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.

Read More......

The Sin of Crank Velocity

Crank and bike speed variations during a pedal stroke

This topic occasionally comes up in discussion in cycling forums – just how much does crank speed vary during a pedal stroke? And how much does this affect the accuracy of power meters?

If you are pedalling along at a steady rate and maintaining a consistent power output (in other words you are not attempting to accelerate or slow down) and are using circular chainrings, then the short answer is: not a lot.

But crank rotational velocity during a pedal stroke is not totally constant, there is some variation.

Of course anyone who has ridden a bike behind a derny or motor pace bike on flat terrain or at a velodrome knows they are able to ride consistently close to the rear guard or roller of the motorbike and not experience significant fore-aft movements during each pedal stroke.

Riders following a motor pacer manage to remain very close
to the pacer and don't experience large fore-aft relative motion.

Riders in a highly skilled team pursuit formation riding at high power outputs are also able to ride within centimetres of the wheel in front without experiencing major changes in velocity between riders during each pedal stroke, which if it did happen would of course be somewhat disastrous. Note the riders below are all at different phases in the pedal stroke:

Track Cycling World Championships 2014: GB women's team pursuit team
Image from: www.telegraph.co.uk

So even without any examination of the research, or doing any fancy modelling of the physics involved, we already know empirically there really isn't going to be large variations in bike and crank velocity.

So how much variation is there and what influences bike and crank speed during a pedal stroke?

When pedalling in a steady state manner, the main factors influencing the variability of crank velocity are:

• The average power being applied
• The manner and level of power variation during a pedal stroke
• The inertial load of the system (i.e. the speed and mass of the bike + rider, plus a little rotational inertia from rotating components)
• The resistance forces in play (i.e. air and rolling resistance, gravity, and changes in kinetic energy) and whether for example air resistance is dominant (e.g. when riding on flat terrain), or overcoming gravity is dominant (e.g. climbing a steep grade)
• The shape of the chainrings, or as in the case of some weirdo bike crank and pedal sets ups, the variable effective radius of the crank arms

Why do we care about crank velocity variation?

Apart from satisfying our curiosity on this somewhat esoteric matter, the answer does have a few practical applications with respect to cycling performance, one of which is to do with power meter accuracy. Others pertain to efforts seeking to eek out minor performance gains though examining mechanical adaptations to the bicycle drive train, such as design of non-circular chainrings. Whether these designs result in a performance improvement is debatable (the research is equivocal on the matter for sustainable aerobic power) and not the topic of this post, so I'll leave it there for now.

Power meter accuracy and crank rotational velocity

Many power meters, e.g. SRM, Quarq, Power2Max, Garmin Vector and Stages, rely on the assumption that crank speed during a pedal stroke does not vary (Powertap on the other hand assumes wheel speed does not vary during their fixed duration torque sampling period of 1 second).

This is an important assumption, since torque is sampled at a fixed frequency (e.g. at 200Hz for an SRM or somewhat lower, e.g. at 50-60Hz for other brands) and then those torque samples are averaged over a complete crank revolution. This averaging of torque over a full revolution to calculate power will only be accurate if the crank velocity does not vary much during the pedal stroke.

If however a rider pedals significantly more slowly during one part of a pedal stroke compared with another, then that slower part of the pedal stroke will be over-weighted in the average of total torque samples. Hence interest in examining the assumption about constant or near constant crank velocity during a pedal stroke.

So let’s look at some of the crank velocity variability factors I mentioned earlier.

Power application during a pedal stroke

It’s well known that when we pedal we apply torque to the cranks in a pulse-like manner, with each leg’s down-stroke moving from a phase of minimal propulsive power when the crank is vertical with the pedal at top dead centre, increasing propulsive force and power as the crank moves down towards the horizontal, and diminishing as the crank moves towards the vertical again with the pedal at bottom dead centre. It looks a little like this:

Image courtesy of:
http://www.rohloff.de/en/company/index.html

In steady state cycling we apply little if any propulsive force on the upstroke and some may in fact apply a little negative force (this is not necessarily a bad thing and is something often misunderstood about pedalling dynamics - but I digress).

This pulse-like power cycle is repeated by the opposite leg and crank arm, so that for each full revolution of the crank, we apply two pulses of power, mostly from the down-stroke push of each leg.

This pulsating nature of power application has been measured and is well reported in the scientific literature, and typically shows a wave-like sinusoidal pattern (i.e. it looks like a sine wave), which should come as no surprise given our legs act like two pistons pushing down on rotating crank arms.

Studies examining this go back many, many decades, e.g. this 1968 paper by Hoet at al as an example reported the following finding:

Those summary findings by Hoes et al have been consistently replicated in many subsequent studies.

Such analysis goes back even further, to the late 1800s. Pedal pressure was measured and shown in this book: Sharp, A. (1896). Bicycles and tricycles: an elementary treatise on their design and construction.

This fabulous old book (which covers a huge range of cycling physics and performance matters over 32 chapters and which Lee Childers at Alabama State University kindly referred me to) is available in scanned form online here:

https://archive.org/details/bicyclestricycl02shargoog

Here are image scans from four of the book's 561 pages showing pedal pressure measurements from various riding conditions on a fixed gear bicycle (flat track riding, ascending and even back pedalling when descending). Read from the bottom of page 268 - Section titled: 214 - Actual Pressure on Pedals.

The charts plot the measured pedal pressure, which is not the same as the tangential (propulsive) forces, a point made on page 270 - but even so we can see the basic shape of pedal forces follows this basic pattern. Indeed Sharp refers to such tangential pedal force measurement pedals designed by Mallard and Bardon, their "dynamometric pedals". I don't have a link to show these unfortunately. This was the late 1800s. What's old is new again.

Below is an image from the 1991 Coyle et al paper showing the measured crank torque applied by one leg through a full pedal stroke for each of the 15 riders in the study. We don’t need to inspect the plots too closely; the main point is we can readily see the approximately sinusoidal shape of torque applied to the cranks during the down-stroke phase, and the minimal torque applied during the upstroke phase.

The primary differences between riders are in the amplitude of the down-stroke phase of curve, and the shape of the upstroke phase, which mostly hovers around the zero line. As always, you can click on an image to see a larger version.

If you then imagine the opposite leg repeating the same type of torque application, then we can see we apply torque to the cranks in a pulsating wave-like, or sinusoidal, manner. This sinusoidal curve was also demonstrated in the 2007 Edwards et al paper which included the following plot of typical pedal torque applied by both legs for a full crank revolution:

So while not perfect sine wave-like application of torque, thinking of the force applied to the cranks as being sinusoidal-like is a very good first order approximation.

Users of indoor bike training systems like Computrainer, Wattbike or SRM's Torque Analysis System may have also seen similar torque output curves. Here’s a random example of an image of a Computrainer SpinScan plot I found with a quick Google search:

Now SpinScan is not as fine a resolution measurement tool as used in scientific study, but at least you can see that the same basic shape of the power output curve during a pedal stroke. Wattbike charts are typically displayed in polar chart format, so to avoid confusing things I won’t post a picture here but the same overall pattern of torque and power application is repeated, as they are with SRM's Torque Analysis system (although this is a very low power example from SRM's website):

One thing we can see with all these examples is how power doesn't generally drop all the way to zero while pedalling, and that it is often not symmetrical for left and right legs.

I have generated a sample sinusoidal power curve to reasonably approximate this pedal power pattern which I'll use for modelling I'll discuss later on. In this case it shows the power curve when pedalling with an average power of 250 watts at 90rpm (click on pic to see larger version):

Now this is by no means a perfect model of actual power application, and as can be seen from the various charts shown earlier, everyone pedals slightly differently, but it’s certainly a very good first order approximation to examine the issue of how much bike speed is affected by application of such a pulsating power curve. It matches the general shape of actual torque delivery delivery and the peak power is nearly double the average power, which also matches the torque profile measured experimentally many times, and at least since Hoet at al reported this in the 1960s.

Naturally the power curve is a function of both crank torque and crank velocity, but as we shall eventually see, the latter does not vary all that much, certainly not enough to make this first order approximation invalid for the purpose of answering this question.

So what effect does this pulsating variable power output have on bike and crank velocity?

Firstly I’ll look at an example of what’s actually been measured and reported in the scientific literature, and then I’ll examine the physics with some modelling.

Actual measurement of crank speed variations

Crank speed variations during a pedal stroke were reported in this paper by Tomoki Kitawaki & Hisao Oka: A measurement system for the bicycle crank angle using a wireless motion sensor attached to the crank arm, J Sci Cycling. Vol. 2(2), 13-19.

Here’s a link to a pdf of the paper I found in a Google search:
http://tinyurl.com/qapfoek

I'm referring to this paper in particular as it provides some helpful images and a full version is available online for anyone interested in examining it in more detail. Other studies have also measured crank velocity during pedalling and found similar results, but the data may not be available in the freely available public domain nor presented in such a convenient and helpful manner as needed for this discsussion.

Figure 6 of this study (shown below) summarises the measured variability in crank velocity over a range of power outputs for riders in three groups categorised as beginner, intermediate and expert level by their relative power to weight ratio being approximately 1.5W/kg, 2.25W/kg and 3W/kg respectively.

Crank velocity for each group is shown at two different cadences (70rpm and 100rpm) and was measured using two different crank velocity measurement systems (the study was primarily to examine the validity of a crank angle and velocity measurement system compared with a standard. As it turns out the two methods matched quite well). They also measured the crank velocity variations at the riders’ freely chosen cadence but did not provide charts for those data.

In this study, riders used their own bike on a CycleOps Powerbeam Pro trainer, which is a fairly typical and relatively low inertia indoor trainer.

It shows six charts. In each the crank rotational velocity relative to the average crank rotational velocity (i.e. the normalized crank rotational velocity) is plotted by crank angle for a complete pedal stroke. There are a series of dots and lines plotted in the charts, and these represent the normalized crank rotational velocity as measured using two different measurement systems.

The maximal variance in normalized crank rotational velocity occurs in the most powerful group of riders, and at the lowest pedal rate (70rpm). The variance in this case was around +/-3% and in all other cases the crank velocity variance was less than +/-2%.

Keep in mind this experiment was performed on a low inertia trainer. Why does this matter? 

It matters because a mechanical system (or an object) with lower inertial load will accelerate (or decelerate) more rapidly when a net force is applied to it compared with a system with greater initial inertial load. Many indoor trainers, like the Powerbeam Pro used in this study, have lower crank inertial loads for the same rear wheel speed compared with what a bike and rider riding out on the road typically possesses.

So what happens when we examine the case of a more realistic road-like inertial load scenario?

Since I’m unaware of published and validated crank velocity measurements readily available from actual on road riding (if anyone can point me to any please let me know), we can instead examine the physics of what happens to a bike’s speed when power is applied in this pulsing sinusoidal-like manner.

Forward integration - Balance sheet accounting for energy

To do that I use the technique of forward integration, a technique that’s really no more complicated than an accounting balance sheet but for energy rather than money.

On one side of the balance sheet is the energy supply coming via our legs, and the other side of the balance sheet is the energy demand, i.e. the power required to overcome various resistance forces such as air resistance, rolling resistance, gravity if changing height, and importantly resistance to changes in speed (kinetic energy). That energy balance sheet must remain in balance. It’s a fundamental law of nature.

At any point in time if we know a rider’s speed, their mass and that of their bike, the moment of inertia of their wheels, their coefficients of air and rolling resistance, the road gradient, and other small frictional loss factors, then we can calculate how much power is required for each of these various resistance forces, and when added together they tell us how much power is required to maintain that speed.

If a rider’s actual power output is different to that required to maintain the same speed, then the balance of power supply must result in a change in kinetic energy, and hence a change in speed.

If a rider is in deficit on the energy balance, then that deficit must come from somewhere and that means their kinetic energy (and hence speed) must reduce by the same amount accordingly. Put another way, they are not supplying sufficient power to maintain their original speed and must therefore slow down.

Conversely, if the rider is providing power in excess of that required to maintain their original speed then they will accelerate, and at a rate so that the increase in kinetic energy matches that energy surplus.

In the model these calculations are made for each brief moment in time, the net energy surplus or deficit for that initial speed is determined and converted to the exact change in speed required to maintain the energy balance.

Let’s examine what happens to a rider’s speed in a sample scenario.
250W, flat road @ 90rpm

Riding along at 90rpm on a dead flat road with no wind and with an average power of 250W at around 36km/h with:

• Bike + rider mass: 80kg (including wheel rim mass of 1kg)
• Coefficient of rolling resistance (Crr) of 0.005 (fairly typical for good road tyres on asphalt/chip seal surface)
• Coefficient of drag area (CdA) of 0.35m^2 (e.g. road bike on the hoods)
• Air density of 1.20kg/m^3 (sea level, 1020hPa, temp 21C, relative humidity 77%)
• Drivetrain efficiency:  100% (just to keep it simple, although ~97% is typical)

Using the forward integration model with the simulated sinusoidal-like power output during a pedal stroke, we can now plot the impact on bike speed during a pedal stroke. Click to view a larger image.

In the chart above we have the power output (yellow line) varying during the pedal stroke, which takes a total of 0.667 seconds to complete each revolution. The plot show 1 full second of pedalling, and so the graph actually shows one and half revolutions of the crank.

The initial velocity is set to a little under 36km/h. The speed resulting from that pulse like power input is also plotted by the blue line with the left hand axis being speed. Note the speed scale ranges from 24km/h to 40km/h and so is already zoomed in a little to amplify the variation. At that slightly zoomed scale we can see that the speed line wavers up and down just a little during the pedal stroke.

Since it’s a little hard to see how much variation in speed happens, let’s zoom in much more by adjusting the speed scale to amplify that speed variation curve.

Note the scale of the speed axis on the left side – each horizontal grid-line represents 0.05km/h, and the variation in speed is easier to see.

When power is higher than that required to maintain a constant speed, then speed increases. Eventually though the power drops below the level required to keep accelerating, and speed levels off then begins to decline as power has dropped such that there is now an energy deficit compared with that required to maintain that speed, and so kinetic energy (speed) must fall. As a result, the speed plot follows a similar sinusoidal-like curve, but out of phase with the power plot.

Here’s a table summarising the average, minimum, maximum and amount of variation in power and speed.

The normalized speed variation is less than +/-0.2%.

As I said, not a lot of variation in bike speeds during a pedal stroke, even though the power is ranging from a low of 20W up to a maximum of 480W twice each pedal stroke.

That's bike speed - what about crank velocity?

Now the next logical step is to assume that this “all-but” constant bike speed is also matched by constancy of chain speed and hence crank speed. Since the chain is moving around the rear wheel's circular cog and the upper drive section of the chain has positive tension then that is what you would expect.

So provided the front chainring is circular, this will also result in a nearly uniform crank rotational velocity.

Hence in this steady state cycling scenario we need not be concerned with any inaccuracies in power measurement due to the assumption used by power meters that crank velocity is constant during a pedal stroke.

For crank velocity not to closely match the bike’s velocity it would require the part of the chain under constant tension to stretch and contract significantly during each half pedal stroke, or for the chainring to not be circular. Chains just don’t do that but chainrings may be all sorts of curved shapes.

Sensitivities and assumptions

As I said earlier, this input power model is only a first order approximation; people apply power slightly differently, and not necessarily symmetrically or consistently. Some of the other assumptions may not necessarily hold, e.g. aerodynamic and rolling resistance coefficients, and drivetrain efficiency remaining constant during a pedal stroke when they may in fact vary a little during pedal stroke. The rider’s legs also slightly vary their kinetic and potential energy as they move through a pedal stroke,

These are second and third order effects that would only make minor changes to the shape of the modelled speed curve, and we can see that the speed variation is already so small such that second and third order modifications are not going to change the outcome to any significant degree.

What about when climbing a steep hill?

When climbing, average speed for same power will be significantly less than when on a flat road. On an 8% gradient our 250W rider will be travelling at closer to 13km/h instead of 36km/h. That’s means a much reduced kinetic energy – which is dominated by translational KE of the rider.

KE = 0.5*mass*velocity^2,  plus a little bit from wheel rotational inertia (which is very small).

The translational KE of our 80kg bike and rider at 36km/h is 4,000 joules, and at 13km/h it’s 522 joules, or only 13% of the KE at 36km/h, even though velocity is 36% of flat road speed.

The next big difference is the resistance forces are now dominated by overcoming gravity rather than overcoming air resistance. This also has an impact on the size of bike speed variations during a pedal stroke, the result being we should expect changes in speed to be greater.

Finally, many riders have a tendency to pedal at a lower cadence when climbing steep hills. Not everyone does of course, but sometimes the available gearing means a lower cadence is inevitable. So for the sake of this scenario, let’s assume the rider’s cadence has dropped to 60rpm (that's about what cadence would be with a 39x23 gear at 13km/h).

This is the power and speed plot:

Since the cadence is 60rpm, it take a full second for each pedal revolution. We can see even with the low zoom level on the speed axis that the bike’s speed line does indeed vary more than when on the flat road.

Here’s what the speed variation looks like using the same zoomed-in view setting as before:

So when climbing there is a much greater variation in bike speed during a pedal revolution than when riding on a flat road at higher speed, but it’s still less than +/-2%.

Is a +/-2% crank speed variance during a pedal stroke something to be concerned with for power meter accuracy? 

As a rough rule of thumb, the error this would introduce to the calculation of power would be approximately 40% of the crank speed variation, or less than 1%. Whether that 1% error matters to you I can't really say, but it's a couple of watts and for most people it's not a significant factor for the purposes they might be using power meter data from climbs for.

If you are doing some aerodynamic field testing though, then such an error would be of concern. Fortunately we don't do such testing on steep climbs all that much, but rather mostly on flatter terrain where any error due to crank rotational velocity variation as we have seen is tiny.

That’s a 3.5W/kg rider. What about a more powerful 5.5W/kg rider climbing that 8% grade?

More powerful riders climb faster, and likely pedal at a higher cadence as well, so let’s assume our 400W rider climbs the 8% grade and pedals at 75rpm (that's roughly the cadence if pedalling a 39x19 gear at 19 km/h). This is the resulting power and speed plots:

So even though the rider is more powerful and has much greater variation in power output, the increased cadence and higher speed means the normalized crank rotational velocity variation is only +/-1%, and power meter error is likely to be less than 0.4%.

Summary

While pedalling in a steady state manner out on the road with circular chainrings, crank speed does not vary all that much. It varies more when climbing than when riding along flatter terrain, but the amount of variation is still small such that the basic assumption of non-varying crank velocity used by power meters to calculate power is sufficiently valid and within their generally stated margins of error.

Crank speed variation is larger when riding on low inertia trainers, such that the level of potential error in reported power may begin to approach the limit of the devices' stated error margins.

Read More......

Anaerobic Stuff - Mr Peabody's WABAC Machine

Time to get into Mr Peabody's WABAC Machine. C'mon Sherman, let's wind the clock back to 2007....


This post is another take on my February 2007 Darth Vader item. Back then I wrote, with considerable assistance from Mr Peabody - er, I mean Dr Andy Coggan, an item about Maximal Accumulated Oxygen Deficit (MAOD).

Andy introduced the concept of using power meter data from a well paced individual pursuit as a means to estimate MAOD (which ordinarily would require lab based testing). He expands on it in the book, Training & Racing with a Power Meter, pp 244-248 (2nd edition).

Just to recap, MAOD is the "gold standard" measure of an athlete's anaerobic capacity. Expressed in litres of O2, it's the difference between the energy produced aerobically and the total energy demand. In an event such as the individual pursuit, a rider's total energy output is typically ~ 70-80% via aerobic means and the balance of course via anaerobic metabolism.

So I thought I'd take the analysis method from that previous post, run it on my recent events and add another twist - the points race.

In recent posts I've mentioned a few track endurance* events I've raced:
- 4km Individual Pursuit (Aussie National Championships - C4 paracycling)
- 2km Team Pursuit (Masters 150+ State champs)
- 20km Points race (Masters 45-49 State champs)

Edit: I've since updated the list to add in the 1-kilometre time trial I raced at the Paracycling nationals the day before the 4km individual pursuit.

It's all part of my comeback to competitive cycling, as these are the events I most enjoy. Well except for the individual pursuit. That's an event impossible to enjoy. But it's fun to do some analysis of pusuiting because it reveals so many things about a rider. Physiologically, technically, aerodynamically and psychologically.

In the weeks and months before my accident in 2007, I rode the same events, the only difference being the individual pursuit was 3km, not 4km and the team pursuit was 3km then vs. 2km this year (different distances for different masters age and paracycling categories).

I've been riding these events for many years but 2007 was my best season up to that point, with a win in the Team Pursuit (in a new state record time), a bronze medal in the National Masters Points race champs and two personal best times in the 3km IP. So for me, relatively speaking, they provide very sound benchmarks for how I've bounced back since then. I'm not going to go into that here though as I've already covered that a number of times.

OK, back to Mr Peabody and the analysis. Here's the chart showing cumulative O2 deficit from my recent races:


Click on the pic to enoxygenate (apologies for the Phil Plaitism).

The picture details the cumulative O2 deficit for four rides - my individual pursuit (red line), the team pursuit (blue line), the 1-km TT, and also a roughly 5-min section from my points race last weekend (the Richie Benaud cream jacket tan line). I'll get to the points race later.

Just to explain the chart - let's take the red line for the individual pursuit. You start the event from a dead stop (your bike is held in a starting gate which releases on count down to zero) and then accelerate over about 15 to 20 seconds to a high cruising pace, which you are then attempting to maintain for the balance of the event. The red line is a measure of how much oxygen "debt" I am incurring as time passes.

I incur this O2 "debt" since my power output in a pursuit is somewhat higher than my sustainable threshold power (which can be produced almost wholly via aerobic metabolism - or in a "pay as you go" sense). Once you ride above threshold, you are tapping into your limited anaerobic work capacity - and it really is limited - meaning that such efforts are by necessity going to be short lived. Harder you go, the less time you'll last. Nothing new about that.

Not only that but once you expend your limited reserve, in order to continue you will have no choice but be forced to ride under threshold in order to recover the O2 deficit. This is why pacing your effort is so crucial in timed events, and in mass start racing why dosing out the hard efforts at the right time is so important. The cost of "blowing up" is considerable in performance terms.

It's also why improving threshold power is so crucial. When you do go into the red zone in a race, you don't incur as much O2 deficit, or can last for longer at that level. And when the pace eases up again and you dip below threshold more quickly, you recover faster meaning you are ready for the next attack before someone else is. Counterattack anyone?

How do we determine this aerobic/anaerobic contribution with a power meter? Well as per the book, it's matter of looking at O2 kinetics of a well paced pursuit:


Andy showed that we can plot, along with the actual power output from a pursuit, a line representing a rider's theoretical maximal aerobic power output based on lab tests of a rider's VO2max** and efficiency***.

Except that in my case, I don't have the latter. Never mind, since the steady state part of a well paced pursuit represents power output at VO2max, we can simply adjust those VO2max and efficiency values so that they match the steady state portion of the pursuit power file. I assumed an efficiency of 22.5% and adjusted my VO2max value until it fairly represented my steady state power output in the pursuit. It came out at 58 mL/min/kg. If you change the VO2max (or efficiency) value, it moves that maximal aerobic (red) line up and down accordingly.

OK, so that's pretty funky, I can estimate my VO2max (or at least a range given that we assume efficiency is in a range typical for trained cyclists).

But by then directly comparing the difference between the maximal aerobic power, and what power I actually produced, we can then attain an estimate of the proportion of energy output from anaerobic contribution.

In my case, it estimates about 17% of my energy was from anaerobic supply. That's a little lower than typical for a pursuit, but my race time was 5:08, which is longer than the 3.5-min to 4.5-min efforts for elite riders in 3km and 4km pursuits and so it's not entirely surprising.

It also means that my MAOD was estimated at 4.16 L. We'll tag that number for now.

OK, so how about those cumulative O2 deficit lines?

In the WABAC machine we saw the way the O2 deficit would climb at different rates when riding a team pursuit as a rider alternately takes a pull on the front (O2 deficit line increases at a faster rate) and then gets back in line and recovers (where the line either rises more slowly or can even fall if the rider is quite powerful and not overly challenged by the team's pace).

If a rider exceeds their MAOD, then there is a pretty fair chance they will crack, which in a team pursuit means they are unable to continue and pull out after their turn on the front, or as sometimes can happen they cannot even maintain the pace of the rider(s) in front and they end up creating a gap in the line, which is bad news.

So I plotted the cumulative O2 deficit line from my recent individual and team pursuits and they shows the same pattern as in 2007. The team pursuit line is much shorter of course since the event is half the distance of the individual pursuit, and in a team, so it is considerably faster.

I also plotted the same line from a section of my points race on the weekend. I chose a starting point very early in the race, it was about lap 6, with 4 to go to the first sprint. My team mate was on the front at the bottom of the track, he slowed the speed down a little in the preceding half lap and then launched an attack, I was on his wheel and went with it.

I had to go pretty hard, with peak power reaching 1184W in order to cover it (he's a world class masters sprinter but not on form right now). The idea was to see what we could get from it - either get a break happening or at least pick up some early points for later strategic benefit.

Problem was, he cracked pretty quickly and I was left with about 3 laps to the sprint line. I was committed, had a gap, so went for it. The cumulative O2 deficit line shows just how deep I went. Very deep.

Once the sprint line was passed I then had to do everything I could to ensure I stayed in the race. You can see how the cumulative O2 deficit line drops away as I reduced my power output and went on the hunt for good wheels to follow. Not long later you can see the line begin to rise again as the next sprint was approaching. I sat that one out just making sure I got through unscathed and could cover any counterattacks.

When you look at the blue line tracing my cumulative O2 deficit from the team pursuit, it reaches a maximum of 4.26 L (about 2.5% higher than from my individual pursuit) and in the points race I reached 4.46L (7% higher than in the IP). What's going on there?

Well, a few things:

- firstly, there is normal day to day variability in performance.

Given that in this analysis we are keeping VO2max and VO2 kinetics**** constant, then the performance is wholly expressed as a difference in MAOD. And since anaerobic contribution to power output is still only 25% or less of total over several minutes, then it still only means a difference in performance of ~ 20-25% of 7% or less than 2% of the total power/energy.

- the next obvious difference is group versus solo efforts, and the influence of motivation/psychology

I would never discount the role that motivation can have on performance and perhaps I am capable of pulling just that little bit more out of myself in a team or a mass start event than I can in an individual pursuit. I can't imagine how I could go any harder in the IP, but it is interesting nonetheless to see if there's any more blood to get from this stone.

- thirdly, as Andy mentioned to me, lab studies indicate that MAOD is independent of the duration of the effort, although he doesn't recall any studies looking at efforts quite as long as this (~5-min). Perhaps that is a factor as well.

So there you have it.

As for the points race, well that attack was a very big risk and a large match to burn so early on. I really needed it to either form a successful break or net 5 points in the opening sprint (3 at least given the race favourite was always going to be very hard to beat). I was overhauled on the line and ended up with 1 or 2 points (I forget exactly) and so it meant I had not gained the desired return on investment. It sure wasn't through lack of trying.

It also meant that since I had gone so deep into O2 debt, I would need every ounce of craftiness to stay in the race. Perhaps in going so hard, the chase was not so easy either and everyone else had to recover too and that was just enough to keep me alive. Thereafter I just took my opportunities to collect points as I felt able. I had to gain 3 points in the final sprint to have a chance but didn't have the legs for that last lap to contest. It was enough for a 4th place finish. Had my initial salvo netted 5 points, perhaps the result may have been different and I made the podium instead.

That's bike racin'.

Edit: Since posting this the other day I also added to the chart the data from the 1-kilometre time trial. As we can see, I reached a MAOD of 4.30L, which is consistent with giving it all and with the MAOD values attained from the other efforts. Not sure if it affected the value attained in the pursuit on the next day, but does highlight the day to day variances.

Thanks again to Andy Coggan for his inspiration, Ric Stern for getting my form to such a good stage and all those team mates and competitors and supporters who help bring the best out of me.


* We call them endurance events, since even though they are about as hard as hard can be and relatively short in duration as far as cycling events go, they are still fundamentally aerobically (with oxygen) "fueled" efforts, albeit with some sizeable contribution from our anaerobic (without oxygen) energy systems.
** VO2max is the maximal rate of oxygen uptake by the body, typically occurs when exercising very hard for several minutes, although it can be induced with efforts lasting over longer periods (VO2 slow component). Expressed as litres of O2 per minute, or in relative terms as litres of O2 per minute per kilogram of body mass.

*** the proportion of mechanical energy output delivered to the bicycle crank as a ratio of total energy metabolised by the body - trained cyclists are typically around 19-24% efficient. The balance is almost all given off as heat (which is why we get so darn hot when going hard).

**** Initial VO2 assumed at 0.5 L/min and half life for VO2 assumed to be 25-seconds.

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Déjà vu

2007 was the last time I rode a Team Pursuit. My team won that day and set a new state record time in the masters' age category. Indeed two of the pics that line the top of this blog are from that day.

I wrote about our 2007 effort in this popular post which looked at Maximal Accumulated Oxygen Deficit using the power meter data from team mate Phil and myself.

Well as most of you know, a few months after that race I had my accident and the subsequent leg amputation.

Yesterday I rode in my first Team Pursuit championship since then. In between times I coached our squads while I made my recovery on the bike myself.

Well we won again and set a new state record time (2:21.379). Phil was also in the team and we both have power data from the event. Déjà vu.

There was one main difference this time - in 2007 we were in the "younger" age category, this time the "older" age category (three youngest riders 150+ years). I suppose another five years does that! It also means the event this time was shorter - 2000 metres compared to 3000m for the younger category.

Interestingly, the power output for each was similar.

In 2007 I averaged 397W in the final.
In 2011 I averaged 411W in the final.

Leg? What leg? More pretty convincing evidence that a lower leg amputation need not be an impediment to cycling performance.

Here's a pic of the power, speed and cadence trace from yesterday's final.


Cadence maxed out at 126rpm, and averaged ~ 119rpm during the "cruise" part of the event. I rode a 51x14 gear (nominal 98").

Here I am with Phil (left) with whom I have been riding Team Pursuit events for the last 10 years. Sneaking into the shot is John Crouchly, a good buddy and former coach of some Aussie Olympic track riders. I had the pleasure of coaching John himself helping him to a win in the State individual road time trial championships in 2009 as well as get him started into the world of training with power.

Our club had five teams riding and our good buddies Peter, David, Alan and Crouch picked up the bronze in our division with two cracking rides a couple of seconds behind our team, the all ages team placed 4th and the 2nd all ages team had a good qualifier setting the early standard. The girls also rode well to get on the podium.

What else can I say? I think I've made a pretty good comeback.

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Team Pursuit Championships

Bicisport Team Pursuit Medallists.

14 February 2009.
22 riders.
6 teams.
3 race categories (Masters all ages, Masters 150+, Elite Women) .
1 Manager.
1 Coach (me).

2 months of weekly team preparation rides (with a break over Christmas / New Year).

When you have 22 riders all wanting to ride in Team #1, it makes for a challenging task to sort out the right combinations.

We had seasoned team pursuiters, some that had barely ridden the track before, strong riders that didn't have the pedigree in team pursuiting, seasoned team pursuit riders with form that needed to pick up, sprint oriented riders, roadies, track enduros, riders from several geographies. We had it all.

Then, once you settle on the combinations, you then need to work on the contingencies. Who are the subs to go up if a rider drops out for some reason? What is the best order of riders in a team? Where are the weaknesses and how can you minimise their impact? All good fun.

Somehow we pulled it all together and at the end of the day:

35 teams entered Championships.
6 Bicisport teams rode.
5 qualified for finals.
4 medalled.
2 Silver.
2 Gold.

2 x Championship record times set in men's qualifying and one again set in final.
Inaugral Women's event (qualified both teams for Gold final)

Bicisport now holds the State record time in both Men's masters categories and Women's elite team pursuits. For a club of ~ 75 riders, I reckon that's pretty impressive.

Cracking rides by all teams. Not a foot wrong all day. While I shouldn't pick favourites, the one that stood out for me was not the record setting rides but Team 2's qualifying ride, which saw them post 4th fastest time and qualify for the bronze ride off. Getting 2 teams into the finals in an ultra competitive category was really a highlight. They missed out in the final, getting nailed by a strong Sutherland outfit. Not to say the other rides weren't worthy, they were all tremendous.

Congrats to the Tuggeranong express train that took out the all ages final by 0.3 seconds. It was a cracker of a race and went down to the wire.

Nice work team!

Special thanks to Stuart Lane for being there at training every week to fill in the gaps as needed.

Coach exhausted.
Coach wants to ride it next year instead.

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Darth Vader Rides the Teams Pursuit

MAOD – Maximal Accumulated Oxygen Deficit is the theme of today’s chat.

This is something I first learned about via The Book (Training and Racing with a Power Meter) and also in subsequent analysis of power meter data kindly undertaken for me by Dr Andy Coggan last year. It’s pretty funky stuff, so hang on for the ride if you can.

Original Wattage list reference here and the Excel file used to generate such analysis is here.

For those interested in delving further, Andy has also prepared a Powerpoint presentation on the topic of the demands and preparation for individual pursuiting which is available for download at the Fixed Gear Fever download page. It's worth a look.

First, let me go back a step or two…

Technique plays a big part in Team Pursuiting

As some would know by now, I’m targeting two predominantly aerobic events, which have an anaerobic twist – the individual pursuit and points racing. Along the way, I get the chance to ride in one of my favourite events, the Teams Pursuit. A description of all these events can be found here. A quick glance at my recent posts and you’ll see that my team had success this past weekend, winning the NSW State Master’s Championship.

Two members of the team (Phil & myself) used power meters during the qualifying and final rides. We also both have power meter data from previous individual pursuit efforts. So, what can we learn from such data, in particular what can it reveal that may assist us?

As is already explained in a discussion about the Individual Pursuit in the book (pp 189-192), the performance of a rider in an Individual Pursuit is primarily determined by the combination of their aerobic and anaerobic work capacities. The discourse demonstrates that power meter data from an individual pursuit can be used to estimate the proportion of a rider’s power that is being generated from each of their aerobic and their anaerobic energy systems.

In particular, it is possible to use this data to estimate a rider’s Maximal Accumulated Oxygen Deficit (MAOD) – the best measure of a rider’s anaerobic capacity.

Based on this information, conclusions can be drawn about a rider’s individual capacities and it can help decide the type of training specific to that individual which is most likely to optimise performance (i.e. what specific training leading into the event will make me go the fastest I can go?).

Of course, in an individual pursuit, a rider typically accelerates up to speed and then settles into a quasi-steady state power output, typically at a level equivalent to their power at VO2 Max. See example here. The time taken to reach that VO2 Max power level does vary by rider and is proportionally longer for athletes with higher anaerobic work capacities.

In a Team Pursuit however, the demands are subtly different. While the overall aerobic and anaerobic demands are similar to an individual pursuit, the Team Pursuit also requires a greater degree of technical skill (for riding at 55+kph in an aero pursuit position just inches from the wheel in front, riding a good line in the bends and to effect smooth change overs of the lead rider).

It also places a greater emphasis on neuromuscular power (as the power demands are significantly variable compared to an individual pursuit – e.g. going from following a wheel to being on the front without changing pace demands a significant & rapid change in power).

So in a sense, not all aerobic monsters will necessarily make good team pursuiters. Riders like Brad McGee, Stuart O’Grady and Graeme Brown however all possess sensational aerobic engines and have the skill and top end power required for success in such an event.

Meanwhile, back in the Death Star....

So can we apply the MAOD analysis to Team Pursuit power meter data given that you never reach a quasi-steady state in such an event? Well originally I didn’t think it would be valid but as is his way, Dr Coggan showed it was possible (there are a couple of caveats which I won’t go into here) and he came up with some pretty interesting results.

Let’s start with Phil’s data. Rather than rewrite what Andy has already written, let me simply quote him here:

“In a laboratory setting, the gold standard for measuring anaerobic capacity is maximal accumulated O2 deficit (MAOD), i.e., the summed difference between the energy you produce aerobically and the overall energy demand. While we obviously don't know Phil's VO2 during his efforts, his VO2 kinetics, his VO2max, or his efficiency, it is possible to make some reasonable estimates and thus to estimate MAOD, as I did for Phil last year.

Evolution of O2 Deficit
(click/right click on chart to see an enlarged version)

As you can see in the graph titled "evolution of O2 deficit", during the individual pursuit his O2 deficit (the dark blue line) increased progressively for the first ~2 min of the event, after which it apparently became strictly "pay as you go", i.e., all of the power was apparently being generated aerobically.

This is exactly what you expect and what you typically find, with the only real difference between individuals of differing ability being the absolute values and the time point at which all of anaerobic capacity is expended (e.g., for me, it only takes ~1.5 min, whereas for my wife it takes 2.5 - 3 min).

So, what happens when you extend the same logic to analyze the team pursuits? Interesting stuff, that's what! :-)

Specifically, during the qualifier Phil's O2 deficit (the purple line) grew rapidly during the first 40 seconds, then held steady while he was on the wheels, then grew again when he took a pull, recovered a bit, and so on. Notably, however, at no point did it achieve the same value as during his individual pursuit last year. Assuming that he's in roughly the same shape now, this implies that he was never completely at his absolute limit, and thus was able to call upon his anaerobic reserves when he had to elevate his power above his aerobic maximum while taking his turn at the front and then getting back on again.

In contrast, during the final the power requirement was significantly higher from 40 seconds on, such that his cumulative O2 deficit (the yellow line), while flucuating a bit due to being in a paceline, essentially followed the same time course of that seen during the individual pursuit. IOW, in this case he *did* appear to be at or near his absolute limit throughout almost the entire race, so he simply couldn't recover after taking that final pull."

~ Andy Coggan

Now I should add that the final was ridden at a pace ½ second per lap faster than the qualifier and that Phil played the role of lead rider (I knew Phil had the experience to pace the start to schedule). In the final after his third pull, Phil had reached his limit and withdrew from the pace line, leaving the three remaining riders to complete the final three laps (in team pursuits, it is the elapsed time of the third rider across the line that determines the result – assuming you don’t catch the other team).

½ second quicker per lap may not sound like much but as you can see from the chart, it can quickly take someone from being “comfortable” to being right on or over a their limit.

Use the Force, Luke

OK, Andy has shown us something pretty funky with Phil’s data, so what did mine look like? Click/right click on pic to see an enlarged version:

Well at first glance it looks similar to Phil’s chart, however there are some significant differences:

- My cumulative O2 deficit in an individual pursuit (the dark blue line) is of a lower overall magnitude than Phil’s

- In the Team Pursuit qualifier (the purple line), it is apparent that I never fully depleted my anaerobic reserves, whereas Phil did slightly during the initial laps (Phil was the lead rider, so that is not unexpected). Indeed looking at the O2 deficit line, it is apparent that I was recovering quite rapidly when back in the pace line.

- In the Final (the yellow line), once again I did not exceed my anaerobic capacity until it was time to do a pull on the front. But note my recovery when back in the paceline compared to Phil’s. While Phil’s cumulative O2 deficit effectively kept climbing (indicating a depltion of anaerobic reserves), I was recovering sufficiently to enable another two strong pulls on the front, especially the final effort on the last lap and a bit (which took us from behind to in front of the other team).

- So it appears that I too am in at least as good a shape as last year but one should never discount the positive impact that motivation has on one’s ability to find a little more from somewhere within. I have always been a highly motivated rider in a group scenario.

In summary, once again this demonstrates the value of power meter data. Would have I done anything differently armed with such information? Perhaps. With data from all riders I may have decided on a different rider order. Certainly we rode as hard as we could but could have we used our resources more effectively and achieved an even faster time? Next year I expect all squad members will have power meters and perhaps I’ll be able to back up my intuitive assessment with a more objective look at the data.

One thing is for sure, be careful when you ask a sprinter to provide sideline-pacing instructions to a team pursuit squad!

Photo courtesy of Action Snaps photography

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