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

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)

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

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

Reality to Stage Profile to Model Turn Stage Profile into Sequence of Inclined Planes

Free-Body Diagram on Inclined Plane

Forces on Bicycle-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)

Model Parameters Bicycle-Rider Mass: m = 77 kg Coefficient of Rolling Friction: μ r = 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) (ample literature to support above values!)

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

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

Angle Data for 2004 Tour de France

Model Results for 2004 Tour de France

Apply 2004 Model to 2003 Tour de France