Watts per Kilogram Explained

Since the invention of the power meter, the watts produced by cyclists, both amateur and professional, have been a frequent topic of discussion for fans and those wishing to evaluate performances. We analyse and compare climbing performances primarily based on estimated watts per kg (w/kg), using a mathematical model that we have refined over the past few years.

Naturally, many questions have arisen regarding our calculation of watts, the accuracy of power meters and why riders achieve the same speed at different w/kg. This is why when calculating and comparing climbing performances, we use a standardised equivalent for a 60kg rider, called “etalon” w/kg. The reasons for this are below, and we hope this will explain why our “etalon” figures are sometimes different to published figures from riders or teams.

Basics

The watt (abbreviated: W) is the unit of power or radiant flux which in one second gives rise to energy of 1 joule within the International System of Units (SI). It is used to quantify the rate of energy transfer.

In cycling, the energy transfer is the pushing of the pedals by the cyclist, transferring mechanical energy to kinetic energy (speed/movement) and potential energy (from gravity when going uphill) on a simplified basis.

Watts per kilogram is a basic power to weight ratio measurement, which displays the relative power produced by the cyclist. The simple way to find out w/kg is dividing the absolute watts by the weight of the rider at the time of the performance. The ratio of a rider’s watts produced per kilogram of bodyweight (w/kg) is the key metric which determines how fast they can ride uphill.

On a flat parcours, absolute power (watts) and aerodynamic drag (CdA, draft) are the deciding factors for the speed of a cyclist. Due to gravity, relative power becomes a more important factor on inclines, but aerodynamic drag (CdA, draft) is still an influential factor, especially on lower gradients, where the speed is still quite high in the professional peloton.

Why W/kg does not equal W/kg

Understanding how w/kg is derived is a relatively simple task and one might assume that our job ends there when comparing climbing performances. However not all w/kg are created equally. Heavier riders will always have to produce less w/kg to achieve the same speed as a lighter rider or, conversely, will go faster if they are producing the same w/kg as a lighter rider.

One of the reasons for this is that the bike weight in the professional peloton is typically a smaller percentage of the body weight of a heavier rider, which means they need to produce less relative power (w/kg), to move the total system. This becomes more relevant the steeper the incline, when gravity accounts for a large majority of the force a cyclist needs to overcome to move forward at a certain speed.

Example:
Rider 1 is 60kg with a 7kg bike. The bike weight is 11,67% of his body weight. If he rides at 360w, he is producing 6w/kg. His rider + bike w/kg is 360w / (60kg+7kg) = 5,37w/*kg.

Rider 2 is 70kg with a 7kg bike. The bike weight is just 10% of his body weight. If he rides at 420w, he is producing 6w/kg. His rider + bike w/kg is 420w / (70kg+7kg) = 5,45w/*kg.

The second reason is especially relevant at higher speeds and lower gradients, where aerodynamic drag still makes up a large part of the force a cyclist needs to overcome in conjunction with gravity. That is, heavier riders are more likely to have a higher watts/CdA ratio, as an increase in weight does not bring a linear increase in CdA. The prime example of this in action is Filippo Ganna’s regular success on the long but shallow Alto del Colorado climb in Vuelta a San Juan.

Why then, if heavier riders have an ‘advantage’ over lighter riders in that they can produce less w/kg to go the same speed, do we not see 90kg or 100kg Tour de France winners? This is due to the physiological reality that it is easier to produce higher w/kg at lower weights and as a rider’s weight increases there is not necessarily a linear increase in their ability to produce more watts.

Etalon W/KG

The reality described above means that comparisons between riders’ climbing performances based solely on unadjusted w/kg are not that useful, as they do not accurately reflect how fast they actually went. Standardisation of the w/kg metric is therefore required for ‘apples to apples’ comparison across the broad spectrum of riders of different weights.

‘Etalon’ is the french word for ‘Standard’ and has been used to describe the results of standardised watt calculations like ours for some time by Frédéric Portoleau. We chose an Etalon weight of 60kg, meaning we calculate how much w/kg a 60kg rider would have had to achieve for the identical performance or speed. This is the reason why our final calculations do not actually represent the unadjusted w/kg value a rider may have pushed (as not all riders are 60kg). Instead they are a metric to compare and evaluate performances.

Example:
In June, we published our etalon watt calculation for Ruben Guerreiro on Mont Ventoux, which had the result of 5,98w/kg for 58’36min. Jonathan Vaughters, manager of Guerreiro’s team EF Education EasyPost, replied to us on twitter, stating that Guerreiro had done 5,92w/kg for the ascent. This might look like a big difference, but when calculating the ascent with Guerreiro’s real weight, which is above 60kg, we obtained an unadjusted result of 5,91w/kg, almost identical to Vaughters’ stated result which presumably came from Guerreiro’s power meter and morning weight.

To clarify that we are generally referring to etalon w/kg, we will start to publish our calculations with the notation of ‘ᵉw/kg’ and not ‘w/kg’. Below you can see the unadjusted w/kg needed to achieve the same speed as a 60kg rider pushing 6.00 w/kg for different rider weights at different gradients, assuming standard values for altitude, temperature and wind.

The significant differences between the unadjusted w/kg required for a 60kg rider vs a 70kg rider to climb at the same speed has, in part, lead to the development of metrics like the Compound Score, which takes absolute watts into account and has been used for rider evaluation at WorldTour teams such as UAE Team Emirates.

Estimation vs Power meter

Power data from professional riders has been accessible through Strava for a number of years. This raises the question of, if many professional riders are uploading the power of all their races, why w/kg calculations are even necessary or valuable? There are a number of reasons.

Firstly, even with countless professionals uploading their full race power data, it is very rare for the top general classification riders to upload their best race performances. Those that used to publish power data in the past usually stop doing so after becoming absolutely elite. One example of this is Tadej Pogačar, who started hiding his power meter values on Strava after the first week of Le Tour de France 2020, in which he broke the Col de Peyresourde climbing record. Egan Bernal catalogues almost all of his training on Strava (including power data), but when performing at a high w/kg level in races, like on Monte Zoncolan in 2021, he will typically not even upload the ride file to Strava at all.

Even if the UCI took the unlikely step of demanding every athlete publicly published their power data from UCI races, power calculations would still be needed to evaluate performances. The reason for this is the margin of error for power meters in conjunction with inter-manufacturer recording variation and uncertainty regarding user calibration. Most power meter manufacturers claim an accuracy of +/- 2% if calibrated correctly. A rider pushing 6w/kg could therefore get a result between 5,88w/kg and 6,12w/kg even when religiously calibrating their power meter. More importantly, power meters sometimes over/under-read way beyond this margin, may not be calibrated frequently enough or may simply be broken.

Example 1:
Before La Vuelta 2022, Jay Vine performed a power test on Col de Beixalis, in which he set the Strava KOM. Unlike his typical upload practices at the time, Vine hid his power for the effort. The reason for this was that his power meter was not working correctly. It displayed 409w at 68kg body weight – 6,01w/kg.

Vine already realised that this could not be correct, considering the speed he achieved on this steep 8,49% incline into a headwind, so we calculated his effort. In reality, Jay Vine rode the climb at 6,53w/kg, which is equal to 6,66ᵉw/kg, meaning his power meter under-read by 8%.

Example 2:
Sepp Kuss is one of the few top climbers that always publishes his power numbers. In 2019 he won the Vuelta mountaintop finish Santuario del Acebo, during which his power meter read exceptionally high – 6,48w/kg. Comparing this with the calculation (6,24w/kg), it turns out that his power-meter was over-reading by 3,8%. When questioned about this, Kuss confirmed that he had realised the over-read himself and even switched power-meters after the stage.

In these examples we actually knew the exact weight of the rider prior to the ride, but generally weight is one more factor that can lead to major inaccuracy in w/kg calculation via power meter data. We have already discussed the +/-2% margin of error for the measurement of the absolute power (watts) by the power meter, however the second part of the equation is knowing the accurate weight of the rider when using this methodology.

What makes this even more difficult, even for WorldTour teams, is that weight is something that not only fluctuates throughout the season, but also throughout stage races and even single stages. After a race last season, Filippo Ganna shared that he lost multiple kilograms on a single stage. The weight of lighter riders will obviously fluctuate less in absolute terms, but they too can have significant relative changes over an entire race. A solution may be for teams to weigh riders immediately after a stage, to find out the exact w/kg of the rider on the final climb, but this is likely impractical and potentially psychologically intrusive. Power divided by a rider’s Strava input weight is consequently not reliable either and can lead to inaccuracies of 5% or even 10%.

The unreliability of power meters and lack of available data regarding rider weights therefore necessitates an alternative method for estimating the w/kg of a performance – one which does not require the rider’s weight or power data.

Calculating Etalon W/kg

We have refined a mathematical model to estimate a rider’s w/kg, expanded upon from the work of James Martin et al, and standardised to a 60kg rider. In the model, the three main forces that the cyclist needs to overcome are:

• Gravity
• Aerodynamic Drag
• Rolling resistance

The following are some of the parameters used to calculate these forces:

• Average Speed (km/h)
• Standard Weight (60kg in our case)
• Weight of bike and every other object the cyclist has with him (kg)
• Rolling resistance (crr)
• Approximate CdA (Cd*A / ft2)
• Gradient (%)
• Contemporary Climb Conditions
• Distance (km)
• Drivetrain loss (%)

Additionally, the effect of drafting has to be calculated. This is done with a reduction of the aerodynamic drag, depending on time spent in the draft and quality of the draft – the size of group and the size of the rider that the cyclist drafts will impact draft quality. To increase the reliability of our elevation, distance and wind parameters, it is necessary to use sources such as geographical institutes and weather station data.

Accurate power calculations are also only possible on climbs above 4% gradient, unless the exact CdA of the cyclist throughout the ride is known and their position on the bike is not changed significantly. Small descents during a climb, and longer flat sections, can make calculation more difficult and lead to wrong results. In such cases, only the uphill parts should be calculated.

Of course, our calculations of etalon w/kg remain just that – calculations. Just like the measurement of power by a power meter is subject to a margin of error, so too are any calculations. We do, however, ensure that our calculations are as accurate as possible, through the use of high quality parameter sources, multiple people reviewing the video footage of each performance and using up-to-date information regarding the riders’ bike and equipment weight. Where there are outlier or surprising performances, such as Evenepoel and Vine on Gaustatoppen in the Tour of Norway, the calculation is performed multiple times and all parameter sources are double-checked – as well as looking for alternative parameter sources.

We hope this article provided some useful background information on watts/kg and our calculation process. This season we look forward to developing new metrics to enjoy as cycling fans, taking into account things like altitude and spent kilojoules prior to a climbing performance. If you have any further questions please leave a comment down below.

Author: Gabriel Stróżyk (@NaichacaCycling)

Editor: Patrick Broe (@LanterneRougeYT)