Choosing a Bicycle Wheel
Danny McNamara, Gabrielle Vasey &
Megan Chisholm
Math Modeling 2012 – Dr. Ping Wang
Our Goal
• Examine the effect of wind and
the wheel type on the
performance of a professional
cyclist.
Assumptions
• Parameters in each of the studies
looked at are the same.
• All conclusions are for professional
cycling at high speeds.
• Focus on Time trail rules and
regulations.
Computational Fluid
Dynamics (CFD)
• A branch of fluid dynamics that uses numerical
methods and algorithms to analyze problems
involving fluid flows.
• In our case, CFD was used to study the effects of
wind speeds on different types of wheels at various
yaw angles.
Drag Force
• Also called air resistance or fluid resistance.
• Forces acting on a solid object in the direction of
the relative fluid velocity.
• Depends on the velocity of an object.
• F  ½CAv2
o
o
o
o
C = Drag Coefficient
 = Fluid density
A = Surface area perpendicular to flow
v = Relative velocity of object and fluid
Yaw Angle
• Angle off from bike axis of apparent wind, Veffect
• Veffect is a vector sum
Wind Tunnel
• A tool used in aerodynamic research to study the
effects of air moving past solid objects.
• Completely closed tubular passage with the test
object mounted in the middle.
• When air is blown into the test section, the fan
blade turbulence is an issue but when the air is
sucked out, it is not.
• When objects are mounted on a force balance, lift,
drag, lateral forces, yaw, roll, and pitching moments
can be measured.
Wind Tunnel
• http://www.youtube.com/watch?v=ZcvFVPweBDQ
Time Trials
• Individual Time Trial vs
Team Time Trial
• Rolling start
• No drafting
• Equipment
• Difference in course
UCI Regulations
• Wheel diameter: 55-70 cm
• Must be marketable
• “Standard wheel”:
o Rim no more than 2.5cm high
o 16 or more round, flat or oval spokes
o Spoke thickness no more than 2.4mm
• Or on list of approved wheels
• Unknown not allowed
Study of Commercial Bicycle
Wheels using CFD.
• Matthew N. Godo, David Corson & Steve
M. Legensky.
• Used Computational Flud Dynamics (CFD)
methodology to study the performance of
6 wheels.
• Various yaw angles between two different
speeds.
• Results for drag and side forces compare to
those from experimental wind tunnel results.
Study of Commercial Bicycle
Wheels using CFD.
• Six Wheels were
looked at:
o
o
o
o
o
o
Rolf Sestriere
HED H3 TriSpoke
Zipp Sub9 Disc
Zipp 404
Zipp 808
Zipp 1080
Study of Commercial Bicycle
Wheels using CFD.
Study of Commercial Bicycle
Wheels using CFD.
Study of Commercial Bicycle
Wheels using CFD.
racing cycle wheels
• Department of Mechanical Engineering, University
of Cape Town, South Africa
• Wind tunnel tests on a number of racing bicycle
wheels
• Wind velocities 30-60 km/h and yaw angles 0o-30o
• Wheel rotation speed had minimal effect
Force Coefficients
• Ca axial force coefficient =Fa/0.5p(Vwb)2A)
o axial drag force Fa experienced opposite to direction of motion
• Cs side force coefficient =Fs/0.5p(Vwb)2A)
o
side force Fs experienced perpendicular to his direction of motion
Force Coefficients
•
•
•
•
Vwb = velocity of air relative to the bicycle, m/s
F = axial/side force, N
p = air density, kg/m
A = projected area (pi*d/4), m2
Wheels Used
•
Wheels Used
Results
•
• 30km/h:
Results: Ca
o Disc wheel lowest to 8o, highest after 18o
o Standard wheel consistently high
o Other four consistently similar
• 40 km/h:
o Standard always highest
o Standard always highest
o Other four consistently low
• 48 km/h:
Results: Ca
o Disc lowest from 0o-4o, Shamal lowest 6o-14o
o Standard always highest
• 55km/h:
o Similar results to 48km/h
Results
•
• 30 km/h:
Results: Cs
o Standard consistently low
o Disc lowest from 8o-14o, peak low at 8o, hits negative value
o All others linearly increase
• 40 km/h
o Disc peak low at 7o, less negative
o Less spaced than 30 km/h, same patterns
• 48 km/h
Results: Cs
o Disc peak low at 4o, even less negative
o Even less spaced that 40 km/h, same patterns
• 55km/h
o Disc only minimal low peak at 4o
o All but disc almost identical to 48km/h
Interpertation
Ca
Cs
• Yaw angle 3o or less, disc
always best
• Standard almost always
worst
• Shamal best 6o-14o for a
Vwb of 48km/h or 55km/h
• All other cases, Shamal,
Cosmis, Spinergy, or
Trispoke are all very close
• Standard or disc always
best
• As Vwb increases,
standard is better for
more yaw angles
• Only one angle for Vwb
= 55km/h that disc is
better than standard
Interpretations
• Yaw angles below 20 degrees:
o Rear deep rim disc wheel.
• Yaw angles between 20 and 30 degrees:
o Wheel choice depends more on the wind for time trials.
o Stick with deep rim wheel with spokes.
• Yaw angles over 30 degrees:
o Unrealistic in professional cycling.
o For nonprofessionals, use a light weight wheel built of carbon with a deeper rim
than a traditional wheel.
Lance Armstrong
July 11,1999, during the 8th stage of the 86th Tour de
France
Tony Martin
Interesting Facts
•
•
•
Power to weight ratio is best indicator of a good cyclist.
10 best cyclists weight range: 135lbs – 180lbs.
Use of bicycles on urban trips:
o
o
o
•
•
•
•
American’s – 1%
Italy – 5%
Netherlands – 30%
• 7/8 Dutch people over the age of 15 own a bicycle.
Before Babe Ruth joined the Yankees in 1920, cyclists were the
highest paid professional athletes.
Lack of Randomness makes for an easily modeled sport.
Time trial is also referred to as a “Race against the Watch”.
Individual time trials were added to the Olympics in 1996 for both
men and women.
Other Time-Reducing
Equiptment
Aero Equipment
From (Original)
To (New)
Drag Difference
(G)
Time Saved In
40km ITT
(Seconds)
Speed Suit
Road bib and
jersey
Nike Swift suit
(Not standard
skinsuit)
-289
134
Body Position
and Aerobars
Upright, on
bullhorns
Normal tuck on
aerobars
-262
122
Aero Helmet
Road helmet
Aero TT helmet
-144
67
Body Position
Normal tuck
Tuned wind
tunnel tuck
-121
56
Front Wheel at
10-Degree Yaw
3-5 spoke
Deep rim 12
spoke
-90
42
Shoe Covers
No shoe covers
Shoe covers
-65
30
Rear Wheel at 0Degree Yaw
Any full disc
3-spoke
-63
29
Front Wheel at
0-Degree Yaw
24 spoke
aluminum boxsection rim
wheel
5-spoke
-50
23
New Aero Bike
Frame
Standard tubing
TT bike
Aero tubing TT
bike
-36
17
Aero Helmet
Decent aero
helmet
Best aero helmet
-29
13
Ryder Hesjedal
• Canadian professional cyclist
• First Canadian to win a grand tour - Giro d’Italia
• Strength - Time Trials