1. Choosing a Bicycle Wheel
Danny McNamara, Gabrielle Vasey & Megan Chisholm
Math Modeling 2012 – Dr. Ping Wang

2. Our Goal
Examine the effect of wind and the wheel type on the performance of a professional cyclist.

3. 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.

4. 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.

5. 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
C = Drag Coefficient
 = Fluid density
A = Surface area perpendicular to flow
v = Relative velocity of object and fluid

6. Yaw Angle Angle off from bike axis of apparent wind, Veffect
Veffect is a vector sum

7. 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.

8. Wind Tunnel

9. Time Trials Individual Time Trial vs Team Time Trial Rolling start
No drafting
Equipment
Difference in course

10. UCI Regulations Wheel diameter: 55-70 cm Must be marketable
“Standard wheel”:
Rim no more than 2.5cm high
16 or more round, flat or oval spokes
Spoke thickness no more than 2.4mm
Or on list of approved wheels
Unknown not allowed

11. A Comparative Aerodynamic 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.

12. A Comparative Aerodynamic Study of Commercial Bicycle Wheels using CFD.
Six Wheels were looked at:
Rolf Sestriere
HED H3 TriSpoke
Zipp Sub9 Disc
Zipp 404
Zipp 808
Zipp 1080

13. A Comparative Aerodynamic Study of Commercial Bicycle Wheels using CFD.

14. A Comparative Aerodynamic Study of Commercial Bicycle Wheels using CFD.

15. A Comparative Aerodynamic Study of Commercial Bicycle Wheels using CFD.

16. Aerodynamics of yawed 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 km/h and yaw angles 0o-30o
Wheel rotation speed had minimal effect

17. Force Coefficients Ca axial force coefficient =Fa/0.5p(Vwb)2A)
axial drag force Fa experienced opposite to direction of motion
Cs side force coefficient =Fs/0.5p(Vwb)2A)
side force Fs experienced perpendicular to his direction of motion
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

18. 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

19. Wheels Used

20. Wheels Used

21. Results

22. Results: Ca 30km/h: 40 km/h:
Disc wheel lowest to 8o, highest after 18o
Standard wheel consistently high
Other four consistently similar
40 km/h:
Standard always highest
Other four consistently low

23. Results: Ca 48 km/h: 55km/h:
Disc lowest from 0o-4o, Shamal lowest 6o-14o
Standard always highest
55km/h:
Similar results to 48km/h

24. Results

25. Results: Cs 30 km/h: 40 km/h Standard consistently low
Disc lowest from 8o-14o, peak low at 8o, hits negative value
All others linearly increase
40 km/h
Disc peak low at 7o, less negative
Less spaced than 30 km/h, same patterns

26. Results: Cs 48 km/h 55km/h Disc peak low at 4o, even less negative
Even less spaced that 40 km/h, same patterns
55km/h
Disc only minimal low peak at 4o
All but disc almost identical to 48km/h

27. Interpertation Ca Cs Standard or disc always best
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

33. Interpretations Yaw angles below 20 degrees:
Rear deep rim disc wheel.
Yaw angles between 20 and 30 degrees:
Wheel choice depends more on the wind for time trials.
Stick with deep rim wheel with spokes.
Yaw angles over 30 degrees:
Unrealistic in professional cycling.
For nonprofessionals, use a light weight wheel built of carbon with a deeper rim than a traditional wheel.

34. Lance Armstrong
July 11,1999, during the 8th stage of the 86th Tour de France

35. Tony Martin

36. 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:
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.

37. 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 0-Degree Yaw
Any full disc
3-spoke
-63 29
Front Wheel at 0-Degree Yaw
24 spoke aluminum box-section rim wheel
5-spoke
-50 23
New Aero Bike Frame
Standard tubing TT bike
Aero tubing TT bike
-36 17
Decent aero helmet
Best aero helmet
-29 13

38. Ryder Hesjedal Canadian professional cyclist
First Canadian to win a grand tour - Giro d’Italia
Strength - Time Trials