Check on Model Robustness: 2004 Tour de France - PowerPoint PPT Presentation

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Check on Model Robustness: 2004 Tour de France

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  1. Check on Model Robustness: 2004 Tour de France John Eric Goff Lynchburg College (Collaborator: Benjamin Lee Hannas North Carolina State University)

  2. Research Background • 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)

  3. Idea Behind Model • 21 Stage Profiles (Prolog + 20 Regular Stages) on Tour de France Web Site www.letour.fr • Turn Stage Profiles Into Sequence of Inclined Planes

  4. Idea Visualization • Example – Stage 16 • 21 Hairpin Turns Through French Alps • Lance Armstrong Won Stage in 39’ 41” • Second Place – More Than ONE MINUTE SLOWER!

  5. Reality to Stage Profile to Model • Turn Stage Profile into Sequence of Inclined Planes

  6. Free-Body Diagram on Inclined Plane

  7. Forces on Bicycle-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)

  8. Model Parameters • Bicycle-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) (ample literature to support above values!)

  9. Biker’s Power Output • Long Stages (2003 Model – 375W in place of 325W and 425W)

  10. Biker’s Power Output • Short Stages – 0, 4, 16, and 19 (new for 2004 model!) • Reduce CDA by 20% for Drafting and Sleek Clothing (except stage 16)

  11. Angle Data for 2004 Tour de France

  12. Angle Data for 2004 Tour de France

  13. Model Results for 2004 Tour de France

  14. Apply 2004 Model to 2003 Tour de France