check on model robustness: 2004 tour de france
DESCRIPTION
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) - PowerPoint PPT PresentationTRANSCRIPT
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Check on Model Robustness: 2004
Tour de FranceJohn Eric Goff
Lynchburg College
(Collaborator: Benjamin Lee Hannas North Carolina State University)
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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)
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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
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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!
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Reality to Stage Profile to Model• Turn Stage Profile into Sequence of
Inclined Planes
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Free-Body Diagram on Inclined Plane
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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)
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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!)
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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
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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
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Angle Data for 2004 Tour de France
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Angle Data for 2004 Tour de France
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Model Results for 2004 Tour de France
Acrobat Document
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Apply 2004 Model to 2003 Tour de France
Acrobat Document