Model of the 2003 Tour de

France( coming soon to AJP! )

Benjamin Lee Hannas* and John Eric GoffLynchburg College, Lynchburg VA 24501

*Now at N.C. State University (applied mathematics graduate student)

Project beginnings …•Computational Physics Course (Spring 2003)•Course textbook – Giordano (some elementary discussions of modeling bicycle motion)

Student project …•Ben Hannas modeled two stages of 2001 Tour de France for course project•Used profile data found on internet•Good results!! (~10%)•Goal: SIMPLE MODEL

Profile data …

Stage 15 of 2003 Tour de France(www.letour.fr)

Incline-plane model …

Stage 15 of 2003 Tour de France

Free-body diagram …

Forces …

• Two resistive forces make

• Air drag:

• Rolling friction:

RF

2

2

1AvCF DD

Nrr FF

Rider’s power input …

vPF bb /

•Power on steep downhills (~4%): Pb = 200W

•Power on steep uphills (only ONE!): Pb = 500W

•Power for everything else (~96%): Pb = 375W

Other parameters …• bicycle + rider mass: m = 77 kg

• air density: = 1.2 kg/m3

• drag coefficient and cross-sectional area: CDA = 0.25 m2 (downhill) and CDA = 0.35 m2 (uphill)

• coefficient of rolling friction: r = 0.003

Velocity profile for stage 15 …

Use only terminal speeds as a check!

Results …

Model sensitivity …

• Model most sensitive to power

• Increase Pb by 5% ~5% faster

• Decrease Pb by 5% ~13% slower

Biker suffers on steep climbs!

• Model not very sensitive to 200W for steep downhills

2vFD

Model improvements …

• Rider-specific parameters

• Wind:

• Account for food and restroom breaks, both of which can take place while the biker is in motion!

• All lead to loss of simplicity!

22 )( wvvv

Student projects …•Long-distance automobile or dog-sled races!•Future Tour de France races!•Individual bikers!