What’s up with all these doping allegations based on predicted power?

For a start we need to take a look at power output and how they are measuring it. The claims are coming from timing a climb with a stopwatch (where we know the elevation gain and length) and using a formula to estimate power output. While from a pure physics point of view this seems straight forward enough, there are several assumptions about some variables which are way too simple:

**rolling resistance**– this is often assumed to be constant, but factors such as variations in road surface, tyre inflation, speed, etc, can all make a significant effect. These are also continually improving too remember if we believe the manufacturers claims.**path**– it is assumed every rider follows the same line up the hill. One rider could travel further by taking the corners wider or travel less by cutting the corners. Riding the inside line will also give a steeper incline through the corner which may well influence the average power compared to the outside line.**wind resistance**– while often dismissed on a climb, this is still a factor. Head, tail and side winds will significantly change pace at the same wattage (think of the times you have set a Strava record, wind makes a difference!). Accounting for the wind with a formula is at best simplistic unless it is able to constantly change for each part of the climb, surrounding structures and fans, drafting position, TV motorbikes etc. Good luck! Oh, and isn’t clothing more aero now too? That’ll mess with the calculations…**rider and bike weight**– while the bike weight will likely be 6.8kg or heavier (to follow the UCI rules), rider weight is often a closely guarded secret. Yes they are easy to find online, but not necessarily correct. An error here can be significant. For example as written in the daily mail aritcle (and others) Dr Pierre Sallet calculated that Froome produced 7.04 watts per kg (w/kg) during his effort (15.3km climb – and yes, there was a slight tail wind). This was based on Froome’s published weight of 71kg, but his actual weight may be more like 66kg (according to Froome’s biographer). So 7.04w/kg x 71kg is 500w, but at 66kg it is 465w, but bear in mind the favourable wind and other variables mentioned here too. Other components such as shoes, clothes, helmets etc have also improved and become lighter and more aero, skewing predictive numbers.**terrible maths –**one thing I’d like to add here is the rather poor maths used in the article to exaggerate the numbers. I think a class of 10 year olds could spot the error. They give Froome as 7.04w/kg for the climb, but then suggest that this will be higher if he was lighter …um…if Froome weighs less, he still needs to do 7.04w/kg to achieve that time up the hill. If he was 100kg and could manage 7.04w/kg, he should climb at the same speed too. If he produces more watts per kg (w/kg) up the hill, he will go faster, if he produces less, he will go slower. Weighing less does not give him more watts per kg.

**Stava Power Estimator**

Another angle to assess the accuracy of these predictions is to look at Strava and it’s predicted power. Comparing real power to Strava’s. Let’s assume Strava has a bit of cash/experts to through at this and that their model is fairly good for the available mathematical models. I personally have several examples where this has been significantly out, but my colleague Steve Bale has written a nice double blog post on this very thing with one example on the road and one on the MTB. He does a range of climb lengths too. Read it here: Steve’s Strava vs real power article part one and part 2

**Finally, power meter differences**

Now I may not have as many power meters on my bike as DC Rainmaker, but I have been known to have two on the road at one time (Powertap and SRM) and three if you include the Computrainer while riding indoors. I have also done several power meter comparisons while testing people (Powertap with Stages, Polar, Quarq, Infocrank, Power2max, SRM, Ergomo, Garmin Vectors etc). One thing I can say is there are significant variations between power meters, and they are not always straight forward e.g. a consistent 10% or +20w etc. SRM for example reads around 5% or so higher than Powertap, but this varies between wattage levels, Stages and Quarq are close to Powertap, but not for all power levels and so on. Many factors affect this from where the power is measured (you will see more power nearer the source e.g. closer to the legs, so cranks should be higher than hubs and Computrainer is the lowest, measuring at the tyre) to how the units go about measuring the forces. Non round chainrings also effect the data.

**Conclusions**

Predicting power is about as useful as predicting energy expenditure. There are so many variations and constantly changing variables that a complex ever adjusting formula would be needed (read that close to impossible). And as with energy expenditure it is easy enough to just measure it, but tread carefully as if I go out one day with my Powertap, then a few days later with my SRM, it would look like I’ve had a little more than a marginal gain (indoor vs outdoor measurement has significant differences too, but that should be a future post). Plus, we have to give the bike companies some credit for improving our times too (remember we are comparing times now to Lance – 1999-2005), otherwise all that stuff they tell us about bikes being faster/lighter, tyres having less resistance, kit being more aero, gears being more efficient has all been just marketing…

**Other links on this topic**

Steve’s Strava vs real power article part one and part 2

The Daily Mail article with poor maths

**Video highlights and live coverage links**

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