When your ride buddy becomes a real drag

A question that comes up from time to time when chatting about aerodynamics stuff is how much impact does another rider in close proximity have on your aerodynamics, or more correctly stated, does having another rider in close proximity change the power required for you to maintain your speed?

We are all familiar with the reduction in power required when riding behind another rider. This "drafting" benefit is substantial and anyone with a power meter can see the big reduction in power when they move from riding directly into the wind to riding behind another rider. Even if you don't have a power meter the difference is certainly large enough to notice the reduction in effort required.

But what about when your buddy is drafting behind you or rides beside you? Does this impact the power needed to maintain the same speed?

The short answer is: yes, both of them do.
But in what way and by how much?

The question as to whether a rider in front gains benefit from having a rider behind them has been researched before, and the consensus is that yes, they gain a small benefit. There is good reason for this slightly counter intuitive result and it's to do with the "bow wave" of air from the rider behind causing a change in the turbulent air flow behind the lead rider and reducing, by a small amount, the depth of the low pressure zone that exists behind the front rider.

This slight reduction in the fore to aft air pressure differential of the lead rider provides a small but measurable gain. This can be expressed as a reduction in apparent CdA, but since a rider's CdA doesn't really change if their position and equipment hasn't, then in reality it's a change in the forces acting on the rider, and as a result, the power demand at the same speed is slightly reduced when compared with having no rider in close proximity (or alternatively, a rider can travel slightly faster for the same power when they have a rider immediately behind them).

In 2010  Andy Coggan examined data from a 2007 track session ridden by his wife, in which she did efforts on the track both with and without having a rider drafting behind her. In Andy's assessment of the data he remarked "having a rider drafting closely behind them apparently lowered their CdA by 3.2%, i.e., from 0.198 to 0.192 m^2.".

The reduction in energy demand will be of a very similar amount to the reduction in apparent CdA. Assuming ~350W, a reduction from a CdA of 0.198 to 0.192 is equivalent to a reduction in power demand at the same speed of ~10W, or 2.8%. In this case the other rider was riding in pursuit set up, and were themselves very "aero" (an elite track pursuit rider).

So that's one example.

This phenomenon has also been reported in the published scientific literature, examples include:

Racing cyclist power requirements in the 4000-m individual and team pursuits, Medicine and Science in Sports and Exercise, v31, no.11, pp 1677-1685, 1999. J.P. Broker, C.R. Kyle and E.R. Burke.
http://www.ncbi.nlm.nih.gov/pubmed/10589873

where amongst their data they report that the lead rider requires 2-3% less power while riding on the front of a 4-man team than if riding solo at the same speed.

Another more recent study examined this using both computational fluid dynamics (CFD) simulations along with wind tunnel validation as described in this paper:
CFD simulations of the aerodynamic drag of two drafting cyclists, Computers & Fluids Volume 71, 30 January 2013, Pages 435–445,. Bert Blocken, Thijs Defraeyeb, Erwin Koninckxc, Jan Carmelietd, Peter Hespelf
http://www.sciencedirect.com/science/article/pii/S0045793012004446

In this paper they report the lead rider of two riders riding in single file receives a reduction in energy demand of 2.6% while riding in the time trial position.

Above are three examples of data from a similar situation, with reported reductions in energy (power) demand to ride at the same speed ranging between 2% to 3% for the lead rider compared with riding solo.

There's another paper that reports a 5% advantage for the lead rider of team time trial, although I'm not able to see more than the abstract:

Aerodynamics of a cycling team in a time trial: does the cyclist at the front benefit?; European Journal of Physics, Volume 30 Number 6, 2009; A Íñiguez-de-la Torre and J Íñiguez
http://m.iopscience.iop.org/0143-0807/30/6/014

Edit: I've now read the paper and it used two dimensional CFD analysis on ellipses as a simple model simulation of multiple riders in a line and is indicative of the principles involved.

I've had the resources to test this for some time but I've hadn't got around to doing the experiment, mainly because exclusive use of track time costs money and I'm focussed on working with clients on answering more important aerodynamics questions for them than doing experiments just for the fun of it.

But today I had the opportunity to do just such an experiment.

I was doing aerodynamics testing as part of a story being written about a woman masters rider preparing for the UCI World Masters track cycling championships being held in Manchester later this year. Cycling NSW kindly offered and arranged for the track time to make this possible, and a client of mine, Rod Wagner, loaned a special power meter to enable the testing on the rider's track bike, while I offered my time for the aero work.

We'd reached the end of our allotted track time, but as luck would have it no one else was ready to ride on the track, so we had some spare time for the experiment, and willing participants.

I won't comment on the primary aero testing session as that's for another to write about for later publication in magazine and online, but I'll expand on the impromptu experiment.

The method of measurement

With the Alphamantis Track Aero System, I record and monitor in real time a rider's aerodynamics as they circulate around the indoor velodrome. Testing is done indoors as this removes the wind variable and provides for a well controlled environment. The system enables us to monitor speed and velocity and along with other key inputs such as air density, track geometry data, centre of mass height, rider mass and rolling resistance variables, the Coefficient of drag x Frontal area (CdA) is also plotted in real time and lap by lap a picture of a rider's aerodynamics is revealed.

I've briefly explained this system before in this post, which also has a video demo. You can also read more on the Alphamantis site linked above.

The experiment

Normally this testing is done with a rider riding solo on the track but for this experiment I asked her coach, another world level master's rider, to join in. His task was to ride in various positions relative to the test rider (who would continuously circulate around the track at approximately 40km/h) while her coach would change his relative position on the track every 4-6 laps as follows and on my instruction, he would:

- ride in front of the test rider to test the level of drafting assistance, then
- ride next to, and on the outside of the test rider, then
- ride immediately behind the test rider, then
- drop off entirely and stop riding, so that we could obtain data from the test rider circulating solo.

This test process was repeated a second time during the long test run to validate the results from the first run.

For reference, the test rider is a slim 60kg female approximately 172cm tall, and the coach weighs approximately 80kg and is ~185cm tall. The test rider was using a track bike with pursuit bars, while the other rider was using a track bike in regular mass start set up.

The system is really reporting the impact on apparent CdA. It's a quick way to measure how beneficial or detrimental having the other rider near you is, and the measurements are not overly sensitive to the changes in speed during the run (this is the nice thing about the process).

The results

Here's a table summarising the results of all the data runs. Click on images to see larger versions.

In the case of the support rider riding behind the test rider, the test rider gained a benefit of a reduction in apparent CdA of around 0.008m^2, or about 3.8%. Note (i) the error range and (ii) the support rider was riding in a more upright mass start position (and consequently has a larger "bow wave") and is somewhat larger than the test rider.

Also shown are the results of the traditional drafting, being a reduction in apparent CdA to nearly half of the solo value, and interestingly, the apparent CdA increase of ~ 0.013m^2, or nearly 6% when the other rider was riding alongside the test rider.

Since apparent CdA differences are a little harder to understand, I've flipped the data around to show, at a normalised velocity of 40km/h, what the power demand for the solo rider would be for each scenario:

The table below summarises the chart data, and also shows the difference in power compared with riding solo:

Compared with riding solo, the test rider gains a ~7W (3%) benefit from having her ride buddy directly behind her; a 76W (39%) benefit from drafting behind her ride buddy; and a 10W (5%)  penalty when her ride buddy is riding alongside.

So in this experiment, I found a 3% energy demand benefit from having a trailing rider, and that's right in line with (but at the top of) the range found by the other reported data referenced earlier.

This result of a 10W penalty when riding alongside another rider is more novel, although it doesn't surprise me it may be news to some.

It is something to ponder when riding in team formation events, especially when the lead rider pulls aside to make their way to the back of the line of riders. They and their team are better off (at least in low yaw conditions) if the rider pulls over and moves well away from their companions until they are near the back and can return to be in the draft of the other riders. 10W is nothing to sneeze at.

Conclusion

So it would seem that if you wish to ride alongside your ride buddy, it might cost you ~10W give or take. If speed is of the essence, then ride in single file, you'll both go quicker that way.

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W/m^2, Altitude and the Hour Record. Part III

In my previous posts on this topic I explored the impact of altitude on the hour record. You can recap by clicking on the links here:

W/m^2, Altitude and the Hour Record. Part I
W/m^2, Altitude and the Hour Record. Part II

In summary, the primary impacts on the speed attainable (or distance attainable for an hour) are:

1. Physiological - the reduction in sustainable aerobic power as altitude increases due to the reduced partial pressure of Oxygen, and

2. Physical - the reduction in aerodynamic drag as altitude increases due to the reduction air density.

Of course there are other factors - variable track surfaces and geometry, logistical, financial, physiological and so on, but for the purpose of this exercise I have confined analysis to the primary physiological and physical impacts.

These primary competing factors - reduced power and reduced drag combine to mean that in general an increase in altitude means a greater speed is attainable. In other words, the benefit of the lower air resistance at higher altitude typically outweighs the reduction in power. But not always.

The level of impact to speed is individual and is a function of each individual's physiological response to altitude - while the physics side of the equation is the same for everybody. I covered this in more detail in Part II of this series, and used data from several studies which provide four formula for the average impact of altitude on power output.

I plotted the different formula depending on whether athletes had acclimatised to altitude or not.

This chart should be fairly intuitive - further up in altitude you go, the more power you lose compared with sea level performance. The vertical scale of the chart amplifies the differences between them, which are not large, but also not insignificant either. A key element was the difference between athletes that had acclimated to altitude and those who had not.

Then I layered on that the physics impact of reducing air resistance, but the resulting chart was not quite as intuitive to follow and so I decided to revisit this another way.

Hence exhibit A below (click on the image to view larger version):

This should be reasonably straightforward to interpret, but even so I'll  provide some explanation.

The horizontal axis is altitude and the dark vertical lines represent the altitude of various tracks around the world.

The vertical axis is the proportion of sea level speed attainable.

The curved coloured lines represent the combined impact of both a reduction in power using each of the formula discussed in Part II of this series, combined with the reduction in air resistance.

So for example, if we look at the green line (Basset et al acclimated), this shows that as an cyclist increases altitude, they are capable of attaining a higher speed up until around 2,900 metres, and any further increase in altitude shows a decline in the speed attainable, as the power losses begin to outweigh the reduction in air density.

The track in Aigle Switerland represents around a 1% speed gain over London, while riding at Aguascalientes would provide for between a 2.5% to 4% gain in speed. Head to Mexico City and you might gain a little more, but as the chart shows, the curves begin to flatten out, and so the risk v reward balance tips more towards the riskier end of the spectrum.

Altitude therefore represents a case of good gains but diminishing returns as the air gets rarer. Once you head above 2,000 metres, the speed gains begin to taper off, and eventually they start to reduce, meaning there is a "sweet spot" altitude.

Caveats, and there are a few but the most important are:
-  any individual's sweet spot altitude will depend on their individual response to altitude - the plotted lines represent averages for the athletic groups studied;
- the formula used have a limited domain of validity, while the plotted lines extend beyond that, a point I also covered in Part II of this series;
- these are not the only performance factors to consider, but are two of the most important.

I suspect that the drop off in performance with altitude might occur a little more sharply for many than is suggested here. Nevertheless, the same principles apply even if your personal response to altitude is on the lower end of the range, and it is hard to imagine why anyone would suggest that heading to at least a moderate altitude track is a bad idea from a performance perspective.

Alex Dowsett rode 52.937km at Manchester earlier this year. At Aguascalientes he could reasonably expect to gain ~3.5% +/-0.5%  more speed, or just about precisely what Bradley Wiggins attained in London.

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Density matters

I saw a question today from someone who read recent comments about how high air pressure resulted in Brad Wiggins' hour distance being less than it might otherwise have been with more favourable conditions.

He was wondering if you can control air pressure in velodromes, or choose a time of year when it is lower. So can we do that?

Climate control

While there are velodromes where the inside air temperature is controllable (mostly northern hemisphere tracks located in cold climates), the control of air pressure is not something possible at any currently existing track that I'm aware of.

It would require quite a deal of engineering, in particular to provide an air lock / sealed environment that enables lots of people (and service vehicles) to enter /exit the building without affecting inside pressures and which meets emergency evacuation requirements for a large crowd, as well as fresh air to breathe. I don't see that happening any time soon.

Air locks do exist, e.g. at Aguascalientes velodrome in Mexico they use an air pressure differential to support the roof, but that means the air pressure inside the velodrome needs to be higher than outside. Not by much, but it will always need to be higher relative to local weather conditions, and inside the velodrome air pressure will still vary relative to outdoors.

So what about picking a better time of year?

Well let's look at the daily barometric pressure readings near London for the past three and a half years. Source for these charts is the National Physical Laboratory in the UK.

Barometric pressure London Jan-Dec 2012

Barometric pressure London Jan-Dec 2013

Barometric pressure London Jan-Dec 2014

Barometric pressure London Jan-June to date 2015

Looking at the above, it's pretty clear there is no obvious pattern to suggest a time of year when barometric pressure will be, on the balance of probabilities, lower.

Air density is what matters.

Air pressure of course is not the only variable. What really matters is attaining as low an air density as is physiological sensible. Air density along with a rider's aerodynamics, ie. their CdA, determines the energy demand for riding at a given speed, and lower air density is desirable for greater speed, provided of course the means to achieve that lower density doesn't reduce a rider's power to the extent performance ends up being worse. e.g. by riding at such high altitudes or temperatures that the rider's power output is compromised to a greater extent than the air density benefit provides.

Air density is a function of:
- air temperature
- barometric pressure
- altitude
- relative humidity

You can pretty much discount the latter as the changes in air density is very small with changes in humidity, although for the record humid air is slightly less dense than dry air (at same temperature, pressure and altitude).

Air density reduces with increasing temperature and altitude, and with reducing barometric pressure.

Since attempting to reduce air pressure either via climate control or by picking suitable times of year is not really an option, that leaves us with adjusting the other two variables - temperature and altitude.

I've discussed altitude before in this item. I'm going to revisit it in a future post in an attempt to simplify the impact of the variables involved.

Heating the air inside a velodrome is common, and this was attempted with some powerful portable heating devices during Jack Bobridge's unsuccessful attempt earlier this year, and in the case of attempts at most northern hemisphere tracks, the temperature has been dialled up to the rider's desired level.

Wiggins did specific heat acclimation work and reports are the temperature inside the velodrome was around 28-30C. That's pretty warm - going too hot can be detrimental as power losses can occur with inadequate cooling. As I said earlier, it's a balance between a physical benefit and a potential physiological cost.

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Wiggo's Hour

Just a short one today to update the chart from the one I posted here and on other social media forums. Click to see bigger version.

54.526km

Different reports of barometric pressure of 1031-1036hPa and air temp of 30.3C inside the track mean that Wiggins must have been exceptionally aerodynamic and recent work on his bike and position at the track suggest some good aero gains were made.

I estimate a power to CdA ratio of 2500-2550W/m^2 was required.

There are of course a range of assumptions:
Total mass: 82kg
Crr: 0.0023
Drivetrain efficiency: 98%
Altitude: 50m
Relative Humidity: 60%

If drivetrain efficiency is better, say 99% and Crr at 0.0020, then it drops the power to CdA ratio down to 2200-2220W/m^2.

and perfect pacing.

Just on that, my colleague Xavier Disley has once again produced a lap pacing chart - here it is:

That's a very slight fade over the course of an hour, which in my humble opinion is pretty much perfect. Opening few laps a bit hard, but that's understandable as a rider seeks to control the adrenaline rush with thousands in the crowd watching on and cheering.

The high air pressure did cost distance, and on another day perhaps 55km was within reach

As for going to high altitude, well there are many variables, but another 1-2km is feasible. See this item for more on that.

Well done to Brad Wiggins. That's sure a fine ride.

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g force

No, not that kind of G-Force!

I mean the extra "weight" we feel pressing us down onto the bike or into the track when riding at speed around the curved banking of a velodrome.

If you really want to read up on g forces, then this Wikipedia page covers it.

First of all, "g force" isn't really a force, rather it's a measure of a rate of acceleration. It's one of those slightly confusing expressions.

g force is a way to "normalise" accelerations relative to that we experience every day due to gravity on the surface of the Earth. It's a way to gauge how much we'd "weigh" when experiencing an acceleration that's more or less than 1g.

When we are standing on the ground, we experience 1g (units are usually expressed a "g", not to be confused with grams). We are not actually accelerating, since the ground is there to stop us from falling, so instead we feel a force we call weight.

While we normally use standard international unit of metres per second squared (m/s^2) to express accelerations, it's common to express accelerations relative to that we experience on the surface of the Earth, which is defined a 1g.

If you have a mass of 80kg and are standing on the ground then you'll weigh 1g x 80kg. That's why many confuse weight with mass. They are not really the same thing, mass is an intrinsic property of an object, weight is the force it pushes down on the ground with. It's just that on when sitting on the surface of the Earth, an object with a mass of 80kg will also weigh 80kg.

However if you are accelerating upwards away from the Earth's surface (imagine you're travelling upwards in a rapidly accelerating elevator or rocket), then you'll experience more than 1g.

How much more depends on the rate of acceleration. If you happens to be accelerating upwards at 9.81 metres per second per second (which equals 1g), then you'd experience 2g, being acceleration due to gravity + the extra acceleration of the elevator or rocket. If you were able to stand on some bathroom scales while that acceleration is happening, then you'll "weigh" 80kg x 2g or feel like you now weigh 160kg. ugh.

Now keep in mind that an acceleration can be a change in speed and/or direction.

e.g. when a travelling in a car that turns around a corner, even through the road speed of the car may not change, we experience what feels like a force pressing us towards the opposite side of the car. Such lateral accelerations can also be expressed relative to 1g. Modern Formula 1 racing cars for example are capable of generating lateral corning accelerations of up to 6g.

g force on a velodrome

So whenever we are riding around the curved path on the turns of a velodrome, we are constantly accelerating towards the centre of the track, even though we may not be changing the bike's forward speed. As a result, we experience some lateral g forces when riding on velodrome, as well as the downward 1g due to gravity. What this means is the total g force we experience will be more than 1g. How much higher depends on our speed and the turn radius.

Calculating the rate of lateral acceleration when riding around a track is a pretty simple:

where:

- rider speed is in units of metres per second 

- 9.81 is the rate of acceleration due to gravity in metres per second squared

- rider turn radius is measured in metres

Estimating rider turn radius

To estimate a rider's turn radius, we start by estimating the track's turn radius.

First an overhead shot of a velodrome to get a sense of the general shape of a track (thanks to Google maps). This one happens to be a local outdoor track not far from where I live. It's a 333.33m concrete track. You can make out the faint blue band around the inside of the track, which is just inside of the track's black measurement line, the inner edge of which = 333.33 metres in length.

Now we can approximate the shape of the track as being two semi-circles joined by two straights. Here I superimposed some circles and lines to demonstrate:

Of course tracks are not exactly like this, in reality the shape of the turns are not perfectly circular, and the length of straights varies. They really do come in many different configurations. But as an approximation you can see from the diagram it's pretty good starting point. So to make a reasonable approximation of a track's turn radius at the black measurement line, all we need to know is the total length of the track, and the length of the straights.

Let's say you are riding a 250 metre track with 44 metre long straights. The turn radius around most of the turn will be approximately (250 - 2 x 44) / (2 x PI) = 25.8 metres.

Like I said, it won't be exactly that as in reality tracks have a variable turn radius but it's close enough for the purposes of this discussion. OK, that's great, we have the track's turn radius.

Now back to our lateral g force formula:

Now this formula asks for the rider's speed and turn radius, not the track's turn radius.

The rider's speed and turn radius is based on the position of their centre of mass (COM). Since a rider leans over when riding around the banked turn of a velodrome, then their COM speed and turn radius is less than the wheel's speed and the turn radius at the track where the tyre is rolling along.

Another diagram to help explain. You might need to look at a larger version - so click or right click on it to view a larger pic. ('The pic of a leaning rider I found on this blog item. Hope they don't mind me borrowing it - I can't however vouch for the physics discussed in that item).

When a rider at speed rides around the turn of a banked velodrome, they are leaning over. That means the turn radius of their COM is less than the turn radius of the track where the tyre is rolling along. So if you want to calculate the g force on a rider you really should be using the COM turn radius and speed, which is a bit of a pain because bikes use speed sensors that measure the wheel's speed.

To calculate COM radius and speed, you then need to know the rider's COM height and their lean angle (from the vertical). It's a little basic trigonometry. 

e.g. if a rider's COM is 1 metre (COM height will be about the same as floor to saddle height for a rider in an aggressive race position), and they are leaning over at 40 degrees from the vertical, then the rider turn radius = track turn radius - sin(40 degrees) x 1 metre. IOW we reduce the track turn radius by ~0.64 metres, which for our 250 metre track is about 2.5% of the track's turn radius. So not much, but enough that for some applications and analysis of track cycling data you need to take these things into account.

That then brings us to the question of how do we calculate the rider's lean angle? Well I'm going to leave that one for now because I'm getting further away from the issue of g forces than I'd really like. Suffice to say that we can reduce the estimated track turn radius and wheel speed by a couple of percent to estimate rider turn radius and rider COM speed.

Are you still with me?

OK, so we can reasonably estimate the lateral g force of a rider travelling around the turns of a track. But of course the rider also feels the force of gravity pulling them downwards. So the total g force acceleration into the track is the sum of those two acceleration vectors:

Which can be expressed as follows:

So there you have it.

How much g force does a rider feel in the turns?

If we use an estimated rider turn radius of ~25 metres for a typical 250 metre track with rider speeds ranging from 40km to 75km/h, here's what the estimated g forces are:

At elite hour record speeds of between 52-55 km/h, a rider will experience around 1.3g to 1.4g when riding the turns.

There is a physiological question to be considered, namely does this higher g force, which occurs twice per lap and lasts for about 2/3rds of the total time on track, cause any problems with blood circulation, is it sufficient to hamper performance?

I don't know, and I'm not sure if there's been anything more than speculation on this question. 1.3-1.4g doesn't sound like it'd cause too much of a problem to me, but who knows?

Track sprinters

Things get much more interesting for the world's best track sprinters, who experience around 2g in the turns during their flying 200 metre time trial. If you have a 95kg track sprinter flying around at 75km/h, the bike, wheels and tyres are supporting the equivalent down force of over 200kg.

This is why track sprint bikes and wheels have to be made extra strong, and also partly why track sprinters run extra high pressure in their specialist tubular tyres.

Would you put a 200kg rider on your bike?

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