Do aerodynamics matter off-road? Yes, more than you might think...

"Aerodynamics doesn't matter below 20 kph"  is something I often hear on cycling podcasts or internet forums.

Sometimes the "20 kph" gets substituted with 15 kph or 25 kph or some other arbitrary speed, but regardless, these kind of statements suggest incorrectly that there is some threshold speed below which the aerodynamic drag suddenly becomes zero, or negligible.

As an aerodynamicist, I tend to get irritated by these kind of statements.  As the plot above shows, the power losses due to aerodynamic drag get progressively larger at faster speeds, but there is no speed 'threshold' at which aerodynamics doesn't matter.  It's a continuum.  A more appropriate question to ask would "How important is aerodynamics at xx kph?".  This is the subject of this blog post: How much does aerodynamics matter off-road, at those slower speeds?

What % of power goes to overcoming aerodynamic losses?

To answer that question, I calculated the power losses for three power outputs, and three scenarios:

    - Power outputs: 150 Watt, 300 Watts & 450 Watts
    - Scenarios: Road Bike, Gravel Bike, Mountain Bike

The 150-450W power range covers a wide variety of rider abilities and situations, ranging from recreational riders doing an endurance event, to a professional rider doing a shorter effort.
The road, gravel and mountain bikes scenarios are represented through changes to the rolling resistance coefficient values (CRR) primarily, but also some small changes to the aerodynamic drag area (CdA) to reflect the more draggy set-ups for gravel and mountain bikes:

   - Road Bike:        CdA = 0.32, CRR = 0.0040

   - Gravel Bike:      CdA = 0.34, CRR = 0.0133

   - Mountain Bike:  CdA = 0.40, CRR = 0.0159

The road bike CRR values comes from my own testing.  The off-road CRR values come from data gathered from the excellent testing performed by John Karrasch, using Cat 2 gravel CRR values for the gravel bike and Cat 3 gravel for the MTB case.  I used values for the Specialized Pathfinder 700x45 mm tyre for gravel (CRR=0.0133) and the Maxxis Aspen 29x2.4" tyre for MTB (CRR=0.0159).  Those are both popular and reasonably fast gravel and MTB tyres.

The plot below shows what percentage of the rider's power output goes into overcoming aerodynamic losses, and what percentages are lost elsewhere.  To keep things simple I've assumed zero gradient, so gravitational losses are zero.

The aerodynamic losses are the largest percentage for most of the nine cases shown in the plot above.  Not surprisingly, for the road bike case, the aerodynamic losses dominate, with those % values having a fairly narrow range of 78-87% even over that very large 150-450W power range.  This is already an important point to note: Although the number of Watts lost to aerodynamic losses varies significantly across the three 150/300/450W rider power cases, but the percentage of the aerodynamic losses is fairly similar for all three cases.

The off-road cases are interesting too though.  The percentage of the power lost to aerodynamic losses is still significant, and accounts for over half the power losses in most of the off-road cases.  It's only the two slowest cases, the 150W cases, where the rolling resistance losses slightly exceed the aerodynamics losses.  Still, in those two cases, aerodynamics still accounts for about 40-50%, which is still a significant proportion.

It's clear then that yes, aerodynamics do matter off-road, even across this wide range of scenarios which cover the vast majority of off-road riding abilities and conditions.

Out of interest, I calculated how much slower you'd need to go for aerodynamics to become insignificant.  I modelled a very slow 16 kph (10 mph) case, which I think represents a low level amateur racing cyclocross in the most foul winter conditions, having a very high CRR of 0.06 and a power output of 250W (which by the way is fairly representative of my own cyclocross races).  In that case, at such so slow speeds, the aerodynamic losses are only 7%, so far less significant than rolling resistance losses through thick mud.  Even so, aerodynamics is still not negligible, even in this extreme case of a muddy cyclocross race.

Are aerodynamic improvements worth making?

This is a slightly more interesting question.  While the percentage of aerodynamic losses, discussed above, show that aerodynamics is important, what most of us really want to know is whether it's worth the effort of improving our aerodynamics when riding off-road.

I did a similar calculation to before, modelling road, gravel and MTB cases at those three different powers (150/300/450 Watts).  However, I calculated how much faster the speeds would be if the CdA was reduced by 0.012.  This 0.012 reduction to the drag coefficient is a 3.0-3.8% reduction.  It represents the kind of aero benefit that you'd achieve by swapping a non-aero helmet for an aerodynamic road helmet, like the Specialized Evade.  In fact, I calculated this 0.012 value from this video posted by Specialized, by reverse-engineering their quoted 40 km time trial time saving of 42 seconds.

The plot below shows how much the speed improves by, as a percentage, by making that same aerodynamic improvement for all nine cases.  Note that the % time saving, to cover a certain distance, is exactly the same as these values, since % speed increase and % time saving are the same:

The plot above shows that the % speed improvement (or % time improvement) from a certain aero improvement are fairly similar whether you're riding on the road or off-road.  Also, the % speed improvements are only slightly dependent on rider power and speed.  That aero helmet would improve Filippo Ganna's speed @450W by 1.24%.  However, it would also improve the speed of a 150W MTBer by 0.70%, which isn't much different.  This, surprised me and I think most people would also find the similarity unexpected.

Remember though, that the percentage of the rider's power that is lost to aerodynamic losses is fairly similar (88% for the 450W road bike case, versus 78% for 150W), even though the number of Watts lost (395W vs 117W respectively) varies significantly.

Still, I think there is a conventional wisdom that says the Pros, who ride faster, are the people that need to - and benefit most from - making aerodynamic improvements.  In fact, that's not really true. 

If you think that's counter-intuitive, it gets better...

The previous plot showed % time savings.  However, if you plot the time saving in seconds instead, the results are truly mind-blowing:

Since faster riders cover a certain distance faster than slower riders, a certain % improvement is a smaller number of seconds-saved for a faster rider than for a slower rider.  The plot above shows the number of seconds saved for a 40 km distance for these nine scenarios, plus the muddy 10 mph cyclocross (CX) case.  As you can see, not only are off-road time savings still roughly similar to road bike savings, the slower 150W riders actually save more seconds through the same aerodynamic improvements.  This is something that I've calculated in the past, but I still find it counter-intuitive.

I expect many people will find this result hard to believe.  Aerodynamic savings are almost as significant at slower off-road speeds as they for a road bike's higher speeds.  This is true for a wide range of riding abilities and scenarios.  Not only that, the time savings for slower riders are actually higher than for faster riders.

Don't believe these results?

If you don't believe me, I urge you to do the calculation yourself and leave a comment below.  The maths needed to calculate power losses due to aerodynamics and rolling resistance isn't too complicated.  The calculations that I did in Microsoft Excel only took about an hour or two to do.  If you need helps with the equations for the various power losses, refer to my old blog post here.

One final example: Unbound 500 + Keegan Swenson

As a bit of fun, let's consider an example that's loosely based on Keegan Swenson's win at the Unbound 200-mile gravel race in 2023.  He completed the 200 mile in 10 hour, 6 minutes, with an average power of 271W.  That's an average speed of 19.8 mph or 31.9 kph. 

If I make some simplifications by assuming he rode the whole distance solo and on flat terrain (both huge over-simplifications, admittedly), that speed and power is achieved with a CRR of 0.01635, which is not unreasonable.  For that ride then, we have the following:

• CRR = 0.01635
• CdA = 0.34
• Rider + bike = 85 kg
• Air pressure = 101,250 Pa
• Air temperature = 20 degrees C
• Air density = 1.203 kg/m3
• Drivetrain efficiency  = 3%
• Speed = 31.9 kph
• Power = 271W

Keegan, 271W, non-aero helmet (CdA=0.340)

->  Aerodynamic losses = 142.0 W (52.5%)

->  Rolling resistance losses = 120.8 W (44.6%)

->  Drivetrain losses = 7.9W (3%)

->  Time = 10 hours, 6 minutes, 0 seconds

If I consider that we make an improvement of 0.012 to Keegan's CdA, which is the aero helmet benefit that we considered previously, we now have: 

Keegan, 271W, aero helmet (CdA=0.328)

->  Aerodynamic losses = 140.9 W (52.1%)

->  Rolling resistance losses = 121.9 W (45.0%)

->  Drivetrain losses = 7.9W (3%)

->  Time = 10 hours, 0 minutes, 23 seconds

So that 0.012 reduction in CdA (3.5% aero improvement) results in 5 minute, 37 second time saving (0.93%).

Now the interesting bit:  If we take the same scenario, but change Keegan's 271W power to half that, 135W, we're now representing an identical rider, bike and course, but we're modelling a fairly low level amateur who just trying to complete the race.  They would obviously be riding slower, due to their reduced power.

For the baseline case, with the non-aero helmet, they would complete the Unbound 200 course in 14 hours, 34 minutes:

Amateur, 135W, non-aero helmet (CdA=0.340)

->  Aerodynamic losses = 47.4 W (35.1%)

->  Rolling resistance losses = 83.7 W (62.0%)

->  Drivetrain losses = 3.9W (3%)

->  Time = 14 hours, 34 minutes, 0 seconds

Now, the same aero benefit gives:

Amateur, 135W, aero helmet (CdA=0.328)

->  Aerodynamic losses = 46.7 W (34.6%)

->  Rolling resistance losses = 84.4 W (62.5%)

->  Drivetrain losses = 7.9W (3%)

->  Time = 14 hours, 27 minutes, 27 seconds

So for the amateur, that same 0.012 reduction in CdA  results in a time saving of 6 minutes 33 seconds, which is more minutes saved than Keegan!

Conclusion

To conclude, aerodynamics do matter off-road.  The % time savings, and % speed increases, are broadly similar to the benefits on the road, despite the slower off-road speeds.  They are the same order of magnitude as the % benefit on the road, because in the vast majority of off-road cases, the aerodynamic losses are still the largest power loss.  Even at very slow speeds, aerodynamics are not negligible and remain an important factor.

If we consider time saving in seconds, instead of % time saving, slower riders will actually improve their time to cover a certain distance by more seconds than a faster rider does.  This is counter-intuitive, but true.

The aerodynamics of aero socks and fabrics - Part 2

In my previous post about aero socks, I explained how the ribs and grooves on the fabric of aero socks can induce boundary layer 'transition', from laminar to turbulent, which helps to keep the airflow around the ankle and calf 'attached' for longer, which then leads to a narrower wake of separated flow and therefore less drag.

I also explained an important aerodynamic parameter called the Reynolds number of the flow, which depends on the speed of the airflow and also the size of the object, and how that affects the behaviour of the flow.  

I showed the plot above to illustrate the factors that determine whether the fabric of the aero socks will cause boundary layer transition to occur at a lower Reynolds number, compared with what would happen naturally on a smooth surface.  This plot shows how the drag coefficient of a cylinder varies as a function of Reynolds number for different surface roughness heights.  "k/d" in the plot is the surface roughness height divided by cylinder diameter.  Surface roughness has a similar effect to aerodynamic fabric ribs in that it causes a the boundary layer to transition from laminar to turbulent earlier (i.e. at lower Reynolds numbers) than what would occur naturally on a smooth surface.

In this post, I'll dive deeper into these effects and discuss what else we can infer from plots like the one above.

Why size is important

The Reynolds number depends on the size of an object, in addition to the speed of the flow.  For a given object shape, for example a cylinder, a larger object will have a higher Reynolds number than a smaller object having the same shape, even if the airflow speed (i.e. the riding speed) is the same.  This is shown in the plot above; the ankle, calf and thigh lines (the red, green and blue lines respectively) are at different Reynolds numbers, different positions on the x-axis, despite the airflow speed being the same 50kph for all three.

This difference in Reynolds number for different body parts is, I think, one of the reasons why we see clothing manufacturers use different fabric textures on different parts of skinsuits.  Looking at the plot above, it's clear that a cylinder with a smaller diameter, such as an ankle, will have a lower Reynolds number, and therefore needs to have a larger surface roughness (or height of the fabric ribs), in order to trigger the boundary layer transition in the optimum way, to achieve the lowest drag coefficient (Cd) at that Reynolds number.  The red ankle line on the plot above would achieve it's lowest Cd at 50 kph by having a roughness of ~k/d=0.005.  For an 82 mm diameter cylinder, which is my ankle diameter, a k/d value of 0.005 corresponds to a roughness height of 0.41 mm.

On the other hand, for a thigh, the plot above shows that the lowest drag coefficient at 50 kph would instead be achieved with a much smaller roughness of about k/d=0.0003.  For an 175 mm diameter cylinder, which is my thigh diameter, a k/d value of 0.0003 corresponds to a roughness height of just 0.05 mm.  To put that in context, the width of a human hair is 0.05-0.10 mm.

So for the ankle, the optimal roughness is 0.41mm and for the thigh it's 0.05 mm. That's an order of magnitude difference in optimal roughness (fabric texture height) values for the ankle and thigh!  This wouldn't be obvious or intuitive to most people I think, and would probably be surprising even for most aerodynamicists too.  This could be why we don't see ribbed aero fabrics being used on the thigh area of shorts and tights, like the offerings shown above from Rule28, despite ribbed fabrics being used on the lower leg.  The natural texture of a standard lycra clothing fabric probably provides the optimal amount of roughness (0.05 mm) for the thigh area at speeds around 50kph.

Interestingly, I remember an Q&A reply provided by Rule28's founder, Sam Calder, in a TrainerRoad forum post. In that post he explained that aero fabrics don't work on the thigh because of the rotating nature of the thigh when pedalling, which makes it difficult to find a fabric texture that reduces drag.  The rotating element might indeed be an additional factor that complicates things, but I believe the difference in Reynolds number that the thigh experiences, compared with the ankle, is another big reason why aero fabrics don't 'work' on thighs.

Why speed is important too

The Reynolds number also depends on the airflow speed, however, in addition to the size.  This is important, because very few of us (sadly) cycle at 45-50 kph, which is the speed that cycling wind tunnel tests are often performed at.  45-50 kph is a suitable speed for professional and high level amateur time triallists.

As a quick aside, another reason why wind tunnel operators prefer to test at the higher end of the speed spectrum is because the drag measuring equipment in the wind tunnel, called the balance, will be more precise at higher speeds.  Higher speeds produce significantly higher forces.   The drag at 50 kph is approximately 2.8 times more than the drag at 30 kph, for a given drag coefficient.  The wind tunnel balance will normally have a certain force precision, in terms of Newtons of force.  Therefore, if testing at 30 kph instead of 50 kph, then the drag force is 2.8 times less, so the precision of the data collection will be 2.8 times worse.  The guys from Specialized made a similar comment in an interview in this BikeRumour interview.

If the riding speed is slower, the Reynolds number will be proportionately lower. The plot below shows the Reynolds numbers for the ankle, calf and thigh for 40 kph, instead of 50 kph shown previously. 40 kph is closer to the speed that I would average for a 10 mile time trial.

Note that at 40 kph, the optimal roughness for the ankle is now a k/c of 0.007, which corresponds to a roughness height of 0.57 mm.  For 50 kph the optimal roughness was a smaller k/c of 0.005 (0.41mm).  Therefore, slower speeds need a larger surface roughness, or more prominent aero fabrics ribs and grooves, to achieve the lowest drag.  If the optimal aero fabric for 50 kph is used at 40 kph, there is a chance that the fabric texture is insufficient to cause boundary layer transition.

At speeds even than 40 kph, the effect is even more significant.  A speed of 25 kph is too slow for anybody riding a time trial or triathlon, no matter how unfit they are, but it's an appropriate average speed for many off-road racing scenarios.  The plot below shows how the Reynolds numbers for the ankle, calf and thigh move to the left on the x-axis when considering 25 kph.

There are a couple of really interesting observations to make from this 25 kph plot, compared withe previous ones:

1) Aero socks probably won't work at 25 kph: The k/d value that gave the lowest ankle drag at 50 kph (i.e. k/d=0.005) is completely ineffective at reducing the drag at 25 kph, according to the plot.  In fact, even the optimal k/d for 40 kph (0.007), is ineffective too.  At 25 kph, the drag coefficient for those k/d lines is at the upper 1.2 value, which is the drag coefficient for cylinder when it experiences fully laminar flow and laminar separation.  Those 0.005 and 0.007 k/d roughness values are not able to 'trip' the boundary layer, to cause the early transition to turbulent flow.  At 25 kph, a k/c of 0.02 is needed instead, which is 1.64 mm, which is larger than what the UCI now allows.

2) Aero fabric might work elsewhere though: The k/d value that provides the optimum drag for the thigh, however (the blue line below), is now 0.004.  For a thigh diameter of 175 mm, this requires a roughness height (k) of 0.7 mm.  Without that roughness, for k/d=0, the plot below shows that the thigh would experience laminar separation and has a Cd of 1.2.  For an optimum roughness height of 0.7mm (k/d=0.004), the drag coefficient would be half that, 0.6.  

What this shows it that the effectiveness of roughness, and therefore the effectiveness of aero fabrics, depends on the size of the object and the speed.

At 50 kph or 40 kph an aero fabric is not needed on the thigh area, and may be counter-productive, whereas at 25 kph it might actually be needed to improve the flow around the thigh and reduce the drag.  This is something that so far, I haven't seen any clothing manufacturers investigate or utilise.

There are a few assumptions behind what I've explained in this post, particularly the use of the roughened cylinder analogy to explain how textured aero fabrics work on the legs and arms.  Still, I think there is a good chance that aero fabrics used in unconventional places, like the thigh, could produce clothing that performs very well at lower speeds associated with off-road events like gravel, mountain bike and cyclocross races.  There is a big market there, and a potential opportunity for a clothing manufacturer to produce something that performs well for those events.

As a final remark, there may be people that read these last few paragraphs and think to themselves that aerodynamic improvements have little benefit at slow speeds.  This is a common misperception, and a wrote a blog post recently (see here) that shows that aerodynamic improvements have a surprisingly similar benefit at slower off-road speeds compared with their benefits at faster road and time trial speeds.

The aerodynamics of aero socks and fabrics - Part 1

 

Aero socks, like the Rule 28 socks shown in the picture to the left, are a popular clothing choice for time triallists and racers seeking and advantage.

In fact, aero socks are often mentioned as being one of the the best value bang-for-your-buck upgrades, considering the performance advantage they provide for their relatively modest price.

In this blog post, I'll explain why aero socks work.

During my 30-year career as a professional aerodynamicist, I've worked on many aircraft R&D projects that involve the same aerodynamic phenomena that apply to sock and leg aerodynamics.  I'm conscious that the majority of readers won't be familiar with many of the aerodynamics concepts I'll talk about, so I'll start with a basic explanation.  More knowledgeable readers might want to skip the early paragraphs.

Bluff body aerodynamics

The legs of cyclists, and cyclist's bodies in general, are what an aerodynamicist would call bluff bodies.  A bluff body is an object that will typically have a wide or irregular shape, and the nature of that shape means that the air cannot flow smoothly around it.  A streamlined body, on the other hand, is shaped so that the air can flow smoothly around it from the front all the way to the back.  An aeroplane wing or a dolphin are examples of streamlined bodies.  Unlike a bluff body, a streamlined body will have much lower drag.

The flow over a bluff body like a cyclist's leg will tend to be smooth only at the front of it, as shown in the right-hand picture above.  Towards the back, often at or close to the widest part, the air is unable to continue flowing smoothly, and it 'detaches' or 'separates' from the surface, as shown above.  In the region of separated flow there tends to be large eddies and a low pressure region, which 'sucks' the object backwards, contributing to the majority of the object's drag.  A cyclist's leg is similar to a cylinder, or a tapered cylinder to be more precise, where the thigh has a larger diameter than the calf and the ankle.  Clearly, the cross section of a leg is not exactly circular, as it is for a cylinder, but for the purposes of explaining leg aerodynamics and aero socks, the cylinder analogy works well.  There have been plenty of studies concerning the flow around cylinders, so we can use cylinder aerodynamic data to understand how aero socks work.

Cylinder aerodynamics

Before getting into the aerodynamics of cylinders, it's important to first explain that the drag coefficient for an object, denoted by the abbreviation "Cd", is in general not a fixed value.  Instead Cd is dependent on the flow conditions like the speed, air temperature and the size of the object.

For cyclists, whose frontal area can be easily adjusted by changing the torso angle and arm position, it's often more convenient to use the drag area parameter, "CdA", which is the drag coefficient multiplied by the frontal area.  Cyclists and time triallists often talk about their CdA as if the CdA value is a constant value for a given setup, but it's not really true.  To be fair, over the range of relevant cycling speeds, the changes in CdA are likely to be fairly small, so for practical purposes, considering CdA to be a fixed value is a reasonable simplification.

Changes in CdA occur because the change of a parameter called the Reynolds Number (Re). The Mach number will also affect CdA, but because we cycle at a small fraction of the speed of sound (which is 1230 kph) we can ignore that dependency of CdA on Mach number and focus only on the Reynolds number dependency.  Reynolds number describes the ratio between the inertial properties of the flow and the viscous properties of the flow.  This won't mean much to many people, so it's more helpful to explain what things change the Reynolds number:

• Doubling the speed will double the Reynolds number.  Riding at 40 kph means your Re number is twice as large as if you are cycling at 20 kph. 
• Doubling the size of the object, even if it has the same shape, will double the Reynolds number.  If an ankle has half the diameter of a thigh, the flow around the ankle will have a Reynolds number that's half the Reynolds number of the flow around the thigh.
• The air density and temperature will also affect the Reynolds number.  Increasing altitude will result in a lower Reynolds number, although there isn't a linear relationship like there is with the first two dependencies, speed and size.

The reason for explaining Reynolds number is because the drag of a cylinder-like object, such as a leg, is highly dependent on the Reynolds number.  The plot to the left shows the drag coefficient of a smooth cylinder as a function of Reynolds number.  Note that the Reynolds number dependency is plotted on the x-axis using a logarithmic scale, so it covers a very wide range of flow conditions.

I've annotated the plot to show the region (in blue) that's relevant for cyclist's legs, covering the 10-60 kph speed range.  Across this speed range, you can see that the drag coefficient is very similar for a smooth cylinder, and the Cd is typically a value around 1.2 for the whole blue range.  However, you will notice that at Reynolds numbers that are slightly higher than the blue region, at about 300,000-400,000, the drag coefficient curve reduces significantly.  This point, where the drag coefficient drops substantially is called the 'critical Reynolds number', and it describes a point where the flow around the cylinder behaves very differently.

At Reynolds numbers below the critical Re number, the flow around a cylinder looks like the flow shown in the top sketch on the left, having a wide wake, often with regular vortex shedding occurring from the cylinder and those vortices are transported downstream in wake.  This is where the drag coefficient is around 1.2.

Once the Reynolds number is larger than the critical Reynolds number, at about 300,000-400,000, the wake becomes much smaller, as shown by the bottom sketch on the left.  A narrower wake causes a smaller low-pressure region at the back, hence less drag.

So what is it about the increase in Reynolds number that causes this difference in the pattern of the separated flow and the size of the wake?  Well, the Reynolds number determines whether the air moving right next to the cylinder surface, called the boundary layer, is a laminar boundary layer or a turbulent boundary layer.  At higher Reynolds numbers, the boundary layer naturally becomes turbulent before the point where the flow separates.  This is important because turbulent boundary layers are much more resistant to flow separation than laminar boundary layers.  Therefore, at higher Reynolds numbers, the turbulent boundary layer resists flow separation at the widest point of the cylinder and instead the flow separates only at the very back of the cylinder, causing a narrow wake and a low drag coefficient.

So, to summarise:

• The drag of a cylinder depends of the size of its wake.
• The size of the wake depends on whether the boundary layer is laminar or turbulent at the widest part of the cylinder.
• The Reynolds number of the flow determines whether the boundary layer is laminar or turbulent.
• Hence the Reynolds number determines the drag of the cylinder.

However, the Reynolds number is not the only thing that determines whether the boundary layer is laminar or turbulent, as I'll explain in the next section.

Boundary layer transition tripping

As explained in the previous section, at higher Reynolds numbers the boundary layer will naturally transition from a laminar boundary layer to a turbulent boundary layer before the point of flow separation, and it's the turbulent boundary layer that enables the flow to resist separation at the widest part of the cylinder.

However, the boundary layer can also be 'forced' to transition from laminar to turbulent at Reynolds numbers below the critical Reynolds number.  This intervention to force the boundary layer to become turbulent is often called 'tripping' the boundary layer.  There are various ways to trip a boundary layer, but most methods involve some kind of protuberance, like a bump, a wedge or a band of roughness, that disturbs the laminar boundary layer and causes transition to turbulent boundary layer.

Hence, at low Reynolds numbers, below the critical Reynolds number, the only way to reduce the drag coefficient of a cylinder is to trip the boundary layer.  This is what the ridges and surface texture of aero socks do, and how they are able to reduce the drag of a cyclist's lower leg.

The plot above is similar to the one shown earlier, in the Cylinder Aerodynamics section, except that instead of showing just a single curve for a perfectly smooth cylinder, the plot shows several curves for cylinders with different levels of surface roughness.

The level of roughness is defined as "k/d", which is the roughness height divided by the cylinder diameter.  The perfectly smooth cylinder is the one with k/d=0, which you can see has a critical Reynolds number of about 300,000, as discussed earlier, above which the drag coefficient drops abruptly.  The other curves are for progressively rougher cylinders.  For example, the curve with triangular symbols is for a k/d of 4/10^3 (=0.004), which is equivalent to 0.4 mm roughness  on a 10 cm diameter cylinder.  0.4 mm roughness is about the same roughness as 40-grit sandpaper, which is a coarse sandpaper you'd use for DIY jobs.

For this k/d=0.004 example, you can see that the critical Reynold number is much lower, because the roughness is tripping the boundary layer at lower Reynolds numbers.  As a results, at a Reynolds number of 100,000, this rough cylinder has a lower drag coefficient, about 0.7, than the smooth cylinder has (which ahs a Cd of 1.2 at Re=100,000).  To non-aerodynamicists this might seems counter-intuitive, that adding surface roughness reduces the drag of the cylinder, but it's true, and it's all related to the state of the boundary layer.

This is how aero socks work.  The ridges in the fabric of an aero sock act like the roughness elements in this example, reducing the critical Reynolds number and therefore the leg drag at the Reynolds numbers that cyclists are operating at.

What trip height for what speed?

As a final word, it's worth mentioning that the transition trip height that's required, to give the lowest drag, depends on the Reynolds number.  Hence the trip height (which means the height of the ridges in the fabric), depends on the rider speed and also the size of the body part it's applied to.

The plot above shows the Reynolds numbers for a 50 kph speed.  This is the kind of speed that a high level time trialist would achieve and is approximately equivalent to a 20 minute time for a 10-mile time trial.  I've annotated the plot to show what the Reynolds numbers would be for an ankle, calf and thigh.  This is rather approximate and is based on my own ankle calf and thigh circumference values (26, 38 and 55 cm) to get an approximate equivalent cylinder diameters.  This is admittedly rather crude, because as mentioned previously, the leg doesn't have a circular cross-section. However, it's just to illustrate a point.

You can see that for the ankle, where (UCI-legal) aero socks are working, the best drag is  achieved with roughness height of about k/d=0.005.  For an 82 mm diameter cylinder, which is typical for an ankle, a k/d value of 0.005 corresponds to a roughness height of 0.42 mm.  This is consistent with the fabric patterns used for aero socks, which have ridges and grooves that are about half a millimetre to one millimetre in depth.  There isn't a direct equivalence here, however, because aero sock fabrics use grooves and ridges, rather than distributed roughness, so it's likely that larger ridge height would be needed to trip the boundary layer in a way that's similar to how roughness behaves.  

Nevertheless, it's reassuring to see that plots of drag data for roughened cylinders is consistent with the fabrics that have been selected by manufacturers of aero socks.

In my next blog post, which I'll write in the coming weeks, I'll discuss this plot further and what other things it may reveal and imply. 

Aerodynamic Garmin Edge 840 out front mount

This is another 3D-printed bike part that I've designed recently.

During the spring this yea I had the idea to make a number of aerodynamic improvements to my road bike, in time for the summer time trial season.  Sadly (and as usual) I've had less spare time than I wanted.  Also, the CAD design work has taken me longer than I had anticipated.

Anyway, this mount for my Garmin Edge 840 computer is the first of several minor aerodynamic improvements that I'll create for my road bike.

What aero improvements are possible? 

I have always been intrigued by the claims made several years ago by Wahoo about the aerodynamic efficiency of their Wahoo Elemnt Bolt.  Those claims are summarised nicely on DC Rainmaker's site.  Wahoo claimed that the Elemnt Bolt had 50% less drag than the leading competitor (i.e. Garmin) with those drag savings equating to a 1.5 Watt saving (although they didn't quote what speed that was for) but apparently that corresponds 12.6 second savings over a 40km time trial.  Those savings are fairly small but not negligible.  To put that in context, 12.6 seconds is about half the penalty of having a round bottle on the down tube, according to Specialized's wind tunnel testing (see here).

DC Rainmaker also performed some wind tunnel tests of his own though, which showed that the savings for a Bolt are actually much smaller than Wahoo's claims, more like a 1 second saving, instead of 12.6 seconds, when the computers are mounted horizontally.  That's very small, a truly marginal gain.

Still, despite this very small saving, it's something I wanted to do.  I felt that the integration with my stem and handlebar could be improved too, which I felt could yield some additional drag savings.  Therefore, I pressed ahead and designed the mount.

Mount design

What I wanted from the mount was to something that:
    1) Had a more aerodynamic profile at the leading edge.

    2) Covers the Garmin's side buttons, which disturb the flow and aren't needed during a ride.

    3) Was blended into my stem and the circular section of my handlebar.

The design consists of a 'sleeve' into which my Garmin 840 easily slips into, and separately a mount that bolts onto the handlebar.  Once the Garmin is inside the sleeve, it can be fitted to the mount so that it's perfectly flush.  The front and back of the sleeve are shaped to help keep the sleeve perfectly flush with the mount, in addition to a central Garmin quarter turn mount (also designed and 3D-printed) that ensures it won't fall out.  All of this is quite difficult to describe with words, so I have uploaded a video to YouTube (see below) that shows it in action:

The sleeve and the mount have two cut outs at the bottom left and bottom right corners. This allows me to press the start/stop button on the right and the lap button on the left, as shown in the second video below.  There's also a small C-shaped cut-out in the left hand side of the sleeve's thin sidewall, that allows the on/off button to be pressed.  I felt that these three buttons were the only three that really needed to be pressed during a ride, with the other computer functions being available via the touchscreen.

Apart from hiding the protruding buttons via the sleeve, what makes this mount aerodynamic is the shape of (1) the leading edge of the fairing and also (2) the blending of the mount around the stem and handle bar.

The mount smoothly curves into the stem face plate and into the round profile of handlebar at the centre.  A lot of trial and error was required to get a shape that fits closely to double curvature shape of my 3T stem.  This is undoubtedly the most fiddly part of creating 3D designs - getting them to fit with existing parts and geometries that I don't have the CAD surfaces for.

For the leading edge of the mount, I chose to use a NACA 0024 aerofoil profile.  This is a general purpose aerofoil with a 24% thickness to chord ratio.  NACA's double-0 series aerofoil profiles are used for all sorts of things and I judged it to be a good choice for this kind of application.

The Garmin quarter turn mount and the handlebar mount are connected using M3 machine screws and nuts.  I used these dome-headed stainless bolts from eBay, which have dome-shaped heads that have a 6 mm diameter and a depth of 1.8mm.  

A few more photos 

I'm pleased with how it turned out.  I've attached a few more photos below.

The design at the moment is customised to the shape of my 3T Apto stem, so it won't fit to many other stems at the moment.  However, if you are interested in printing one of these for yourself, for your bike, then leave a comment below.  If I get enough interest, I'll create a generic version that will work with most alternative bar and stem set-ups and will upload it to Makerworld.

Updated 31st Jan 2026: 

As requested, I have uploaded the STL, STP and CAD model files so they are accessible to anybody that wants to print this.  I have uploaded two versions:

3T Apto stem version:  3T Apto version link

Generic version that will fit more bike stems:  Generic version link  

Please read the description before printing and using.  There will still be a lot of bikes and stems that even the generic version won't fit onto, unless you adapt the CAD geometry yourself, so please be aware of that.

The Drop Bar MTB - Is it faster for Cyclocross?

In my previous blog post, I described the drop bar conversion that I did for my hardtail MTB.  I did that conversion in an attempt to create a bike that's as fast as possible for 'light' off-road duties - faster than a hardtail MTB and faster than a traditional gravel or cyclocross bike.

Based on the testing that I've done in recent years, this drop bar MTB bike should be faster on a grass surface like a cyclocross (CX) course than my CX bike, somewhat counter-intuitively.

During the latest 2023 CX season I therefore decided to use my drop bar MTB for any CX races that were dry enough to be suitable for the semi-slick Schwalbe Thunder Burt tyres.  For the muddy races, I used my CX bike with mud tyres, knowing that the grip from the Thunder Burt tyres would be terrible in mud.  It's worth mentioning that my local Cyclocross League doesn't apply the UCI rule of 33mm maximum tyre width, and doesn't have other bike restrictions, so anything is allowed.  MTBs are often used by people that don't have CX bikes.  Given the lack of restrictions around bikes, my general approach is to use the fastest bike possible, rather than sticking with tradition.

The question is, was the drop bar MTB actually faster or not?

How I judged the bike performance

I did seven CX races this season, from September through to early December.  The last one I did was a regional race, with riders entering from two Leagues (Western League & Wessex League), so that 7th race was much more competitive than the other six races, so my result was worse than the others.

For the first six Western League races, I felt that my fitness was broadly similar, and therefore my results in those six races, and my speed relative to my competitors, would provide a good indication whether or not the drop bar MTB was faster than the CX bike.

It has been a very wet autumn here in the South West of England, so unfortunately there weren't many dry races this year.  Of the six races, only two races were dry enough to use the drop bar MTB.  Even for those two, the courses were still muddy in places.  So for two of the races, I used the drop bar MTB, and for the other four races I used my CX bike with 33mm Challenge Handmade Tubeless Ready Clincher mud tyres, with the tyre model choice based on the level of muddiness (either Baby Limus or Limus).

I analysed my performance relative to my competitors in two ways:

1) What my finishing position was relative to the size of the field, calculated as a percentile.  For example, if I finished 20th out of a field of 50 people starting the race, that's a 40th percentile finishing position.

2) Secondly, what my finishing time was relative to the winner.  For example, if the winner finished in 1 hour and I finished in 1 hr 6 minutes, my 6 additional minutes make me 10% slower than the winner's time of speed.

Of these two methods, I think the first one is a slightly more reliable method, because the second method is influenced by a single person; the winner's performance. It therefore depends on whether the fastest rider in the region raced in a particular weekend and how he performed in that race.

It's worth noting that although I changed bike and tyre width for each race depending on the conditions, almost everybody else in the field, especially the top riders, used the same cyclocross bike with 33mm tyres for all their races. 

Results

The plot below shows the results using these two methods.  Regardless of the method, it's clear that I achieved better race results using the drop bar MTB than my CX bike.  Like many things, this is not 100% conclusive, but I still think it's a strong indication that the drop bar bike is faster.

Weight comparison for my mountain bikes

Weight is not the most important consideration when it comes to cycling performance, as discussed previously in one of my older blog posts.

Having said that, I still weigh the components of my bikes whenever it's convenient to do so.  By doing that, it gives me the information to know whether it'd be good value for money, or not, to upgrade a component, or swap something over from one of my older bikes.  Nevertheless, it's not something I pay a large amount of attention to these days, having understood how important (or rather how not important) bike weight is on cycling performance. Still, it remains slightly interesting to me, hence this comparion.

I recently bought a Specialized Epic Evo as a new full suspension mountain bike.  I already own a 14-year old first generation 26 inch-wheeled Giant Anthem full suspension MTB and a Scott Scale 29-inch wheeled hardtail MTB.  I thought it would be interesting to compare the weights.  For all of the bikes, I've made some improvements to make them lighter, prioritising the items that would provide the best value for money (best gram saved per £).

Perhaps not surprisingly, the carbon-framed Scott Scale hardtail is the lightest of the three.  Most of the difference is coming from the frame, obviously, but I'm also running SRAM XX1 carbon cranks on it, and these are a fair bit lighter than the alloy Shimano XTR cranks on the other two.

What's most interesting is that my Giant Anthem is lighter than the Specialized Epic Evo, despite having an alloy frame, alloy wheels, and a triple chainset (versus the Epic's carbon frame & wheels, and 1x transmission).  Although the Anthem's wheels are on 26", which helps, I think it still shows that alloy wheels can be very light. The 3x9 transmission of the Anthem is also almost as light as the Epic's, despite the hefty triple crankset, but this is helped by the 11-32 XTR cassette, which is about 60% of the weight of the Epic's enormous 11-52 cassette.

Finally, the other big difference comes from the Epic's dropper post, and the Epic is the only bike that has a dropper.  That alone adds about half a kg.

Despite all this, I'm happy with the Epic's build and 10.9kg (23.9lb) total weight.

The benefits of unlocking Zwift's rear disc wheel

Today I got to Level 35 in Zwift, which that means I was able to get the Zipp Super 9 rear disc wheel.

It looks better on any Time Trial (TT) bike, of course (if you care about such things for your Zwift avatar!).  However, I wanted to know how much faster it is.  This post explains my calculation to determine just that.  The quick answer, if you don't want to read the full post, is 2.5 Watts.

I've been using Zwift since September 2015, which was not long after the launch of Zwift.  I'm not a massive fan of Zwift, I must admit, but I quite like it and I use it for a few months every year to help take some of the monotony out of winter indoor riding.  It's taken me that long time, about eight years, to get enough XP to get up to level 35 (approximately 5,700 Zwift miles).

Fastest Zwift Wheels

When talking about the fastest wheels in Zwift, it is worth clarifying that this applies only to wheels on TT bikes.  Why?  Because once you unlock the Zwift Concept Z1 road bike (aka the 'Tron bike'), then all other road bikes are slower, with a few caveats, regardless of the wheelset you put on them. See this Zwift Insider post for more information about that.

TT bikes are different though, and will always be faster than a road bike, including the Tron bike, when riding solo or in a no-draft TT event.

Zwift Insider's analysis

The guys at Zwift Insider do an excellent job of analysing bike and equipment choices within Zwift, amongst other things.  Their post here explains the fastest TT wheels, using their testing protocol, whereby they recorded the time required to ride the Tempus Fugit route (17.4km / 10.7miles) twice at 300W.

As shown in the table to the left, the faster wheelsets provide larger time savings.  However the fastest wheelset can only be unlocked at the higher levels within Zwift.

For some years, since Level 13, I've been using the Zipp 808 wheels on the TT bike, which are the fastest wheels for people at lower Zwift levels.  Now having the Zipp Super 9 disc wheel on the back, saves me 9 seconds on that 2 x Tempus Fugit route, versus two 808s, according to the Zwift Insider table above.  Given that the entire route takes "approximately 50 minutes" when ridden at 300W, then 9 seconds doesn't sound like very much!  In fact, the time/speed improvement is only 0.3% (9 seconds divided by 3000 seconds).

What I wanted to calculate is how much that time saving equates to, in terms of power savings and CdA reduction.

Important: As with all power saving values, it's crucial to keep in mind the associated speed, which in this case was 41.52 kph (25.79 mph), because any power savings due to aerodynamic changes are proportional to speed cubed.  Beware anybody that quotes power savings without also giving the associated speed!

CdA and Watt savings

I used my performance modelling spreadsheet (described here) to model the Zwift Insider test, where they completed two laps of the Tempus Fugit route at 300W, for a 75kg rider, in about 50 minutes, as shown below:

In addition to the parameters above, I had to make a few other assumptions to calculate the CdA, and these are simply guesses, because I don't know what assumptions Zwift makes.  I'm confident, however, that the power and CdA increments won't be particularly sensitive to this choice of conditions:

• Air pressure = 1012.5 bar (i.e. sea level pressure using the International Standard Atmosphere, ISA, conditions).
• Air temperature = 15 degrees C (i.e. sea level ISA conditions).
• CRR = 0.004 (which ZwiftInsider says here is the CRR that Zwift assumes for the road).
• Bike weight = 9kg
• Drivetrain losses = 2.5%

Using these assumptions, I calculated the baseline CdA to be 0.2710 m^2.  Then, by increasing the speed by 0.3%, giving a 9 second time saving, I calculated:

Either: 0.0025 m^2 CdA improvement (0.2710 -> 0.2685, or a 0.92% CdA reduction) at the same 300W power to achieve that 9 second saving.

Or: 2.5 Watt power saving at 41.52 kph (0.83% power saving) for the same 50 minute time, with that reduced CdA of 0.2685.

I think these numbers, especially the power saving, can be understood more intuitively by the average person.  A 2.5 Watt power saving is not large, but is not negligible either.

Are the numbers valid also for me?

Finally, I also wanted to check whether these values are valid for me, because I'm a slightly smaller and less powerful rider than was assumed by Zwift Insider.

Firstly, I calculated my CdA to be 0.2415, for my Zwift time trial bike using Golden Cheetah.  This is relatively easy to do (compared with real life), because in Zwift there is no braking, no wind and no other vehicles to mess things up!

Something to note is that my Zwift CdA is about 10% lower than the CdA for the Zwift Insider analysis, and this will be because I'm probably shorter (at 5 foot 10 inches) and slightly lighter (at 73 kg) than for the Zwift Insider study, and we know that Zwift adjust the CdA based on weight and height.

Next, I applied this CdA to my spreadsheet analysis.  Interestingly, for a 50 minute time to complete the 2 x Tempus Fugit distance, the power requirement was 270.6W, which is approximately what I could hold for 50 minutes, so I didn't adjust it any further.  Then, I reduced the CdA by the same 0.0025 m^2 value, and calculated the power saving in the same way as before:

The Zipp Super 9 rear disc wheel give the following benefits, both at 41.52kph:

                     Zwift Insider (75kg, 300W, 41.52kph)           Me (73kg, 270.6W, 41.52kph)

CdA              0.2710 -> 0.2685 (-0.0025 or -0.92%)      0.2415 -> 0.2390, (-0.0025 or -1.04%)

Power saving           2.5W saving (-0.83%)                               2.4W saving (-0.89%)

In summary, the Zipp Super 9 disc wheel will save me about two and a half watts at typical flat TT speeds.  This benefit is fairly small, but certainly not negligible.