Check on Model Robustness: 2004 Tour de France

Check on Model Robustness: 2004

Tour de FranceJohn 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 www.letour.fr

• Turn Stage Profiles Into Sequence of Inclined Planes

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!

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: FN = mg cosθ•Biker’s Force: Fb = Pb/v•Retarding Forces: FR = FD + Fr

FD = CDAv2/2 (Drag Force) Fr = μrFN (Rolling Friction)

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 (θ ≥ 0, uphill) CDA = 0.25 m2 (θ < 0, downhill)

(ample literature to support above values!)

Biker’s Power Output• Long Stages (2003 Model – 375W in

place of 325W and 425W)

)09.0(500)09.0062.0(425

)062.0055.0(325)055.0(200

WWWW

Pb

Biker’s 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)

)09.0(500)09.0055.0(475

)055.0(200

WWW

Pb

Angle Data for 2004 Tour de France

Angle Data for 2004 Tour de France

Model Results for 2004 Tour de France

Acrobat Document

Apply 2004 Model to 2003 Tour de France

Acrobat Document