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 a 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 face-on 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 better-outperform "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, 1967-1996: 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

Unsuprisingly the most accurate option for measuring a riders CdA is with a wind tunnel, it is also the easiest option (depending 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 Caros 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

Since the development of the "Chung Method" it's no longer absolutely necessary to use a flat, windless enviornment such as a velodrome for CdA estimation with a power meter. This is an apealing method of real world CdA estimation which owners of power meters can use over and over again to make progressive improvements in terms of drag minimisation. The Chung Method is outlined in greater detail and made available as the Chung Method CdA Estimation  model.

An alternative to the Chung method which may be better suited to flat roads and velodrome environments estimates CdA using a regression method. The Regression Method of Martin et al (2006) is available as the Regression Method CdA Estimation  model.

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 1-h 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.