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Model of the 2003 Tour de France ( coming soon to AJP! )

Model of the 2003 Tour de France ( coming soon to AJP! ). Benjamin Lee Hannas * and John Eric Goff Lynchburg College , Lynchburg VA 24501 * Now at N.C. State University (applied mathematics graduate student). Project beginnings …. Computational Physics Course (Spring 2003)

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Model of the 2003 Tour de France ( coming soon to AJP! )

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  1. Model of the 2003 Tour de France( coming soon to AJP! ) Benjamin Lee Hannas* and John Eric Goff Lynchburg College, Lynchburg VA 24501 *Now at N.C. State University (applied mathematics graduate student)

  2. Project beginnings … • Computational Physics Course (Spring 2003) • Course textbook – Giordano (some elementary discussions of modeling bicycle motion)

  3. Student project … • Ben Hannas modeled two stages of 2001 Tour de France for course project • Used profile data found on internet • Good results!! (~10%) • Goal: SIMPLE MODEL

  4. Profile data … Stage 15 of 2003 Tour de France (www.letour.fr)

  5. Incline-plane model … Stage 15 of 2003 Tour de France

  6. Free-body diagram …

  7. Forces … • Two resistive forces make • Air drag: • Rolling friction:

  8. Rider’s power input … • Power on steep downhills (~4%): Pb = 200W • Power on steep uphills (only ONE!): Pb = 500W • Power for everything else (~96%): Pb = 375W

  9. Other parameters … • bicycle + rider mass: m = 77 kg • air density: r = 1.2 kg/m3 • drag coefficient and cross-sectional area: CDA = 0.25 m2 (downhill) and CDA = 0.35 m2 (uphill) • coefficient of rolling friction: mr = 0.003

  10. Velocity profile for stage 15 … Use only terminal speeds as a check!

  11. Results …

  12. Model sensitivity … • Model most sensitive to power • Increase Pb by 5% ~5% faster • Decrease Pb by 5% ~13% slower Biker suffers on steep climbs! • Model not very sensitive to 200W for steep downhills

  13. Model improvements … • Rider-specific parameters • Wind: • Account for food and restroom breaks, both of which can take place while the biker is in motion! • All lead to loss of simplicity!

  14. Student projects … • Long-distance automobile or dog-sled races! • Future Tour de France races! • Individual bikers!

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