Endurance Analytics

Our blog - covering sports analytics and EA products


Somebody recently got in touch to provide feedback on Cycling Power Lab (we love your feedback, thoughts and ideas). Among other useful observations was that the site looks "a bit 90s". While we'd beg to differ - the technology we used to start CPL came out of the "millennial" decade - it's also a fair comment that has not escaped our own notice. In due course CPL will get a new look and feel.

Right now we are working on some exciting sports analytics projects which go beyond the scope of Cycling Power Lab. For that reason we thought it an opportune time to update our blog. Going forward this blog will variously cover all of these projects, hence the change of name. The opportunity to switch onto a more modern blog engine was a nice bonus.

The image that goes with this post is a tribute to cycling in the 1990s. We can still remember many of the wacky go-faster bike designs that came out of that era though we wonder if there was ever much objective aerodynamic testing. Wacky they may have been, but we have to remember that research and development is a process in which the limits have to be pushed, whether you're building bikes, shark fin saddles, or analytics software.

Many of those 90s bike designs (there are some great examples here) are of course now UCI illegal. The UCI has an important role to play in reining in innovations that could be considered to lead us into exclusive equipment arms races, not in keeping with the aesthetics of the sport, or just unsafe. At the time of writing we would join calls for them to rule definitively on the usage of disc brakes, considering in particular the last two criteria.

Weather data for performance modelling

In cycling performance the most fast moving variables are always those attributed to weather. Courses don’t change, rider’s weight or power profiles are slow moving, but weather is relatively more dynamic. Understanding or predicting weather therefore has great importance in terms of modelling and optimising performance.

Advance but reliable knowledge about wind conditions can be pivotal in deciding race tactics, effective equipment or pacing strategies. Riders whose grand tour hopes have been dashed by unexpected side winds are a high profile example of getting the weather component of tactics wrong. Knowledge of air pressure fluctuations can be useful too where, for example, a rider planning an hour record attempt may use this data to determine the viability of a ride.

At CPL we use three different regimes of weather information, depending on how the date of the event relates to the date of modelling.

Pre-Event, 8+ days before

While “longer range” weather forecasts are often available more than a week before an event they tend to be unreliable. In this scenario we believe that the best prediction of event weather, the one we will use for modelling, should be based on historical data. What does the weather “normally” do in the time window of the event, at the event location, and what is the frequency distribution of weather at this time and place? “Wind Roses” give a great visual depiction of “normal” winds and we default our modelling assumptions to be based on the most frequent or probable wind vector. Air pressure is simply taken as “normal” for the location and elevation adjusted.

Pre-Event, 0-7 days before

In the week before an event weather forecasts become more accurate. Actual time-series weather (wind vectors and air density) for the day of the event can reasonably be expected to play out and represent the best basis for predictive modelling. We refresh event day weather forecasts every morning such that assumptions are defaulted to the most up-to-date view of the expected weather.


For post event modelling we have the benefit of hindsight and our modelling can “replay” the actual weather (wind vectors and air density) experienced during the event. This can be matched up with time stamps from a ride file, facilitating the most accurate modelling. One feature of our post-event models is estimation of CdA – rider’s aerodynamic drag metric – and the incorporation of local weather makes this sort of analysis applicable to days which cannot be considered “windless”.

As you use CPL to do Performance Modelling you may notice the weather chart that we display switching between a Wind Rose (frequency based or “normal weather”), a race day forecast, or actual race day history. This happens automatically so you can be sure that your modelling is based on the best assumptions.

Ride Review with Post-Event Performance Modelling

The opportunities to use power based performance modelling in a pre-event context, for Goal Setting, Scenario Analysis, Equipment Optimisation (EO), and Optimal Pacing Strategies (OPS) should by now be compelling for all serious cyclists and triathletes. For the price of a few carefully collected details describing a rider's physical attributes, power-duration curve, and bike setup, it is now possible to first predict a given rider's time on a given course and then to apply scenarios on the underling model to make the same rider go faster. Analytical intelligence equals free speed...if you want to put the work in.

While the pre-event context has always been the most compelling there are also significant opportunities to use the same performance modelling techniques in a post-event context. Nobody wins a race by looking back at the day's data but but you can, perhaps, use it to win the next one...if you know what to look for and have the right tools. We have invested a lot of effort recently creating performance modelling tools for the post-event context and this article outlines what they might be able to do for you.

It's not (just) about the bike (data)

Pre-Event modelling combines data about a rider, his or her bike and equipment, the course, and the weather. Weather can mean historical trends or the actual race day forecast. We then simulate the rider's performance on the given course, under the given weather conditions. A simple simulation, based on the maxium power a rider should be able to sustain for the course duation gives us a time-on-course prediction. Many variations of power output, sector by sector, allow us to find an Optimal Pacing Strategy. Variations of rider parameters or equipment allow us to see the effect of scenarios. Variations of weather allow us to build a complete picture of which equipment is "probably" the fastest, on a "normal" day.

Post-Event modelling replaces weather forecasts with actual, observed weather. It also takes the ride power and speed data (via a .fit. .srm. .tcx, .pwx or .gc file) as a precise description of how the ride was executed. This gives us analytical possibilities and opportunities to combine and compare "model" versus "actual" performance not possible in the Pre-Event context.

Performance Modelling is more than race planning

Some people see performance-modelling as a way to predict race-day performance and then create a plan. That is Pre-Event modelling, but there is more to offer. Post-Event modelling, with the extra second-by-second information provided by the ride file, has some powerful applications. Let's review some of them:


The Virtual Wind Tunnel has never been more available

In our experience the most versatible, and now most used, field test protocol available for determining a rider's aerodynamic drag is the "Virtual Elevation" method a.k.a. "Chung" method (after it's inventor Robert Chung) a.k.a. the method of the "Virtual Wind Tunnel". Some very serious operations routinely use this method, in a velodrome setting, to provide riders with drag data and aerodynamic optimisation advice. In simple terms this methodology takes ride file data (power and speed) to build a "virtual elevation" (VE) profile for the ride. If you vary CdA, or let a computer do that for you, until the VE profile closely matches the actual course elevation profile of the same ride, then the CdA you finish with can be a very good estimate of the rider's actual CdA.

Post-Event Modelling, by combining the rider data, course data, ride data, and environmeental conditions, already has all of the information necessary to estimate CdA using the VE methodology. There is one caveat - wind. Rather than assume zero wind, as velodrome operators can, making VE available for any rider requires us to factor in the wind. Since we already have weather data, at times of day covering the event, and we know rider's time's of day on all sectors of the course, from the ride file, then we can do a reasonable job of factoring in air density and effective winds. VE under observed winds isn't perfect, but if estimating CdA is important to you it is better than nothing...a lot better!

Physics + Power Data = Power & Energy Attribution

Imagine a ride file says that a rider averaged 200 watts on a short climb. Now imagine we model that rider's performance on the same climb, we take all of his parameters, then plug his time into a "power given speed" model to estimate the power required to complete that climb at the given speed. If we're using the right parameters, including VE CdA, then our estimate will be 200 watts. But we have more information... Those 200 watts are composed of some watts required to overcome gravity, some to overcome aerodynamic drag, some to overcome rolling resistance, and a few others. By combining the actual power data from a ride file with theoretical power demands from a performance model we can achieve what we call a "Power Attribution" or "Energy consumption study". (Remember that energy, in joules, is just watts multiplied by time in seconds). This is an interesting capability of Post-Event Modelling.

Pacing Quality Evaluation - How well did you execute?

The identification of theoretically Optimal Pacing Strategies is one of the most compelling applications of Pre-Event Performace Modelling. But how can we know how well a strategy was executed? Sure, we can compare race normalised power with the prediction from the plan, and we can eyeball ride power and speed data relative to the sector by sector plan, but we felt that some better tooling was required.

"Pacing Quality Evaluation" is a software based comparison of actual, sector powers and speeds, from a ride file, verus a theoretically optimal plan calibrated to the rider's power-duration curve as exhibited in the ride it'self. Having looked for some magic number to describe pacing quality we eventually settled on the one number that counts...time! This analysis can also highlight something very interesting - good riders can be very good at pacing. Often the way a rider executes, with the freedom to vary power on every little hill or under every little gust of headwind, results in a time that is better than what we might predict from an "optimal" strategy simple enough to understand and execute. Nevertheless, Pacing Quality Evaluation is a fantastic gross error check and has some great applications in learning lessons and executing better in the future.

Rider Benchmarking with Virtual Competitor

We have always emphasised the application of performance-modelling in the key coaching disciplines of rider profiling, performance benchmarking, and goal setting. It is a powerful thing to be able to compare a rider's actual performance against some theoretical competitor, a better version of the rider's future self, or even a worse version of the rider's past self. A virtual competitor study, in the post-event context, makes this possible.

Real World What-If Analysis

Have you ever agonised about the race you or one of your riders lost, perhaps by a matter of a few seconds? Wouldn't it be great to know the size of the winning (or losing) margin, not in terms of time but in terms of parameters you can work to improve such as power, weight, or drag? Post-Event what-if analysis does exactly this because we can re-simulate performance given certain improvements. No more agonising.

Post-Event modelling is now available at our usual Performance Modelling link. Simply select "Post-Event Modelling" near the bottom of the page. CdA estimates via the virtual wind tunnel are open and free. The full Post-Event report, with all of the above analytical features, can be configured below.

Intelligent Event Selection : Comparative Advantage & CPLPercentile

The concept of "comparative advantage", attributed to the economist David Ricardo in 1817, says that it is better to capitalize on your strengths than to shore up your weaknesses. Back then Ricardo was pointing out the futility with which England might compete with Portugal on wine production and how the English should instead leverage their textile industry to trade cloth for wine, but there is far wider relevance across many aspects of life. In competitive sport, and especially in a sports like cycling and triathlon where there are a multitude of different events and courses available, the idea has a lot to offer.

In our blog article on the measure of a cyclist we outlined 8 metrics of a cyclist's ability. Strengths or weaknesses in each one of them will tend make a rider more or less suited to specific events. For example, a rider with a high FTP/Weight ratio will probably be good in events with long climbs. A rider with high AWC/Weight (Anaerobic Work Capacity) and fast AWC recharge may be better in events with lots of short, punchy climbs. A rider who is relatively heavier but also powerful is likely to have a higher power to drag ratio "Watts/CdA" and excel in flatter time trials. The full set of metrics will interplay to make every rider uniquely better or worse than another rider in every event.

Imperceptible Differences

Identifying comparative advantage is not so easy. Of course we can immediately say that a Fabian Cancellara is better suited to time trials than summit finishes in the Dolomites. And that a Nairo Quintana is unlikely to win a world championship time trial. In between these extremes, however, there is a very large population of more "average" riders whose morphology is similar, whose weight is visually similar, and whose only differences lie in the subtleties of their power numbers, their actual weight, and their aerodynamic drag. This population includes you, your competitors, or if you are a coach then your athletes and their competition.

It is not just riders who are often imperceptibly different. The same goes for courses. A typical, rolling, neither extremely hilly nor extremely flat course may suit one rider more than another, or it may not. To the naked eye and the human imagination there is no way to tell. It's a similar problem to deciding between a light climbing bike or an aero time trial bike for a rolling course. Apply some Performance Modelling though and the answer, rider versus rider, course versus course, just falls out in front of you. All you have to do is simulate both riders then compare their time on course estimates.

Comparing Riders

We have always advocated using Performance Modelling to compare any two riders on a particular course. For example, given metrics for "Rider A" it is very easy to simulate his/her performance on the course in question, then to simulate an alternative or competitor "Rider B", and decide who has comparative advantage. If you were managing a team then you might use this sort of approach to recommend one rider over another for a certain event. If you are a coach then you might use this approach to estimate the shortfall between your rider and a competitor. The latter "gap analysis" is the foundation of the key coaching practises of rider profiling, performance benchmarking and goal setting.

Comparing Events

A logical extension of Performance Modelling is to change the problem, forget about the specifics of any one alternative rider or competitor, and ask "which of several events should this rider enter to maximise his chances?" This is a question equivalent to the problem (for time triallists) "on which course can I maximise my ranking?" or (for triathletes) "which course gives me the best chance of qualifying for Kona?" Until recently we didn't have an answer to that, but now we do.

CPLPercentile is a metric we have developed to indicate a rider's comparative advantage on a specific course. Very simply: Every time you use CPL to simulate a given rider on a given "official" course we show a time on course estimate. Below that we show a "CPLPercentile" which is a number from 1 (best) to 100 (worst) indicating the simulated rider's ranking relative to the theoretical performance of every other rider in our database. Without going into numbers that is now a very comprehensive population of average and not so average riders. The actual value of CPL percentile doesn't matter. It could be 25 (stronger than average), 50 (average), or 75 (weaker than average). The reason it doesn't matter is because it's simply an indication of where the rider might finish in a typical field of typical but anonymous competitors. What does matter though, and what is a very powerful indiation of which event a rider should favour, is the way CPLPercentile changes across events.

Intelligent Event Selection

By example: Let's say we simulate a rider in Event A. The CPL percentile is 50. This means that with a large number of typical competitors the rider might finish exactly mid-field. We dont' care aboout that the absolute level because we dont know who the field are. Now we simulate the same rider in Event B. The CPL Percentile is 45. Again we dont care about the absolute level. What we do care about is that the percentile is 5 lower. The rider's attributes are giving him/her a comparative advantage in this event. The lower the percentile the higher the comparative advantage. Logically the rider would choose Event B to maximise his/her chances. It's that simple.

In conclusion, CPLPercentile is a new metric to indicate rider's comparative advantage across events. It has become possible thanks to the large population of riders in our database, whose attributes we compare 100% anonymously, and a fair deal of computing power. Finding the event where a rider's metrics give comparative advantage really is as simple as checking the CPLPercentile for two or more candidate events and favoring the one with the lowest CPLPercentile. CPLPercentile is visible absolutely free from our Performance Modelling resource. We would of course be keen to see any questions or feedback.

3D Visualisation, applications in Performance Modelling

Anybody who has ever been fortunate enough to pilot an aeroplane has probably experienced an eerie realisation that the world is far more 3 dimensional than most of us ever really think about. Up there, a couple of thousand feet or more above ground level, there is almost a sensation of diving somewhere in the middle of an aquarium while the place that once represented the 3D world feels like nothing more than the gravel and the weeds down at the very bottom of the tank. The opportunity to see the world like that has a lot to do with why many of us stop, gaze and enjoy the vista on high mountain passes.

Modelling cycling courses relies on what we call “triplets” of GPS data – latitude, longitude, elevation – and we have recently been looking for better ways to visualise data in these 3 dimensions. We were incredibly fortunate to hire a guy whose recent projects included some pretty serious geospatial work – software used to remap the bed of the Panama Canal – and the image with this blog is an example of the capability he came up with. In this image we’ve rendered the gradient of every road sector as a kind of “4th dimension”, now quite a familiar technique, but the possibilities go way beyond that.


CPL predictive race modelling typically includes projections of riders speed given power, variable power levels required to execute an Optimal Pacing Strategy, and even cadence ranges given that power, rider attributes and gearing. We can now map any of these projections onto 3D visualisations of a course and we think this opens up a world of possibilities in terms of understanding race planning and execution. Imagine being able to look at the course of a forthcoming event and see the “hotspots” where a rider will be travelling particularly slowly – often the best candidate sectors for pacing improvement – or where a particular range of gearing may be inadequate.


There is more too. One of the big benefits of Pre-Event Performance Models is scenario analysis. What is the impact of a rider’s time on course given more power (CPL Power Delta), less weight (CPL Mass Delta), less aerodynamic drag, or changes in equipment? Currently we can illustrate these impacts for the 4 quarters of a course, and for the course in aggregate, but imagine if these impacts could be visualised through every single sector. Where does a heavier but more aerodynamic wheel cost time and where does it buy time? To the best of our knowledge the cycling world has not seen this sort of analytic detail in 3D before.

We expect to incorporate more and more 3D visualisations into what we do. The image with this blog is from a rather special pacing project that came across our desk this week. In the meantime, if you the reader should have any particular visualisation ideas or problems with which we may be able to help, then we are always happy to hear them.

Mean Maximal Gradient, Predictive Cadence and Gearing Analysis

Bike riders and coaches of all levels understand the importance of informing themselves about the demands of a forthcoming event or race. At it's most informal this process might be a quick glance at the route and profile, while at it's most rigorous a formal analysis of demands may include power analysis, pacing and equipment options, nutrition and hydration strategies. CPL's Event Models are ideal for this level of detail.

One of the factors frequently overlooked, or simply not considered in sufficient detail, is analysis of gradients and gearing. Sure, it's easy enough to look at a profile and see the length and average gradient of climbs, maximum gradient is often indicated too, but is this enough?

Most Gradient Analysis Is Misleading

A number of software products will readily show you a bucketed summary of "Total Distance at Gradient", either for a particular climb, or for an entire course. By "bucketed" we mean they will break the road down into small sections, calculate the gradient on each, then add up the total distance in sensible gradient "buckets" or bands. For example, 300 metres of road at 1.5% gradient goes in the 1-2% bucket, another 200 metres at 1.8% goes into the same bucket (the total distance in bucket total is now 500 metres), and so on.

The main limitation of this approach is that it fails to consider how close or how far apart these sections of gradient will be hitting the rider, or their order on the road. 1 kilometre of 10% gradient sounds pretty tough, but if it's really 100 metres of 10%, on 10 separate sectors, with several hundred metres of flat or event descent in between, then it becomes clear that this sort of analysis is at-best misleadiing and at-worst useless.

There is a paralell here with power and heart rate analysis. 10 minutes above FTP or above threshold heart rate tells us little about a ride unless we know how that time was distributed. Was it continuous?. Was it just a few seconds here and there, many times over? Gradient analysis has exactly the same considerations and what we really want is something equivalent to "Mean Maximal Gradient".

Max Distance At Average Gradient

A better way to do gradient analysis is in terms of "Max Distance At Average Gradient". Define some gradient buckets, as above, but this time scan the entire course looking for the maximum distance with an average gradient falling inside that bucket. By example, a 100k course from point A to point A is going to have 100km at a 0% average gradient. If the biggest climb is 10k at 5% then the max distance at 5% average is 10k and the max distance at -5% average may also be 10k. If that climb has a steeper section peppered with short pitches varying between 6 and 8% this analysis will reveal the max distance at averages of 5-6%, 6-7%, and 7-8%. Total distance in any of these buckets, by comparison, could be misleading or useless.

"Total Distance At Gradient" is an easy analysis to make, in fact it can be done manually, "by eye". "Max Distance at Average Gradient" is much tougher for humans, but relatively easy for a computer, which is well suited to scanning and calculating all continuous combinations of all sectors across an entire course.


CPL Pre-Event Models now include an analysis of Max Distance At Average Gradient in addition to Total Distance at Gradient.

Predictive Cadence & Gearing Analysis

The logical goal of gradient analysis is to make informed decisions about gear choice, given some range of acceptable cadence. But there are no good "rules of thumb" about the right minimum (climbing) or maximum (descending) gear for a certain course or certain gradients. Cadence is a product of road gradient and speed on the road. Speed on the road is a product of a rider's sustainable power output, weight, and to a lesser extent other components of resistance such as aerodynamic drag and rolling resistance. A 60 kilo pro who can hold 350 watts on a climb is not going to need the same minimum gear as an 85 kilo amateur with 200 watts.

In practise this means that the only way to make good decisions g is by relying on predictive event modelling. You want to know 1) what are the maximum and minimum average gradients encountered for at least some minimum critical difference. A 500 metre pitch works well for most riders. And 2) What cadence would a certain rider achieve on these pitches, through a range of different minimum and maximum gearing options. Only then can gearing decisions be considered optimium, adequate, or in some cases low enough to avoid catastrophe!

All CPL Pre-Event Models now include an analysis of minimum and maximum cadences achievable with a range of gear combinations including chainrings: 34, 39, 42, 50, 52, 53 and sprockets: 27, 25, 23, 13, 12, 11.

Think power is complicating cycling? Think again.

People make a lot of excuses when they dont want to pay for something. It's a waste of money. I dont need it. What would I want with one of those? We've heard all of these procrastinations from cyclists and triathletes on the verge of buying a power meter. Another objection that we hear a lot is "it's too complicated". The purpose of this article is to highlight why power is in fact simplifying, not complicating, cycling.

"The amateur wants the gimmick but the expert sees the beauty in simplicity"

There are a lot of gimmicks in cycling. Go-faster wheels, frames, and components, for example. Some of them are worth your money, but some of them aren't. And sometimes you can only take that decision when you know what magnitude of improvements you are looking at. At CPL we use performance modelling to evaluate potential gimmicks in the simplest possible language. We use science to reduce cycling to a set of energy demands (climbing, aerodynamic resistance, etc), a set of scenarios relevant to you, and then the simplicity of the answer - speed effects and time savings.

Performance questions

At CPL our guiding principles and objectives correlate well with the idea of "performance questions", a term we first heard from the E.I.S.

  1. What data do we have or can we get?
  2. What questions do we have?
  3. What really matters? And the answer is almost always "speed!"

There is one phrase of which we all should be aware when discussing the merits of equipment, strategies, or riding scenarios and that phrase is "it depends". Too often "it depends" means "I dont know", even when it's coming from a supposed expert. One of the reasons we created CPL was a chronic tiredness with "it depends" and a need to properly answer performance questions.

Seek clarity, not fuzziness

A lot has been written about the finer aspects of the coaching process, in cycling, in triathlon, and wider. But for sports which are supposedly so advanced some really important parts of the process are still in the dark ages. Only power gives riders a concrete evaluation of current ability and concrete assessments of progress. But accurate goal setting requires power based predictive performance modelling of the type that we've developed. Fuzzy goals lead to fuzzy preparation and fuzzy performances. Fuzziness is hard to understand, whereas things that are clearly defined promote simplicity.

Mind your ifs and buts

On the quest to become, or train, a better bike rider there are a lot of if's and but's. "If we drop 5 kilos, what's the benefit?". "If we find 20 watts, what's the effect?" Too many if's and buts make life complicated. At CPL we prefer simple answers which is why we apply performance modelling for scenario analysis. We coin the term "Mass Delta" to provide a simple metric of how much faster a given rider will go, on a given course, with a reduction in weight. "Power Delta" is the equivalent, when the "if" is increased power. These sorts of capabilities, rooted in power, undoubtedly simplify cycling.

The new language of cycling

Power has not just changed the language of cycling, it has created it. Coaches and riders can now communicate with an accuracy and expressiveness that was never before possible. We now have names for training patterns, like "2x20" and "FTP", that convey the same details to us as "suspension" or "cantilever" might convey between engineers. Sensations of form or lack of form can be communicated in terms of ability to hold a certain power for a certain duration. And injuries can be described in terms of the power output or torque that causes the problem. Many of us have have come to take this language for granted, but how often do we stop to reflect on just how much power has in fact simplified our lives?

Put a number on it

The things that win races - times and speeds - are measured in numbers, as are finishing positions. If these criticial aspects of success can be defined with numbers then why not the things that make them possible? Form, fitness, weight, endurance, explosiveness, etc. Plan your race or your season, dont't speculate. Power and all of the numbers that follow are there to simplify life, not complicate it.

The Measure of a Cyclist

August is wedding season here in Europe and we were recently involved with having a suit fitted and tailored. The process, done properly, involves an awful lot of measurements that together could do a pretty good job of describing the form and physique of the customer. No one measurement defines the perfect suit and this got us thinking about how, in the modern world of power meters and sport science, no one metric is sufficient to define the ability of a bike rider.

So what is the measure of a cyclist? There are romantics and journalists who might turn to words such as "class", "panache", or "tenacity" but let's suspend the BS for a few minutes and look at the set of metrics that we have come to understand are required to comprehensively define the ability of a cyclist. Even for natural number fans there is much more to consider than one simple "watts per kilo" - equivalent to an off-the-peg but poorly defined "size 50 suit"...

Critical Power (Watts)

Critical Power (CP) is what’s left when we strip away the power a rider can produce on a short term basis, “in the red zone”. That means it’s equivalent to power that can be produced aerobically, through “aerobic energy pathways”, and for a relatively long time. The gold standard model for identifying a rider’s CP, from just 2 or 3 short field tests, is the Monod Critical Power Model. Of all rider metrics CP is the most important for the vast majority of cycling events.

Anaerobic Work Capacity (Joules)

Anaerobic Work Capacity (AWC) is the size of a rider’s “red zone”, or the amount of energy they can produce over and above CP, before they need to slow down and recharge. Because AWC is an amount of energy it’s measured in joules. Since a joule is “1 watt for 1 second” AWC can be spent very quickly, at a power output way above CP, or more slowly, for example riding just a bit above CP for several minutes. The Monod Critical Power Model is also the tool of choice to identify a rider’s AWC. Some sport scientists refer to AWC as W’ - “W prime”.

AWC Recharge Velocity (Tau)

When a rider’s power output dips below Critical Power he isn’t spending his anaerobic work capacity, so if it’s depleted then there is an opportunity for the body to recharge it. Consistently riding above and then below CP isn’t particularly efficient, but the demands of a race or considerations of a pacing strategy may win the argument. Speed of recharge is key, and recent research (primarily by Dr Phil Skiba) has provided a framework in which to model AWC recharge. The lower a rider’s power output, relative to critical power, the faster AWC will recharge. Another determinant of that speed is a mathematical function known as the “Tau function” which can either be based on a general population of cyclists, or calibrated to the individual using power based field tests.

Velocity of Oxygen Dynamics (Seconds)

Imagine a rider accelerates from a standing start and upto Critical Power - the level at which all power is still assumed to be coming from the aerobic pathway. He’s never exceeded CP, so did he use any AWC? The answer is yes, because it takes a bit of time for his aerobic system to fire up to full capacity, and in the meantime the energy that’s not being produced aerobically has to come from somewhere. The faster a rider’s aerobic system can accelerate the better, because AWC is preserved and the cost of recharging it is avoided. This can be important in events with highly variable power demands, or for events that involve hard efforts straight from the gun, such as the pursuit. Acceleration of the aerobic system is typically modelled as an exponential function where velocity is explained by it’s half life in seconds.

Neuromuscular Power (Watts)

Sprinting requires explosive efforts that rely on an energy system distinct from the aerobic and anaerobic pathways, as well as a rider’s ability to activate and deploy muscle. Aside from very specific track applications we’ve yet to be convinced of the need for a formal model of neuromuscular power. The metric here is simply “best average power over 5 seconds”. Perhaps more than others this metric is sensitive to the quality of a rider’s power meter (how frequently does it capture data, and how does it measure angular velocity of the crank?).

Fatigue Index (%/Tx2)

The Critical Power model suggests that if we strip the power a rider can produce from anaerobic sources then we arrive at one number – critical power – that he ought to be able to maintain aerobically, and indefinitely. Of course this isn’t realistic – ride beyond an hour or two and everyone will fatigue, even though their aerobic engine isn’t actually getting smaller. So what’s going on? Lots of complex processes and factors contribute to fatigue but rather than try to model all of these factors we like the concept of the “Fatigue Curve” – a model which simply fits a curve to the tendency for a rider’s power output to decay with time, though at an ever reducing rate. The underlying mathematical function gives us a very useful summary number – by what percentage does a riders power output reduce when ride time doubles – and we call this %/Tx2.

Body Mass (Kilos)

The more a rider weighs, the more power he needs to climb at a given speed, accelerate at a given speed, or even to move across a flat road at a given speed. That last bit may be surprising, but it’s a fact that the amount of power needed to roll across any road is a function of tyre rolling resistance and the amount of weight pressing down on those tyres. There is nothing complicated about measuring rider weight, but it is still an essential metric.

Aerodynamic Drag (CdA)

At race speeds some 80 – 90% of a rider’s power is being used to overcome aerodynamic drag, so some measure of how aero or not the rider is must be important. A rider’s “coefficient of drag” multiplied by “frontal area” (CdA) is the standard metric. The whole of a rider’s morphology – including height and weight – will have an impact, as well as flexibility and core strength. We can do a good job of estimating rider’s CdA from height and weight alone. With a suitable field test, involving power data, we can do an even better job. No description of a rider can be complete without some estimate of CdA.

So there you have it – 8 measurements that together describe the ability of a cyclist. Not all are easy to measure, and not all are important to every type of event, but the good news is that the metrics important to the most popular events are also the most measurable using nothing more complicated than a power meter. Now what can we do with these metrics? First, this kind of total description of a rider can be invaluable to coaches looking to deliver improvements having excellent specificity for target events. But by extension these metrics have great applicability in CPL performance modelling.

One way to define performance modelling is simulating the performance of a given rider, on a given course, under given conditions, and the better we can define the given rider then the further we can go. By defining a rider in terms of the above metrics performance modelling can deliver the best possible insights in terms of performance prediction, performance benchmarking, goal setting, optimal pacing, equipment evaluation, and more.

In conclusion we would encourage all riders and coaches to take a multi dimensional view of testing and defining ability, using at least the metrics relevant to current goals. And of course, with benefits like the above, to embrace the considerable potential of performance modelling.

Sustainable Power is a moving target

The trouble with rider’s power output is it falls over time. Not in the course of a season, when we hope it increases due to training stimuli, but as a response to the duration of a ride. Whether we’re interested in short efforts, when sustainable power decreases as a function of anaerobic work capacity, or relatively longer ones, when fatigue is the problem, there is an inescapable reality that we become weaker as the clock ticks over. This reality can be visualised as a rider’s “Power Duration Curve”.

In some way stronger riders enjoy a double advantage. As well as going faster from the outset they also arrive at the finish line way before weaker riders, putting their effort on a very different section of the curve. Indeed pro level ironmen face a completely different race to the typical age grouper who will be out on course for hours more. What may be a tempo ride for someone can be a test of endurance for another. A layman might conclude that we should all ride full gas from the off, thus completing whatever course asap and aiming for some shorter (but higher) point on the curve. Unfortunately the realities of physiology quickly undermine such a strategy.

Completing any course as quickly as possible comes down to intelligent pacing. Even if we discount the opportunities presented by a computer optimised, variable power strategy, there is a problem to be solved. A rider needs to know the highest power output he can expect to be able to sustain for the duration of the course, to leave everything on the road and get the best ride out of himself. But what is his expected duration on course?! Only predictive analytics, performance modelling, can do a good job of revealing that.

There is a chicken and egg problem here. To estimate time on course we need to know (average) sustainable power, something to feed our model. But to identify sustainable power we need to know time on course! Thankfully computers are pretty good at solving these kind of problems…we can “iterate” a power value until we “solve” for a rider’s best sustainable power. Best means the number that leads to the fastest time on course, but rests no higher than the rider’s curve at that duration.

CPL Event Models have always solved for best sustainable power based on your inputs, but we haven’t done a great job of explaining this. That’s why, as of now, where you see our power prediction, you can click on “why this number?” to open an insightful chart. You’ll see two lines 1) Power Duration Curve… based on observed power inputs & 2) Power For Time on Course. Where these lines cross (and a rider’s fitness would have to be critically unsuited to the event if they don’t) is best sustainable power.

Best sustainable power is clearly a key number for any rider wanting to go as fast as possible, even if a variable power pacing strategy has been discounted. So of course we’d encourage everyone to use the free analytics here on CPL in uncovering that number. No rider can out-perform his fitness but the number comes with two guarantees. First, said rider will finish about as fast as he can, no guess work. And second, the suffering will end about as soon as it can do. Smart riders should like the sound of both.

Where are you on the Power Learning Curve?

We’re celebrating an anniversary this month – 10 years since our first SRM training system arrived from the factory. As if you didn’t know it already this particular sample of German engineering has given us years of gold standard accuracy and unwavering reliability, much like most SRMs we’re aware of. We've learned an awful lot about power since the turn of the century, and the purpose of this post is to share our thoughts on the learning curve that comes with integrating power into your cycling. The accompanying graphic is an extract from a presentation we give on the subject - drop us a line if you'd like to host one.

Basics - A better heart rate monitor

The first justification for training with power is often “a more real time measure of intensity”. Power output doesn’t lag heart rate response, so it’s far superior for the monitoring of effort (the basics of pacing) and the execution of intervals. It’s also a measure of output that is not subject to external factors, so training by reference to power zones is frequently more accurate. Given such an objective measure of output it becomes clear that power is a great tool for comparing rider’s abilities and “power profiling” is the term for that. Together these are the immediate benefits of using power.

Paradigms - Descriptive analytics

The richness of power data has facilitated a number of new analytical techniques or metrics which expand on the idea of profiling rider’s ability and help to diagnose where improvements can be made. The Critical Power curve is an essential tool for expressing and explaining how a rider’s ability to deliver power decays as duration of effort increases. Simply looking at where a rider pushed his limits on this curve is a useful way of diagnosing racing performances or failures.

Several tools were developed in quick succession by Dr Andrew Coggan of the Peaks Coaching Group. Quadrant Analysis represents a way to uncover the neuromuscular demands of different types of event, pairing power and cadence data, and to improve training specificity. Training Stress Score (TSS) is a power enabled metric of training load, adjusted for intensity. Training Stress Balance (TSB) compares short term and long term TSS as a method to predict a rider’s form assuming Form = Fitness + Freshness = Chronic Training Load (long term TSS) minus Acute Training Load (short term TSS).

Finally in the area of descriptive analytics power data, used carefully and appropriately, can allow us to estimate and iteratively improve a rider’s aerodynamic drag. These are all retrospective techniques relying on the study of past ride data.

Performance modelling – Predictive analytics

The greatest opportunities in the use of power data are now in the area of forward looking, predictive analytics. This is the area CPL has been working to develop and the principle here is - “How can we use holistic performance modelling, enabled by power data, to deliver intelligence that will make riders faster, or just more successful?”

The first benefit of Performance Modelling is the ability to set real goals. When you can convert power output into a projected time on course, or a target time on course into a required power output then, aside from the motivational benefits, there are real possibilities to intelligently choose, prepare for, and target events. A simple extension of this is scenario analysis – how much faster or slower are certain conditions or rider attributes and can these be targeted?

Performance modelling, with good data, enables Equipment Optimisation. Read “free speed” (at least in terms of effort). Another route to free speed is Optimal Pacing Strategy. The fastest way to the finish line is rarely a constant power output - but it takes some serious analytics and computing power to identify the optimal strategy for a given rider. We do that.

Some cutting edge applications of performance modelling are energy budgeting and management of Anaerobic Work Capacity – the latter inspired by Dr Phil Skiba at Physfarm Training Systems.

Wherever you are on the power learning curve, or wherever your clients are, there is always more to learn. Investing in a power meter is really only the beginning. Riding a bike – fast – is no longer just a physical challenge and the more you learn, the more achievable speed is out there.