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 ½CAv2

o C = Drag Coefficient o = Fluid densityo A = Surface area perpendicular to flowo 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 higho 16 or more round, flat or oval spokeso Spoke thickness no more than 2.4mm

• Or on list of approved wheels• Unknown not allowed

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.

A Comparative Aerodynamic Study of Commercial Bicycle Wheels using CFD.

• Six Wheels were looked at:o Rolf Sestriereo HED H3 TriSpokeo Zipp Sub9 Disc o Zipp 404o Zipp 808 o Zipp 1080

A Comparative Aerodynamic Study of Commercial Bicycle Wheels using CFD.

A Comparative Aerodynamic Study of Commercial Bicycle Wheels using CFD.

A Comparative Aerodynamic Study of Commercial Bicycle Wheels using CFD.

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

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•

Results: Ca• 30km/h:

o Disc wheel lowest to 8o, highest after 18o

o Standard wheel consistently higho Other four consistently similar

• 40 km/h:o Standard always highesto Standard always highesto Other four consistently low

Results: Ca• 48 km/h:

o Disc lowest from 0o-4o, Shamal lowest 6o-14o

o Standard always highest• 55km/h:

o Similar results to 48km/h

Results•

Results: Cs• 30 km/h:

o Standard consistently lowo Disc lowest from 8o-14o, peak low at 8o, hits negative valueo All others linearly increase

• 40 km/ho Disc peak low at 7o, less negativeo Less spaced than 30 km/h, same patterns

Results: Cs• 48 km/ho Disc peak low at 4o, even less negativeo Even less spaced that 40 km/h, same patterns

• 55km/ho Disc only minimal low peak at 4o

o All but disc almost identical to 48km/h

InterpertationCa 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 American’s – 1%o Italy – 5%o 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 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

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