We modeled the 2003 Tour de France bicycle race using stage profile data for which elevations at various points in each stage are known. Each stage is modeled as a series of inclined planes. We accounted for the forces on a bicycle-rider combination such as aerodynamic drag and rolling resistance and calculated the winning stage times for an assumed set of bicycle and rider parameters. The calculated total race time differed from the sum of all actual winning stage times by only 0.03%.

1.
J.
Fajans
, “
Steering in bicycles and motorcycles
,”
Am. J. Phys.
68
,
654
659
(
2000
).
2.
Ricardo E.
de Souza
and
Giovani L.
Vasconcelos
, “
Visual appearance of a rolling bicycle wheel
,”
Am. J. Phys.
64
,
896
897
(
1996
).
3.
Cliff
Frohlich
, “
Effect of wind and altitude on record performances in foot races, pole vault, and long jump
,”
Am. J. Phys.
53
,
726
730
(
1985
), Sec. V.
4.
J.
Lowell
and
H. D.
McKell
, “
The stability of bicycles
,”
Am. J. Phys.
50
,
1106
1112
(
1982
).
5.
Daniel
Kirshner
, “
Some nonexplanations of bicycle stability
,”
Am. J. Phys.
48
,
36
38
(
1980
).
6.
J.
Liesegang
and
A. R.
Lee
, “
Dynamics of a bicycle: Nongyroscopic aspects
,”
Am. J. Phys.
46
,
130
132
(
1978
).
7.
William M.
Wehrbein
, “
Collecting and recording bicycle speed data by CBL
,”
Phys. Teach.
41
,
243
244
(
2003
).
8.
Manfred
Euler
,
Gert
Braune
,
Soenke
Schaal
, and
Dean
Zollman
, “
Collecting kinematics data over long time intervals
,”
Phys. Teach.
38
,
434
436
(
2000
).
9.
Chris
Waltham
and
Brian
Copeland
, “
Power requirements for rollerbladding and bicycling
,”
Phys. Teach.
37
,
379
382
(
1999
).
10.
Nathan H.
Rich
, “
Bicycle computers and kinematics
,”
Phys. Teach.
27
,
627
628
(
1989
).
11.
Robert G.
Hunt
, “
Bicycles in the physics lab
,”
Phys. Teach.
27
,
160
165
(
1989
).
12.
Nicholas J. Giordano, Computational Physics (Prentice Hall, New Jersey, 1997).
13.
The Tour de France Web site is 〈www.letour.fr〉. (We used the English version.)
14.
Private communication with Jeff Jones, editor of 〈cyclingnews.com〉.
15.
David Halliday, Robert Resnick, and Jearl Walker, Fundamentals of Physics—Extended (Wiley, New York, 2001), p. 57.
16.
Jerry B. Marion and Stephen T. Thornton, Classical Dynamics of Particles and Systems (Harcourt, New York, 1995), p. 59.
17.
Chester R. Kyle, “Selecting cycling equipment” in High-Tech Cycling, 2nd ed., edited by Edmund R. Burke (Human Kinetics, Champaign, IL, 2003), pp. 1–48.
18.
Eugene Hecht, Physics, 2nd ed. (Brooks/Cole, Pacific Grove, CA, 1998), p. 113.
19.
Chester R. Kyle, “Mechanical factors affecting the speed of a cycle” in Science of Cycling, edited by Edmund R. Burke (Human Kinetics, Champaign, IL, 1986), pp. 123–136.
20.
P. E.
DiPrampero
,
G.
Cortili
,
P.
Mognoni
, and
F.
Saibene
, “
Equations of motion of a cyclist
,”
J. Appl. Physiol.: Respir., Environ. Exercise Physiol.
47
,
201
206
(
1979
).
21.
Frank Rowland Whitt and David Gordon Wilson, Bicycling Science (MIT Press, Cambridge, MA, 1982).
22.
Obviously, if a biker is not outputting enough power on a steep incline, the biker is not exerting enough force. For too small a power in our model, the biker’s velocity can switch directions, which means the biker is no longer going up the hill.
23.
Jeffrey P. Broker, “Cycling power: Road and mountain” in High-Tech Cycling, 2nd ed., edited by Edmund R. Burke (Human Kinetics, Champaign, IL, 2003), pp. 147–174.
24.
A.
Lucia
,
J.
Hoyos
, and
J. L.
Chicharro
, “
Physiology of professional road racing
,”
Med. Sci. Sports Exercise
31
,
325
337
(
2001
).
25.
Tao Pang, An Introduction to Computational Physics (Cambridge University Press, UK, 1997), pp. 5 and 57.
26.
J. Hagberg and S. McCole, “Energy expenditure during cycling” in High-Tech Cycling, 2nd ed., edited by Edmund R. Burke (Human Kinetics, Champaign, IL, 1996), pp. 167–184.
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