Check on Model Robustness: 2004 Tour de France

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 Giordanos 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 cos?
• Bikers 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 (? 0,
  uphill)
• CDA 0.25 m2 (? lt 0,
  downhill)
• (ample literature to support above values!)

9
Bikers Power Output

• Long Stages (2003 Model 375W in place of 325W
  and 425W)

10
Bikers 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