Cycling Aerodynamics & CdA  A Primer
A riders aerodynamic drag is a critical factor in the speed he can achieve at a
given level of power output and therefore a given level of fitness. New users of
cycling power models frequently observe that all of the parameters to a power or
speed model  weight, gradient, windspeed, air pressure, temperature, etc  are
relatively easy to find, but that the aerodynamic drag (CdA) parameter is not so
easy. With a bit of experimentation it becomes apparent that CdA has the greatest
effect on the "speed given power" or "power given speed" output from the model
on all but the hilliest courses and that minimising drag is key to faster
cycling. In fact the ratio of a riders power to CdA is probably far more
important that the often quoted "watts per kilo" measure, this is why Power:CdA
summary statistics are included on the
Power Data
page, while this page focusses
entirely on aerodynamic drag  what it is, ways to find it, and typical values.
What is Aerodynamic Drag or CdA?
Aerodynamic drag is air resistance
atttributed to an object. It is a product of an objects drag coefficient (Cd) or
"slipperyness" and it's size, criticaly it's frontal area (A). Hence the
scientific measurent of aerodynamic drag and the input required by a cycing
power model is Cd x A written as CdA.
Coefficient of drag is a dimensionless number that relates an
objects drag force to its area and speed, it ranges upwards from 0. An object
with a drag coefficient of 0 could not exist on earth, while teardrops or wing
shapes have some of the very lowest drag coefficients. Typical drag coefficients
are as follows:
Wing or Teardrop 
0.005 
Ball 
0.5 
Person stood upright 
1.0 
Flat plate faceon to airflow 
1.17 
Brick 
2.0 
Cyclist (Tops)* 
1.15 
Cyclist (Hoods)* 
1.0 
Cyclist (Drops)# 
0.88 
Cyclist (Aero Bars)# 
0.70 
How these drag coeficients are calculated is not so important
here, suffice to say that with a wind tunnel it's possible to derive an objects
drag coefficient from measurable drag forces. Technically drag can be decomposed
into "form or pressure drag", due to the shape of an object, and "skin friction
drag" (how shiny is your skinsuit?!), but the difference is also of lesser
importance in practical terms.
Frontal area is typically measured in metres
squared. A typical cyclist presents a frontal area of 0.3 to 0.6 metres squared
depending on position.
Frontal areas of an average cyclist riding in different positions are as follows
Tops* 
0.632 
Hoods* 
0.40 
Drops* 
0.32 
*Source = "Bicycling Science" (Wilson, 2004). It is unlikely these values included helmets.
#Source = "The
effect of crosswinds upon time trials" (Kyle,1991)
It follows that an average sized cyclist riding on the drops (having a frontal
area at the lower end of the spectrum) might ride with an effective CdA of 0.88 * 0.36 =
0.32.
As to what a CdA of 0.32 means, there is a
formulaic relationship between CdA, air density, and cycling speed which is
built into any model of cycling power and which determines the amount of power
(i.e. watts) that would be required to overcome air resistance at that speed.
This is written as
F= CdA p [v^2/2]
where:
F = Aerodynamic drag force in Newtons.
p = Air density in kg/m3 (typically 1.225kg in the "standard atmosphere" at sea level)
v = Velocity (metres/second). Let's say 10.28 which is 23mph
In our examle of CdA 0.32 aerodynamic drag generates a force of
0.32 x 1.225 x
[(10.28^2)/2]= 20.71 Newtons
And the power required to overcome this force at
10.28 metres/second is
20.71 N x 10.28 m/s= 213 watts.
Clearly CdA has an important effect on the speed of a cyclist, making it a
desirable characteristic to estimate and minimise.
Yaw
No primer on cycling aerodynamics would be complete without a mention of yaw. Briefly, in this context, yaw describes the idea that airflow doesnt always hit a rider head
on or at "0 degrees yaw", rather at some other "yaw angle" infuenced by wind. Intuitively and in practise riders, bikes, wheels, or the whole unit considered together have
different drag characteristics and therefore present different CdA's depending on the yaw angle of airflow. Yaw is highly relevant in component choice because aerodynamic components tend
to betteroutperform "standard" components when a cyclist is experiencing airflow at significant yaw angles, something which happens a lot in road environments.
For more discussion of yaw take a look at
Component Choice & Yaw
The CdA's mentioned or quoted on this page or anywhere else on this site (unless otherwie stated) refer to a CdA which is nonspecific in
terms of yaw angle. This is because the theoretical models of cycling power work well enough with one, constant CdA input applied in conjunction with
a wind vector adjusted to zero yaw; because the 0 yaw CdA is the most commonly quoted test value; and because CdA field tests (see below) compute a CdA
in terms of one constant number assumed to have been experienced throughtout the test.
Estimation of a Cyclists CdA
There are a few options to arrive at a realistic estimate of a riders CdA..
1) Find frontal area (A) with a digital photograph and some software, estimate Cd
One way to find a riders
frontal area is with a digital photo and some photo editing
software similar to photoshop (such as the freeware
Paint.NET
).
Consider the following which is a just a "cut out" of Mark Cavendish from a
digital photo taken at the Tour de France. Creating a cut out like this is
fairly trivial depending of course on familiarity with the software.
At the bottom of the screen, having selected the image representing Cavendish
and his bike,
the software is giving us a frontal area in pixels: 33,087. All we need to
arrive at a frontal area is metres squared is some way to relate pixels and
metres using known dimensions in the picture. A reasonably reliable measurement
to use is the height of the front wheel including tyre which in the picture
measures 185 pixels. Now if we assume it's a 700c wheel with 23mm tyres it
should correspond to a diameter of 622+(2*23) = 668 mm. (622 is the standardised
tyre bead diameter of a 700c wheel). Simple maths can then
reveal frontal area in metres:
Pixels per square metre = (185/0.668)^2 = 76,699
Frontal area = 33,087 / 76,699 = .4314 metres squared
This estimate of frontal area can easily be multiplied with a suitable estimate
for a coefficient of drag, such as 0.88 from above, to derive a CdA of
0.88 x .4314 = 0.3780. Interestingly enough this CdA is very close to the value
for a 175cm, 69 kilo rider (such as Mark Cavendish) riding on the drops as will
be estimated using the next option and this evokes some confidence in this
method which could be replicated by any rider who can find a friendly
photographer.
2) Use CdA estimation formula developed from historically observed relationships.
A number of cycling focussed sports scientists have attempted to estimate riders
frontal area based on body size (anthropometric) parameters, the most accessible
ones being height and weight. They have typically used regression analysis to
develop an equation predicting frontal area from these measurements. One such
effort was published in a very popular study "Comparing cycling world hour
records, 19671996: modelling with empirical data" in which the authors sought
to estimate and compare the power output of hour record holders by adjusting for
differences in aerodynamic drag. This study suggests formula to predict frontal
area in both the time trial and road bike (drops) position so it's particularly
useful.
Without labouring the details these formulas were found to be reasonably
predictive when compared with wind tunnel drag data. They can be seen, and used,
below where they are combined with the above coefficient of drag estimates to
provide CdA estimation formula.
3) Use a wind tunnel to accurately measure CdA
A wind is generally accepted as the most accurate way to measure rider's CdA and is also the easiest option (depending of course on availabiliy of a local low
speed wind tunnel!) although unlikely the cheapest. Wind tunnel measurement of CdA can reveal the impact of incredibly minor changes to riding position as we
might deduce from the following photos of Carlos Sastre combined with views from the reporting software. (Incidentally this testing was done in the spring before
his yellow jersey defending time trial at the conclusion of the 2008 Tour de France).
In the first picture Carlos is registering a CdA of 0.26 which on a flat, windless course ridden at 300 watts might result in a 25 mile time of
56:46. In the second picture his position is apparently a bit flatter and he registers a CdA of 0.25. On the same flat, windless course
riden at 300 watts this reduced drag might result in a 25 mile time of 56:04, saving 42 seconds..
4) Use a power meter to find CdA
There exist several field test protocols which can be used to estimate CdA in a realistic, road or velodrome, environment. At CPL we have experimented with many of them and
have long offered calculators to help with posttest CdA calcualtion. Building on our experience we have now moved our CdA calulation resources into a dedicated aero analysis
site fastaerolab.com which, we beleive, makes aerodynamic field testing as easy as it possibly can be given only a power meter. Please check it out!
Typical CdA Values
It is important that whatever method one uses to "measure" or estimate CdA
delivers a number that can be trusted because it "looks right" compared with
some previously established measurements. Equally readers may be interested in
these numbers for their own sake, so what follows is a collection of CdA
observations drawn from some established sources.
Are you aware of further prolific sources of cycling CdA values that could be
shared here? Send us an email!
Source 
Test Format 
Scenario 
CdA 
High Performance Cycling (Jeukendrup, 2002) 
Wind Tunnel 
Tops 
.4080 
" 
" 
Hoods 
.3240 
" 
" 
Drops 
.3070 
" 
" 
Aerobars (Clip on) 
.2914 
" 
" 
Aerobars (Optimised) 
.2680 
Bikeradar Article "How Aero Is Aero" (2008) 
Wind Tunnel 
Road Bike, Road Helmet, Drops 
.3019 
" 
" 
Road Bike, Road Helmet, Aerobars 
.2662 
" 
" 
Road Bike, TT Helmet, Aerobars 
.2547 
" 
" 
TT Bike, Road helmet, Aerobars 
.2427 
" 
" 
TT Bike, TT Helmet, Aerobars 
.2323 
Scientific approach to the 1h cycling world record: a case study (Padilla et
al, 2000) 
Complex Estimation 
Mercx 1972 (Road bike, Std. Helmet, Drops) 
.2618 
" 
" 
Moser 1984 (TT bike ex. Aero bars) 
.2481 
" 
" 
Obree 1994 (Obree position) 
.1720 
" 
" 
Indurain 1994 (TT Bike, TT Helmet, Aero bars) 
.2441 
" 
" 
Rominger 1994 (Superman position) 
.1932 
" 
" 
Boardman 1996 (Superman position) 
.1838 
Cycling Power Lab
Many of the models on this website require a rider CdA input which should be as representative as possible to ensure that the model outputs are meaningful.
Cycling Power Models provides a range of ways to estimate CdA inputs with the objective of maximising the accessibility, utility and real world applicability
of the relevant models.
 Use an estimate based on a riding position (tops, hoods, drops, aero bars, etc)
 Specify a custom value (such as a known value or a value calculated with the Chung method)
 Specify height, weight and riding position. A CdA value will be calculated as
per "option 2" above
 Select the name of a professional rider and choose between a time trial and road
position. Using his or her height and weight data (the list includes some of the
biggest and smallest known professionals) a CdA will be estimated as per the previous method.
Play with our CdA estimator here >

