An Aerodynamic Study of Bicycle Wheel Performance Using CFD

An Aerodynamic Study of Bicycle Wheel Performance using CFD

Matthew N. Godo, Ph.D. FieldView Product Manager

 Wind Tunnel testing used extensively in cycling for over 20 years  Typical test for Zipp, 85h at $850/h, conducted 3 or 4 times per year

 Advertiseme Benefits to cyclists from Wind Tunnels nt ca 2007  Improved knowledge of positioning  Significant improvement in the performance of equipment (helmets, clothing, frames, wheels, spokes,…)  Enhanced awareness of the role of aerodynamics in the community

 Current status  Still considerable variation in design  UCI rule changes & enforcement can be rapid & unpredictable  Wind Tunnel reaching its limit today  Interpretation of results „controversial‟

How much does it matter? 2

3 3.0%

4 From Greenwell et.al. 5

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 Wheel drag is responsible for 10% to i s

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15% of total aerodynamic drag i 9

n i F 10  Rider makes up the majority of overall 11

aerodynamic drag 12

 Improvements in wheel design can 14 reduce drag between wheels by as 15 0 1 2 3 4 5 Percentage Time Difference much as 25% IronManTM Lake Placid Triathlon 2008 Male 45-49 Age Group Q 1 2  Overall reduction in drag can be on the Q 3.3% Q 3 order of 2% to 3% Q 4 Q 5

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In the ‟05 Tour of Germany, Ullrich‟s Xentis front wheel

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was mistakenly fitted backward for the Stage 8 time n i trial. Although he won the trial, he finished second F 10 overall to Levi Leipheimer, behind by a final margin of 11

31 seconds. If the wheel had been the right way round, 12

might Ullrich have won stage 8 by a greater margin, 13 perhaps enough to win the race overall? Wheel 14 manufacturer Xentis says „Yes!‟. 15

0 1 2 3 4 5 6 7 8 Percentage Time Difference

] Wheel onlyWheel m 8

c Zipp 404

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 Wheels* (700c) t p

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 Zipp 404 R 4  Zipp 1080 3 2 1  Forks 0  Reynolds Full Carbon Aero  Blackwell Time Bandit (slotted)

 Frame (partial) Carbon Reynolds  Based on 2005 Razor Elite

 RANS calculations run for  2 speeds (20mph & 30mph)  10 yaw angles (0o thru 20o)

 120 total cases Bandit Blackwell

*Continental Podium 19mm tubular tire

 STARCCM+ v4.06.011

 Meshing models  Polyhedral Mesh, prism layers

 Physics models  Steady, incompressible, segregated solver  RANS Turbulence  K-Omega model  SST Mentor  All defaults applied  Low Re Damping Modification turned ON  Force Report convergence after 600 iter  Low y+ wall treatment

 FieldView 12.2.1 (Intelligent Light)  FV-UNS exported from STARCCM+  Parallel export compatible with FV

 Surround Boundary  Set upstream flow speed  20mph or 30mph  Set yaw angle for specific case  0o thru 20o  Ground Plane  Set forward axial speed  20mph or 30mph  Matches constant direction of travel of bicycle  Wheel, hub & spokes  Set rotational speed to match forward axial speed  Wheel contact  Rotational speed matches ground plane axial velocity

 Nonconformal interface applied to inner region of wheel  Permits accurate ground contact  Allows for easy spoke count changes  For steady case,  Use Moving Reference Frame  For unsteady case,  Use rotational mesh motion

 Fork & Frame  No-slip surface in relative reference frame

For the wheel… Resolved Forces Top View Turning Moment Wind Velocity  Drag, Vertical & Side (effective)  Pressure & Viscous Axial Drag Force

 Wheel components Bike Velocity Side (Lift) Force (relative)  Circumferential variations Turning Moments

 Based on side forces Vertical Force Side View For the fork… Wind Velocity (effective) Resolved Forces Axial Drag Force  Drag & Side

Showing Flow Field Features Direction of Wheel Rotation

 Use streamlines

Wind Tunnel Protocols vary widely!  “Wheel-only” studies mount wheel to floor with upright supports  Tests start at 30 degrees yaw, angle gradually reduced  Rotational wheel speed independently adjusted at each yaw  Ground plane boundary condition differs (wind tunnel floor doesn‟t move)  Results are often „normalized‟

Drag Force vs. Yaw Angle Drag Force vs. Yaw Angle 1.5 1.5

30mph, Blackwell Fork 1.2 30mph, Reynolds Fork 1.2 30mph, wheel only 20mph, Blackwell Fork 20mph, Reynolds Fork 0.9 0.9 20mph, wheel only 0.6 0.6

0.6 0.6

0.5 0.5

] ]

0.3 0.3

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e 0.4 0.4

r o o 0 0

30mph, Blackwell Fork

30mph, Reynolds Fork g

g 0.3 0.3 a

a 30mph, wheel only r

r 20mph, Blackwell Fork

D D 20mph, Reynolds Fork 0.2 0.2 20mph, wheel only

0.1 0.1 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Yaw Angle [degrees] Yaw Angle [degrees]

 Drag force varies significantly with yaw angle  10 to 15 degrees yaw is considered a design target by manufacturers  Significant differences seen comparing wheel/fork combinations  Blackwell slotted fork w/ Zipp 1080 shows considerable promise

Circumferential Variation, Drag Force Zipp 404 Zipp

D i r e c t i o n o f F l o w Zipp 1080 Zipp

No Fork Reynolds Carbon Blackwell Bandit

Side Force vs. Yaw Angle Side Force vs. Yaw Angle 6 8 20 30mph, Blackwell Fork 30mph, Reynolds Fork 30mph, wheel only 20mph, Blackwell Fork 20mph, Reynolds Fork 12 16 20mph, wheel only 6

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4 r

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i S 2 S

4 2 30mph, Blackwell Fork 30mph, Reynolds Fork 4 30mph, wheel only 20mph, Blackwell Fork 20mph, Reynolds Fork 20mph, wheel only

0 0 0 0 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Yaw Angle [degrees] Yaw Angle [degrees]

 Side force varies significantly with yaw angle  Dependence on yaw from wind tunnel studies is generally linear  Fork has only small influence on wheel side force  Note: Side force scales are different for each wheel

Turning Moment vs. Yaw Angle Turning Moment vs. Yaw Angle 0.35 30mph, Blackwell Fork 0 30mph, Reynolds Fork 30mph, wheel only 0.3 20mph, Blackwell Fork 20mph, Reynolds Fork 20mph, wheel only -0.2

0.25

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0.15 e

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M M 0.1 30mph, Blackwell Fork 30mph, Reynolds Fork 30mph, wheel only 0.05 -0.8 20mph, Blackwell Fork 20mph, Reynolds Fork 20mph, wheel only 0

-1 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Yaw Angle [degrees] Yaw Angle [degrees]

 Turning moment varies significantly with yaw angle  Direction of moment for Zipp 404 acts opposite to Zipp 1080  Significant differences seen comparing wheel/fork combinations  Both forks dampen moment on Zipp 404,  Blackwell fork amplifies moment on Zipp 1080

Circumferential Variation, Side Force Zipp 404 Zipp

D i r e c t i o n o f F l o w Zipp 1080 Zipp

No Fork Reynolds Carbon Blackwell Bandit

Zipp 404 Suction Side Zipp 1080

 At low yaw,  Strong recirculation observed at top, outer edge of wheel  Weaker recirculation observed at bottom half, inner edge of wheel  As yaw angle increases,  Top recirculation extends along front of wheel, combines with inner wheel recirculation

Zipp 404 Pressure Side Zipp 1080

 At low yaw,  Backflow zone is created between fork and top of wheel  As yaw angle increases,  Inner wheel recirculation being driven from pressure side

Drag Force vs Yaw Angle Drag Force vs Yaw Angle

1 1

0.9 0.9

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N N

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0.4 0.4

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r r

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F F

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r 0.3 0.3

D D 30mph, Blackwell 30mph, Blackwell 20mph, Blackwell 20mph, Blackwell 30mph, Reynolds 30mph, Reynolds 0.2 20mph, Reynolds 0.2 20mph, Reynolds

0.1 0.1 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Yaw Angle [degrees] Yaw Angle [degrees]

 Significant differences seen between forks  Blackwell Bandit slotted fork has much higher drag force (>2X)  Choice of wheel does not significantly affect fork drag  Dependence on yaw angle is very low

Zipp 404 Zipp 1080

Reynolds Carbon Reynolds Blackwell Bandit Blackwell

Zipp 404 Suction Side Zipp 1080

 Flow is drawn into fork slots for all yaw angles, both wheels  Flow is pulled away from the wheel rim & tire  At higher yaw angles,  Flow gets trapped behind fork  Strong recirculation pulls flow upward

Zipp 404 Pressure Side Zipp 1080

 Flow is drawn into fork slots for all yaw angles, both wheels, AGAIN!  Even on the pressure side, flow is pulled away from the wheel rim & tire  Pressure side flow at high yaw does not predominantly cross the center axis

Zipp 404 Zipp 1080 Production Challenge  18 months from concept to shelf wheel only wheel only  Only a few weeks available to make design changes

Reynolds Reynolds FieldView Automation Methodology Carbon Carbon

 Use FVX high level programming language 20mph  Customizable environment, one-time investment Blackwell Blackwell Bandit Bandit  Run FieldView Parallel  5X speed-up on 8 processor system wheel only wheel only  Operate concurrently using Batch-only licensing  Create spreadsheet-ready files, figures of merit & animations all at the same time Reynolds Reynolds

Carbon Carbon 30mph

Blackwell Blackwell Bandit Bandit

10 yaw angles for each folder, 120 sim files + 120 FV-UNS files ~500 GB (approx 2400 files in total)

45-49M Age Group Eagleman ‘09 Triathlon (World Championship Qualifier)

 Pick target speed (23mph) & wattage (275W) (use data from Cobb et.al. to get total drag)

 Estimate time spent at different yaw angles  Wind (usually relatively) calm  Course is flat

 Use Zipp404/Blackwell combination to obtain baseline drag  Linear interpolation 20mph & 30mph

 Exchange front wheel & fork  Calculate wheel drag for yaw angles  Add to baseline drag  Recalculate speed, same wattage  Compare seconds saved

 Examine transient effects  Shedding frequency  Force fluctuations

 Wheel/Component interactions  Front fork can choke flow  Calipers can cause significant disruption  Effect of downtube position relative to wheel/faired to wheel unknown

 Automate postprocessing  Cheaper compute  Faster solvers  More & more data  Transient will add to this! “Rarely can one‟s bike set-up compensate as profoundly as improving the human on it.” Maffetone, P., Inside Triathlon, 1995, 10(3), p 20.