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