top of page

What is W' (W-Prime) - FKA Anaerobic Work Capacity?


How much is too much when the exercise intensity is above your critical power (CP)? What's the actual cause of this sudden onset of fatigue when they go above CP? Obviously there are a number of variables that influence the amount of time or power you can hold above CP.



However, in most cases it involves something called the W’ (pronounced “W prime”), and it is the subject of a scientific paper which you can now read in Medicine and Science in Sports And Exercise.


It is important for you to understand the difference between work and work rate. Work is how much exercise you do. Work rate is speed you do it. For example to run a mile would be classed as work, but we don't know the speed or intensity. However, you may have run it at 5 minutes per mile (CP) or 10 minutes per mile (endurance pace). In other words, you can think of the distance as the work, and the speed you do it at as the work rate. With regards to cycling, work is equal to joules. Power expressed as wattage is equal to joules per second. (1 watt is simply equal to 1 joule per second. If you are riding at 200 watts, you are spending 200 joules per second.)


Once you go above CP, the amount of additional work you can do becomes fixed. This amount of additional work is called the W’ (formerly known as the ‘anaerobic work capacity’, or AWC). You can use it quickly (by going really hard), or you can use it more slowly (by limiting your surges above CP), but either way, once you use it all up you are going to have to slow down, or maybe even stop. You won’t be able to get above CP again until you take some recovery. Think of pacemakers in running and cycling, leading out their teammates to the point when they literally come to a standstill.


Michal Kwiatkowski stops for a rest after riding himself into the ground for Chris Froome on the Col D'Izoard 2017 - Tour De France


A good way of thinking about it is like this: Imagine you unplug your mobile and start using it to do your Zwift workout (something i did this weekend!). The battery starts running down. So, you plug it back in and it starts to recharge. Now, it doesn’t charge right away…it takes a little while. How fast the recharge happens depends on how much you keep using it. In my case i had another 40 minutes to go so the charge was very slowly topping up the battery whilst i was still using the phone. Had i turned the screen off, closed background apps etc it will recharge much more quickly.


We can use the performance metrics established through the INSCYD PPD testing to define a cyclists CP. If i prescribe intervals above CP by a fixed amount (e.g. unplug the phone and start using it a lot), they will start to use up W'. Rather than ride through to exhaustion we include a predetermined recovery period. This will could be in their optimal lactate combustion range (e.g. to recharge the battery a little). We don't want the rider to fully recover so they repeat, over and over again until they had to quit (e.g. they ran the battery down to zero and the phone shut off). You can use the INSCYD PPD results to experiment at different intensity and recovery power levels. What we wanted to find out was how quickly the athletes recharged their W’, and if recovery was dependent upon how hard or easy the recovery is. We formulated a model based on calculus which allowed us to calculate the speed of the recharge.


What we found was that when athletes dropped their power far below CP during recovery (e.g. rode at 20W, or just used the phone a little) they recharged their W’ at a particular speed. In contrast, when they recovered at a harder power output (e.g. rode at 100W, or kept using the phone a lot), they recovered much more slowly. It turns out that the relationship is defined by the difference between CP and the recovery power. Thus, a person with a CP of 300W will recover more quickly when they drop to 20W than a person with a CP of 200W. In the former case, the person is recovering 280W below CP. In the latter case, the person is recovering only 180W below CP. This helps explain why great athletes seem to recover so quickly.


In 2012 Skiba et al, sought to model W’ use during bouts above Critical Power (roughly equivalent to the functional threshold power you likely have heard about – the power you can sustain for about an hour*), followed by recovery at different workloads. Each effort involved a 60 s hard interval followed by a 30 s recovery interval, with each recovery phase at a different intensity ranging from easy (20 Watts) to moderate, then hard, then severe.


They established a few notable observations:


• The absolute size of W’ in their subjects ranged between 14 and 28 Kilojoules, with a mean of 21 Kj. Recall that a Kilojoule is simply a thousand joules, and a joule is equal to watts x seconds (J= W x s). So when you are doing 333W for 3 seconds you’ve used 999 joules, or roughly 1 Kj! That’s not a very big basket, about a minute all-out!


• They affirmed that W’ began to be immediately depleted once power rose above Critical Power and that reconstitution of W’ did not start until subject power was under CP.


• The time of reconstitution (Tw) was impacted by the intensity of the recovery. Indeed at the 20W recovery level, reconstitution ranged between 370-380 seconds, while it was 452 seconds for the “medium” recovery effort and averaged 580 seconds for the “hard” recovery interval. The “severe” recovery constant averaged over 7000 s, indicating no W’ reconstitution within the 30 s recovery phase of the trial.


To give you some ballpark figures, let’s take a pretty average athlete with a CP around 220W who has completely used up their W’. Assuming recovery at 20W, it will take them roughly 380s to recover about 60% of their W’. To totally recharge the W’, the athlete will have to crawl along at 20W for about a half hour! Now imagine that same athlete is trying to recover at around 150-175W. It may take them much, much longer!


This is the reason why doing a lot of surges above CP (i.e. ‘burning matches’ in cycling parlance) is such a bad idea. You are using up precious W’, and W’ takes a VERY long time to recharge. For triathletes, if you come into T2 with a low “W’ balance” remaining in the tank, you are going to feel terrible and run quite poorly. For cyclists, if you come into the final 1-2k of a race with a low W’, you won’t be able to make the final break or be a contender in the final sprint.


Hopefully, the above examples should at least give you some practical ideas for how to better pace your training and racing.


Co-authors Prof. Andy Jones, Dr. Anni Vanhatalo, and Weerapong ‘Tony’ Chidnok at the University of Exeter for their assistance with this work.

bottom of page