Choosing a Bicycle Wheel

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 • http://www.youtube.com/watch?v=ZcvFVPweBDQ

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 • ZippSub9 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 30-60 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

18. Force Coefficients • Vwb= velocity of air relative to the bicycle, m/s • F = axial/side force, N • p = airdensity, kg/m • A = projected area (pi*d/4), m2

19. Wheels Used

20. Wheels Used

21. Results

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

23. Results: Ca • 48 km/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: • 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 • 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 Yaw angle 3o or less, disc always best Standard almost always worst Shamalbest 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

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