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%): P b = 200W Power on steep uphills (only ONE!): P b = 500W Power for everything else (~96%): P b = 375W

9. Other parameters … bicycle + rider mass: m = 77 kg air density:  = 1.2 kg/m 3 drag coefficient and cross-sectional area: C D A = 0.25 m 2 (downhill) and C D A = 0.35 m 2 (uphill) coefficient of rolling friction:  r = 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 P b by 5% ~5% faster Decrease P b 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!