You can't touch this, Part II

In my previous post, I reviewed the concept of Average and Normalized Power, more as an introduction to some further thoughts about the topic of NP Busters. I also said that this would be a two part discussion, with Part II on the topic of NP Busters. Well I am getting to that but it will actually require three parts, so here continues the discussion on Normalized Power, as another prequel to an NP Buster chat. I will at least introduce what is meant by an NP Buster.

Previously I demonstrated by way of an example of a proposed interval session how average power can be a misleading indicator of metabolic strain, especially when power output is highly variable, and that Normalized Power represents a better means of measuring metabolic strain. Well we don't need to make up theoretical examples, we can turn to real data.

Criteriums versus Time Trials

Let's consider the Normalized and Average power from hard rides of different types but of similar durations. An obvious example would be to compare a time trial with a criterium race.

A TT is typically ridden solo and involves sustaining a high power in a relatively steady state manner, with perhaps some variability if the terrain is not flat or has some technical elements, while a criterium involves substantially variable power outputs as one deals with or dishes out the attacks and surges, the braking and/or coasting into and accelerations out of turns, the inevitable driving of the pace in or to establish a break, and sitting in the slipstream of others when recovering. As rides, they are poles apart.

The following chart (click on it to see a larger version) shows a comparison of the power output over time for a time trial and a criterium race by the same rider, performed within about five weeks of each other and both on relatively flat courses. There are two plots for each race. The lines that jumps up and down are the second by second power data trace, and the two straight horizontal lines are the average power from each race. The time trial (blue) is a little shorter in duration than the criterium (red).

The instantaneous power output is a little hard to follow since it jumps up and down so much, but even so, it's clear that the criterium power line (red) is far more variable than the time trial power line (blue). This is pretty typical. So while both of these races were hard efforts by the same rider and over reasonably similar durations, there was a substantial 40 watt difference in the average power.

On closer inspection we can see a period in the crit race from around the 33-minute mark where power dropped substantially. It happened that the rider had a puncture and "took a lap out" to replace a wheel and rejoin the race (annoyingly as they had established a breakaway prior to that). So we would expect this lower power period would account for some of the lower average power overall, even so, the average power up to that point was 272W, still 25W less than the average power in the time trial.

But let's not forget that time spent not pedalling affects what you can do when you are pedalling, and so that mini break no doubt meant a little freshening up before rejoining the race, and an ability to go a little harder than might have been the case with no recovery.

A good way to gain some insight is to view the power trace after applying a filter to the data, and one simple filter is a rolling 30-second average (i.e. each point on the chart represents the average power for the preceding 30-seconds). Here's the same plot showing the rolling 30-second average power:

The vertical scale is now halved which means variances are amplified. The 30-second rolling average makes it easy to spot differences in the power sustained during sections of a ride. In this example we can readily identify periods during the criterium of sustained harder and easier effort. Likewise, the time trial also shows two brief drops in power output, which correspond to a steep decline on the course with speeds too fast for continued pedalling.

A 30-second rolling average power filter is of particular interest as metabolic responses to changes in effort really start to kick in at around that time frame - many have what we call a "half-life" of around 30-60 seconds. Very brief forays (a handful of seconds) at higher powers are not all that metabolically stressful but sustain the higher power for longer (>20-30 seconds) and it gets ugly, fast. How fast depends on how hard you go.

Hence it's no coincidence the algorithm used to calculated Normalized Power is based (partly) on a rolling 30-second average power filter. There's a couple more important elements to the NP formula than that (although it's not a very complicated formula) but it starts with this 30-second rolling average.

So what was the Normalized Power for these two races? Well here they are plotted on the chart as the two horizontal lines:

In effect, the Normalized Power from each race was the same (OK, one watt different). So even though the races were very different in style, they were both hard and produced a Normalized Power that was more representative of the metabolic strain experienced.

OK, so that's pretty nifty, and is why Normalized Power is a good way to glean from races how your fitness is tracking despite the lack of a formal testing protocol.

It should also be of no surprise there is very little difference between the Average and Normalized Power for the time trial (297W and 299W respectively), since the effort was already relatively steady state, and NP is about providing a steady state power equivalent (hence the name "Normalized").

By definition, Normalized Power will be equal to or greater than Average Power, and the gap between them will depend on the amount of variability there is in the rolling 30-second power, and especially the duration and number of forays at very high power levels.

Using Normalized Power to estimate Functional Threshold Power

Since Normalized Power is providing a steady state power equivalent for longer (dominantly aerobic) durations, then it follows that one can consider NP from hard rides/races of about an hour as one means to estimate FTP.

The well established rule of thumb is for durations of about an hour, Normalized Power will be no more than 5% higher than the maximal quasi-steady state power a rider is truly capable of. Since maximal quasi-steady state power for about an hour is the definition of Functional Threshold Power, then we can simply state:

~1-hour NP <= 105% of FTP

or at least that it will be for the large majority of riders, a large majority of the time.

So if you notice from a hard ride/race of about an hour that NP is > 105% of FTP, then it's quite possible your FTP is higher than you think it is.

Caveats and fruit salad

There are of course caveats to this rule of thumb. I'll go over these as they impact the definition of an NP Buster and can help explain what some perceive to be anomalies when interpreting their own NP numbers.

The duration caveat
Since we are primarily concerned with obtaining a measure of equivalent aerobic metabolic demand/strain, then the duration of any comparison of highly variable versus steady state efforts needs to be sufficiently long to reduce the confounding impacts from individual differences in anaerobic work capacity and neuromuscular power capabilities relative to a rider's aerobic capabilities.

For this reason, NP numbers from rides or parts of a ride of less than 20-minutes duration are not suitable for such comparisons, nor as an indicator of a metabolic steady state power equivalent. I generally take more notice of NP for durations of at least 30-minutes, but it depends on the rider's individual circumstances and capabilities. As the duration of a ride reduces (e.g. down towards 20-minutes), then the difference between NP and a rider's actual maximal steady state power can become somewhat wider.

The circumstantial caveat
There are circumstances where no matter how one rode (steady state or variable), their power output would be somewhat different when compared to another circumstance. Examples of this might be comparing riding on an indoor trainer to an outdoor ride as some people experience a sizeable difference in the power they can sustain indoors versus out.

Another might be comparing long steep hillclimb to flat terrain, or on a road race bike versus an aggressive time trial bike position that might compromise power output for some aerodynamic gains, or really hot day, or at altitude and so on. Another is the use of frequent out of the saddle efforts engaging upper body musculature versus staying in the saddle.

So while Normalized Power enables a comparison of some apples with some oranges, we need to be thoughtful when using it to compare all types of fruit.

The power meter data accuracy caveat
Well it should go without saying that power data needs to be accurate for the interpretation to make sense. While basic accuracy is a factor, there are ways in which data integrity can be compromised even though the individual data points might still be accurate. This mostly concerns the way some power meter head units collect and store data, especially the sampling rate. If the fruit is bad, well no point in trying to use it.

An example of this is/was Garmin's use of "smart recording", which should in current firmware versions be automatically disabled when using a power meter, but it makes sense to ensure it really is disabled. This was also a factor for older model power meters with memory space restrictions, and options to "down-sample" data (e.g. older Powertap head units). You could get away with 2-second sampling (just), but any more than that would compromise data integrity to the extent that the data might not be all that useful.

The software algorithm caveat
While the Normalized Power algorithm is pretty straightforward and in the public domain, not all software (be it commercial desktop software such as WKO+, home designed spreadsheets or websites) produce the same results. There may be a number of reasons for that, e.g. use of an incorrect algorithm (I've seen it many times with people claiming an NP that was incorrectly calculated) or more subtle matters such as how gaps in power data or variable duration time stamps are handled.

So when doing such analyses and/or comparisons, then consider the software you are using as well and validate it is correctly applying the algorithm. Some food processors take the goodness out of the fruit.

So what is an NP Buster?

An NP Buster is a ride that breaks the rule of thumb, or put this way:

~1-hour NP > 105% of FTP

provided:

1. the above caveats are taken into consideration (especially power data accuracy, correct calculation of NP, but also the circumstantial caveats), and
2. FTP at around the time of the claimed buster ride has been well established using one or all of Andy Coggan's Sins 5, 6 and 7 referenced in this post on establishing Functional Threshold Power, i.e.:

• using critical power testing and analysis
• from the power that you can routinely generate during long intervals done in training
• from the average power during a ~1-hour TT

Such NP Buster rides have occurred, and there are riders who can produce them. They are however rare, and I'll talk more about them in Part III.

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You can't touch this, part I

NP Busters 

are the spark for today's musing. It's an old topic but a fun one. I am however going to break this into two parts, first (Part I) to review the concept of Average and Normalized Power, and then (Part II) to chat a little on NP Busters.

An NP Buster?

So before getting into the discussion of NP Busters and just WTF I'm on about, let's just go back to Power 411 to remind us what Average and Normalized Power is all about. This is mostly for those that are new to the concepts, even though NP has been with us for a decade, the number of people beginning to use power in training and racing is ever growing and besides, a refresher is never a bad idea.

For those well versed in power meter analysis and associated software, they are no doubt familiar with the concept of Normalized Power and perhaps don't need to go over old ground the rest of this post covers. Much of what I am covering in Part I is also in this original item by Andy Coggan introducing Normalized Power. I suggest reading it if you have not done so before (and you're interested in learning about this stuff).

In summary, Normalized Power is neat a way of enabling us to make sense of rides that are, by their nature, highly variable in power output, especially when a straight numerical average of a rider's power output is often not that helpful in assessing the "damage" done during a ride.

With that said, you can wait for Part II, the NP Buster chat, or read on...

Average Power

Average Power is by definition fairly straightforward – being the average of a rider’s moment by moment power output over part or whole of a ride. For example, 5-minutes at 100 watts followed by 5-minutes at 200 watts equates to a 10-minute Average Power of 150 watts.

A measure of work done
Average Power tells us how much mechanical work was performed during a ride. This knowledge has numerous benefits, in particular when assessing daily energy intake requirements:
Average Power (watts) x Ride Duration (seconds) = Mechanical Work Performed (joules).
e.g. 150 watts x 600 seconds (10-minutes) = 90,000 joules (90kJ) 

Of course that's just the mechanical work done at the cranks propelling the bike forward, and not the total energy metabolised, which will be approximately 4-5 times that value depending on a few things, primarily a rider's individual gross mechanical efficiency (GME - the ratio of energy reaching the cranks as a proportion of total energy metabolised). The vast majority of energy we metabolise ends up as waste heat. That's just the warm blooded Mammalian way.

A (good) indicator of energy metabolised
Somewhat serendipitously, since 1 Cal (kcal) ~= 4.2kJ, we can as a reasonable first approximation use the kJ reading from a power meter file (e.g. 700kJ) and make a straight conversion of that number to energy metabolised (e.g. 700 Cal) since the GME and conversion of kJ to Cal (almost) neatly cancel each other out. The real conversion is probably more like in the range of:
1.05 - 1.15 x kJ of mechanical work done  = Calories metabolised.

A measure of fitness
The Average Power a rider can maximally sustain in a well-paced steady state effort such as during a flat time trial or on an indoor trainer is one of the most direct and objective measures of fitness. It is usually expressed in terms of maximal average (mean maximal) power for various durations (e.g. 1-minute, 5-minutes, 1-hour), and in terms of watts per kilogram of body mass (W.kg^-1).

It should come as no surprise that we can sustain a higher power output over shorter durations. Over the course of a training block, we seek to raise the power a rider can maximally sustain per kilogram of body mass for durations of relevance to the rider's target events. The higher the mean maximal W.kg^-1 number, the faster one can ride and/or the longer a rider can sustain a given pace. Along with a consideration of the specific demands of a rider's events, this is a fundamental principle that should guide a rider's training.

Normalized Power

So what happens when power output is highly variable, such as typically happens when we ride outdoors over variable terrain, or with a group, in a road, criterium or track race or over a mountain bike course; or perform interval efforts at various power levels with rest periods interspersed?

Racing, group rides, hills all provide for highly variable efforts.

In these common scenarios, Average Power can be a misleading indicator of intensity and understate the level of difficulty of a ride (often substantially so).

That’s because, and to quote Andy Coggan:

1. the physiological responses to rapid changes in exercise intensity are not instantaneous, but follow a predictable time course, and

2. many critical physiological responses (e.g., glycogen utilization, lactate production, stress hormone levels) are curvilinearly, rather than linearly, related to exercise intensity.

This latter point is really important. As power output goes up, the level of strain experienced increases exponentially.

Steady state
By way of example, let’s say a rider is capable of maximally sustaining 200 watts for about an hour . If we asked them to perform a 20-minute steady paced effort at 200 watts, then assuming they are not unduly fatigued, we should expect the rider could actually complete such an effort, since by definition they are capable of sustaining that power output for longer than 20-minutes. It would be hard, but do-able (indeed, over 20-minutes, a rider could typically maximally sustain ~ 104-109% of their 1-hour power).

Not so steady state
But what if we asked the same rider to perform a 20-minute effort with the same average power of 200 watts, except this time the rider is asked to perform 10 x 2-minute interval repeats comprising 300 watts for 1-minute followed by 100 watts for 1-minute?

Those with any experience of this sort of effort will know the rider would be very unlikely to successfully execute the prescribed session, despite the average power being the same. This is because the strain experienced during the 300 watt sections is far greater than the relative increase in power, and is not equally matched by the reduced level of strain experienced when riding the 100 watt '"recovery" sections.

Normalised Power is a clever means by which reported power output is adjusted to take into account the typical and natural variability in power output. To quote Dr Coggan:

“Normalised power provides a better measure of the true physiological demands of a given training session - in essence, it is an estimate of the power that you could have maintained for the same physiological "cost" if your power output had been perfectly constant (e.g., as on a stationary cycle ergometer), rather than variable. Keeping track of normalised power is therefore a more accurate way of quantifying the actual intensity of training sessions, or even races.”

This is one reason why we track Normalised Power, as it represents a more accurate indicator of the level of difficulty and is a helpful guide to changes in fitness over the medium and longer terms when the vast bulk of training data comprises rides of variable effort levels.

Feasible training sessions

Interval training, i.e. the use of periods of higher intensity work coupled with recovery periods, is quite a common feature in many training plans (usually because it can be highly effective in improving fitness). Normalized Power is very helpful in establishing whether a proposed training session is "physiologically feasible".

In the interval example quoted earlier (the 10 x 2-min 300W / 100W intervals), the Normalised Power for such a session would be 234 watts, meaning the equivalent physiological cost of riding at a sustained steady state 234 watts. Typically you would expect a rider with an FTP of 200 watts to be able to maximally sustain ~ 104-109% of their FTP for 20-minutes, or ~ 208-218 watts.

Hence the original prescribed session was unrealistic from the outset. You can use Normalised Power in this manner to guide the level of difficulty of training sessions, so that they are hard enough to provide sufficient stimulus to improve fitness but are not so hard they become impossible to execute. Nifty huh?

The underlying physiological principles and the mathematics of the Normalised Power algorithm are described in more detail in an article by Dr Coggan quoted earlier in this post.

Caveats
There are limitations and caveats to how one uses and interprets Normalized Power, and that's for Part II, so stay tuned....

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A time for a bit of sensitivity (analysis)

The Performance Manager Chart is a tool that's been with us for a while, being first released into the wild by Andy Coggan, and the guys from Training Peaks circa 2006. Before then it was tested by a dozen or so lunatics in a power meter users' asylum known as "TSTWKT".

In the years since, it and its off-shoot variants have become a ubiquitous tool for power meter users to inspect the "forest" that represents our overall training loads, as well as giving additional insight into our training patterns and as a indicator of likely form, either prospectively, or as a retrospective analysis tool.

People use the tool as one guide to their overall training progress, to check their actual and planned workload is appropriate for their current training cycle and training objectives. Of course it's only one part of the picture and as always, one must tend to the individual trees, that is, be concerned with the composition of one's training to ensure the specificity principle of training is not lost in the undergrowth.

There's been plenty written about these issues and the use and sometimes misunderstanding of the use of the tool. I'm not going to delve into the whole shebang here, rather just touch upon one small element about the Performance Manager Chart that the more experienced and/or astute user of this tool will understand.

A quick recap:
The basic Performance Manager Chart plots three things - Acute Training Load (ATL), Chronic Training Load (CTL) and Training Stress Balance, where today's TSB = yesterday's (CTL - ATL). It can also show other information if desired, such as daily training stress scores, best power performances and so on.

In layman's terms, ATL is an indicator of how hard you've been training in recent weeks, and CTL is an indicator of how hard you've been training in recent months. ATL and CTL are both exponentially weighted moving averages of the daily Training Stress Scores (TSS), which in turn are calculated from a rider's power meter data and their current threshold power.

Since ATL and CTL are exponentially weighted moving averages, a key input into their calculation is a time constant. The default time constants used for the PMC are 7-days for ATL and 42-days for CTL.

I thought I'd demonstrate with a video animation what happens if you change these defaults settings and comment on whether and/or why you should or would do so. Cue the (94-second long) video:

Occasionally the question asked is - what time constants should I adopt?

The answers usually include the following points:

• Suggest that you create a range of Performance Manager Charts, each with a different combination of time constants, and see which you consider best reflects your actual performances.
• Note that the chart is not particularly sensitive to changes in the CTL time constant, so you may as well leave that at the default 42-day setting.
• The chart is far more sensitive to changes in the ATL time constant, and some have suggested using a longer time constant for older/masters age riders, and a shorter one for younger riders with faster recovery time, although I'm unsure I would necessarily use such as rule of thumb, as there's more to it than just age.
• Even so, changes to the ATL TC (such that one would still consider it an acute indicator) don't radically change the fundamental patterns displayed on the chart, just the absolute values along with a slight time phase shift in the TSB. Keep in mind that it's the patterns that are more insightful than the absolute numbers.
• If you really want to go there, there is software (RaceDay Apollo) and a method described by Dr Phil Skiba to test yourself regularly such that the "ideal" time constants for you can be calculated, although there is likely a sizeable error range in such calculation of ideal time constants and the effort required to do the frequent regular performance testing to narrow that range is likely beyond the training desire of most.
• If you are a multi-sport athlete, then it gets pretty complicated, as the stress scores from different exercise modalities are not linearly additive, nor will they necessarily use the same time constants.

In my opinion, for vast majority of users there really isn't any need to deviate from the default values, as the additional insight to be gained is likely to be fairly limited. That's not to say it doesn't exist but keep in mind that some won't have TSS data for all rides, and/or TSS values that are possibly subject to errors from an incorrect estimation of threshold power (let alone the chosen source of power data).

But by all means this is not meant to dissuade you from playing with the options. Go forth and explore. Or let coach worry about it. We're good at that.


If you want to read more on the Performance Manager, I suggest the following links as starting points:
My Performance Manager Chart by me
Season Review with a Performance Manager Chart by me again
What is the Performance Manager Chart by Hunter Allen
The scientific inspiration for the Performance Manager by Dr Andrew Coggan

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More ZO Zen

A follow up to my post the other day about the setting of zero-offset / torque zero on power meters, and how we need to be sceptical about how auto-zero functions operate (if your power meter uses one).

I received feedback to suggest that auto-zero on SRM could not be as bad as I am suggesting, and that it might indeed be more accurate to leave the auto-zero on.

Well it hasn't been my personal experience that the auto-ZO is as reliable as theory might suggest, so I thought I'd do a test when I got the chance. More backyard science.

So today happened to be a lovely day, and I decided to go for a ride. Not a long one mind you because right now I'm about as fit as Harry the Hairy Nosed Wombat, but a long enough ride outdoors under fairly typical riding conditions for me.

For those that know Sydney - the ride went from Annandale, through Stanmore, past Sydney University, Redfern and onto Centennial Park where I did a 20-min "test" and rode back home again. I've done that ride about a bazillion times.

And before leaving I set my Powercontrol VI to use SRM's auto-zero function, and had my phone camera along to take a few snaps, to see what I noticed along the way. Here's the Powercontrol screen showing zero-offset before starting my ride:

The bottom line is the zero-offset value stored by the Powercontrol, and is the value used when calculating (and storing) power values. The middle, larger number, is the "live" zero-offset reading, akin to the offset number shown in the video in my previous post. i.e. if you apply some force to the cranks, that's the number that will fluctuate along with the force being applied. The "Auto" along the top just tells you that the auto-zero function is enabled.

The temperature inside and outside my home was not all that different, and my meter  had about 10-minutes outside before this initial check. This is a different SRM to the one in the video (different bike), although it's the same model of SRM.

So, my starting zero-offset was 409Hz.

After about 15-minutes I'm at some traffic lights near Redfern Oval, so I take the chance to pull over to the side and see what the zero-offset has done.

We can see that at some stage along the way in that initial 15-minutes, auto-zero has reset the zero-offset value to 417Hz, while the actual zero-offset is 407Hz, 2Hz less than when I left home 15-minutes earlier.

Just so that's clear, that incorrect zero-offset value is now being used to calculate all my power numbers. I have no idea when or how many times during that initial 15-minutes of riding the zero-offset was changed, nor what the size of those changes might have been, other than when I stopped to make this check.

OK, so I continue on to the Park and do a 20-minute test effort. Then after that I leave the Park to head back home, stopping on the bikeway alongside Moore Park to do another check. This is what I see:

Auto-zero has set zero-offset to 419Hz, when the actual zero-offset is 409Hz, same as when I left home about 50-minutes earlier.

Continue on home, and this is the final check I made after about 75 minutes of riding:

Auto-zero has set zero-offset to 403Hz, when the actual zero-offset is 407Hz.

So, to summarise in table format:

So, I have four actual zero-offset readings in a 1:15 ride that vary by only 2Hz (and this is pretty typical for my SRMs, i.e. not much drift in zero readings), yet the auto-zero function has reset the zero-offset value with a range spanning 16Hz. And that's just what I know it's done, let alone what I don't know it's done. As Rumsfeld would say, it's a known unknown.

Perhaps now you can see why I don't use auto-zero on my SRM Powercontrol.

The possible impact to my average power on this ride of a 16Hz differential in zero-offset is 3.5% and for my modest 20-minute test effort today, that's 8 watts. I reckon 8 watts is worth knowing about no matter how fast you are. If it were true, that's nearly one second per km in a time trial. But it ain't.

Now I have no idea whether the auto-zero performed better or worse than that on average because we just don't know. We can never know since no power meter keeps a log of zero-offset changes.

As I said in my previous post, such anomalous changes in zero-offset would make some analysis not worth doing (e.g. aero field testing when you are fine tuning equipment and position choices). I don't know about you, but I think a possible 3.5% variance is pretty significant. It's not something you can correct post-hoc either, since there is no record of what and when changes to zero-offset were made (power values are calculated based on the zero-offset value used at the time of recording).

At least with the Powercontrol, you can easily turn off the auto-zero function (just press the "Pro" button on the zero-offset screen), and checking the zero-offset is trivial press of the Mode & Set buttons at same time.

That's far better than having to navigate through various menus to perform one of the most important checks a power meter user needs to make every time they ride, let alone not being able to disable the auto-zero.

Of course YMMV

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Three, Two, One, Zero Offset

Some more backyard science. Well, training room science perhaps.

This one was prompted by occasional power training forum discussions relating to the setting of torque zero on a power meter, and the auto-torque zero feature on some crank based power meters.

It was also prompted by an addition to my training room set up, which now means I am able to view on a computer screen my SRM zero-offset numbers. That's kind of handy as anyone with an SRM Powercontrol knows, the zero-offset screen only stays on long enough to do a check and set the zero-offset, but then reverts back to the main display screen after a short delay, which is fine for its intended purpose. Since I'm doing something unintended, having the zero-offset on permanent display helps.

So for some fun I put my phone in front of the screen to video record my SRM's zero-offset numbers while testing a few things, namely, how the zero-offset numbers vary from unclipped to being clipped into the pedals. How stable was zero-offset when clipped in? When moving a little but still not attempting to put pressure on the pedals? And what happens when I back pedal?

And while this was on an SRM, the issues arising are applicable to all crank based power meters.

This was the result. It's a 3-minute long video.

OK, so my video ed skills ain't quite up to Francis Ford Coppola standards. The white noise you can hear is my fan that I had left running. Summary thoughts are shown in the video.

Just for the record - here are some more thoughts on this subject:


SRM have an auto-torque zero feature on their wireless units. If you are using an SRM Powercontrol, the auto-zero feature can be enabled or disabled. How the auto-zero function operates is not documented in SRM public literature or on their website, so when and how it invokes is a bit of a mystery. as follows:
1. Speed must be > 0.
2. Cadence must be 0 for at least 5s.
3. The Zero offset must not vary by more than +/- 4 Hz.
If all three of these conditions are met, the new zero offset is the average of the values over the 5s.
Thanks to the contributor that updated me on the SRM function from the German manual.

It's my personal experience that it can generate zero-offset values that are way off. I recommend disabling auto-zero and doing manual zero-offset checks (the same as you do with older wired models). Interesting that SRM says it requires speed > 0, as that implies it also requires a speed separate speed sensor for auto-zero to work.

However, if you use a Garmin device as your head unit with your SRM, then you will have no choice as you presently cannot disable the auto-zero function. In my view that's a significant functional flaw that Garmin and SRM should fix. How significant? For example, I would not rely on Garmin captured data from an SRM when performing aerodynamic field tests. Use an SRM Powercontrol.

Quarq does not have an auto-zero function, the user needs to choose to perform a torque zero (which is fine by me, it's far better than having an auto-zero you can't disable and have no control over or knowledge of when it happens). A torque zero can be done manually as normal or by back-pedalling the cranks a sufficient number of rotations (at least four).

Back pedalling to set a torque-zero is convenient for sure but introduces an error similar to that described in the video. The size of that error will vary and depends on how different your individual reading is compared to the fixed back pedal torque value assumed by Quarq. Best to check and set your torque-zero manually, and unclipped from the pedals, and preferably not when coasting either (on many bikes this latter item is no big deal but some have a bit of freehub drag that can apply positive torque to the cranks while coasting).

Power2Max enables you to do a manual torque zero check as normal and it also uses an auto-zero function which you cannot disable (at least not with a Garmin). P2M have publicly stated the auto-zero function will only trigger if the torque readings are stable for a period and presumably the crank is not rotating for a few seconds. The maximum torque variance that would trigger an auto-zero being no more than one "ppm", with "ppm" being the unit the P2M uses for torque measurement (each power meter reports using different units).

Using a filter of stable torque readings makes sense to prevent erroneous torque-zero values but I wonder how often that actually happens given it was not easy for me to keep a stable zero-offset even when on a trainer and able to focus on doing just that.

P2M's reported torque units are about one-quarter to one-fifth as sensitive as those displayed by an SRM. So the torque values a P2M would interpret as being a stable zero point and trigger an auto-zero, would be the equivalent of an SRM zero-offset value being within a range of ~5-10Hz. So while it seems likely that the P2M will trigger an auto zero when coasting with reasonable frequency, the consequence of this level of (in)sensitivity in the torque range used to trigger an auto-zero means it could well introduce a random error of up to +/- 5W in power readings.

Powertaps of course are not subject to the same issue of trying to deal with pedal forces when coasting since they are measuring torque at the freehub, and so an auto-zero can be invoked as the hub will know when it is coasting (and hence no torque is being applied). It's not perfect either, and there are situations when it might be fooled, but in general it works reasonably well.

Note that the Powertap auto-zero feature when using a Powertap Cervo head unit (Little Yellow Computer) will only work if the torque-zero is not too far out of range to begin with (up to 8 Powertap torque units I think but that's from the dark recesses of my memory), so it's important to perform a manual torque-zero check before starting any ride. I don't know if this function is the same when using Garmin head units. Auto-zero on a Powertap can be disabled on both the LYC and Garmin.

Finally, the torque units reported by a Powertap and used to invoke an auto-zero are about one seventh as sensitive as those on an SRM (it depends on the gearing used and the range is typically one-quarter to one-tenth as sensitive as an SRM for an equivalent crank torque), but at least it has the advantage of being isolated from pedal forces by the freehub.


As a general comment, power meter head units really should be recording torque-zero values and keep a log of when and to by how much those torque-zero values have changed. This is important data to enable forensic examination of a power meter's performance and accuracy. At present, the only power meter head unit to record a torque-zero value in its file is an SRM Powercontrol. Even then, it only records the most recently set zero-offset value.

So while we keep seeing a stack of features being implemented in each new generation of head units, the most basic, fundamental and important feature of a power meter, i.e. the quality of the power data, does not always get the attention it deserves.

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Pour me a draft

Drafting in cycling is a term that refers to practice of riding in close proximity to another rider or riders ahead of them or riding behind other moving objects, such as a motor bike or other vehicle. Taking draft, riding in the slipstream, and keeping your nose out of the wind are some of the phrases used to describe this phenomenon. It even has a Wikipedia entry.

The fact that far less energy is required to ride at a given speed when behind another moving object than when you are the one pushing the wind is without dispute, and many have measured the benefits.

It's a tactic that bike racers make good use of, in order to save as much energy as possible during a race, so they can use that energy when it really matters, such as the final sprint. Often in racing it is those that are least fatigued that win, and is why teams send their workhorses to the front of the group to "do all the work". There is even an anecdotal report from Prof. Asker Jeukendrup of one professional cyclist completing a stage of the Tour de France with an average power of 98W. Now that's an impressive level of drafting skill.

In some cycling events though, drafting is akin to a bowler chucking a cricket ball down the wicket, it's just not cricket. It's against the rules to take draft in events such as individual time trials and in many forms of triathlon (e.g. Ironman) which are also solo competitor timed events. It is cheating. And when it happens it annoys the crap out of many people.

For a cycle racer, drafting is a skill, a craft to be learnt, developed and honed.

However, in time trials and non-draft triathlon, someone accused of illegal drafting usually also has their parentage questioned.

Of course there are rules that apply when two riders end up in close proximity, and usually it involves a  minimum distance the rider behind must maintain, and/or move to another side of the road, and/or pass the other rider within a set amount of time.

The minimal distance in triathlon varies depending on the event, and can be 5, 7 or 12 metres. In cycling under UCI rules, the distance between riders must be at least 25 metres and 2 metres laterally, unless of course they are passing the rider ahead. And of course support vehicles and other vehicles (e.g. TV) in cycling must remain behind the rider (a minimum of 10 metres for support vehicles). It does get tricky in the biggest races though, with police motorbike escorts clearing the crowds sometimes providing unintentional wind assistance.

In road cycling time trials, the issue of riders flaunting the drafting rules (deliberately or otherwise) is not all that common as the number of competitors in any event is usually strictly limited and each rider commences their timed ride over the fixed course at specified time intervals designed to ensure most competitors don't end up in close proximity to another. It does happen of course, but nothing like to the extent it occurs in the sport of triathlon.

Triathlon however have set themselves up for an endemic drafting problem. It's a natural consequence of a mass participation event resulting in far more riders being on the course than there is room on the road to enable everyone to obey the rules without pretty much coming to a halt. Just go to any triathlon forum and monitor the number and tone of discussion threads on drafting and passing. It's normally treated with a level of discourse usually reserved for doping topics.

A scene from a non-draft triathlon. Best of luck to those attempting to abide by or enforce the rules.

Well I'm not really intending to debate the merits or otherwise of such rules and their applicability or enforceability - but what I will do is to publish the results of an impromptu experiment to measure the impact on power of a type of drafting legally permitted in triathlon.

The outcome surprised me, and explains why the drafting rules create big problems and often result in heated exchanges between riders and officials.

The experiment

Last November, Rob (aka Fishboy - blog link) mentioned he would do some test runs at his local outdoor track, collect the power meter data and report back. I suggested he send me the power file with no notes attached, and that I would take a look to see what I could discern from the data without actually knowing what he did. All I did know was that he would do some riding behind and in front of another rider also riding at the track.

OK, so what did I find?

This is a chart tracing Rob's power and speed, with horizontal axis being distance. It's shown with 30-second averaging to make it easier to see what happened.

I have also placed several horizontal lines on the chart to help. The power lines are at 200W, 240W and 280W, and the speed lines are at 38km/h, 40km/h and 42km/h.

We can see Rob rode about 35km total, with three intervals of ~10km each, with a bit of warm up and short recovery between each interval. So on that basis I decided to examine each 10km interval in more detail. The speed and average power for each interval was a little different, which each being ~ 20W harder and 0.7 - 1km/h faster than the previous effort.

Upon closer examination, it was clear to me Rob's air resistance (apparent CdA*) varied during each 10km interval. Within each interval, there were four distinct sub-interval sections with relatively stable aerodynamics, each of approximately 2.5km in length. To see this properly requires re-plotting the data using a technique known as virtual elevation, which helps us make aerodynamic sense of what can appear to be quite noisy data. I'm not going to show those charts as there are too many, but I will summarise the results into three charts, one for each 10km interval.

In each summary of results chart I have indicated on the bottom axis where I think the start and end of each of those sub-interval sections was, and the columns show my estimated CdA for each of those sections. Note that the CdA numbers won't be absolutely correct since I am making some other global assumptions about Rob and environmental conditions, but what's important is the measured differences in apparent CdA. I may not have the absolute values exactly spot on, but the differences in the absolute values will be on the money. Here's the first summary chart:

You will see some blue and red columns, showing Rob's apparent CdA was either "low" or "high" during these sections. This can be as result for instance of being in the aero position, and then sitting upright, then back into aero again etc. But for the purpose of this exercise I know he rode with another rider on the track, and was either in front of, or behind the other rider. I didn't know how far the gap between the riders was in any of the intervals, all I am showing is the estimated difference in apparent-CdA between "leading" (red) and "drafting" (blue).

Also shown, are horizontal lines, which are the average apparent-CdA for "drafting" (blue) and "leading" (red), as well as the difference in apparent CdA between each (the fat vertical double headed arrow).

So we can see that the average difference in apparent-CdA for draft vs non-draft in the first 10km interval was 0.035m^2.

Here's the chart summarising the second 10km interval:

which shows an average difference in apparent-CdA between drafting and non-drafting of 0.033m^2, which is similar but slightly less than the difference measured in the first 10km interval.

And the third 10km interval:

which again shows a drafting benefit, but now that benefit has been reduced somewhat to 0.026m^2. There is also a slight increase in non-draft CdA in this interval compared to the first two intervals.

So in summary, the gain by drafting the other rider was a reduction in apparent-CdA of:

Interval 1: 0.035m^2
Interval 2: 0.033m^2
Interval 3: 0.026m^2

In terms of energy benefit for for Rob when drafting over leading, when riding at 40km/h this equates to wattage savings of:

Interval 1: 29W
Interval 2: 27W
Interval 3: 21W

What's interesting is that the non-draft CdA values are pretty consistent across all runs (a little higher in third interval), but that the draft-CdA values in the third 10km interval had increased somewhat more, IOW the drafting benefit had been reduced for some reason. There can be several reasons for this, such as environmental condition changes, on bike position changes due to riding at higher power and/or fatigue (creeping forward on saddle for instance), change in equipment/clothing and so on.

After I had done the analysis, Rob then revealed all the details of what he actually did - these are his words in green, although I have re-ordered some paragraphs for clarity:

The procedure was to ride sections of the interval drafting and non-drafting. It was attempted to hold a constant speed during each section (were aiming for 40kmh, but my front rider went a little slower on the first interval).
In all intervals I trailed on the first segment, then swapped to the front twice.
In all intervals I tried to hold the same aero position. This was very consistent on the first interval, but possibly less so on the final interval.

All intervals were the same draft distance +/- 0.3m, 12m front wheel to front wheel. A laser pointer was taped to the frame to aim at the back wheel of the rider in front for a 12m front wheel to front wheel distance. Rig checked after the session and laser was still accurate, so didn't move during the session.

The intervals got harder (3 x 10km E, M, H)

The wind went from dead calm to moderate on the H interval. Distinct head, tail and cross winds on interval 3 (the H one), possibly more than what Moorabbin airport recorded as there was a rain shower that came through with much stronger wind.

The other rider is small, ~65kg, on a very aero bike, in a good aero position. Probably 0.250m^2 or so CdA. If there was something smaller or more aero to draft off, it would be hard to find.

The BOM data for Moorabbin airport, 10km away approx was:
Date/Time EDT Tmp°C AppTmp°C DewPoint°C RelHum% Delta-T°C Wind PressQNH hPa Press MSL
hPa Rain since 9 am mm Dir Spd km/h Gust km/h Spd kts Gust kts -
08/06:00am 12.6 11.3 11.2 91 0.7 NNW 9 13 5 7 1010.6 1010.5 0.0 

08/05:45am 11.9 11.4 10.6 92 0.7 NNW 4 9 2 5 1010.5 - 0.0 

08/05:33am 11.5 11.6 10.2 92 0.7 CALM 0 0 0 0 1010.3 - 0.0 

08/05:30am 11.5 11.6 10.2 92 0.7 CALM 0 0 0 0 1010.2 - 0.0

My weight and bike 95kg.
Crr previously measured many times on this velodrome at 0.0044.
Air density pretty consistent around 1.227.

Bike is TT (P3) with H3 front, H Jet Disc rear, eKoi helmet (no vents).

Track location is Carnegie Velodrome in Packer Park just near East Boundary Rd and North Road. 363m circuit.

Anyone suggesting there is no benefit at 12m is totally incorrect, even in head, cross and tail winds on interval 3 there was close to 20w difference - which is significant. When it is calmer, there is more benefit, which makes perfect sense.

There is also a high likelihood that there could be even more benefit that could be found from a bigger test rider in front, being 3rd or 4th wheel, or being closer than 12m.

So, there we have it. Even under the 12-metre rule the power savings from drafting are quite significant, and as Rob says, if you are following a larger rider, and add more of them into the line of riders on the road ahead, one can only imagine the power demand will reduce further. Not by as much as this initial benefit of course but it all adds up.

A larger rider adhering to the 12-metre draft rule when following a single smaller rider at speeds of ~40km/h   in calm conditions gained a benefit of ~27-30W reduction in power required, and ~20W saving in moderate cross winds.

It's no wonder there are big problems with riders deciding they can go faster than the guy ahead, attempting to pass, and then being unable to maintain the pace because the power demand is still so much higher even with a 12-metre draft rule, creating all sorts of headaches for riders who find themselves stuck in drafting hell.

Aside from the drafting issue, this was a nice example of being able to correctly infer a lot from analysis of a naked power meter file, and with no specific prior knowledge of its content other than it was from a ride at a track somewhere looking to test the impact of drafting. OK, so it's not a formal scientific test, but I have to say, as a way of blinding one element of the analysis, this is a pretty cool outcome.

It's not the only time I've done this - I used this blind analysis technique to spot things like a rider's bike position changing during an event, as well as assess rider's physiological capabilities in events such as team pursuits.

Big thanks to Rob and his mate for conducting the experiment. Nice one Fishboy!

* I say an apparent-CdA, because when riding in a slipstream it's not Rob's actual CdA that changes so much, it's the air flow he is riding through that is changing. What these numbers represent is the equivalent impact of that beneficial air flow in both CdA and in wattage saving terms.

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The bathroom scale analogy

Power meter accuracy and calibration 101

This is not a complex item, but I often see confusion* over the issue of power meter calibration, torque zero, zero-offset etc, so I thought I would use a simple analogy to help people understand the basic differences in what these terms mean.

There are many things that can affect the accuracy^ of power meters, but let's talk about one of the most important, i.e. the person using the power meter.

Most common on-bike power meters in use today (e.g. SRM, Powertap and Quarq, and more recent offerings from Power2Max and others) require a user to do three things for accurate data:

1. Pair the handlebar computer with the right power meter – this might be via a wireless protocol such as ANT+, or by simply plugging the two together via their wiring harness
2. Check the torque zero before and occasionally during a ride (torque zero or "zero-offset" as referred to by SRM are interchangeable terms in this context)
3. Check / validate the correct slope calibration of the power meter is being used

How you do #1 will vary depending on the type of handlebar computer and power meter used and as always, reading the manuals is a worthwhile investment of your time (ugh I hear you say). Typically it's not a difficult thing to do.

However I want to elaborate on #2 (torque zero / zero-offset) & #3 (slope calibration) via an analogy – the ubiquitous bathroom scales that many have a love/hate relationship with.

To demonstrate the difference between  "zero-offset" and "slope calibration" and their importance, I'm going to share with you a simple experiment - checking the accuracy of an old set of bathroom scales I have. They are the old fashion type with an “analogue” display that rotates around when you hop onto the scales.

Here’s a pic of the scale's reading before I place a known weight on the scales. The lower scale is kilograms (kg) and the upper scale is stone and pounds. I'll stick with kg for now.

We can see they are reading +4kg when there is nothing on the scales. Clearly the “zero-offset” is wrong. So if I placed a known mass on the scales, I should expect the scales will read 4kg too high.

So, let’s place an accurately known weight on the scales. I just happen to have an accurately known weight of 31.210kg. Rounding to 31.2kg will do for this example. This is what we see: 

That’s reading 34kg. But hang on, shouldn't we expect the scale to read 35.2kg  = 31.2kg (actual weight) + 4kg (the "zero-offset")? 

Well yes, we should, but it isn’t. Hang on to that snippet - we'll get back to it shortly.

The scales have a small “zero control” knob, which I can turn so the scales are reading zero when I am not standing on them. All we are doing is validating that, when no weight is on the scale, it displays a zero value. OK, so let's correctly set the “zero-offset” on the scales: 

and now put the weight back on the scales again: 

Now it says 30kg. Hmmm, so even though the “zero-offset” setting is correct, my scales are under reading the actual weight by 1.2kg or about 4%.

Let’s plot those readings.

There are four readings. The two for when the scale’s zero-offset was +4kg (the green triangles and line), and the two when the scale’s zero-offset was 0kg (the red squares and line).

The horizontal axis is the actual weight placed on the scales, which in this case is either 0kg or 31.2kg. The vertical axis is the reading provided by the scales.

So now we can visualise two things:

• the “zero-offset”, which shows us how much the scales read when there is no weight applied, and 
• the “slope”, of the scale – in other words, how much weight the scales report increasing by for every kg of actual weight placed on the scale.

This slope can be calculated as follows:

[Reported weight - Zero-offset weight] / Actual weight

In this case for both sets of readings, the slope is 0.96.

Hence, if I stood on these scales, and the zero-offset had been set correctly to 0kg, and the scales read 83kg, I would actually weigh 83 / 0.96 = 86.5kg.

So even though the “zero-offset” has been correctly set to zero, this does not mean the scales have been calibrated, nor that they are accurate. All we know after performing a "zero-offset" is they will read correctly when there is no weight on the scale - but that does not ensure accuracy when we step on the scales. 

In order for the scales to be accurate, we need to know not only the zero-offset is correct but also their slope is correct. In this case the slope of the scales is wrong, and hence the weight reading will be wrong unless I apply the correct slope to the "raw" data.

The exact same principle applies to bicycle power meters. Instead of weight on a scale, most power meters measure the torque (twisting force) applied to a bicycle component (using special gauges). The most common meters measure the forces at the crank spider or at the rear hub but forces can also be measured at the pedal or cleat, the crank arms, or the rear cog (or even the chain). Besides measuring the torque applied to the component, all that is required to determine power is the the rotational velocity of the component (revolutions per unit time).

So to complete the analogy:

• The zero-offset (or torque zero) of a power meter is the torque reading when there is no force being applied to the crank (or hub) and is analogous to the bathroom scale's reading with no weight on them. Various power meters report in different units.
• The slope of a power meter is a value indicating the increase in the reported torque readings per unit of actual torque applied to the crank (or hub) and is analogous to knowing how much the bathroom scale's reading changes for each kg of actual weight we put on them.

Checking and/or re-setting the torque zero (zero-offset) of your power meter before and occasionally during a ride is a necessary and sound practice, 

however

unless you also know the correct slope of your power meter is being used, then the data may still be inaccurate.

Torque zero / zero-offset is something that will naturally vary, in particular with ambient temperature, but other things can affect it too, which is why it is good practice to always check it and do so regularly. The better meters have predictable and minimal zero-offset "drift", and some have firmware designed to automatically adjust the torque zero while riding, which may or may not be user enabled (depends on the meter).

This auto-zero / correction feature may or may not be a good thing depending on how it has been implemented. In my opinion, I consider knowing how and when such changes occur to be useful and valuable information when evaluating the possible errors in reported power data.

There are also some things that can affect the slope of your meter between when it left the factory to when it is finally installed on your bike, so I encourage you to have the slope validated while the meter is actually on your bike. Slope checks are best done at a 6-12 monthly intervals, or whenever you make changes to the crank's set up (such as changing cranks arms or chainrings).

Some power meters have far more stable slopes than others. It’s not a difficult thing to check yourself, but I’ll look at providing an example of that process in another post.

In the meantime, the good folk at Quarq have provided a video to demonstrate the slope checking process for their power meter. It's a similar process for other meters but the means to obtain the torque numbers and calculate the slope will vary.

As a final comment - it's possible to post-hoc correct power data that has had an incorrect slope applied but an incorrect zero-offset/torque zero can be a lot more difficult (if not impossible) to correct, and especially so if that zero-offset has been drifting. For SRM users, applying a slope or zero-offset correction is pretty trivial to perform using SRMwin software.

*  The confusion hasn't been helped when one of the major manufacturers of bicycle computer recording devices (i.e. Garmin) use the terminology "calibration" for their device, when the specific function they refer to as "calibration" it is not a true calibration. If you use a Garmin computer, and "calibrate", I suggest in your own mind to replace the Garmin word "calibration" with the words "torque zero".

^  When using a power meter, we want to ensure that the data is as accurate and precise as possible. We do this for many reasons, in particular so we can make valid comparisons of performance changes over time (keeping in mind that the gains at high levels of relative fitness are only a handful of percent and people may not use the same power meter their entire lives). There are also many performance analyses that require accurate and precise data to make valid but important choices about performance matters, e.g. the testing of aerodynamics, or tyre rolling resistance. Anyway, I’m not going to labour why accuracy and/or precision is important, that’s for another discussion.

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An hour at a time - photos

Refer to yesterday's post for details on Jayson's record ride.

I'll post images, credits and links to images here.

Thanks to Donncha Redmond:
http://www.flickr.com/photos/47663040@N00/sets/72157632721745241/

Only one hour to go...

Getting lap splits, pacing instruction and time checks from coach

hold a good line Jayson...

387 turns...

last lap c'mon!!

A couple thanks to Nour "TrinewB" on Transitions:

can be lonely out there even though people are watching

on target...

These came from Jayson, from Ernie Smith I think...

track's that a way Jays!

tight suit

coach showing off his coach's physique

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An hour at a time

A short and sweet entry today. I'm just back from the Dunc Gray Velodrome, having coached rider Jayson Austin to a new world masters hour record for M40-44 category.

48.411km

which adds 1.284km to the previous record of 47.127km held by Dave Stevens (December 2011).

Great work Jayson, it was a bit of a fight with some challenges during the ride.

Coach is pretty darn pleased with his chargers - Jayson having previously set the record for M35-39 back in 2009 (you can read about that here) and just recently Charles McCulloch of the UK set the M50-54 record a few months back at the Manchester velodrome.

Charles' record for M50-54 is 47.96km. 

Across town and across the world. Good work fellas.

For those interested, here's Jayson's speed and cadence plot. I'm leaving the power data out for now, for reasons I won't go into here.

Photos later.

Post script: For reference, Jayson's ride is the second fastest hour ride ever by an Australian. Brad McGee holds that record at 50.052km, set in 1997 aged 21. Different and slightly more relaxed aero equipment rules back then.

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The sum of the parts

A perennial favourite argument on cycling forums is the cost-benefit of choosing a wheelset with superior aerodynamics vs a wheelset that is lighter (or an aero vs a lighter frame).

It is of course a false dichotomy that one must chose only one or the other. But that does not stop people having fun arguing the merits of each, or of holding onto beliefs/myths/folklore handed down through the generations. Of course there are a multitude of things that go into what is a suitable choice of wheels, and I'm not going to delve into those, suffice to say they involve a range of factors aside from aerodynamics and mass, including, inter alia (and not in any particular order):

• strength
• durability
• ability to stay round and true
• lateral stiffness
• cost
• repair-ability and service cost
• suitability for the purpose/race/riding situation
• braking demands
• handling characteristics
• available tyre choices
• bearing and freehub quality etc
• rules of competition
• suitability for the bike (e.g. will it fit?)
• sex appeal / bling factor
• and so on.....

Then one needs to weigh up those factors and apply their own personal judgement as to which factors matter most. That will of course be different for everyone. It's no wonder wheel manufacturers have a field day with all the various possible points of difference available when marketing their wares.

But let's get back to the issue of wheel mass and aerodynamics, and what actually matters if for instance we could assume that all other factors between two wheel sets were identical.

Just before diving into that - to slightly complicate matters, one might assume the rotational inertia of a wheel plays a big part in its performance during accelerations (over and above the simple difference in wheel mass itself). Well of course one should expect some difference between wheels with different moments of inertia, but is it really a factor of significance when it comes to acceleration performance?

Now this question has already been examined by others, including a good item on wheel performance by Kraig Willett at Bike Tech Review. In that item, Kraig runs through the physics and demonstrates how (in)significant a difference in wheel rotational inertia during accelerations is, relative to the other primary resistance forces encountered on a bike. In another, more simplified look, Tom Anhalt also examined this and illustrates the same finding in this article on Slowtwitch.

So one can reasonably ignore the difference in moments of inertia when considering overall acceleration performance. But for those who still care, the equations of motion for a cyclist have been developed, thoroughly tested and do include the moment of inertia. I'll get back this this soon.

So, back to weight v aero - the classic prize fight.

First let's consider the relative energy demands of the various resistance forces encountered when cycling, primarily:

1. air resistance (bike and rider's aerodynamics, speed and wind)
2. gravity (weight of bike and rider, and gradient)
3. rolling resistance (tyres and road surface)
4. drive-train friction losses
5. changes in kinetic energy (accelerations)

We can examine the difference in relative energy demand of the various resistance forces a rider encounters when riding at steady state speed on roads of various gradients. An example is shown in the chart below:

In this example, we can see the relative importance of each resistance force, as gradient changes from flat terrain (0% slope) to very steep (10% slope). As the road gets steeper, the influence of gravity takes over, and as the road flattens, then air resistance is the dominant force.

Our speed when climbing steeper gradients is directly and almost linearly proportional to our power to mass ratio. Hence why weight is a primary consideration when the road tilts upwards. Lose 2% mass for same power, as you'll go nearly 2% faster. Pretty simple.

However when the terrain is flatter, then it's not so simple as the relationship between speed and power is not pseudo-linear, but rather a cubic relationship with relative air speed, meaning that to sustain a speed that's 2% faster (1.02 times), you'll need nearly 8% 1.02^3 or approximately 6% more power*. Ouch. Talk about diminishing returns. That's why aerodynamics matters so much.

* when you really account for all the forces correctly, then the increase in power demand for an increase in sustained speed from say 40.0 to 40.8km/h (a 2% speed increase) is more like 5.5%, and you can use a exponent of 2.7 rather than 3 as a slightly better ROT.

But what about accelerations?

Well the power required to accelerate is directly proportional to the mass and the rate of acceleration. Of course there will also be a power demand to overcome the varying air and rolling resistances at those varying speeds, as well as deal with gravity for any hill we might be climbing at the time.

So it all starts to get a little more complicated. Bear with me...

Back in the 1990s, a group of bright sparks did a lot of testing to develop and validate a mathematical model for the physics of road cycling, and have that published in the peer reviewed scientific world. The model was developed after extensive testing at highly variable wind speeds and yaw angles, and has been tested against real world data collected using SRM power meters. It's since been adapted and validated for velodrome track scenarios including standing start accelerations by world class track sprinters. I don't have a website link for the paper, but here's the reference details. OK, I found the website link to the paper:

Validation of a Mathematical Model for Road Cycling Power

James C. Martin, Douglas C. Milliken, John E. Cobb, Kevin L. McFadden, Andrew R. Coggan. Journal of Applied Biomechanics, 1998, 14, 276-291

Some of you might recognise a few of the author's names. In summary, the equations look like this (as per a slide from one of Dr Coggan's powerpoint presentations):

At first glance it looks a bit OTT, but really it's not that bad once you break it down to its constituent parts.

What this fancy pants maths enables us to do is something called forward integration - which is a way of being able to predict the second by second speed of a rider if we know their second by second power, and a handful of key variables like their aerodynamic drag coefficient, weight, tyre rolling resistance, gradient, wind and so on.

Now there are some websites that have been doing this stuff for years, and the best example I can think of is Tom Compton's analyticcycling.com. Check it out, Tom does some cool modelling.

For a bit of fun though, I thought I'd examine two acceleration scenarios using the forward integration technique to examine the performance trade off between a wheel set that's more aerodynamic versus one that's a bit lighter.

Here are the two scenarios.

Scenario 1:
A rider accelerates from a standing start with an average power of 1000 watts for 10 seconds.

Scenario 2:
A rider accelerates from 30km/h with an average power of 1000 watts for 10 seconds.

I'm going to use the following as assumptions on the differences in key variables:

Bike set up A: CdA of 0.320m^2 and mass of 80.0kg (lighter but less aero)

Bike set up B: CdA of 0.297m^2 and mass of 80.5kg (heavier but better aero)

and the following assumptions apply to both bike set ups:

Air density: 1.2kg/m^3

Crr: 0.005

Drivetrain efficiency: 100%

No wind

I chose that difference in CdA as it is representative of a real world difference I have measured between two rear wheels (one a low profile light-ish 32 spoke wheel, the other a wheel designed solely for aerodynamic performance), although for the purpose of this exercise, I have exaggerated the mass difference.

By using the equations of motion, and the technique of forward integration, in this case using a time interval of 0.1 seconds, we can show what happens when we accelerate from a standing start. Here is the speed plot for those 10 seconds for each bike set up:

Well, the lines pretty much overlap, but as you get closer to the end of the acceleration  we can see that the heavier, but more aero set up results in a higher top speed after 10 seconds. But does that mean they are ahead? If they were initially slower in the early phases of the acceleration, will they catch up? Well to examine that, we simply inspect the difference in cumulative distance travelled at each time point:

So, now we can see that initially after starting together, the rider with the heavier but more aero wheel falls behind slightly in the opening seconds and the distance grows initially until they lose a maximum of 4.6cm on their "rival" after 4.3 seconds. But after that point, the rider on the heavier and more aero wheel begins to catch up, eventually overtake his rival after 7 seconds, and wins the 10-second sprint by 17cm, or about 1/4 of a wheel. For even just a half lap track sprint, that's way more than enough to justify the aero option over the weight penalty. But if your speciality events lasts less than 6 seconds from a standing start, then go for the lighter rim.

OK, but what about accelerating from a rolling start?

Well let's examine the same scenario, with the only change being that we start at 30km/h, then apply an average of 1000W for 10 seconds. Speed difference plot:

Again we can see that the speed lines are closely matched, except now the top speed reached after 10 seconds is higher and the top speed difference of 0.5km/h between each set up is larger than the top speed difference in the standing start scenario. And the gap in distance? 

Well this time the lighter/less aero wheel loses out straight away and never gains an advantage. The guy with the heavier but more aero wheel wins the 10-second sprint by 60cm - nearly a full wheel width.

OK, so if flattish terrain is your thing, and regular accelerations are part of the game, then perhaps a re-think about the relative merits of aerodynamics and weight when considering which wheels to use. And keep in mind that for the purpose of this exercise I over exaggerated the typical mass difference, while using a fairly typical improvement in aerodynamics attainable from using a deep section aero wheel set over a lighter low profile wheel.

For my next trick, I will examine the shape of a typical power curve during such accelerations, and apply that variable power supply to the models, since nobody really accelerates with a flat power curve. Look out for Part II.

And as they say in the trade, YMMV.

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