Content uploaded by William Bertucci
Author content
All content in this area was uploaded by William Bertucci
Content may be subject to copyright.
Aerodynamic drag in cycling: methods of assessment
PIERRE DEBRAUX
1
, FREDERIC GRAPPE
2
, ANELIYA V. MANOLOVA
1
,&
WILLIAM BERTUCCI
1
1
LACM-DTI (EA 4302, LRC CEA 05354) UFR STAPS, Universite
´de Champagne-Ardenne,
Reims, France, and
2
De
´partement de Recherche en Pre
´vention, Innovation et Veille Technico-Sportive
(EA 4267 - 2SBP), UFR STAPS, Universite
´de Franche-Comte
´, Besanc¸on, France
(Received 2 October 2010; accepted 25 May 2011)
Abstract
When cycling on level ground at a speed greater than 14 m/s, aerodynamic drag is the most impor tant
resistive force. About 90% of the total mechanical power output is necessary to overcome it.
Aerodynamic drag is mainly affected by the effective frontal area which is the product of the projected
frontal area and the coefficient of drag. The effective frontal area represents the position of the cyclist on
the bicycle and the aerodynamics of the cyclist-bicycle system in this position. In order to optimise
performance, estimation of these parameters is necessary. The aim of this study is to describe and
comment on the methods used during the last 30 years for the evaluation of the effective frontal area
and the projected frontal area in cycling, in both laboratory and actual conditions. Most of the field
methods are not expensive and can be realised with few materials, providing valid results in comparison
with the reference method in aerodynamics, the wind tunnel. Finally, knowledge of these parameters
can be useful in practice or to create theoretical models of cycling performance.
Keywords: Aerodynamic drag, coefficient of drag, cycling, projected frontal area, theoretical model
Introduction
In cycling, among the total resistive forces on level ground, aerodynamic drag is the main
resistance opposed to the motion (Millet & Candau, 2002). At racing speeds greater than
14 m/s, with a classical racing bicycle, aerodynamic drag represents about 90% of the overall
resistive forces (Candau et al., 1999; di Prampero, 2000; Martin et al., 2006; Millet & Candau,
2002). Aerodynamic drag is a major concern of cycling research to enhance performance.
During a cycling race (e.g. a time-trial), the time difference in performance between elite
athletes can be small. The optimisation of aerodynamic drag could be a determinant to
enhance the cyclist’s performance for the same mechanical power output. In order to minimise
this resistance, it is important to know the determinant’s parameters, how to evaluate them,
and what the evolution of these parameters would be as a function of the position of the cyclist
and his or her displacement velocity. The purpose of this review is to present the different field
and laboratory methods available for assessment of aerodynamic drag and its most essential
parameter, the effective frontal area, in order to enhance cycling performance.
ISSN 1476-3141 print/ISSN 1752-6116 online q2011 Taylor & Francis
DOI: 10.1080/14763141.2011.592209
Correspondence: Pierre Debraux, UFR STAPS, Universite
´de Reims Champagne-Ardenne Ba
ˆtiment 25, Chemin des Rouliers,
Campus Moulin de la Housse, BP, 1036 – 51687, Reims Cedex, France, E-mail: pierre.debraux@sci-s port.com
Sports Biomechanics
September 2011; 10(3): 197–218
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
Characteristics of the aerodynamic drag
The major performance parameter in cycling is the displacement velocity of both cyclist and
bicycle (v, in m/s). At constant velocity, the ratio of the mechanical power output generated
by the cyclist (P, in W) to the total resistive forces (R
T
, in N) is given by:
v¼P
RT
ð1Þ
By definition, the power output is the quantity of energy output per unit time. At constant
speed, the mechanical power output can be assumed to be the sum of the energy used to
overcome the total resistive forces (De Groot et al., 1995; di Prampero, 2000). Since
aerodynamic drag is about 90% of the total resistive forces at high speed (.14 m/s), for a
constant power output decreasing aerodynamic drag would result in an increase of the
velocity of the cyclist-bicycle system. In all forms of human-powered locomotion on land,
aerodynamic drag is directly proportional to the combined projected frontal area of the
cyclist and bicycle (A
p
,inm
2
), the drag coefficient (C
D
, dimensionless), air density (
r
,in
kg/m
3
) and the square of the velocity relative to the fluid (v
f
, in m/s). R
D
can be expressed by
(e.g. di Prampero et al., 1979):
RD¼0:5·ApCD·
r
·v2
fð2Þ
For a given velocity, aerodynamic drag is dependent on air density and the effective frontal
area (A
p
C
D
,inm
2
). Air density is directly proportional to the barometric pressure of the fluid
(PB, in mmHg) and inversely proportional to absolute temperature (T, in K) (di Prampero,
1986):
r
¼
r
0·PB
760
·273
T
ð3Þ
Where
r
0
¼1.293 kg/m
3
, the air density at 760 mmHg and 273K. Air density is also
affected by air humidity but this effect is very small and can be neglected (di Prampero,
2000). Moreover, at a given temperature, the barometric pressure of fluid decreases with the
altitude above sea level (Table I). At a temperature of 273 K, the decrease in barometric
pressure of the fluid with altitude (Alt, in km) can be described by (di Prampero, 2000):
PB ¼760·e20:124·Alt ð4Þ
As seen in Table I, for the same parameters, the increase of altitude decreases aerodynamic
drag by about 24% from 0 m to 2250m above the sea.
Table I. Effect of air density on aerodynamic drag
Track Alt (km) PB (mmHg)
r
a
(kg/m
3
)R
D
b
(N)
Bordeaux (France) 0 760 1.20 29.8
Colorado Springs (USA) 1.84 605 0.96 23.9
Mexico City (Mexico) 2.25 575 0.91 22.6
Alt ¼Altitude; PB ¼Barometric Pressure;
r
¼Air density; R
D
¼Aerodynamic drag; A
p
¼Projected frontal
area; C
D
¼Coefficient of drag; v
f
¼Velocity relative to the fluid.;
a
With a temperature equal to 208C;
b
Based on
Equation 2, for a cyclist with A
p
C
D
¼0.221 m
2
and v
f¼
15 m/s.
P. Debraux et al.198
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
The projected frontal area
The projected frontal area represents the portion of a body which can be seen by an observer
placed exactly in front of that body, i.e. the projected surface normal to the fluid
displacement. Some authors assume that the projected frontal area is a constant fraction of
the body surface area to establish mathematical descriptions of aerodynamic drag (e.g.
Capelli et al., 1993; di Prampero et al., 1979; Olds et al., 1993, 1995). This assumption is
helpful since the body surface area (A
BSA
,inm
2
) is easily estimated from the measurement of
two anthropometric parameters, body height (h
b
, in cm) and body mass (m
b
, in kg) (Du Bois
& Du Bois, 1916; Shuter & Aslani, 2000):
ABSA ¼0:00949·h0:655
b·m0:441
bð5Þ
However, Swain et al. (1987) and Garcia-Lopez et al. (2008) have shown that the
projected frontal area is not proportional to the body surface area because the A
BSA
/m
b
ratio
tends to be smaller in larger cyclists. Heil (2001) reported that the assumption that the
projected frontal area and body surface area are proportional is correct for cyclists with a
body mass of between 60 and 80 kg. It is generally considered that the body surface area is
proportional to m0:667
b(Astrand & Rodahl, 1986), whereas the projected frontal area is
proportional to m0:762
b(Heil, 2001). The projected frontal area also can be expressed with the
position of the cyclist on the bicycle from the seat tube angle (
b
, in degree) and the trunk
angle (
d
, in degree) relative to the horizontal (Figure 1). The trunk is represented by the body
segment between the hip and shoulder. A goniometer was used to measure the trunk angle:
Ap¼0:00433·
b
0:172·
d
0:096·m0:762
bð6Þ
Nonetheless, Garcia-Lopez et al. (2008) observed a weak correlation between the trunk
angle and the projected frontal area (r¼0.42, p,0.05). Finally, as logically expected, the
results of the different studies show that the projected frontal area is dependent on body
height and body mass, position on the bicycle, and equipment used (e.g. helmet, shape of the
Figure 1. Illustration of the seat tube angle (
b
, in degree) and the trunk angle (
d
, in degree) used by Heil (2001) to
determine the projected frontal area of a cyclist and bicycle, and the helmet inclination angle (
a
1
, in degree) used by
Barelle et al. (2010).
Aerodynamic drag in cycling 199
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
frame, clothes). Faria et al. (2005) reported a method to determine the projected frontal area
in the aerodynamic position with aero-handlebars using body height and body mass:
Ap¼0:0293·h0:725
b·m0:425
bþ0:0604 ð7Þ
Barelle et al. (2010) established two models to determine the projected frontal area in the
aerodynamic position with aero-handlebars and a time-trial helmet, as a function of body
height, body mass, length of the helmet (L, in m), and its inclination on the horizontal (
a
1
,in
degree) (Figure 1):
Ap¼0:107·h1:6858
bþ0:329·ðL·sin
a
1Þ220:137·ðL·sin
a
1Þð8Þ
Ap¼0:045·h1:15
b·m0:2794
bþ0:329·ðL·sin
a
1Þ220:137·ðL·sin
a
1Þð9Þ
However, the accessibility of direct measurement methods of the projected frontal area, as
described further, reduces the interest of such mathematical estimations.
The drag coefficient
The drag coefficient is used to model all the complex factors of shape, position, and air flow
conditions relating to the cyclist. The drag coefficient is the ratio between aerodynamic drag
and the product of dynamic pressure (q, in Pa) of moving air stream and the projected frontal
area (Pugh, 1971):
CD¼RD
qAp
ð10Þ
Where the dynamic pressure is equivalent to the kinetic energy per unit of volume of a
moving solid body, and defined by the equation:
q¼1
2·
r
·v2
fð11Þ
The drag coefficient is dependent on the Reynolds number. The Reynolds number is a
dimensionless number that gives a measure of the ratio of inertial forces to viscous forces.
Thus, the drag coefficient depends on the air velocity and the roughness of the surface. For a
given position on the bicycle, the relationship between aerodynamic drag and velocity
relative to the fluid is not linear.
In recent wind tunnel investigations, Grappe (2009) showed that the relationship between
the effective frontal area and the air velocity was hyperbolic (Figure 2). Measurements were
obtained on an elite cyclist with a traditional road bicycle in the traditional aerodynamic
position, where the torso is parallel to the ground, with the hands in the drop portion of the
handlebars and the elbows flexed at 908. These data indicated that the effective frontal area
decreased between 4.2 and 11.1 m/s and increased between 11.1 and 27.8m/s. The lowest
effective frontal area was found between 11.1 and 13.9 m/s. However, for three cyclists on a
track bicycle in the dropped position, where the torso is partially bent over with hands on the
drop portion of the handlebars and elbows fully extended, the effective frontal area decreased
between 5.6 and 19.4 m/s (Figure 3). The position and the air velocity can have a significant
effect on the Reynolds number.
P. Debraux et al.200
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
Oggiano et al. (2009) observed, using a wind tunnel, that aerodynamic drag was also
dependent on the velocity and the roughness of the textile worn by the cyclist. Their
conclusion highlights the fact that using a rougher fabric can permit an aerodynamic drag
reduction at lower displacement speeds, whereas a smoother fabric will perform better at
higher speeds.
Grappe (2009) also studied the effect of roughness on the effective frontal area in actual
conditions. In a velodrome, the mechanical power generated by a cyclist on a track bicycle
was measured with a SRM powermeter (Schoberer Rad Messtechnik Scientific version,
Welldorf, Germany) in the traditional aerodynamic position. The power output produced
by the cyclist was compared at different velocities between 8.7 and 13.9 m/s in two
Figure 3. Influence of the air velocity (v
f
, in m/s) on the effective frontal area (A
p
C
D
,inm
2
) for three cyclists in static
dropped position on track bicycles, in wind tunnel. Data from Grappe (2009).
Figure 2. Influence of the air velocity (v
f
, in m/s) on the effective frontal area (A
p
C
D
,inm
2
) for one elite cyclist in
static traditional aerodynamic position on a standard road bicycle, in wind tunnel. Data from Grappe (2009).
Aerodynamic drag in cycling 201
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
conditions: 1) with the cyclist-bicycle system covered with a special ’wax’ supposed to
improve the roughness and 2) without any treatment (Figure 4). Between 11 and 12 m/s, no
difference was shown between the two experimental conditions. Between 8.7 and 11 m/s, the
surface treatment allowed an increase in the velocity of the cyclist-bicycle system for the
same mechanical power output. However, at velocities of displacement higher than 12 m/s,
the velocity did not increase when the ’wax’ was used. These results show the complexity
of the relationship between the drag coefficient, air velocity, and surface roughness. Heil
(2001, 2005) showed that, in cycling, the drag coefficient can be related to the body mass
according to data collected in the wind tunnel:
CD¼4:45·m20:45
bð12Þ
Heil (2001) noted that the drag coefficient decreases when the body mass increases, e.g.
when the body mass increases from 50 to 100 kg, the drag coefficient decreases from 0.76 to
0.56. In view of the findings of Grappe (2009) on roughness and the evolution of the drag
coefficient with displacement velocity, these data have to be examined closely. Indeed, a body
mass of 100 kg corresponds to a higher body surface area than a body mass of 50 kg, thus
resulting in greater skin surface area and a higher drag coefficient. Additional studies are
needed to understand the evolution of the drag coefficient as a function of cyclist parameters.
At a given velocity, the effective frontal area is the dominant component of aerodynamic
drag. In assessing the effective frontal area, it is possible to evaluate the aerodynamic profile
of an athlete and to determine the optimal position on the bicycle for decreasing aero-
dynamic drag. The measurement or estimation of the effective frontal area allows an
evaluation of the aerodynamics of the position and equipment (Faria, 1992), which enables
them to be optimised. It is also useful to establish mathematical models to predict
performance. Jeukendrup and Martin (2001) used a model with multiple factors concerning
the effective frontal area (e.g. body position, bicycle frame and wheels) to show the decrease
in the predicted time to assess a 40 km time trial in modifying these factors.
Figure 4. Evolution of the mechanical power output (P, in W) as a function of the velocity of displacement of the
cyclist-bicycle system (v, in m/s) for a cyclist in a velodrome with a track bicycle in traditional aerodynamic position
in two conditions: 1) with the cyclist-bicycle system covered with a special ’wax’ supposed to improve the roughness
and 2) without any treatment. Data from Grappe (2009).
P. Debraux et al.202
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
Methods of assessment of aerodynamic drag
Different methods are used to evaluate aerodynamic drag under actual conditions or in the
laboratory (Garcia-Lopez et al., 2008). Once the aerodynamic drag is known, the effective
frontal area can be computed. If the projected frontal area can be directly measured, the drag
coefficient can then be determined. Although drag coefficient is the main coefficient in
evaluating the aerodynamic profile of an athlete, the validity, sensitivity and reliability of the
many methods of effective frontal area and projected frontal area assessment must be
discussed. In actual situations, the projected frontal area could help to give indications about a
position in a short time with minimal equipment. With the assessment of the effective frontal
area, the measurement of the projected frontal area can be a tool to calculate a mean drag
coefficient for the most frequently used positions. With this approximation for each position
tested, coaches and cyclists could have an aerodynamic profile of a position at low cost.
Results of the determination of projected frontal area and effective frontal area in the
literature, using different methods, are presented in Table II. Despite the fact that body mass
and height of cyclists affect the measurements, and that position on the bicycle is not always
clearly stated, large differences can be observed between methods for a given position. This
may be because not all publications clearly describe the position adopted by the cyclists.
Also, it is not always clear if the measurements of the projected frontal area take into account
the projected frontal area of the bicycle. These methods of assessment are described and
discussed in the next sections.
Two ways can be used to determine the effective frontal area. On the one hand, the
aerodynamic drag can be directly measured in a wind tunnel. On the other hand, the
mechanical power output can be measured by a powermeter (e.g. SRM powermeter
Scientific version, Welldorf, Germany) at different speeds and, using Equation 1, the total
resistive force to motion is calculated in order to estimate the effective frontal area with
respect to air density.
Wind tunnel
Wind tunnels are commonly used to evaluate the effective frontal area. The wind is
artificially generated from a fan on the cyclist-bicycle system, and assessment of aerodynamic
drag is based on quantification of the ground reaction forces through a plate force
measurement (e.g. Davies, 1980; Garcia-Lopez et al., 2008; Martin et al., 1998). In wind
tunnel, the cyclist is placed on the bicycle in a test position: i) motionless on a stationary plate
force; or ii) pedalling on a treadmill or on a home trainer on a plate force. Before the
aerodynamic drag measurement, the force plate must be calibrated and the fan must blow a
moderate wind in order to heat the wind tunnel to an optimum temperature. The
aerodynamic drag is the parallel force in the same direction as the fluid displacement. It can
be evaluated in the wind tunnel and the effective frontal area can be calculated as:
ApCD¼RD
0:5·
r
·v2
f
ð13Þ
If this method is used in conjunction with an assessment method of the projected frontal
area, the value of the drag coefficient can be quantified. The wind tunnel is the reference
technique to assess aerodynamic drag because of its validity and reliability (Garcia-Lopez et al.,
2008; Hoerner, 1965). This technique is sensitive to wheel type (Tew & Sayers, 1999), yaw
angle (i.e. the angle of alignment between the bicycle and the air stream) (Martin et al., 1998),
Aerodynamic drag in cycling 203
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
Table II. Measure of A
p
(m
2
) and estimation of A
p
C
D
(m
2
) in different positions with different methods. (M^SD).
Subjects Positions
Study Methods n
Body height
(m)
Body mass
(kg)
UP
(m
2
)
DP
(m
2
)
AeroP
(m
2
)
BHP
(m
2
)
TAP
(m
2
)
Measure of A
p
Olds & Olive (1999) 17 1.76 ^0.08 68.3 ^9.2 0.605 ^0.069 0.563 ^0.071 0.493 ^0.057
Garcia-Lopez et al.
(2008)
Weighing
Photographs
5 1.79 ^0.03 71.6 ^2.7 0.301
a
^0.011 0.364 ^0.012
Padilla et al. (2000) 1 1.88 81.0 0.375
Davies (1980) 15 1.77 ^0.08 69.0 ^5.9 0.50
b
Capelli et al. (1998) 10 1.81 ^0.09 70.5 ^6.0 0.42 ^0.028
b
Capelli et al. (1993) 2 1.85 ^0.01 73.0 ^2.8 0.394
b
Heil (2002) 21 1.82 ^0.06 74.4 ^7.2 0.525 ^0.01 0.531 ^0.008 0.46 ^0.0091
Dorel et al. (2005) Digitalization 10 1.81 ^0.04 83.0 ^5.0 0.531 ^0.014
Debraux et al.
(2009)
9 1.77 ^0.03 70.5 ^5.4 0.533 ^0.031 0.426 ^0.031
de Groot et al.
(1995)
Planimetry 7 0.39 ^0.028
b
Debraux et al.
(2009)
CAD 9 1.77 ^0.03 70.5 ^5.4 0.565 ^0.037 0.45 ^0.04
Estimation of A
p
C
D
Martin et al. (1998) 6 1.77 ^0.05 71.9 ^6.3 0.269 ^0.006
Garcia-Lopez et al.
(2008)
Wind Tunnel 5 1.79 ^0.03 71.6 ^2.7 0.297 ^0.013 0.481 ^0.017
Padilla et al. (2000) 1 1.88 81.0 0.244
Defraeye et al.
(2010)
1 1.83 72 0.270 0.243 0.211
Davies (1980) 15 1.77 ^0.08 69.0 ^5.9 0.280
b
Martin et al. (2006) Linear
Regression
Analysis
1 1.83 96.0 0.332
2 1.73 ^0.12 77.5 ^13.4 0.2 ^0.021
P. Debraux et al.204
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
Table II – continued
Subjects Positions
Study Methods n
Body height
(m)
Body mass
(kg)
UP
(m
2
)
DP
(m
2
)
AeroP
(m
2
)
BHP
(m
2
)
TAP
(m
2
)
Debraux et al.
(2009)
7 1.77 ^0.03 70.5 ^5.4 0.361
c
^0.021
Grappe et al. (1997) 1 1.75 67.0 0.299 0.276 0.262
0.216
d
Capelli et al. (1993) Towing 2 1.85 ^0.01 73.0 ^2.8 0.255
a
di Prampero et al.
(1979)
2 1.75 63.0 0.318
Candau et al.
(1999)
Simple
Deceleration
1 1.72 66.2 0.355 0.262-0.304
A
p
¼Projected frontal area (m
2
); A
p
C
D
¼Effective frontal area (m
2
); UP ¼Upright Position; DP ¼Dropped Position; AeroP ¼Aerodynamic Position with
aero-handlebars; BHP ¼Brake Hoods Position; TAP ¼Traditional Aerodynamic Position;
a
Without helmet;
b
Position unclear;
c
In mountain bike;
d
Obree’s Position.
Aerodynamic drag in cycling 205
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
and cyclist position (Garcia-Lopez et al., 2002, 2008). The results can be dependent on
whether the cyclist is motionless or moving. Indeed, during the pedalling exercise the cyclist
significantly increases the aerodynamics. Accordingly, the plate force records the generated
forces during pedalling. To obtain a valid measurement of the drag forces, a first step could be
to record the forces while pedalling in order to subtract these from the forces measured in a
wind tunnel.
Although the wind tunnel technique is still a reference method, it is very expensive
(between 5,000 and 10,000 euros per day) and few studies have been published on the
assessment of aerodynamic drag using wind tunnels. Furthermore, wind tunnel
measurements have some limitations. Candau et al. (1999) explain that testing conditions
present limitations: i) if the tested body does not move, the air flow around the bicycle is
modified by the floor; ii) if the wheels of the bicycle are stationary, the effect of wind is not
measured; and, iii) the cyclist’s position on the bicycle during the tests is not necessarily
identical to the position in actual conditions. Slight lateral movements that can occur in
actual conditions are not present in the wind tunnel. When the cyclist rides on a motor-
driven treadmill or a home trainer, limitations ii and iii are resolved, but another limitations
appears: iv) the pedalling motion introduces noises in the force measurement system such
that there are changes in the forces applied to the treadmill within each pedal revolution; and,
v) slight lateral movements (e.g. shoulders) are dependent of the intensity of pedalling.
Few studies have simulated actual conditions of pedalling in a wind tunnel. In Davies’
study (1980), the cyclists were instructed to pedal on a motor-driven treadmill at a set speed
of 4.7 m/s against wind velocities varying from 1.5-18.5 m/s. To be closer to riding
conditions, Martin et al. (1998) simulated pedalling at 90 rotations per minute (rpm), but
without resistance, and the front wheel was rotated by a small electric motor. Garcial-Lopez
et al. (2002, 2008) tested five different positions to measure the aerodynamic drag of
professional cyclists in a wind tunnel using two bicycles, a special time-trial bike with aero-
handlebars and a standard bike with standard handlebars. These tests occurred with and
without pedalling against a resistance ergometer.
In order to model actual conditions more closely, it could be more practical to use a field
method to assess the effective frontal area. This permits lower cost testing in actual
conditions and enables selection of the most appropriate position and equipment.
Method of linear regression analysis
When cycling on level ground at constant velocity, the total resistive forces are mainly
composed of two forces, aerodynamic drag and rolling resistance (R
R
, in N). Thus, the total
resistive forces can be described by Equation 14 (Capelli et al., 1993; Davies, 1980; di
Prampero et al., 1979; Grappe et al., 1997, 1999):
RT¼RDþRRð14Þ
With
RR¼CR·M·gð15Þ
Rolling resistance represents the contact forces between the ground and the pneumatics of
the wheels, and the frictional losses at the bearing and transmission chain (Grappe et al.,
1997; Millet & Candau, 2002). Rolling resistance depends on the rolling coefficient (C
R
,
dimensionless), the mass of the cyclist-bicycle system (M, in kg) and the gravity acceleration
P. Debraux et al.206
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
(g¼9.81 m/s
2
). According to Equations 2, 14 and 15:
RT¼0:5·
r
ApCD·v2
fþCR·M·gð16Þ
The total resistive forces can be determined by measuring mechanical power output as a
function of velocity (Grappe et al., 1997):
RT¼P
vð17Þ
This method consists of measuring mechanical power output using a powermeter (e.g.
SRM powermeter Scientific version, Welldorf, Germany) at different velocity to determine
the total resistive forces. To do this, the cyclist performs several trials at different velocities in
a selected posture. According to Equation 16:
a¼0:5·
r
·ApCDð18Þ
b¼CR·M·gð19Þ
Thus
RT¼av2þbð20Þ
Based on Equation 20, the total resistive forces vary in a linear way with the square of the
velocity (Figure 5).
With a linear regression analysis, it is possible to determine the effective frontal area value
for the selected posture according to Equation 18 (A
p
C
D
¼a/0.5
r
) from the slope aof
Equation 20. If this method is used with a method of determination of the projected frontal
area, the value of the drag coefficient can be quantified (Capelli et al., 1998). However, the
relationship between the total resistive forces and v
2
is not necessarily linear (Grappe, 2009).
Figure 5. Illustration of the evolution of the total resistive forces (R
T
, in N) as a function of the squared displacement
velocity of the cyclist-bicycle system (v
2
,inm
2
/s
2
) on level ground with a mountain bike.
Aerodynamic drag in cycling 207
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
The reliability of this method is good (Coefficient of variation (CV) ¼3.2%) (Grappe
et al., 1997). Grappe et al. (1997) did not observe a significant difference, using the Max One
powermeter (Look SA, France), between the aerodynamic position with aero-handlebars,
where the lower arms are on the aerodynamic handlebars, and the dropped position. The
difference in the effective frontal area between the two positions was 4.6%, and the authors
concluded that this method reaches the limit of the sensitivity of the measurement. The
powermeter used (Max One, Look SA, Nevers, France) to measure the mechanical power
output has a weak sampling frequency (i.e. 4 data per 1 rpm) and the tests were performed in
an outdoor velodrome. The use of a more accurate powermeter like the SRM, which has a
higher sampling frequency, could lead to a more sensitive measure in the field. It could be
helpful in discriminating different positions or levels of roughness.
To verify whether the SRM system could provide a valid measure of cycling power, Martin
et al. (1998) compared the SRM measured power with that from the Monark cycle
ergometer (Model 818). The statistically valid results indicate that the power measured by
the SRM was significantly different ( p,0.01) than the power delivered to the Monark
ergometer flywheel; the difference was 2.35%. It appears that this difference is characteristic
of power loss in chain drive systems (Martin et al., 1998). These authors assume that the
SRM provides a valid and accurate measure of cycling power compared with the Monark
cycle ergometer.
Measurement of the tractional resistance (dynamometric method): the ’towing’ method
With this method, tractional resistance is determined by towing a subject with a vehicle (e.g.
car, motorcycle) by means of a cable (e.g. a nylon cable of 0.003 m of diameter) on a flat
track at constant speed. The length of the cable (e.g. 10 m, 25 m) was chosen to minimise the
air turbulence caused by the moving vehicle (di Prampero et al., 1979; Capelli et al., 1993).
However, air turbulence set up by the towing vehicle and alterations in atmospheric
conditions can affect the results (Candau et al., 1999; Garcia-Lopez et al., 2008). During the
test, the cyclist’s selected posture does not change while being towed by the vehicle. The
cyclist can pedal at a selected cadence without a transmission chain to reproduce the air
turbulence induced by moving legs during actual cycling (Capelli et al., 1993).
The total resistive forces to the motion were measured with a dynamometric technique
from a load cell mounted in series on the cable. The total resistive forces were assessed over
several trials at different velocities to obtain a R
T
-vrelationship. As for the method of linear
regression analysis, the curve of the total resistive forces in function of the square of the
velocity has to be plotted, based on Equation 20. With a linear regression analysis, it is
possible to determine the effective frontal area value for the studied position according to
Equation 16 (A
p
C
D
¼a/0.5
r
) from the slope aof Equation 20. Capelli et al. (1993) tested
the repeatability of the towing method by measuring the total resistive forces twice each at six
speeds. They found no significant difference between the paired sets of data (p.0.10). The
fact that this method cannot be used routinely is an important limitation.
The coasting-down and deceleration methods
These methods of measuring aerodynamic drag are based on Newton’s second law
(SF¼m·a), where the sum of the resistive forces (F) is equal to the product of mass (m) with
acceleration (a). The tests performed in descent (coasting-down method) measure the
acceleration of the cyclist in free-wheel and those performed on flat terrain (outdoor and
indoor) measure the cyclist’s deceleration, also in free-wheel. In a specified position i) in a
P. Debraux et al.208
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
descent (Gross et al., 1983; Kyle & Burke, 1984; Nevill et al., 2006) or ii) on flat ground, in a
field, or in hallways (Candau et al., 1999) the cyclists brought the bicycle to a defined velocity
before they stopped pedalling. The riding position was unchanged and, to reproduce actual
conditions with turbulence induced by movement of the lower limbs, the cyclists can pedal
without transmission of force to the rear wheel during coasting trials (Gross et al., 1983; Kyle &
Burke, 1984; Candau et al., 1999). In this way, the cyclists slowed down due to the air friction
and rolling resistive forces over several timing switches.
For the coasting-down method (Gross et al., 1983; Kyle & Burke, 1984), there are six timing
switches. The distance between switches is 6 metres and the time is recorded using a
chronometer system (to 1/1,000 s). The mean velocity between each switch is calculated to
assess linear regression of mean velocity as a function of the distance. The slope of the linear
regression multiplied by the mean velocity of the third interval determines the mean acceleration
of the bicycle-cyclist system. The total resistive forces are the product of the mass and the
acceleration of this system. The aerodynamic drag and the rolling resistance are calculated from
the relation between the total resistive forces and the square velocity as shown in Equation 16.
As the coasting-down method is a field method, climatic conditions and the nature of the
ground can potentially induce some errors. Kyle and Burke (1984) reported measured
variations of nearly 10%. To avoid such errors, the method can be used in hallways (De
Groot et al., 1995). De Groot et al. (1995) have developed a small infrared light emitter and
detector mounted on the front fork of the bicycle. This system can measure velocity as a
function of time during the deceleration phase but there is no information concerning the
reliability and sensitivity of this approach.
For the deceleration method (Candau et al., 1999), three switches are disposed in a
hallway. The distance between the first and the second switch is 3 metres and the distance
between the second and third switch is 20 metres (Figure 6).
The time is recorded using a chronometer system (accurate to 30 ms). The total resistive
forces were assessed with several trials (<20) at different velocities by iterations with a
mathematical model describing the deceleration of the trajectory of the cyclist-bicycle system
(Candau et al., 1999). The reliability (CV ¼0.6%), sensitivity and validity of this method of
measuring the effective frontal area (in comparison with the wind tunnel) are excellent.
Although this method permits measurement of the rolling resistance of the tyres according to
a specific ground surface, it is limited by the significant number of trials needed to determine
an evaluation of the effective frontal area.
Of these four methods of assessment of the effective frontal area, the wind tunnel method
and the method of linear regression analysis are the most sensitive and reliable. The method
Figure 6. Schematic view of the measurement system for the deceleration method in a hallway and the placement of
the three switches.
Aerodynamic drag in cycling 209
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
of linear regression analysis with the use of a powermeter such as SRM provides
measurement of the resistive forces in actual conditions. It could also help to discriminate
between the effective frontal area values at different positions. However, the wind tunnel
allows more accurate and reliable measurements of aerodynamic drag, resulting in a higher
sensitivity to small adjustments of the cyclist’s position (Defraeye et al., 2010) or equipment
(e.g. the helmet) (Barelle et al., 2010). Nevertheless, this method is very expensive. Most
coaches and sport scientists have easier access to a powermeter system like the SRM or
PowerTap models. The field method could serve to prepare and/or optimise and/or verify
wind tunnel results. Finally, Defraeye et al. (2010) showed that computational fluid
dynamics provided measurements of drag in good agreement with those obtained by wind
tunnel tests. Computational fluid dynamics could be a valuable numerical alternative for
evaluating the drag of different cyclist positions with high sensitivity. The advantage of this
method is that it allows more detailed insight into the flow field around the body of the cyclist.
Although the effective frontal area is the main parameter in aerodynamic evaluation, it can
be highly influenced by the projected frontal area. For a constant drag coefficient, the effective
frontal area is proportionally affected by the change of projected frontal area. Moreover, a
decrease in the projected frontal area would result in a decrease in the effective frontal area
(Defraeye et al., 2010). Two different methods are used to measure the projected frontal
area: i) with a calibration frame of known area, such as the method of weighing photographs
(e.g. Capelli et al., 1993, 1998; Debraux et al., 2009; di Prampero et al., 1979; Heil, 2001;
Olds et al., 1993, 1995; Padilla et al., 2000; Pugh, 1970, 1971; Swain et al., 1987), the
method of digitalisation (Barelle et al., 2010; Debraux et al., 2009; Dorel et al., 2005; Heil,
2001, 2002)); and ii) without calibration frame, such as planimetry (Olds & Olive, 1999),
digital methods using computer-aided design (CAD) software (Debraux et al., 2009)).
The method of weighing photographs
This method consists of taking a photograph in a frontal plane of the cyclist and bicycle
(Figure 7A). A calibration frame with a known area located midway between the subject’s
hip and shoulders and facing the camera is also photographed. The photograph is printed
and the cyclist and calibration frame are cut from the photograph. These separate pieces are
weighed using an accurate balance with a high sensitivity (^0.001 g). The actual projected
Figure 7. Example of photographs of cyclists used to measure A
p
with different methods: method of weighing
photographs (A), method of digitalisation (B), and computer-aided design method (C).
P. Debraux et al.210
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
frontal area in square metres is calculated for each image by multiplying the known area of
the calibration frame by the ratio of the projected frontal area image weight over the
calibration frame image weight (Capelli et al., 1998; Debraux et al., 2009; Heil, 2001;
Olds et al., 1995; Padilla et al., 2000).
The method of weighing photographs requires only a calibration frame, a digital camera, a
balance with high sensitivity, and a cutting instrument, but it cannot be used in actual
conditions because of the need of the calibration frame. Although this method has been used
for a long time (Pugh, 1970, 1971; Swain et al., 1987), it is very reliable (CV ¼1.3%)
(Debraux et al., 2009) and has been used to test the validity of new methods of assessment of
the projected frontal area (e.g. Debraux et al., 2009; Heil, 2001).
The method of weighing photographs presents some inconvenience which can be resolved.
The cutting of the printed photograph following the outline of the cyclist has to be very
accurate, and this operation takes at least 5 –6 minutes. Moreover, for the classical format of
digital photographs, it is easier to measure only the projected frontal area of the cyclist
without the bicycle, unless the photographs are enlarged. To be sure that colour did not
influence the mass of photographs, Debraux et al. (2009) weighed five photographs with five
different colours. They concluded that colour did not influence the results in this method.
Planimetry
In planimetry, the outline of the cyclist and bicycle is traced with a polar planimeter, and a
triangulation method is used to calculate the enclosed area (Olds & Olive, 1999). Olds and
Olive (1999) compared a method based on weighing pictures and planimetry while
measuring A
p
cyclist in three positions: i) Upright position: where the torso is upright with the
hands placed near the stem of the handlebars; ii) Dropped position: partially bent over torso
position with hands on the drop portion of the handlebars and elbows fully extended; and
iii) Aerodynamic position: where the arms are resting on aero-handlebars. The authors
observed a significant mean difference (,3.3%) between the projected frontal areas
determined by the two methods. Both methods were extremely reliable but weighing
photographs gave a more precise result than the planimetry-based method. The mean
differences were 0.25% vs. 2.90% respectively for the weighing photographs and planimetry.
Digitalisation
Like the method of weighing photographs, the digitising method (Barelle et al., 2010;
Debraux et al., 2009; Dorel et al., 2005; Heil, 2001, 2002) requires the use of a calibration
frame with a known area placed near the cyclist and bicycle. However, this digital method
does not require the cutting of photographs; instead, it consists of digitalising a paper picture
with the help of a digitiser (Heil, 2001), or with a computer-based image analysis software
application (e.g. Scion Image Release Alpha 4.0.3.0.2 for Windows, Scion Corporation,
Frederick, Md., USA or ImageJ software) if the pictures are in numerical format (Barelle
et al., 2010; Debraux et al., 2009; Dorel et al., 2005; Heil, 2002). Accurate preparation is
needed in order to be able to use numerical pictures. The zones to be measured must be
darkened. This can be done in two ways, either by converting the picture into a black and
white file using computer-based imaging software (e.g. Gimp, Adobe Photoshop) (Debraux
et al., 2009) or by using a light placed behind the cyclist and bicycle (Dorel et al., 2005).
In a computer-based image analysis software application (e.g. Scion Image Release Alpha
4.0.3.0.2 for Windows, Scion Corporation, Frederick, Md., USA), the black and white
image is imported, and the zones of the cyclist with the bicycle and the calibration frame are
Aerodynamic drag in cycling 211
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
selected (see Figure 7B). The software measures the number of pixels included in the zones.
The actual projected frontal area in square metres of the digitised image is obtained by
determining the ratio of pixels of the two zones then multiplying this ratio by the actual
known area of the calibration frame. To measure only the cyclist projected frontal area, it is
necessary to take a picture of the cyclist and bicycle, and one of the bicycle alone, then
manually subtract the pixel count from the picture of the bicycle alone from the pixel count
of the picture representing both cyclist and bicycle.
The digitising method needs a personal computer (but the software is free and easy to use)
and a digital camera or a scanner to digitise the printed photographs. However, it requires
the investigator to correct the photographs (e.g. darken the measured zone, change the
extension of the image file) before opening them in the software Scion Image, which will take
time and practice. This method is valid in comparison with the method of weighing
photographs (Heil, 2001; Debraux et al., 2009).
Method based on computer-aided design (CAD) software
The methods based on CAD software do not require a calibration zone to be placed near the
cyclist and can be used in actual conditions. The calibration is assessed by entering a known
distance (vertical or horizontal) corresponding to a distance in the photographs (e.g. the
width of the handlebars, the height of the front wheel) in the software (Figure 7C). The digital
photographs are opened in CAD software. The outlines of the area measured are traced with
a spline curve tool in a 2D plane. The software calculates the area enclosed (Debraux et al.,
2009). This method is valid in comparison with the method of weighing photographs and
reliable (CV ¼0.1%) (Debraux et al., 2009). It is a fast method, but it needs a personal
computer and CAD software, which are both relatively expensive. As this method can be used
in actual conditions, it is possible to test the aerodynamic drag of different positions at a lower
cost by using it together with linear regression analysis or towing.
Among the different methods described to assess the projected frontal area, the
digitalisation method and the methods based on a CAD software are better adapted for the
digital image format. Planimetry and the method of weighing photographs both require more
procedures and more time for a measurement which could be done in five minutes utilising
the new digital methods (Debraux et al., 2009). However, all these methods are reliable, and
there is no significant difference between weighing photographs, digitalisation, and the
method based on CAD software (Heil, 2001; Debraux et al., 2009). The new methods are
simply faster and more convenient.
Nevertheless, all these methods have in common the need to take a photograph of the
cyclist-bicycle system. Since the measurement of the projected frontal area is dependent on
the photograph, the placement of the calibration frame and the optical calibration of the
digital camera can be source of errors. To study these measurement errors, Olds and Olive
(1999) determined the effects on the projected frontal area of the calibration frame position
and the position of the camera relative to the cyclist-bicycle system. The authors made some
recommendations in order to standardise the measurement protocol of the projected frontal
area using a calibration frame, or not: i) The frontal plane of the calibration frame has to be
located approximately midway between the cyclist’s hip and shoulder. Olds and Olive (1999)
showed that when the calibration frame was moved back to the rear wheel-tip, the projected
frontal area increased by 61%, and when it was placed at the front wheel-tip, the projected
frontal area decreased by 46%; ii) The digital camera has to be directed straight towards
the cyclist at the height of the handlebars in the axis of the bicycle. An angular deviation of
108of the digital camera could induce a 7.5% increase of the projected frontal area measure
P. Debraux et al.212
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
(Olds & Olive, 1999); and iii) The digital camera has to be located at least 5 metres away
from the cyclist-bicycle system. This is to minimise distortion due to focal length and the
differences in apparent size of the parts of the cyclist closer and further from the digital
camera (Olds & Olive, 1999).
How to minimise aerodynamic drag
In cycling, aerodynamic drag is composed of two forms of drag: pressure and skin-friction
drag (Faria, 1992; Millet & Candau, 2002). Pressure drag is the most important part of
aerodynamic drag. It represents the difference of air pressure that exists between the front
and rear of a moving body. Within a fluid, a moving body creates a boundary layer due to the
fluid pressure on the body and leads to backward turbulence resulting in pressure drag.
Pressure drag is mainly dependent on the general size and shape of the body. Skin-friction
drag is the resistance generated by the friction of fluid molecules directly on the surface of the
body in motion. It increases with the size and roughness of the body surface (Millet &
Candau, 2002).
As explained previously, the effective frontal area is the determinant parameter of the
cyclist-bicycle system aerodynamic. Both general size and shape of the moving body affect
the effective frontal area, and can be decreased in different ways according to Kyle and Burke
(1984) and Millet and Candau (2002). A cyclist can lower aerodynamic drag in reducing the
projected frontal area. The angle between the trunk and the ground is important, the nearer
the angle to 0 degrees, the more the projected frontal area decreases (Heil, 2001). Faria
(1992) reported a decrease of 20% of the aerodynamic drag when the cyclist’s elbows are
bent with the torso nearly parallel to the ground. The position of the arms is a supplementary
factor to modify in order to enhance the projected frontal area. A decrease of 28% in
aerodynamic drag was observed when the hands were on the centre of the upper handlebars,
trunk resting on the hands, crank parallel to the ground (Faria, 1992). The hands can be
placed forwards in relation to the body in using aero-handlebars, and this can increase
comfort and decrease the projected frontal area. Moreover, Berry et al. (1994) did not find
significant differences between aero-handlebars and standard racing handlebars in terms of
exhaustion, power output and oxygen consumption.
The effects of the moving cyclist-bicycle system shape on the aerodynamic drag are
quantified by the drag coefficient (di Prampero, 1986). To reduce the drag coefficient, the
shape of the moving body has to be streamlined. The position, an aerodynamic bicycle
frame, aerodynamic helmet, aerodynamic wheels (Tew & Sayers, 1999), and clothes and
accessories can significantly reduce the drag coefficient (Faria, 1992; Faria et al., 2005). Tew
and Sayers (1999) showed that aerodynamic wheels could reduce the axial drag of up to 50%
in comparison with the spoked wheels. Different techniques exist to enhance the effective
frontal area for the cyclist-bicycle system, and every improvement must be tested and
quantified to find out whether the decrease in effective frontal area can save significant time in
actual racing conditions (e.g. time-trials) (Atkinson et al., 2007). This is why mathematical
models of cycling performance are necessary to simulate mechanical power output, which
depends on many parameters.
Importance of the effective frontal area in modelling cycling performance
A theoretical model can provide a helpful simulation tool for researchers, coaches, and
cyclists who do not have access to the technologies indicated above (e.g. powermeter,
computer). Indeed, a model permits the effect on cycling performance of physiological
Aerodynamic drag in cycling 213
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
changes, biomechanical, anthropometric, and environmental factors to be predicted (Olds
et al., 1993). Many authors have established a mathematical cycling model (e.g. Atkinson
et al., 2007; Broker et al., 1999; di Prampero et al., 1979; Heil et al., 2001; Martin et al.,
2006; Nevill et al., 2006; Olds, 1998, 2001; Olds et al., 1993, 1995; Padilla et al., 2000),
most including terms for power output produced by the cyclist and power required to
overcome aerodynamic drag, rolling resistance, and other parameters (Martin et al., 2006).
At displacement velocity greater than 14 m/s where the aerodynamic drag is about 90% of the
total resistive forces, according to Equations 1 and 2, it can be assumed that the mechanical
power output is proportional to the product of aerodynamic drag and velocity. The
mechanical power necessary to drive the cyclist-bicycle system through the air will increase
with the cube of the velocity (Faria, 1992).
Gonzales-Haro et al. (2007) and (2008)have compared nine theoreticalmodels for estimating
the power output in cycling using the SRM powermeter in a velodrome. The most important
variables in these models are: velocity, mass of the cyclist-bicycle system, and aerodynamic
variables: the projected frontal area and the drag coefficient. Other secondary variables are the
slope, rolling coefficient and climatic conditions (barometric pressure of the fluid and
temperature). Gonzales-Haro et al. (2007) found the equations of di Prampero et al. (1979) and
Candau et al. (1999) the best estimates of power output in comparison with measurements with
the SRM powermeter, whereas Gonzales-Haro et al. (2008) found the equation of Olds et al.
(1995) best to estimate peak power output because of the few variables to measure.
As on level ground, at racing speeds greater than 14 m/s, aerodynamic drag represents
about 90% of the overall resistive forces (Candau et al., 1999; di Prampero, 2000; Martin
et al., 2006; Millet & Candau, 2002) and consideration of the effective frontal area in a
mathematical model is important. Its estimation can strongly influence the model. However,
some simulations did not take it in account or are based on approximation (Table III).
Olds et al. (1995) established a relationship between the projected frontal area and the
body surface area considering that the projected frontal area is a constant fraction of the body
surface area in a given position:
Ap¼0:3176·ABSA20:1478 ð21Þ
These equations do not take into account the differences intra- and inter-individual for the
same position on the bicycle, or different bicycles. In these authors’ model, the drag
coefficient was a constant and equal to 0.592. For comparison, we estimate the projected
frontal area according to Olds et al. (1995) and we measure the projected frontal area using
the CAD method (Debraux et al., 2009). The revisited equation of the body surface area by
Shuter and Aslani (2000) was used (see Equation 5), where the body surface area is expressed
in square metres but the body height is expressed in cm. Table IV presents the results of the
difference between the two methods on seven cyclists in traditional aerodynamic position.
The mean results show an increase of 0,021 m
2
(þ4.9%) for the projected frontal area with
the method of Olds et al. (1995). The two methods are compared with a paired t-test and the
difference is significant ( p,0.05). However, additional studies should be performed on the
accuracy of the methods for the projected frontal area determination.
In order to be valid, the mathematical model for an estimation of the projected frontal area
must consider various parameters (e.g. the position of the cyclist, the wearing of a helmet). In
this way, the drag coefficient that changes with position and velocity has to be determined.
Martin et al. (2006) found that the effective frontal area values determined in field trials with
the SRM powermeter were similar to those measured in the wind tunnel. This method is very
useful to assess the effective frontal area in actual conditions as routine and the cyclists can
P. Debraux et al.214
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
Table IV. Comparison of the estimation of A
p
with the equation developed by Olds et al. (1995) using A
BSA
calculated according Shuter and Aslani (2000) and the measure of A
p
with the CAD method (Debraux et al., 2009)
for cyclists in traditional aerodynamic position with modern bicycle
Subjects h
b
(m) m
b
(kg) A
p
(m
2
) Olds et al. (1995) A
p
(m
2
) Debraux et al. (2009)
Subject 1 1.74 78 0.456 0.406
Subject 2 1.81 70 0.443 0.425
Subject 3 1.90 75 0.481 0.424
Subject 4 1.85 72 0.459 0.425
Subject 5 1.70 64 0.397 0.385
Subject 6 1.80 64 0.417 0.416
Subject 7 1.75 65 0.412 0.401
Subject 8 1.80 75 0.459 0.461
Subject 9 1.75 91 0.501 0.488
M^SD 1.79 ^0.06 72.7 ^8.6 0.447*^0.034 0.426*^0.031
*Significant difference at p,0.05
A
p
¼Projected frontal area (m
2
); A
BSA
¼Body surface area (m
2
); h
b
¼Body height (m); m
b
¼Body mass (kg).
Table III. Mathematical expression of the aerodynamic parameters in modelling of the power output
Study Method of calculation of the aerodynamic parameters
Whitt (1971) A
p
has to be determined
di Prampero et al. (1979) Based on a percentage of A
BSA
with ABSA ¼0:007184·m0:425
b·h0:725
b
Kyle (1991) C
D
¼0.8
A
p
has to be determined
Menard (1992) SC
x
¼0.259 m
2
SC
xv
¼0.012 m
2
Olds et al. (1993) Based on a percentage of A
BSA
ABSA ¼0:007184·m0:425
b·h0:725
b
CF
A
¼A
BSA
/ 1.77
Broker (1994) K1¼Kd·Kpo·Kb·Kc·Kh
A
p
has to be determined
Olds et al. (1995) C
D
¼0.592
Ab¼0:3176·ABSA20:1478
Total Ap¼0:4147·ðAb=1:771Þþ0:1159
Candau et al. (1999) A
p
C
D
¼0.333 m
2
Shuter and Aslani (2000) ABSAðm2Þ¼0:00949·h0:655
b·m0:441
bwith h
b
in cm
Heil (2001) Ap¼0:00433·STA0:172·TA0:096·m0:762
b
CD¼4:45·m20:45
b
Faria et al. (2005) FA ¼0:0293·h0:725
b·m0:425
bþ0:0604
Martin et al. (2006) A
p
C
D
has to be determined
Barelle et al. (2010) Ap¼0:107·h1:6858
bþð0:329 ðL·sin
a
1Þ220:137·ðL·sin
a
1ÞÞ
Ap¼0:045·h1:15
b·m0:2794
bþð0:329 ðL·sin
a
1Þ220:137·ðL·sin
a
1ÞÞ
A
p
¼Projected frontal area (m
2
); A
b
¼Projected frontal area of the body (m
2
); A
BSA
¼Body surface area (m
2
);
m
b
¼Body mass (kg); h
b
¼Body height (m); C
D
¼Coefficient of drag; SC
x
¼Coefficient of air penetration
determined in wind tunnel (m
2
); SC
xv
¼Wheel’s coefficient of air penetration determined in wind tunnel (m
2
);
CF
A
¼Correction factor for body surface area (m
2
); K
1
¼Aerodynamic factor; K
d
¼Air density; K
po
¼Rider
position; K
b
¼Cycle components; K
c
¼Clothing; K
h
¼Handlebar type; FA ¼The total frontal area of the
cyclist in the aerodynamic position with Aero-Handlebars (m
2
); L¼Length of a time-trial helmet (m);
a
1
¼
Helmet inclination on the horizontal (degree).
Aerodynamic drag in cycling 215
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
test several positions and bicycles. Considering the mathematical model of Olds et al. (1995)
as the best estimate of the peak power output (Gonzales-Haro et al., 2008), it could be more
appropriate to use this model with the effective frontal area estimated by the method of linear
regression analysis.
Conclusion
The effective frontal area is the most important parameter to characterise aerodynamic drag.
The techniques of estimation of the effective frontal area are now well recognised in cycling,
and this parameter can be reliably evaluated in laboratory or actual conditions. However,
although the projected frontal area is a well-known easily quantifiable factor, the variation of
the drag coefficient is more complex. Its evolution as a function of velocity is still difficult to
understand fully. More research will be necessary to study the characteristics of drag
coefficient variation. New methods such as computational fluid dynamics could be a great
help in achieving this. Knowledge of these parameters can be very helpful in developing
theoretical models. A mathematical simulation can provide an estimation of performance,
and is thus a tool for cyclists, coaches and scientists. Moreover, if the effective frontal area
can be accurately estimated, the model will be more reliable.
References
A
˚strand, P. O., & Rodahl, K. (1986). Body dimensions and muscular exercise. In P. O. A
˚strand, and K. Rodahl
(Eds.), Textbook of work physiology,(3
rd
ed.) (pp. 391– 411). New York, NY: McGraw-Hill.
Atkinson, G., Peacock, O., & Passfield, L. (2007). Variable versus constant power strategies during cycling time-trials:
Prediction of time-savings using an up-to-date mathematical model. Journal of Sports Sciences,25, 1001 –1009.
Barelle, C., Chabroux, V., & Favier, D. (2010). Modeling of the time trial cyclist projected frontal area incorporating
anthropometric, postural and helmet characteristics. Sports Engineering,12, 199– 206.
Berry, M. J., Pollock, W. E., van Nieuwenhuizen, K., & Brubaker, P. H. (1994). A comparison between aero and
standard racing handlebars during prolonged exercise. International Journal of Sports Medicine,15, 16 – 20.
Broker, J. P. (1994, November). Team pursuit aerodynamic testing, Adelaide, Australia. USOC Sport Science and
Technology Report, 1 – 24. Colorado Springs, CO
Broker, J. P., Kyle, C. R., & Burke, E. R. (1999). Racing cyclist power requirements in the 4000-m individual and
team pursuits. Medicine and Science in Sports and Exercise,31, 1677 – 1685. Retrieved from http://journals.lww.
com/acsm-msse/Abstract/1999/11000/Racing_cyclist_power_requirements_in_the_4000_m.26.aspx
Candau, R., Grappe, F., Me
´nard, M., Barbier, B., Millet, G. P., Hoffman, M. D., ... Rouillon, J. D. (1999).
Simplified deceleration method for assessment of resistive forces in cycling. Medicine and Science in Sports and
Exercise,31, 1441– 1447. Retrieved from http://journals.lww.com/acsm-msse/Abstract/1999/10000/
Simplified_deceleration_method_for_assessment_of.13.aspx
Capelli, C., Rosa, G., Butti, F., Ferretti, G., & Veicsteinas, A. (1993). Energy cost and efficiency of riding
aerodynamics bicycles. European Journal of Applied Physiology,67, 144– 149.
Capelli, C., Schena, F., Zamparo, P., Dal Monte, A., Faina, M., & di Prampero, P. E. (1998). Energetics of best
performances in track cycling. Medicine and Science in Sports and Exercise,30, 614– 624. Retrieved from http://
journals.lww.com/acsm-msse/Abstract/1998/04000/Energetics_of_best_performances_in_track_cycling.21.aspx
Davies, C. T. M. (1980). Effect of air resistance on the metabolic cost and performance of cycling. European Journal
of Applied Physiology,45, 245– 254.
De Groot, G., Sargeant, A., & Geysel, J. (1995). Air friction and rolling resistance during cycling. Medicine and
Science in Sports and Exercise,27, 1090 – 1095. Retrieved from http://journals.lww.com/acsm-msse/Abstract/
1995/07000/Air_friction_and_rolling_resistance_during_cycling.20.aspx
Debraux, P., Bertucci, W., Manolova, A. V., Rogier, S., & Lodini, A. (2009). New method to estimate the cycling
frontal area. International Journal of Sports Medicine,30, 266–272.
Defraeye, T., Blocken, B., Koninckx, E., Hespel, P., & Carmeliet, J. (2010). Aerodynamic study of different cyclist
positions: CFD analysis and full-scale wind-tunnel tests. Journal of Biomechanics,43, 1262 – 1268.
di Prampero, P. E. (1986). The energy cost of human locomotion on land and in water. Inter national Journal of Sports
and Medicine,7, 55– 72.
P. Debraux et al.216
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
di Prampero, P. E. (2000). Cycling on earth, in space and on the moon. European Journal Applied of Physiology,82,
345– 360.
di Prampero, P. E., Cortili, G., Mognoni, P., & Saibene, F. (1979). Equation of motion of a cyclist. Journal of Applied
Physiology,47, 201– 206. Retrieved from http://jap.physiology.org/content/47/1/201.abstract
Dorel, S., Hautier, C. A., Rambaud, O., Rouffet, D., Van Praagh, E., Lacour, J.-R., & Bourdin, M. (2005). Torque
and power-velocity relationships in cycling: Relevance to track sprint performance in world-class cyclists.
International Journal of Sports and Medicine,26, 739–746.
Du Bois, D., & Du Bois, E. F. (1916). Clinical calorimetry: A formula to estimate the approximate surface area if
height and weight be known. Archives of Internal Medicine,17, 863 – 871. Retrieved from http://archinte.
ama-assn.org/cgi/content/summary/XVII/6_2/863
Faria, E. W., Parker, D. L., & Faria, I. E. (2005). The science of cycling: Factors affecting performance – Part 2.
Sports Medicine,35, 313 – 337. Retrieved from http://adisonline.com/sportsmedicine/Abstract/2005/35040/
The_Science_of_Cycling__Factors_Affecting.3.aspx
Faria, I. E. (1992). Energy expenditure, aerodynamics and medical problems in cycling. Sports Medicine,14, 43 –63.
Retrieved from http://adisonline.com/sportsmedicine/Abstract/1992/14010/Energy_Expenditure,_Aero
dynamics_and_Medical.4.aspx
Garcia-Lopez, J., Peleteiro, J., Rodriguez, J. A., Cordova, A., Gonzalez, M. A., & Villa, J. G. (2002). Biomechanical
assessment of aerodynamic resistance in professional cyclists: Methodological aspects. In K. E. Gianikellis
(Ed.), Proceedings of the XXth International Symposium on Biomechanics in Sports (pp. 286 – 289). Caceres:
University of Extremadura.
Garcia-Lopez, J., Rodriguez-Marroyo, J. A., Juneau, C.-E., Peleteiro, J., Cordova Martinez, A., & Villa, J. G. (2008).
Reference values and improvement of aerodynamic drag in professional cyclists. Journal of Sports Sciences,26,
277– 286.
Gonzales-Haro, C., Galilea Ballarini, P. A., Soria, M., Drobnic, F., & Escanero, J. F. (2007). Comparison of nine
theoretical models for estimating the mechanical power output in cycling. British Jour nal of Sports Medicine,41,
506– 509.
Gonzales-Haro, C., Galilea, P. A., & Escanero, J. F. (2008). Comparison of different theoretical models estimating
peak power output and maximal oxygen uptake in trained and elite triathletes and endurance cyclists in the
velodrome. Journal of Sports Sciences,26, 591 – 601.
Grappe, F. (2009). Re
´sistance totale qui s’oppose au de
´placement en cyclisme [Total resistive forces opposed to the
motion in cycling]. In Cyclisme et Optimisation de la Performance (2
nd
edn.) [Cycling and optimisation of the
performance] (p. 604). Paris: De Boeck Universite
´, Collection Science et Pratique du Sport.
Grappe, F., Candau, R., Belli, A., & Rouillon, J. D. (1997). Aerodynamic drag in field cycling with special reference
to the Obree’s position. Ergonomics,40, 1299– 1311.
Grappe, F., Candau, R., McLean, J. B., & Rouillon, J. D. (1999). Aerodynamic drag and physiological responses in
classical positions used in cycling. Science et Motricite
´,38–39, 21–24.
Gross, A. C., Kyle, C. R., & Malewicki, D. J. (1983). The aerodynamics of human-powered land vehicles. Scientific
American,249, 126–134.
Heil, D. P. (2001). Body mass scaling of projected frontal area in competitive cyclists. European Journal of Applied
Physiology,85, 358– 366.
Heil, D. P. (2002). Body mass scaling of frontal area in competitive cyclists not using aero-handlebars. European
Journal of Applied Physiology,87, 520– 528.
Heil, D. P. (2005). Body size as a determinant of the 1-h cycling record at sea level and altitude. European Journal of
Applied Physiology,93, 547– 554.
Heil, D. P., Murphy, O. F., Mattingly, A. R., & Higginson, B. K. (2001). Prediction of uphill time-trial bicycling
performance in humans with a scaling-derived protocol. European Journal of Applied Physiology,85, 374– 382.
Hoerner, S. F. (1965). Re
´sistance a
`l’avancement dans les fluides [Fluid-dynamic drag: Practical information on
aerodynamic drag and hydrodynamic resistance]. Paris: Gauthier-Villars.
Jeukendrup, A. E., & Martin, J. (2001). Improving cycling performance: How should we spend our time and money.
Sports Medicine,31, 559 – 569. Retrieved from http://adisonline.com/sportsmedicine/Abstract/2001/31070/
Improving_Cycling_Performance__How_Should_We_Spend.9.aspx
Kyle, C. R. (1991). Racing with the sun. Philadelphia, PA: Society of Automative Engineers.
Kyle, C. R., & Burke, E. R. (1984). Improving the racing bicycle. Mechanical engineering,9, 34–45.
Martin, J. C., Gardner, A. S., Barras, M., & Martin, D. T. (2006). Modelling sprint cycling using field-derived
parameters and forward integration. Medicine and Science in Sports and Exercise,38, 592 – 597.
Martin, J. C., Milliken, D. L., Cobb, J. E., McFadden, K. L., & Coggan, A. R. (1998). Validation of a mathematical
model for road cycling power. Journal of Applied Biomechanics,14, 245 – 259. Retrieved from http://journals.
Aerodynamic drag in cycling 217
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
humankinetics.com/jab-back-issues/jabvolume14issue3august/validationofamathematicalmodelforroadcycling-
power
Menard, M. (1992). Improvement of the athlete’s performance. In First International Congress of Science and Cycling
Skills. Malaga: Spain.
Millet, G. P., & Candau, R. (2002). Facteurs me
´caniques du cou
ˆte
´nerge
´tique dans trios locomotions humaines
[Mechanical factors of the energy cost in three human locomotions]. Science & Sports,17, 166 –176. Retrieved
from http://www.em-consulte.com/article/24078
Nevill, A. M., Jobson, S. A., Davison, R. C. R., & Jeukendrup, A. E. (2006). Optimal power-to-mass ratios when
predicting flat and hill-climbing time-trial cycling. European Journal of Applied Physiology,97, 424 – 431.
Oggiano, L., Troynikov, O., Konopov, I., Subic, A., & Alam, F. (2009). Aerodynamic behaviour of single sport jersey
fabrics with different roughness and cover factors. Sports Engineering,12,1–12.
Olds, T. (1998). The mathematics of breaking away and chasing in cycling. European Journal of Applied Physiology,
77, 492– 497.
Olds, T. (2001). Modelling human locomotion. Sports Medicine,31, 497– 509. Retrieved from http://www.
ingentaconnect.com/content/adis/smd/2001/00000031/00000007/art00005
Olds, T. S., & Olive, S. (1999). Methodological considerations in the determination of projected frontal area in
cyclists. Journal of Sports Sciences,17, 335 – 345.
Olds, T. S., Norton, K. I., & Craig, N. P. (1993). Mathematical model of cycling performance. Jour nal of Applied
Physiology,75, 730– 737. Retrieved from http://jap.physiology.org/content/75/2/730.abstract
Olds, T. S., Nor ton, K. I., Lowe, E. L. A., Olive, S., Reay, F., & Ly, S. (1995). Modeling road-cycling performance.
Journal of Applied Physiology,78, 1596– 1611. Retrieved from http://jap.physiology.org/content/78/4/1596.
abstract
Padilla, S., Mujika, L., Angulo, F., & Goiriena, J. J. (2000). Scientific approach to the 1-h cycling world record: A
case study. Journal of Applied Physiology,89, 1522– 1527. Retrieved from http://jap.physiology.org/content/89/4/
1522.full
Pugh, L. G. C. E. (1970). Oxygen intake in track and treadmill running with observations on the effect of air
resistance. Journal of Physiology,207, 823– 835. Retrieved from http://jp.physoc.org/content/207/3/823
Pugh, L. G. C. E. (1971). The influence of wind resistance in running and walking and the mechanical efficiency of
work against horizontal or vertical forces. Journal of Physiology,213, 255– 276. Retrieved from http://jp.physoc.
org/content/213/2/255
Shuter, B., & Aslani, A. (2000). Body surface area: Du Bois and Du Bois revisited. European Jour nal of Applied
Physiology,82, 250– 254.
Swain, D. P., Richard, J., Clifford, P. S., Milliken, M. C., & Stray-Gundersen, J. (1987). Influence of body size on
oxygen consumption during bicycling. Journal of Applied Physiology,62, 668–672. Retrieved from http://jap.
physiology.org/content/62/2/668.abstract
Tew, G. S., & Sayers, A. T. (1999). Aerodynamics of yawed racing cycle wheels. Journal of Wind Engineering and
Industrial Aerodynamics,82, 209–222.
Whitt, F. R. (1971). Estimation of the energy expenditure of sporting cyclists. Ergonomics,14, 419 – 424.
P. Debraux et al.218
Downloaded by [SCD DE L'Universite De Franche Comte], [Fred Grappe] at 00:14 07 October 2011
