# aerodynamics by zhangyun

VIEWS: 110 PAGES: 22

• pg 1
```									                                                 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)
 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
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
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)

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.

```
To top