The Case for a Variable CdA in Cycling

If you need a refresher on what Cd is, or on the difference between Cd and CdA, read What is Aerodynamic Drag and CdA first; it is foundational for this section. In addition, some literature will refer to Drag Area, which is the same thing as CdA.

In brief

• Cars and planes: one Cd works. The shape of the airflow, flow regime, or streamlines for cars and subsonic airplanes is relatively constant across the speeds at which they are used. This means that their drag can be well modelled by a dimensionless number called the coefficient of drag.
• Cyclists: the flow changes with speed. Due to the size and shape of cyclists and the speeds they ride at, the flow around the cyclist changes with speed; therefore, a constant coefficient of drag is much less accurate than in most other aerodynamic domains.
• Fine for estimates, not for measurement. When making coarse approximations in cycling, such as an application where an error of 5% is not significant, a constant drag coefficient with speed can be used. However, when the purpose is precise measurement, many researchers and modellers in cycling have used a constant drag coefficient without being aware that the model can have errors 5 to 10 times greater than when used on cars or aircraft.
• A constant CdA is the exception. Just as a broken watch can be right twice a day, there are cases where the drag coefficient appears constant over several speeds in cycling; these are exceptions and should not be used as the basis for precise measurement. Both aerodynamic theory and experimental evidence show that in cycling, the drag coefficient changes with speed and that in measurement applications, it should not be ignored.

The Reynolds number should not be ignored

This article relies heavily on the term Reynolds number (Re). If you need a quick primer, the theory section below covers what is needed and also includes external links.

Widely documented resources describe a drag crisis starting at Re 200,000 for smooth cylinders and spheres, and at a much lower Re of 50,000 for rougher surfaces.

The drag crisis refers to a distinct change in the flow regime as it moves from laminar to turbulent resulting in:

• More attached flow, i.e. a delayed separation point.
• A narrower wake profile and reduced drag coefficients.
• For extreme cases such as polished spheres and cylinders, the drag coefficient can be 80% lower than its pre-crisis value. For cases with more roughness, the reduction can be about 30%.

Reynolds number is primarily driven by the size and speed of the object.

• The length cannot be precisely defined for complex shapes, but can be approximated.
• A cyclist in an aerodynamic position can be approximated as having a torso reference length of 700 mm.
• Legs and arms can be approximated at 70–300 mm depending on orientation. Vertical limbs can be approximated with their actual diameter. Inclined limbs are longer: at 60° from the vertical, the length doubles.

The textbook start of the drag crisis for rough and smooth cases is (50k -> 200k Re):

• For a 70 cm inclined torso, between 4 and 16 km/h (1.1–4.4 m/s)
• For an upright upper arm or lower leg with a 7 cm diameter, the crisis will theoretically begin between 40 and 160 km/h (11–44 m/s).

Considering the complex shape of a cyclist, from textbook values we can expect variations in CdA across the entire cycling speed range from 4 km/h to over 100 km/h (1–28 m/s).

What do actual wind tunnel tests on cyclists show?

• CdA changes can be greater than 10% or 0.06 on CdA, from 15 to 40 km/h (4–11 m/s)
• CdA generally decreases from 15 to 40 km/h; however, the minimum can be as low as 40 km/h (11 m/s), above which it rises at higher speeds. In other cases it may decrease steadily from 15 to 55 km/h (4–15 m/s).

As a note, there is an absence of data below 15 km/h (4 m/s), which is related to the difficulty of measuring these speeds in wind tunnels. Consequently, the actual start of the drag crisis on the torso region can only be estimated. None of the high-precision sources reviewed showed CdA levelling off at any speed, i.e. none showed the drag crisis finishing.

Finally, field tests at 35–50 km/h (10–14 m/s) show significant changes in CdA values, similar to what is seen in the wind tunnel.

The rest of this document will go into greater detail about the points raised above.

As a bonus, this section explains how the astronaut could uncover The Real Truth, just from looking at the image.

Theory: Reynolds numbers, shapes and speeds

Rounded bluff-body flow

We will begin the theoretical discussion with the statement: A cyclist should be considered a bluff body (yes, all of you). This simply means that there are large areas of airflow separation and that these separations are the dominant source of drag. An airfoil section does not fit this description. Its flow stays attached over most of the shape, and when it is not producing lift its drag comes mainly from skin friction. (When it is producing lift, induced drag from the tip vortices dominates.)

We will also divide bluff bodies into two categories: those with sharp distinct separation edges, and those with more rounded edges. A flat plate perpendicular to the airflow will separate very sharply and predictably around its perimeter, and provide a very constant Cd. A sphere will not have an obvious separation region and, as has been very strongly verified, has a variable separation region. We will classify all cyclists as having rounded separation regions.

The table below gives the measured Cd of five shapes at three Reynolds numbers.

The table shows that rounded bluff bodies such as spheres and cylinders have the largest variance in aerodynamic drag coefficient with speed. Airfoils have significant proportional changes in aerodynamic drag coefficient, but much smaller absolute changes. The flat plate at 90 degrees to the airflow is generally considered one of the most stable drag references.

This article will not go into the full definition of the Reynolds number. For an in-depth understanding, you can read the Wikipedia article. But you can also understand this article just by treating Re as proportional to airspeed × length, where length is a very approximate number. If you double the speed OR the size, Re will double; if both, it will be 4 times as large. If you double the size and halve the speed, Re is unchanged.

Published Reynolds numbers for critical speeds are very approximate, sometimes to only about two significant digits, which makes them very different from physical constants such as the gravitational constant, the gas constant or π. The reasons for the imprecision are a vast topic which we will not delve into in this article. It should also be remarked that the extreme drops seen in the polished cylinders and spheres are very unstable and require very low turbulence. Different experiments show quite different values, and should be seen as similar to limit values, rather than something encountered in practical applications.

Everything will be treated as a cylinder

Essentially, the majority of a cyclist's drag comes from the body, and the body can be very roughly modelled as a series of cylinders. An upright torso might be thought of as a cylinder with a diameter of 0.3 m, an inclined torso 0.6 m. A lower leg might be abstracted as a cylinder of diameter 0.15 m. At the same speed, an upright torso would have 2 times the Re number of the leg, and an inclined torso 4 times. Note: Torso measurements for a rider usually measure between 60–80 cm. 70 cm is used as an average in other places in this document, 60 cm is used here to keep a simple multiple of 4.

In terms of Reynolds numbers, cylinders and spheres have very similar transition zones, just different Cd values. We will generally refer to everything as a cylinder, though the torso of a TT cyclist is probably better approximated as a sphere. But since we are concerned with approximating the transition speeds and not the actual Cd values, it doesn't matter, since experimental results have shown the transition Re numbers to be similar.details

If you require exact numbers, this is the wrong subject for you. The important part to remember: The Reynolds Number is not applied directly to the calculation, instead it indicates how the subject should be modelled.

A crude analogy would be that a standard Mercator projection map is perfectly suitable for navigation at tropical and temperate latitudes. But if the latitude is near the poles, a different projection would be needed for navigation. Knowing only that you are at about 80°N ± 10° is a very coarse measurement, but it is enough to tell you which map to use.

I am not claiming an exact geometric relation for a cyclist's Reynolds number. The claim is that simple shapes that roughly resemble a cyclist, tested at equivalent Reynolds numbers, show a variable drag coefficient, so we should not be surprised when a cyclist's measured drag follows the same trends.

How cylinder drag varies with Reynolds number

A circular cylinder does not have a drag coefficient. It has a range, and which part of that range you get depends on Reynolds number and surface finish. Three curves here representing different turbulence / surface roughness cover the practical span. Note: Surface roughness creates small-scale turbulence; the effect on the cylinder is similar.

All three share a subcritical plateau at Cd = 1.20. Roughness does not change that plateau; it decides when the cylinder leaves it and how far it falls. A smooth cylinder drops by a factor of 5.7, to 0.21. A rough one only reaches 0.83 and is back above 1.0 at high Reynolds number. The delayed sharp drop requires a polished cylinder, which is quite different from the rider.

The same three curves can be drawn against air speed for cylinders of different diameters, because for a given diameter the Reynolds axis is just the speed axis scaled by D/ν.

How did the astronaut realise that CdA was variable for cyclists?

From the image, the astronaut saw a gradual separation on the rider's back. Knowing that the reference length of the rider is about 0.7 m and a cyclist might travel at 20 km/h (5.6 m/s), their Re number would be around 2.6×10⁵, which is in the highly variable range.

Whenever air separates along a continuous surface, as opposed to a sharp edge, there is almost always a Re dependency and a variable drag. On a sharp edge the separation point is fixed by the geometry. On a curved surface it depends on the state of the boundary layer. A laminar boundary layer separates early, while a turbulent one holds on further round the curve, leaving a narrower wake. Which state the boundary layer is in depends on Reynolds number, so on convex surfaces like a rider's back the separation point, and with it the drag, moves as speed changes.

What do wind tunnel results show?

The first wind tunnel test we will use is an often-cited study from Grappe (2009). The cyclist is described as a racing cyclist (though the CdA is a bit high) and the airspeed was varied from 15 km/h to 100 km/h (4–28 m/s).details The measurements are shown in Figure 4 and listed in Table 2.

This set shows a distinct drop across the 18 km/h (5 m/s) region, a steady descent to a minimum at 40 km/h (11 m/s), followed by a gradual rise.

This plot shows 12 different drag curves. The skinsuit, which introduces its own turbulence, gives the largest benefit at the two lowest turbulence levels.

It is also worth noting that at the minimum test speed for each series, there is already a strongly descending slope.

It is worth noting that the Grappe test, which predates textured skinsuits, shows the largest rise above its minimum, 15% from 40 to 100 km/h. These plots are just to show that CdA is highly variable with speed and although there are trends, testing at a number of speeds is a strict requirement to establish the shape of the CdA curve.

Correlating cylinders with the wind tunnel results

So far we have seen cylinders with fairly predictable speed sweep curves, and cyclist data which appears far more unpredictable.

We will now look at a PIV study from Terra, Sciacchitano & Scarano (2020), which gives direct velocity measurements of a cyclist's wake. In this case it is a static mannequin of a professional cyclist in a TT position. Figure 7 is redrawn from the study's data. It shows the critical speed, where the drag crisis occurs, at each measurement height on the limbs, and the cylinder size that would explain it. The torso was added here for reference.

It is worth noting that this cylinder comparison is not part of the PIV study, but it helps to show how the experimental results correlate with the more abstract cylinder results. Drag cannot be measured accurately from the PIV data in this type of experiment, so the wake width at each speed is used instead.

From the wake iso-surfaces in Figure 8 (right), it can be seen that the majority of the wake occurs in the upper thigh and buttocks, but below the torso. Importantly, the larger wake section from the upper thigh is relatively constant when compared to many of the smaller sections. An interpretation of this result is that the larger diameter regions began the flow transition below 18 km/h (5 m/s), reaching a minimum at around 36 km/h (10 m/s), while the upper arms and the lower legs with the smaller diameter show a general decrease from 18 to 90 km/h (5–25 m/s).

The actual flow patterns are quite complicated and even more complex with a pedalling cyclist. But the PIV does show that the sections at y = 950 mm, the thigh (d_w/d between 1.21 and 1.34) and the arm near the elbow (0.72 to 0.74), change little between 18 and 90 km/h (5–25 m/s), while the upper arm at 1000 and 1050 mm narrows its wake steadily (from 1.09 to 0.84, and from 1.37 to 0.99). That is evidence that the transition is happening very early, maybe as low as 7 km/h (2 m/s).

What does outdoor data show?

How the measurement is made

The Streamlines field testing method solves for aerodynamic drag over a GPS-gated course in four steps:

1. A probe measures dynamic pressure, yaw angle and barometric pressure; a power meter measures rider power; and a wheel-based speed sensor measures the ground speed.
2. Each run is divided into traverses. Rider power is varied between two levels, which, combined with an upwind and a downwind traverse, gives four air speeds, usually with a spread of 7–11 km/h (2–3 m/s).
3. For each traverse, an energy balance equation using rider power, kinetic and gravitational changes and a fixed rolling resistance gives the aerodynamic energy, which is divided by dynamic pressure to give a raw CdA, along with the traverse's average wind speed, yaw angle and, optionally, rider head and chest position.
4. The raw CdA is normalised for airspeed (Reynolds effects), yaw (sail effects) and, in some tests, rider position.

The data below are normalised for airspeed and yaw only. In the future, there will be an additional section showing the full yaw and speed normalisation process.

For these tests, a Crr value from roller tests is used with a road roughness offset estimate. In addition, a temperature adjustment is applied. The nature of the energy balance equation is that the higher the Crr value, the lower the CdA and vice versa.

In brief, when CdA really is constant with speed, only the correct Crr value gives a flat speed curve. When it is not, forcing a flat curve needs the wrong Crr:

The full relationship between estimated Crr and CdA slope is outside the scope of this article, but will be addressed in the future.

Mattie Dodd, 17 November 2025

The test below is a Streamlines test with Mattie Dodd. The full write-up and session report are on the Streamlines blog.

The tyre and environment details are:

This configuration was not full race gear. The cold-temperature Crr is probably an overestimate, so no road roughness offset was applied.

This resulted in a CdA slope of −0.00406 CdA per m/s.

We can calculate what Crr would be required to flatten the slope to 0.0 CdA per m/s.

Mattie Dodd is a tall 82 kg rider; a CdA of 0.179 seems far too low, especially considering he was not in full race kit. The variable CdA in this case provides absolute numbers which match much more closely to a rider's race performance and expected tyre Crr.

Anna Kiesenhofer, 28 October 2025

This wheel test was part of a larger series of tests that Anna Kiesenhofer ran herself over two weeks. A write-up and session report are on the Streamlines blog.

The tyre and environment details are:

This resulted in a CdA slope of −0.00399 CdA per m/s, within 2% of Mattie Dodd's slope on a rider whose CdA is 20% lower.

A CdA of 0.153 on the road would be very low and, considering that this is not in race trim (no skinsuit, shoe covers, etc.), quite implausible. In addition, a Crr of 0.0065 for a Continental GP5000 TT on a smooth Swiss road seems unlikely even if the temperature is 15 °C.

Casper von Folsach

This test was part of a disc test / Tom Compton challenge. A write-up and session report are on the Streamlines blog.

The tyre and environment details are:

This CdA is high for Casper, even when accounting for the bar attached for the disc test. More tellingly, the Continental S + 111 configuration has repeatedly measured higher rolling resistance than the GP5000 TT, and this test is on a Majorcan farm road which is significantly rougher than the Swiss road in Anna Kiesenhofer's test. They are at a similar temperature, yet assuming a constant CdA gives Casper a Crr about a third of Anna's, which is the opposite of what the roads and tyres would predict.

Why a variable CdA and not an incorrect Crr

The three sessions side by side:

In practice, almost any actual decreasing CdA slope, and mildly increasing CdA slopes, will have a Crr value greater than zero that flattens the CdA slope, giving a constant CdA value. However, at higher air speeds, the Crr values become increasingly implausible. This is due to the Crr term being the remainder of a force that increases with speed², so any error arising from a variable CdA becomes larger with the square of the speed.

The asymmetry is the key point. Crr is only 10–25% of the energy at testing speeds (32–54 km/h, 9–15 m/s), so a Crr error barely moves CdA. A small CdA error, however, produces a large Crr error. So the fixed-CdA model shows up as Crr values that cannot be reasonably explained. As long as a road is relatively smooth, those Crr values can be checked against roller values, which are themselves slightly inflated by the roller curvature.

Streamlines rider testing

The field tests above are those for which Streamlines is allowed to show the data publicly. During a typical winter testing period Streamlines equipment will be used to test 15–20 riders on the same road with the same tyres in similar temperatures for multiple teams. This field data, like the teams' wind tunnel and tyre data, cannot be shared publicly, but all of it strongly correlates with a variable CdA with airspeed and predictable tyre Crr values.

Field tests by Streamlines approximate the drag reduction over a 7–14 km/h (2–4 m/s) band and use a linear fit for the drag slope. These tests rely on estimations of rolling resistance, which has an effect on the drag slope. With reasonable rolling resistance estimates, the Streamlines slopes, −0.004 to +0.0012 m² per m/s, fall inside the range of the Brown et al. (2023) wind tunnel sweeps.

Published research

It should first be noted that with the exception of the field tests, all of the other information listed above is in the public domain, and well known in aerodynamic fabric research. In particular, in 2010 Luca Oggiano at the Norwegian University of Science and Technology criticised di Prampero (1979) for treating CdA as a constant, and emphasised the need for a variable CdA in aerodynamic fabric development.

I think the gap between fabric research and field testing exists because some researchers are unfamiliar with the drag crisis and assume, following earlier studies, that a constant drag coefficient is adequate.

The two most cited sources for a constant CdA in cycling are Bassett (1999) and the aforementioned di Prampero (1979).

The Bassett paper states:

In the range of speeds in endurance track racing (50–60 kph), the drag coefficient of cyclists Cd is typically constant as long as the rider position, equipment, and environmental conditions are constant. This was shown by full scale tests in the General Motors Automotive wind tunnel, Warren, MI (Broker 1995). For a fixed riding position, when the air drag was plotted versus velocity squared in the range from 40 to 56 kph, the result was linear with the average r2 = 0.998.

Broker (1995) is Broker, J. P., and C. R. Kyle. Pursuit Aerodynamics, Project 96: Wind Tunnel Test Results. USOC Sport Science and Technology Report, Colorado Springs, December 1995, pp. 1–46, which is not publicly available.

Since I have only the text above to understand the research, I will take the stricter view that the regression passed through zero. A line through the origin forces drag to be proportional to speed squared, which is exactly a constant CdA, so any change in CdA with speed shows up as scatter about the line and lowers r². With a free intercept, a CdA that changes steadily with speed is largely absorbed by the intercept, and r² stays close to 1 almost regardless. Using the through-zero definition, an r² = 0.998 is not as definitive as it initially sounds; it still allows ±0.0017 CdA per m/s. It is worth noting that 3 of the 12 Brown (2023) wind tunnel speed sweeps have a slope within this range, while the other 9 sit below −0.0017. The von Folsach field data, while clearly rising, sits within the criterion, and the Grappe (2009) data sits above it at +0.0028. If the regression did not pass through zero, almost all of the wind tunnel CdA sweeps would pass the r² = 0.998 criterion.

Also worth noting is that a co-author of this study is Dr Chester Kyle, who has numerous other papers that show CdA varying with speed. One possibility is that the constant value was considered a decent approximation for the purpose of studying human record attempts. What is clear from looking at other citations is that this invariability was then taken up in the measurement context.

García-López (2014) is a velodrome study. I will quote the following:

Nevertheless, the SCx in the velodrome decreased (0.0013 m2 each 1 km · h − 1) when the bicycle speed increased. This is consistent with a previous study which showed that the underestimation of the power output increased at the highest bicycle speeds [ 11 ]. In theory, for a fixed riding position, the critical Reynolds’s number did not change from 36 to 72 km · h − 1 [ 1, 6 ].

Several things are worth noting here. Firstly, the slope of 0.0013 m2 each 1 km · h − 1 translates to −0.0047 CdA per m/s, which is very typical. Secondly, source 6 is the paper Defraeye (2010), which states:

Possible Reynolds number effects could play a role due to the use of different wind speeds although CD is usually fairly constant in the Reynolds number range for cycling (Basset et al., 1999)

So 'fairly constant' can be fine for estimating world records where power is increasing at v³ or validating a CFD study; however, it is completely different to use it as a diagnostic of a measurement system.

The second paper that is often cited is di Prampero (1979). It is an experiment where a bicycle is towed behind a car to measure the drag. The resolution of the measurements is not suitable to determine if CdA can be held constant, so it relies on a paper, Pugh (1971), The Influence of Wind Resistance in Running and Walking and the Mechanical Efficiency of Work against Horizontal or Vertical Forces. In this paper, Pugh estimates a human as a cylinder of diameter 0.15 m and then states that from Reynolds theory drag should be constant from 5 to 67 km/h (1.5–18.5 m/s), which is somewhat reasonable; however, I will point out that the typical chest depth is about 0.25 m, which would reduce this speed to 40 km/h (11 m/s).

Di Prampero then states:

The dimensionless Cd is a function of the Reynolds number. However, in the range of air velocities of interest in cycling and for a given posture, Cd is constant (for a detailed treatment of this subject, the reader is referred to Pugh 1971).

Elsewhere in the paper, the cyclist position was referred to as "fully dropped", which would increase the unit length by 2–3 times, meaning that the end of the constant CdA regime would be about 18 km/h (5 m/s). We can see from the wind tunnel tests that 18 km/h is still probably an overestimate. Either way, a reference length chosen for a walking man does not carry over to a cyclist in the drops.

Where the constant CdA came from

The chain of citations runs roughly as follows. Pugh (1971) modeled a runner as a 0.15 m cylinder and concluded that Cd would be constant on the subcritical plateau up to about 67 km/h (18.5 m/s). di Prampero (1979) carried that conclusion across to a cyclist in the drops without rescaling the reference length. Broker (1995) and Bassett (1999) found a straight line of drag against speed squared over 40–56 km/h and reported r² = 0.998, which was read as proof of a constant Cd. Defraeye (2010) cited Bassett to justify a single-speed CFD validation, and García-López (2014) cited both to explain away a measured slope of −0.0047 m² per m/s. Each step was a reasonable approximation for its own purpose. None of them measured a constant CdA over the cycling speed range, and the two sources that did sweep speed, Grappe (2009) and Brown (2023), show it varying by 10% or more.

This is not a complete picture of all the studies in this domain; there are other paths as well. As the fabric research data, which is strongly focused on the drag crisis, percolates through the cycling community, the concept of a constant CdA will further diminish, but this process is far from complete.

Conclusion

This article lays out the application of Reynolds number theory with experimental data showing that a variable CdA should be expected in cycling. The wind tunnel force data shows a similar picture, and the wind tunnel PIV data shows where the separation points on the cyclist are changing. Finally, the outdoor field tests correlate well with the drag changes seen in the wind tunnel.

This conclusion does not go against any pre-existing experimental data; the pre-2000 data was not precise or complete enough to provide a conclusion about the invariable or variable nature of CdA with speed. Regardless, the Reynolds number calculation should have aroused suspicions about the variability.