**Aerodynamics of Cycling** Stephen Kulju http://www.mira.co.uk/Services/images/bike.jpg

**Outline** • Introduction • Basic Fluid Mechanics • Drag and Friction • Bicycle Aerodynamics • 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 • Due to the fluidity of air. • Composed of normal (Pressure) force and tangential (frictional) force. • Extremely geometry dependent.

**Fluid Mechanics & Dynamics** • 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) • Viscosity (μ) Shear Force Velocity Gradient Velocity of fluid is zero along surface due to friction . (No slip condition)

**Fluid Mechanics & Dynamics** • Streamline • Lines tangent to the velocity vector throughout the flow field Figure from Fundamentals of Fluid Mechanics pg. 97

**Fluid Mechanics & Dynamics** • Stagnation Point • Largest pressure obtainable along a streamline • Velocity is zero Figure from Fundamentals of Fluid Mechanics pg. 108

**Fluid Mechanics & Dynamics ** • Air as a fluid • 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 http://pico1.e.ft.fontys.nl/aot/newton.jpg

**Fluid Mechanics & Dynamics** • Continuity equation • Mass is conserved • V1A1=V2A2 • Bernoulli equation • P1+1/2 ρV12 +γz1 = P2+1/2 ρV22 +γz2 • Relationship between Pressure, Velocity, and Elevation • Based on conservation of linear momentum (Kinetic Energy) V2 V1 A2 A1

**Aerodynamics** • Two effective forces • Pressure • Friction • For 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

**Aerodynamics ** • Drag 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 • Drag • The force in the direction of relative flow. • Propulsion power to overcome drag: • Ŵ = drag force x relative vehicle velocity

**Aerodynamics** Drag coefficients of various geometries Figure from Bicycling Science pg. 191

**Aerodynamics** • Laminar Flow • Layers of fluid flow slide smoothly over one another • Turbulent 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 Aerodynamics** • Bicycle is responsible for 20-35% of drag. • Loose Clothing increases drag by up to 30%.

**Bicycle Aerodynamics - Position** • Positions • Goals: reduce frontal area & reduce drag coefficient

**Bicycle Aerodynamics - Position** Figure from Bicycling Science pg. 188 • Drag Coefficients

**Bicycle Aerodynamics - Position** • Rearward 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 Aerodynamics ** • Fairings • Reduce Drag Coefficient up to 50 % http://www.lightningbikes.com/sf40blu.jpg Image from Bicycling Science pg. 191

**Bicycle Aerodynamics - Drafting** • Drafting • 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 http://pro.corbis.com/images/AX933548.jpg?size=67&uid={51D3B79C-B5D0-4A72-B318-B002D5C78EBC}

**Bicycle Aerodynamics - Drafting** • Drafting Negative drag propels object forward at close distances(~ 1 diameter and under) Image from Bicycling Science pg. 199

**Bicycle Aerodynamics - Drafting** • Drafting • No advantage to side by side drafting. Higher CD occurs at distances less than the of the width of the strut (or rider) Aerodynamic interference of two side by side struts. Image from Bicycling Science pg. 201

**Bicycle Aerodynamics -Crosswinds** • Aerodynamic drag is usually calculated assuming calm weather • Crosswinds create aerodynamic moments and instability. • CP (point of action of aerodynamic forces) should be behind the CG for maximum stability. Fcrosswind CP CG Fcrosswind CP CG 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.