aerodynamics by zhangyun

VIEWS: 110 PAGES: 22

									                                                 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          Shear Force
   Density (ρ)
                                                           Velocity Gradient
   Specific weight (γ)
   Specific Gravity (SG)
   Viscosity (μ)           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           V1
                                                       V2
    V1A1=V2A2                                    A2
                                  A1



 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)
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           (a) Normal pressure and friction forces (b) Attached and
                                separated flow around a cylinder (c) Attached flow and
  separation of fluid           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/electrochemist
ry/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


           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 - Position
 Drag Coefficients    Figure from Bicycling Science pg. 188
   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




http://www.lightningbikes.com/sf40blu.jpg   Image from Bicycling Science pg. 191

      Reduce Drag Coefficient up to 50 %
 Bicycle Aerodynamics - Drafting
   Drafting
                                        Traveling close behind
                                         another rider
                                        Broken up air vortices
                                         propel second rider
                                        Offers advantage to
                                         both front and rear
http://pro.corbis.com/images/AX93354
8.jpg?size=67&uid={51D3B79C-B5D0-        rider
4A72-B318-B002D5C78EBC}
                                        Riders in group
                                         expend 40% less
                                         energy than solo
                                         riders
   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

Higher CD occurs at
distances less than the
of the width of the strut
(or rider)



  No advantage
 to side by side
 drafting.
                            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          Fcrosswind
                         CG
                              Fcrosswind
                   CP                             CG

                    stable                 instable




 CP (point of action of aerodynamic forces) should be
 behind the CG for maximum stability.
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.

								
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