Unconventional aero. How did he go so fast?

Like Chris Froome in an unconventional riding position, the Summer seems to have flown by (I’m an engineer, similes do not come easily). Thankfully there’s been a bumper crop of sporting spectacles to sate our appetites. In this post I’d like to focus on a pet topic of mine, cycling aerodynamics.

Right at the start of the Summer we saw Chris Froome pedal to his third Tour de France victory. He grabbed an initial lead over his rivals while flying downhill in an unconventional tuck position.

The interest surrounding the move had many speculating on the advantages gained and even some computational analysis which concluded that the safer, standard descent style may have been quicker (his extra speed could have been down to the use of a 54 tooth front ring as opposed to his usual 53 tooth ring).

It wasn’t Froome’s risky descending which caught my imagination though, it was a video I spotted a short while back which showed a much riskier (and arguably much more effective) descending technique.

In the video we see a cyclist riding a fixed-wheel bike (one gear, no freewheel) before they’re passed by a group of cyclists pedalling standard, geared bicycles. With a fixed gear he isn’t able to pedal much faster and so he adopts a crazy position — a solid, horizontal plank propped on top of the saddle. A number of things are clear from this point on.

  • Despite the fact he’s stopped pedalling he begins to accelerate.
  • Despite the fact the other cyclists are still pedalling, he passes them all.
  • The lead cyclist, in a tucked position and pedalling furiously, is unable to accelerate to match his speed.

It may seem strange that without putting in any effort (pedalling effort, holding a full plank on a racing saddle can’t have been easy) the cyclist is able to pass a train of riders who are all expending large amounts of energy. Can a change in position be so effective?

To try to answer this question I turned to what is perhaps my favourite datasheet (found through the sadly inactive cozy beehive cycling-tech blog)

The Data

drag_chart

Useful aero data for human powered vehicles (click to enlarge)

The datasheet shows a number of human powered vehicles and their associated aerodynamic properties. I really like this because it proposes real and theoretical scenarios (I’m holding out for a go on the moon bike). It contains lots of important, key information.

Cd, Coefficient of drag: This value is a way of combining lots of complex aerodynamic behaviour into a single number. In short, it describes how effectively a particular shape can move through the air (or any fluid). Long thin shapes have lower values and short wide shapes have higher values. Have a look at the Wikipedia entry to see the values for simple geometric shapes and some further description.

NB: Due to the complex behaviour this number hides, Cd is not constant, it changes with speed, surface texture etc. However, for the purpose of this blog post I’m assuming constant values.
A, Frontal area: Quite simply, how much air you are pushing aside. You can reduce your frontal area by changing your shape. In the simplest case, you duck down onto your drop handlebars to hide yourself from the air. In the extreme example above, you only present your head and shoulders to the oncoming air, dramatically reducing your frontal area.Of course by doing this, you’re unable to access to the pedals (unless of course you redesign the whole bike so it can be used in this position).

Cr, rolling resistance: Quite simply, how much resistance is created by the rolling elements of the bike (gears, tyres, bearings etc.) the single value is used to calculate a total force value.

Examining the datasheet we have some options available to try and recreate the video.

Reduced datasheet

The information above  gives us appropriate values to re-create the scenario. We have two examples of cyclists in a traditional racing position (with and without aero-components). We have the values for a cyclist in a ‘perfect prone’ position and for a bike with a dragless human. By combining the latter two examples we have a way of representing our brave, aero-cyclist (I’m going to refer to him as the prone cyclist from now on).

A few caveats to mention before we get started, the values above are not going to be perfect. For the perfect prone cyclist it mentions that it’s for a small person of around 50 kg. Also, it’s unlikely that our cyclist is in a ‘perfect’ position. We’re going to have to adjust some of these values upwards to account for the discrepancies.

The Model

I’ve constructed a simple differential model of a cyclist which balances the propulsive and resistive forces and calculates the resulting motion (for a more detailed description of aerodynamic forces see a previous blog post). Using the model we’re able to alter parameters such as the slope of the road (increasing or decreasing gravitational propulsion), and aerodynamic characteristics (to match those from our datasheet).

I’ve used the model to explore certain scenarios. I pondered trying to recreate the video as closely as possible but I decided against it. It’s hard to calculate what the slope of the road is from the footage and judging relative speeds is equally difficult. I did consider using a typical fixed-gear ratio and measuring the cyclists cadence to determine speed but, to be honest, I had better things to do. Instead I’ve decided to look at how each cyclist would perform in a head-to-head race. For the sake of this simulation I’m going to assume that the prone cyclist is able to lie perfectly horizontally on their seat at any speed. I’ve also made a few other assumptions.

  • Both cyclists + bike have a mass of 85 kg.
  • The prone cyclist’s frontal area has been scaled up from the data sheet by 0.52/3
  • I’ve increased the coefficient of drag of the prone cyclist by 20%
  • For the normal cyclist I’m using the non-aero values
  • The slope of the road is 10% (5.24 degrees).

I’ve used the results of the model to create an animation to show the relative speeds of each cyclist (it should be obvious which is which). Please ignore the frames per second number in the corner, it should be running at 10 fps which will illustrate speed and time elapsed correctly. (Again, I’m an engineer, not an animator so try to look past the aesthetics and the fact the road is flat!).

For the first animation, neither cyclist is pedalling (0 Watts of power from each cyclist).

animation1

As you can see, after a few seconds the superior aerodynamics of our prone cyclist begin to yield an advantage until his increased speed results in him disappearing from view.

However, we’d expect this wouldn’t we? Neither cyclist is pedalling and we know our prone cyclist is more aerodynamic. I think the real question is how much of an advantage does the improved aerodynamics give?

For my second animation I’ve given our normal cyclist an advantage — he’s elite level. This cyclist is able to generate a continuous output of 500 Watts (have a look at this datasheet to see how it compares to other athletes).

How does this head-to-head look? (It may take some time to load)

animation

This animation is much longer, I advise you to watch until the end…

The beginning of the race is not surprising. Our normal cyclist is able to generate a large amount of power to accelerate quickly while our prone cyclist only has gravity. At low speed aerodynamic forces are very low and the prone cyclist is left in the dust.

After some time our normal cyclist reaches a happy equilibrium. The propulsive forces are equal to his drag. What may come as a surprise is that after some time our un-powered, prone cyclist comes from behind to race past!

In the original video we can see the group of cyclists pedalling furiously to keep up. It’s no wonder they weren’t able to accelerate to match him!

Here’s a plot of the distance between the cyclists over a period of two minutes (a negative value means our prone cyclist is behind).

Distance figure

I also modified the simulation so that both cyclists stayed exactly level. The plot below shows how much power the normal cyclist had to generate to keep up!

Power figure

Only the very best cyclists are able to generate 1,200 watts for more than a few seconds!

You can see from the plot the exponential nature of the curve and the unavoidable nature of aerodynamics. If you double your speed, you quadruple your drag. If you want to go quickly, go aero!

So to round this up let’s look back at the points I stated at the beginning of the post.

  • Despite the fact the prone cyclist has stopped pedalling he begins to accelerate.
  • Despite the fact the other cyclists are still pedalling, he passes them all.
  • The lead cyclist, in a tucked position and pedalling furiously, is unable to accelerate to match his speed.

Now we’ve explored the physics of it all, none of these things seem so unbelievable. Aerodynamics give a huge advantage to the rider. So much so that excellent aerodynamics are more than a sufficient replacement for huge power outputs (providing you’re going downhill).

Of course, if you’re not on a slope then you’ll need to combine aerodynamics with the ability to pedal. If you haven’t already I implore you to explore the world of human powered vehicles. Where innovation isn’t stifled by regressive rules about riding position or construction types. Superior aerodynamics is why Bradley Wiggins’ 1 hour cycling distance record is 54.526 km and the human powered vehicle record is 91.55 km!

What we’ve explored here are extreme examples, large changes in position to yield large aerodynamic advantages. Of course less extreme examples won’t give such extreme benefits, but there are countless examples where paying attention to aerodynamics might have given the crucial edge.

Anyway, now I have a nice cycling model and a Matlab toolbox that allows me to create childish animations. If anyone has any ideas of how to explore differences in cycling performance (my model can go uphill as well as down!) then let me know and I might do a blog.

Simon Choppin

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About wiredchop

Simon Choppin Simon’s sports engineering career began at the age of six when he loosened the wheels of his skateboard in order to make it go faster. While the experiment was chalked up as his first failure, his resulting dimpled skull has provided an aerodynamic advantage in more recent sporting pursuits. Academically, Simon completed a degree in Mechanical Engineering with Mathematics at Nottingham University before joining the Sports Engineering Research Group at Sheffield to start his PhD. His main interests include work with high speed video, mathematical modelling of various sorts and experimental work involving machines with big buttons. As a sportsman, Simon has an unfortunate lack of talent for anything requiring skill, tactical awareness or the ability to learn from mistakes. He does however seem to posess the ability to move his legs around for a long time until other people get tired, for this reason you’re most likely to see him on a bike of some sort or running up a hill in offensively small shorts. Simon was fortunate enough to have a stint at the Guardian newspaper as part of the BSA’s media fellowship, which gave him the idea for this blog. Other than this, his writing experience includes his PhD thesis and various postcards to his Mum.

4 Responses

  1. Russell Gordon

    Fascinating reply, thank you very much.
    On the topic of Froome’s descending style it’s a bit of a problem for any of us coaching junior riders because they will of course copy his technique. In fact they have already! It would be very powerful to be able to teach them that not only is it clearly dangerous but also not very effective / necessary.
    On my ‘hobby’ topic of aero kit: All bike and component manufacturers are busy bringing out new, more aero kit and making substantial claims: 5watts less here, 8watts less there. We all want “free” speed since it’s much easier than training harder but we are all getting lost without any sensible comparative data. Still, I guess that is what Twitter and bike cafes are for!
    I’m off to buy some more over-priced aero…

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