreamline

Lines tangent to the velocity vector throughout the flow field

Figure from Fundamentals of Fluid Mechanics pg. 97

Fluid Mechanics & DynamicsStagnation Point

Largest pressure obtainable along a streamlineVelocity is zero

Figure from Fundamentals of Fluid Mechanics pg. 108

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

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)

A1A2

V1V2

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

AerodynamicsDrag Coefficient

CD = drag/(area x dynamic pressure)

Dynamic Pressure can be approximated for speeds under 100 mi/h as:Dynamic pressure = ρV2/2gc

gc = 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

Aerodynamics

Drag coefficients of various geometriesFigure from Bicycling Science pg. 191

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

Bicycle AerodynamicsBicycle is responsible for 20-35% of drag.Loose Clothing increases drag by up to 30%.

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 W

Drops .88 .36 m2 .32 m2 176 W

Bicycle Aerodynamics - PositionDrag Coefficients Figure from Bicycling Science

pg. 188

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

Bicycle AerodynamicsFairings

Reduce Drag Coefficient up to 50 %http://www.lightningbikes.com/sf40blu.jpg

Image from Bicycling Science pg. 191

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

Bicycle Aerodynamics - DraftingDrafting

Negative drag propels object forward at close distances(~ 1 diameter and under)

Image from Bicycling Science pg. 199

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)

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

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.