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Three-Year Study of Tour de France Modeling

Three-Year Study of Tour de France Modeling. John Eric Goff Lynchburg College. CS-AAPT Fall 2005 – American Center for Physics College Park, MD. November 5, 2005. History of Research.

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Three-Year Study of Tour de France Modeling

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  1. Three-Year Study of Tour de France Modeling John Eric Goff Lynchburg College CS-AAPT Fall 2005 – American Center for Physics College Park, MD November 5, 2005

  2. History of Research • Ben Hannas (LC ’03) – Computational Physics Course Project (Spring ’03) • Ideas from Giordano’s Computational Physics • Ben Modeled Two Stages of 2001 Tour de France for Project • After May ’03 Graduation, Ben and I Modeled Entire 2003 Tour de France • American Journal of Physics (May 2004) • Ben and I Modeled Entire 2004 Tour de France • European Journal of Physics (February 2005) • Contacted by Richmond Times-Dispatch and Asked to Model 2005 Tour de France

  3. Ben’s Seminal Idea • Get stage profiles from www.letour.fr . • Convert each profile into a series of inclined planes. Stage 16 of 2005 Tour de France

  4. Forces on Bike-Rider Combo • Weight: W = mg • Normal Force: FN = mg cosθ • Biker’s Force: Fb = Pb/v • Retarding Forces: FR = FD + Fr FD = CDAv2/2 (Drag Force) Fr = μrFN (Rolling Friction)

  5. Physicists LOVE the Inclined Plane!

  6. Parameters • Bike-Rider Mass: m = 77 kg • Coefficient of Rolling Friction: μr = 0.003 • Air Density:  = 1.2 kg/m3 • Drag Coefficient ● Cross-Sectional Area: CDA = 0.35 m2 (θ ≥ 0, uphill) CDA = 0.25 m2 (θ < 0, downhill)

  7. Biker’s Power Output • 2003 Tour de France

  8. Biker’s Power Output • 2004 Tour de France

  9. Other Changes for 2004 • Short Stages – 0, 4, 16, and 19 • Reduce CDA by 20% for Drafting and Sleek Clothing (except stage 16)

  10. Model Successes

  11. Angles for 2005 Tour de France

  12. Biker’s Power Output • 2005 Tour de France (Not much change!)

  13. On to 2005’s Tour de France We are too slow!!!

  14. What Happened?!? • Tailwinds permeated the first week of the race. • Wind speeds measured in the 10-20 mph (16-32 km/hr) range. • Easy way to account for tailwind – increase power input. • How much???

  15. Add Power from Tailwind • Terminal speed reached when forward force matches sum of retarding forces. • Tailwind means biker’s speed relative to air goes down. • Only considering the dominate air drag: Pb~ vt3 • Add about 50W to main 325W power.

  16. Results

  17. Results (continued)

  18. Lance Armstrong • 7th Straight Tour de France Win! • Winning Time: 86h 15’ 02” • 3593-Kilometer Race: vave ≈ 11.6 m/s ≈ 41.7 km/hr ≈ 25.9 mph vmax ≈ 15.9 m/s ≈ 57.2 km/hr ≈ 35.5 mph (average for stage 4)

  19. Other Tour Races in 2004(Use 2004 Model) Thanks Brett Taylor at Radford University!

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