AERODYNAMIC DRAG

FROM CYCLINGPOWERLAB

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 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. 

Format Cd (Estimate) A (Frontal Area, Rider Height   cm, Weight   kilos) CdA

Time Trial Bike 0.7 A = 0.3262 = 0.0293 x 1.75 ^ 0.725 x 69 ^ 0.425 + .0604 CdA = 0.2284 = 0.7 x 0.3262

Road Bike (Drops) 0.88 A = 0.4151 = 0.0276 x 1.75 ^ 0.725 x 69 ^ 0.425 + .1647 CdA = 0.3653 = 0.88 x 0.4151

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 post-test 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.

Source Test Format Scenario CdA

High Performance Cycling (Jeukendrup, 2002) Wind Tunnel Tops .4080

High Performance Cycling (Jeukendrup, 2002) Wind Tunnel Hoods .3240

High Performance Cycling (Jeukendrup, 2002) Wind Tunnel Drops .3070

High Performance Cycling (Jeukendrup, 2002) Wind Tunnel Aerobars (Clip on) .2914

High Performance Cycling (Jeukendrup, 2002) Wind Tunnel Aerobars (Optimised) .2680

Bikeradar Article "How Aero Is Aero" (2008) Wind Tunnel Road Bike, Road Helmet, Drops .3019

Bikeradar Article "How Aero Is Aero" Road Bike, Road Helmet, Aerobars .2662

Bikeradar Article "How Aero Is Aero" Road Bike, TT Helmet, Aerobars .2547

Bikeradar Article "How Aero Is Aero" TT Bike, Road helmet, Aerobars .2427

Bikeradar Article "How Aero Is Aero" 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

Scientific approach to the 1-h cycling world record: a case study (Padilla et al, 2000) Moser 1984 (TT bike ex. Aero bars) .2481

Scientific approach to the 1-h cycling world record: a case study (Padilla et al, 2000) Obree 1994 (Obree position) .1720

Scientific approach to the 1-h cycling world record: a case study (Padilla et al, 2000) Indurain 1994 (TT Bike, TT Helmet, Aero bars) .2441

Scientific approach to the 1-h cycling world record: a case study (Padilla et al, 2000) Rominger 1994 (Superman position) .1932

Scientific approach to the 1-h cycling world record: a case study (Padilla et al, 2000) Boardman 1996 (Superman position) .1838

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.
  
  
  Yaw Drag & Component Choice
  
  

"Ignore your aircrafts crosswind limits and yaw'll be sorry" reads a popular safety poster aimed at trainee pilots. This has little to do with cycling but it gives a big clue what yaw is all about - the idea that, in crosswind conditions, the direction of airflow hitting a moving object - such as an aeroplane or a bike - is some combination of the direction of motion and direction of the wind. For the poor trainee pilot this poses certain control challenges, while for the cyclist it has real relevance to drag and equipment choice. 

To help in our discussion of yaw, let's define two kinds of wind. There is the wind that blows due to weather, perhaps a south westerly breeze blowing at 10 kph, from now on we'll call it the meteorological wind. And there is the "wind" that we perceive due to cycling at speed, even on a flat-calm day with zero meteorological wind you experience some of this "wind" in your face. Of course this isnt wind in the true sense, rather a cyclist moving through a (still) body of air experiences a sensation the same as if the rider was static and the wind was blowing at the speed of the rider. Many people would refer to this wind as wind resistance and so we'll call it resistance wind. 

It follows that in a real word environment a rider experiences some meteorological wind, which has a strength and a bearing you might figure from a weather report, and some resistance wind, depending on the speed he is riding but always with a bearing directly in his face. It also follows that these two winds combine or offset to create just one wind on the rider. This wind we can call the "effective wind" and the angle it hits the rider is known as it's yaw angle. 

Given that most of us ride significantly faster than the meteorological wind is blowing, most of the time, the resistance wind tends to dominate. For example, if we ride at 40kph with a 10kph full-on sidewind (meteorological wind approaching at 90 degrees to our ride direction) the effective wind has a yaw angle of just 14 degrees. In fact modelling suggests that somewhere between 50 and 70 percent (let's say 2/3rds) of effective wind yaw angles experienced by a rider are lower than 10 degrees, the faster your ride, the higher this percentage. The same research suggests that a further 30 percent (let's say 1/3rd) of effective wind yaw angles are between 10 and 20 degrees. 

You might arrive at the same conclusion after a few trials with this Yaw calculator: 

• Bike Velocity (KPH)

• Wind Velocity (KPH)

• Wind Angle (Degrees)

• Yaw Angle (Effective Wind in Degrees)

• Effective Wind (KPH)

• Axial (Head) Wind Component (KPH)

• Lateral (Cross or Side) Wind Component (KPH)

The Relevance of Yaw

So why does yaw matter? Life is never simple and it so happens that cyclists, bike frames and wheels, as well as the whole lot together, present different drag profiles depending on the yaw angle of the wind. On the other hand much aero equipment offers less advantage at the lowest (eg zero) yaw angles, hence why aero frame and wheel manufacturers are now particularly keen to demonstrate the advantages of using their equipment in terms of drag reductions at specific, meaningful yaw angles, especially the 0-20 degree kinds that most of us experience, most of the time. 

Consider the following extracts from the current Zipp technical literature (left) and from an aero frames review comissioned by VeloNews (right) which graph drag numbers attributed to various aero components at various yaw angles. Note - "AOA" in the first example denotes "Angle of Attack" which is simply aerodynamicists (or aviators) speak for effective wind yaw angle. 

What could we conclude from the above?

1. Most cycling equipment, including in these examples, tends to be drag tested with airflow at 30mph so the quoted drag numbers apply only at this speed, they can however be normalised to other speeds. The benefits accruing to an individual rider depend on ability - the faster we ride, the more we benefit from aero equipment.

2. All of the wheels tested by Zipp experienced basically the same drag at 0 degrees yaw (the very left of the chart). To explain this consider whether one 700c wheel looks any different from the next when viewed head-on.

3. Differences between the wheels become more pronounced as the yaw angle increases, peaking in the 10-15 degree range before levels of drag converge again. This is unsuprising - manufacturers know the distribution of yaw angles experienced by most cyclists and design their wheels to be optimal.

4. The aero frames (as complete bikes) tested by VeloNews also display the lowest drag differentials around zero degrees yaw, only in this case "0 degrees" is plotted in the middle of the chart with negative yaw angles off to the left. There may be some merit in testing frames with left and right yaw due to asymmetric design that is less relevant to wheels.

5. Differences between drag applicable to the bikes peaks between 10-20 degrees yaw.

6. For the reaons mentioned above we should be particularly interested in drag differentials in the 0-10 degree range, followed by the 10-20 degree range.

7. Drag savings quoted in terms of grams (or sometimes pounds) can appear quite abstract and have little meaning to the layman. When deciding which wheels to invest in we want to know savings in terms of watts or benefits in terms of speed...
   
   

From drag to wattage savings...and speed effects

So what does it mean to save X grams of drag at 30mph, besides what the manufacturer promises us it means? You may have seen a rule of thumb that "50 grams of drag at 30mph is worth 5 watts" but, on a practical level, it is far nicer to be able to transform drag at a specific measurement speed to wattage savings at this or another speed. Some simple rearrangements of the equations of motion that make up cycling power models allow us to do this. 

Use the following calculator to find wattage savings applicable to drag numbers, it also calculates "equivalent" CdA (meaning the change in a riders CdA that would be explained by the drag number) since this is one of the intermediate values in the calculation. 

• Drag

• Measured at Speed

• Equivalent CdA *  

• Target Speed

• Watts *
  
  

*These measurements assume a "standard" sea level air density of 1.225 kg/m^3

The "advantage" of watts is something you can think about in terms of

Training. How hard is it to increase threshold power by X watts?

Speed. The speed benefit of "X watts saving" really depends how fast you are assumed to be riding before applying the saving. We suggest the Scenario Model to study the effect of watts on speed, although keep in mind that your wattage number has been derived from a drag number applied to a specific speed.