Endurance Analytics

Our blog - covering sports analytics and EA products

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.

"Air pressure is everything"

The hour record is a hot topic at the moment and we have seen great interest in predicting how far both Alex Dowsett could go and how far Bradley Wiggins will go this Sunday June 7th. Based on comments in the media it is clear that Wiggins was hoping for unusually low air pressure this first week in June but just how much of a difference can this make?

Accompanying this article is a chart from the UK National Physics Laboratory (NPL) in Teddington, just across London from the Olympic Velodrome, which shows a time series of local air pressure during the last year. You can see that 1013mb, the typically accepted average global air pressure at sea level, is around about the average observation while 990mb and 1030mb could be considered towards the low and high ends of normal. By applying these numbers in our popular Power Calculator we see that, with some sensible estimates and at hour record pace, the difference between 990 and 1030 is very significant – at least 600 metres – and for less gifted riders might represent the difference between smashing the record and a near miss.

We can’t overemphasise the importance of air pressure when the goal is riding as fast as possible. It’s the very reason riders go to altitude – either for the physiological effects or, in the case of record attempts, to gain what could almost be considered an unfair advantage over sea level times. Our Effects of Altitude model demonstrates the extent of speed &/or power savings that can be had with increasing altitude, versus typical physiological costs. And if Wiggins does as predicted, setting an almost unacheivable mark for the hour, then just maybe the only way to beat it will be some future plan at altitude.

Turning back to the air pressure in London we have long used historical data from the NPL to consider the relative benefits of riding a time trial event based on forecast weather. One of the inputs to our Time Trial Sector Model is air pressure and we can show you just where a forecast value stands in the normal distribution of UK pressures. We display “faster days in the year”, “slower days in the year”, and relative speed and power advantages of the range of pressure percentiles.

At the time of writing the forecast for Wiggins’ ride is not looking favorable. Heat and possibly humidity can be determined by climate control at the velodrome, set at the preference of Wiggins’ team, but air pressure is forecast at a very high 1033mb. Just to recap – if that forecast comes to pass then Wiggins has been unlucky and could go 600m slower than in an atmospheric pressure at the luckier end of the scale. One final thought – track and field records in athletics have long been rectified for wind assistance...is it time cycling did the same for air pressure?

The New Language of Cycling

This month like never before the cycling press is awash with power meter stories. We’ve seen price cuts from Quarq, Pioneer and Power2Max. New devices from Powertap, Rotor, and Garmin – plus several other projects somewhere between prototype and mainstream. It would be fair to say that the power meter market is progressing at a speed few can keep a track of. So where is all of this precision hardware heading? Well, we’ve been saying for years that power meters are destined for ubiquity, like heart rate monitors and cycling computers before them. In fact they are significantly more useful, so ought to achieve even greater uptake. Indeed the only thing standing between where we are now, and a power meter on every serious cyclist’s bike, is the realisation that power is absolutely key to cycling.

But why is power so important? Well it’s what we like to call “the unifying variable” of cycling performance. It’s the one thing that completely explains everything a rider has got (in terms of human output) at the same time as everything he needs (in physical or engineering terms) to achieve a given speed on the road. Speed of course is the essential element of racing, so power is becoming the language of racing. Now take a look at the diagram accompanying this post – we’ve been opening power seminars with this for the last couple of years.

Power Supply

Power supply is really the sum product of all physiological energy systems (aerobic, anaerobic, etc) factored by a rider’s state of motivation and fatigue. All of cycling physiology can be boiled down to “how much power can I/he/she produce” while how it’s produced almost doesn’t matter. Almost we say, because the details and complexities have a role in developing training strategies that improve output, and in the finer points of performance modelling.
Notice how we said power supply is more than just physiology. Yes, power is the product of the human body mixing fuel with oxygen, then converting that into mechanical work, but it’s more than that. There is no better metric of fatigue or psychological factors too. Power is, as sport scientists would say, an inderdisplinary factor and it’s corollaries Watts/Kilo and Watts/CdA are continually demonstrated as the greatest explanatory factors in cycling performance.

Power Demand

Think of power demand as the combination of 1) the demands of the event (that set of prerequisites so famously analysed by Team Sky) including course, weather, required speed; 2) the state of the rider, size, weight, etc; and 3) equipment choices. Change any one of these elements and power demands change. The key point is that, once again, they can all be explained in terms of power.
Consider these “performance questions”:

• What ability does rider X need to complete course Y in time Z?
• How will that change if he’s fitter, lighter, or more aero?
• Which equipment choices will maximise his speed given predicted conditions?
All of these question and many more can be answered with a little research, power data, and the appropriate modelling techniques.

It will take a while yet before the current wave of power meters breaks across the cycling world. But when it does we expect to see a great realisation - that power is much more than just a number reported by the most fashionable cycling accessory. To think of it like that is to be stuck in the dark ages of heart rate monitoring. No, power IS modern cycling – the language of ability, the metric of goals and objectives, and the benchmark of equipment. And as physiologist Allen Lim put it recently “power has changed the language of professional cycling”. Parlez vous power?

Aerodynamic interaction effects in group riding

As little as 5 years ago cycling aerodynamics was still in the wild west. Very few riders had ever seen the inside of a wind tunnel, myths prevailed, and we all had much to learn. But things have moved on...serious cyclists are now routinely using aero data to optimise race preparation, and we understand not only what positions or equipment are faster but how and why. It would help if all manufacturers were forthcoming with performance data, but we digress...

If you have seen any of the recent wind tunnel videos from Specialized, or the series presented by Chris Boardman with ITV4’s Tour de France coverage, then you’ll have noticed that with the basics well understood more efforts are being focussed on the nuances of drafting and group riding. “Interaction efforts” are the big new direction, understanding them offers a lot to anyone participating in team or mass start events, or simply with some cheeky drafting opportunities, and we ought to pay attention.

But there is a problem. Wind tunnels weren’t built for groups of riders, and they certainly weren’t built to evaluate individual drag forces on multiple riders at the same time. Studies of drafting effects began in a more practical manner with power meter data, where Broker et al. (1999) revealed that “man 2” in a 4 man team pursuit (at 57-60kph) needed about 71% of man 1’s power, while men 3 and 4 needed about 64%. More recently researchers such as Blocken et al. (2013) have used CFD (Computational Fluid Dynamics) software to simulate the theoretical effects of group riding, with similar conclusions.

Though power data can be converted to drag data using the "Martin et al." mathematical model adopted by CPL there are some problems with relying on this approach to estimate changes in a more useful number, drag. It’s really difficult for a group of riders to maintain constant wheel-wheel separation in a field test, and as we know on an intuitive level this makes a big difference to drafting effects. Meanwhile CFD simulations require simplifications which may spoil their ability to reflect the real world.

Just last month the journal “Sports Engineering” featured a key article from a team (Barrey et al, 2015) working at Monash University, Australia.  Uniquely they have worked with modifications to their wind tunnel, allowing 4 riders to be evaluated individually and simultaneously. They’ve shown how, with a 12cm separation, man 1 can expect a 5% reduction in drag, man 2 gets around 45%, while men 2 and 3 can expect around 55%. These are averages of all possible combinations of the 4 riders because, crucially, optimising these things depends on the anthropometrics and baseline CdA’s of the riders. When you plug these drag reduction factors into a power model the results compare well with the power based study mentioned above.

If anyone has put more than 4 riders together in a wind tunnel then we haven't heard of it, so CFD simulations can still add some valuable insights. For example, Blocken et al have shown how, in a pace line of upto 8 riders, there is a gradual reduction in drag force through positions progressively further back in the group. This occurs due to a gradual downstream widening of the group’s wake. In groups of 5 or fewer it is the last rider who enjoys the greatest drag reduction. But in larger groups the place to be is last-but-one, since the diminishing benefits of wake are eventually offset by the reduction in pressure drag that comes with a following rider. Important lessons here for anyone involved in group riding.

What does all of this mean for ride modelling? First of all, to do a good job of modelling team pursuit or team time trial events requires a matrix of drag reduction factors. Every rider has a baseline CdA, which falls by a certain amount given their position in the group, who is ahead and behind. Team performance still hinges on the Watts/CdA of the lead rider, rather than some notion of “group average Watts/CdA”, but the drag experienced by drafting riders can be important in modelling recovery. Secondly, the insights here will allow us to do a better job of modelling mass start events. If the type and extent of drafting achievable can be factored into an Event Model then we would expect time-on-course predictions to get even closer to reality. For the mean time, when using CPL, you may wish to apply “rule of thumb” adjustments to CdA - but watch out for some more sophisticated modelling options.

Evaluating Optimal Pacing Plans

Performance Analysis & Modelling in sport probably began in field games such as football and baseball where the objective is to turn analytical intelligence into real tactical advantage which increases the probability of victory. In cycling the highest objective or “holy grail” is free speed - faster race times for equivalent physical effort - and no application promises more of this than the development of Optimal Pacing Plans.

At CPL we’ve been developing optimal pacing algorithms since 2010, when we provided the first web based tool for experiments in variable power pacing highlighting the importance of sector-by-sector constraints on rider's ability to deliver power. This has always been a “beta” tool (further development intended) but we have recently had the opportunity to do a lot more research and development in this area. Since we are no longer the only resource for optimal pacing plans some of our conclusions may be of even greater interest in light of what others are offering.

Beware Simplification

In the same way that climbing and descending a mountain is not the same as riding an equal distance on the flat (though both propositions equal zero net elevation gain) any efforts to simplify a course take us a long way from the realities of rider-on-course modelling. Smoothing away even the smallest ups, downs, and changes of direction can seriously compromise and result in overly optimistic pacing plans. We have always done performance modelling at the highest resolutions made possible by GPS profiles and observe poorer correspondence to reality when that resolution is dialled down. So beware simplification.

Compute Time

The Optimal Pacing Plans included in our Popular Event Models leverage the full resolution of the course profile for the best achievable accuracy. In fact it takes a lot of computing power to come up with a plan from this kind of model. So much so that we don’t pretend to offer plans you can calculate in a couple of seconds on the internet. Our plans take several minutes of compute time to generate so sending you a pdf is the only way to keep things honest and useable. The ten sector summary we show you is just that - a summary – hiding the intricacies of the real model.


Can you control your power output to the nearest watt? Can you even hit an exact average for a certain interval or stretch of road? Probably not. Most people would struggle to hit this accuracy on a turbo trainer, never mind in the varying environment of road cycling. So beware pacing plans that expect you to execute in terms of single digit resolution. We work to the nearest 10 watts - just about executable – with insignificant effects on best time on course predictions. The only exception to this is in the final sector of the course where there is only one number that will solve for an overall target power.


One way to solve the optimal pacing problem is to look at the impact of small changes in sector powers on 1) time in sector & 2) target power at the course level. Logically the sectors which offer the greatest reduction in time-on-course for the least impact on target power (dt[s]/dNP if you’re into maths) may be the ones where a rider should “power up”, and vice versa. Various optimisation techniques can exploit this kind of theory but we have found better results using simulations. The way we develop Optimal Pacing Plans is conceptually similar to having a rider tackle the event 10,000 different times. Every time this rider tries a different pacing strategy – sometimes he blows up, sometimes he’s too conservative. We simply keep the details of the fastest ride where he doesn’t blow up and that is your plan.

Want to try a performance model with Optimal Pacing Plan? Simply choose an event here.

The Hour Record - Predict, Execute, Analyse

Sport science and engineering as applied to cycling is a double edged sword. On one hand the discipline uncovers countless truths about the nature of racing. We can make some really informed decisions about equipment choice, pacing strategies, and race execution in general. All of these things can deliver “free speed” and take us closer to “the perfect ride”. On the other hand some bike racing disciplines are now really predictable, a question of plugging rider’s power and other parameters into a mathematical model to calculate speed and race time. Not everybody likes that because sporting events were often designed to turn uncertainty into excitement.

On the spectrum of predictability the hour record is right up there, possibly the perfect example of preparing a rider to turn known knowns into a certain result. Hour record rides take place in a controlled environment, indoors, and recent attempts have been ridden with power meters. Preparing for the event boils down to making smart equipment choices then asking a simple question: how high can we get the ratio of this rider’s FTP (sustainable power output for one hour) to CdA (the aerodynamic drag metric). The answer determines the number we’re all waiting for...how many kilometres can this guy cover in an hour?

If modelling and predicting the hour record isn’t for you then browse away now. But if it is, and if you intend to take even the slightest interest in cycling during 2015, then you may be interested in our hour record calculator. The defaults are set to estimates of  Jens Voight’s parameters, indicating a distance of 51.11km, but you can tweak them endlessly to run your preferred scenario. We believe that when the big guns weigh in the record is going beyond 53km.  Our calculator will help reveal just what that takes in terms of power output. Want the quick answer? Quite a lot!

Model any riding event, anywhere on the planet

Since the winter of 2012 CPL has been providing self-service event modelling analytics on a wide range of popular cyclosportive and triathlon events.  We have prioritised coverage of Ironman branded triathlons (i.e. the complete series of 70.3 and full Iron events) as well as the most popular sportives and gran fondos on the European and US calendars, around 200 events per year. Also in our event database are Olympic distance triathlons (the ITU and 5150 series), selected major time trials, and key World Tour events. In fact, at the time of writing, we have almost 500 events mapped and modelled for your analysis, insight, and most racing scenarios you could care to evaluate.

We are always grateful for coaches and athletes who get in touch to request new event coverage or to put us right when a course has gotten out of date. The quality and depth of our event database is really important to us and we have usually been able to turn around updates in a matter of hours.  But hours are a long time and, going forward, we’re excited to be able to offer event creation that’s just as self-service as the modelling itself. So starting this week CPL is providing functionality that enables any user to create and specify any cycling or triathlon event anywhere on planet earth. This event is then immediately available for modelling.

To create an event you simply login, navigate to our event manager (there's a link below the event map on our home page), then EITHER upload a gpx or tcx course file OR “point and click” on the map to define a course. At the moment you save that course our software looks up it’s elevation profile, you specify a name, date, and a couple of other event parameters, and the event goes straight into our database, private to you. If your event is likely to be of interest to the wider population of CPL users then you can tell us to review it for public access too. We and other CPL users will thank you.

As always, if you have feedback or ideas on CPL functionality, then don’t hesitate to get in touch. Meantime we hope you find immediate event creation and modelling useful, insightful, and a valuable tool in smarter race prep, wherever your battleground!


Your Clients. Our Analytics. Your Website.

Are you a coach working with power meter equipped athletes? Then you will understand the importance of managing client’s critical power data. Keeping up-to-date metrics of rider’s best-case ability (mean maximal power) at key durations likely forms the basis of 1) tracking changes in their fitness, 2) specifying workouts of appropriate intensity, and ...somewhat related... 3) defining correct power based training zones.  A lot of your time may be spent managing this data and keeping keen clients abreast of their latest levels.

There are now a few software options in the market that will do a good job of managing this data. But what if you want to make it accessible, directly, on the website of your coaching business?  That is where our new client data management functionality can help.

If you 1) Register with CPL ...it’s FREE... and 2) check the box “I’m running a coaching business...” then your user profile will display the tab “Client Data”.  The main use of this tab is to manage current and historic power and anthropometric data for an unlimited number of clients, for use in performance modelling. But there is more...

You “Client Data” is now available to a widget that you can display on your website. You simply include the html indicated in the image above (zoom if you can't quite read it), replacing youremail@domain.com with the address you used to register at CPL.  Clients can then visit the page where you host this widget, login, and see their current Critical Power curve, FTP, AWC, training zones, and history.  But there is more...

All of your client’s data can now be used to load the parameters of our Popular Event Models. Power, weight, CdA & Crr can all be saved, driving the fastest possible estimates of rider’s power-based performance in a wide range of popular cyclo-sportive and triathlon events.  You simply login to the site and adjust the “Load Models As...” dropdown where you see it. There is more too...

Set up a “Coach Subscription” (it’s a very reasonable GBP 99 per month and affords you up to 25 event models per month) and you can create unlimited “Critical Power” reports at the click of a button from the “Client Data” tab.  These are PDF reports featuring current and previous critical power data and training zones and will be emailed to your registered email address from where you can add commentary and dispatch.

Tour de France 2014 Bergerac Time Trial Analysis

Regular users of CPL will be familiar with our efforts to evaluate pro rider's time trial performances in quantitative terms, especially estimated average power output and realised Watts/m^2 CdA (the power to aerodynamic drag ratio). We’ve been doing this for a while, since 2011 in fact, and in many ways this is the time trial equivalent of the climbing Performance Analysis made popular by others such as our friend on Twitter @ammattipyöräily. You can access this analysis in the World Tour category of our Popular Event Models (see the Results Analysis tab).

How does it work? Well, the first requirement is a GPS profile of the course. Then we factor in riders finishing times, height and weight estimates, atmospheric conditions, and our computer model is almost there. Almost…because we don’t know the rolling resistance of riders machines or their aerodynamic drag metric, CdA. The approach we take is to estimate a Crr of .003, about as good as it gets for high quality race tyres or tubulars on tarmac, and then we use “anthropometric estimators” established by empirical research to estimate CdA from rider's height and weight.

Now some people point out that this CdA estimate will introduce error, and it does. But the reality is we don’t really care. Why?.. Because our goal isn’t to calculate rider's power output, rather to “solve" the Watts/m^2 CdA achieved on the course. Within the range of error we get very similar results, whether or not we over/underestimate CdA and consequently over/underestimate power. More importantly these estimates have proven to be an excellent predictor of future time trial performances, within a few seconds from one event to the next.

So what do we make of the Bergerac Time Trial? Well, the first thing to note is that this event was run off under very light winds, a nice environment for Performance Analysis. Estimating Tony Martin’s CdA at 0.222 metres squared we compute an average power output of 477 watts and a “Watts per CdA” of 2147 Watts/metre^2. Martin is almost certainly more aero than that and his power in the final, long time trial of a grand tour was almost certainly lower...but the benchmark Watts/CdA stands. Only the top 3 riders seem to have broken the significant and indeed World Class 2000 Watts/CdA mark. Meanwhile 1700 Watts/CdA was good enough for 50th place.

How fast would you or an athlete you know have gone on this course? Use the Power & Pace tab on the same page to find out!