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.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: F N = mg cosθ Biker’s Force: F b = P b /v Retarding Forces: F R = F D + F r F D = C D  Av 2 /2 (Drag Force) F r = μ r F N (Rolling Friction)

5. Physicists LOVE the Inclined Plane!

6. Parameters Bike-Rider Mass: m = 77 kg Coefficient of Rolling Friction: μ r = 0.003 Air Density:  = 1.2 kg/m 3 Drag Coefficient ● Cross-Sectional Area: C D A = 0.35 m 2 ( θ ≥ 0, uphill) C D A = 0.25 m 2 ( 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 C D A by 20% for Drafting and Sleek Clothing (except stage 16)

10. Model Successes ActualModelDifference% 2003 82h 33’ 53”82h 32’ 37”- 01’ 16”- 0.03% 2004 82h 47’ 07”82h 44’ 38”- 02’ 29”- 0.05% 2003 (2004 model) 82h 33’ 53”84h 01’ 34”1h 27’ 41”1.77%

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 StageActualModelDifference% 1 0h 20’ 51”0h 21’ 59”0h 01’ 08”5.44% 2 3h 51’ 31”4h 16’ 51”0h 25’ 20”10.94% 3 4h 36’ 09”4h 57’ 23”0h 21’ 14”7.69% 4 1h 10’ 39”1h 18’ 23”0h 07’ 44”10.95% 5 3h 46’ 00”4h 18’ 31”0h 32’ 31”14.39% 6 4h 12’ 52”4h 45’ 29”0h 32’ 37”12.90% 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: P b ~ v t 3 Add about 50W to main 325W power.

16. StageActualModelDifference% 1 0h 20’ 51”0h 21’ 59”0h 01’ 08”5.44% 2 3h 51’ 31”4h 04’ 05”0h 12’ 34”5.43% 3 4h 36’ 09”4h 42’ 43”0h 06’ 34”2.38% 4 1h 10’ 39”1h 18’ 23”0h 07’ 44”10.95% 5 3h 46’ 00”4h 05’ 43”0h 19’ 43”8.72% 6 4h 12’ 52”4h 30’ 49”0h 17’ 57”7.10% 7 5h 03’ 45”5h 04’ 44”0h 00’ 59”0.32% 8 5h 03’ 54”5h 21’ 13”0h 17’ 19”5.70% 9 4h 08’ 20”4h 00’ 41”- 0h 07’ 39”- 3.08% 10 4h 50’ 35”5h 01’ 39”0h 11’ 04”3.81% 11 4h 47’ 38”4h 26’ 26”- 0h 21’ 12”- 7.37% Results

17. StageActualModelDifference% 12 4h 20’ 06”4h 12’ 43”- 0h 07’ 23”- 2.84% 13 3h 43’ 14”3h 55’ 34”0h 12’ 20”5.52% 14 5h 43’ 43”5h 37’ 48”- 0h 05’ 55”- 1.72% 15 6h 06’ 38”5h 34’ 42”- 0h 31’ 56”- 8.71% 16 4h 38’ 40”4h 39’ 00”0h 00’ 20”0.12% 17 5h 41’ 19”5h 22’ 59”- 0h 18’ 20”- 5.37% 18 4h 37’ 36”4h 36’ 08”- 0h 01’ 28”- 0.53% 19 3h 33’ 04”3h 37’ 44”0h 04’ 40”2.19% 20 1h 11’ 46”1h 06’ 06”- 0h 05’ 40”- 7.90% 21 3h 40’ 57”3h 08’ 13”- 0h 32’ 44”- 14.81% TOTAL 85h 09’ 17”84h 49’ 22”- 0h 19’ 55”- 0.40% Results (continued)

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

19. Other Tour Races in 2004 (Use 2004 Model) RaceActualModelDifference% Giro (stage 1) 3h 41’ 56”3h 30’ 21”0h 11’ 35”- 5.22% Paris- Tours (stage 3) 5h 33’ 03”5h 49’ 10”0h 16’ 07”4.84% Liege- Bastogne- Liege (stage 2) 6h 20’ 09”6h 10’ 52”- 0h 09’ 17”- 2.44% Thanks Brett Taylor at Radford University!