What is W Prime?

Watts Prime (W’) is also often referred to as a person’s anaerobic capacity (AC) – your reserve or ‘battery’ – and is measured in joules (J) or kilojoules (KJ). It is used as a template on which to base how long a certain wattage above Critical Power (CP) can be sustained for, and how long it takes (in theory) for the battery to be recharged. 

NB: CP can be used as the critical power for a certain time (e.g. CP5min & CP20min) but for the purposes of this article it is determined as the maximal sustainable wattage for extended (>60min) durations. Theoretically it can be sustained indefinitely but many other thresholds come into play during this (neuromuscular, substrate utilisation and heat for example).

There are two common ways of determining someone’s W’, with both methods also requiring CP testing. 

The first is the 3 minute test: this consists of 3 minutes at absolute maximal effort from the off, so starting with a sprint. The aim is to drain the W’ by the 2 minute 30 second mark. At that point, the theory is that you cannot sustain power above CP, so the average power for the last 30 seconds should be your CP measurement. Then, for the first 2 minutes 30 seconds, the work done (J) above CP is determined as your W’. This test can be tricky to do reliably and requires the athlete to fully empty the tank early in the effort. 

Another method is the 3 and 12 minute power test: this requires the athlete to complete a 3 and 12 minute paced time trial where they should feel spent and empty by the end of each effort. Between each effort is 40 minutes of very low intensity to fully recharge the W’. Using these results and a formula to determine the power curve, CP can be derived as well as the W’. An example graph below shows the W’ in the shaded area – note how the volume of the blocks is the same.

A power curve showing both the CP and the W’ battery (represented by the red blocks)

The reason W’ can be useful for both athletes and coaches is that it provides not only a way of measuring improvement for repeated efforts capacity and anaerobic efforts, but also a means of determining the number of efforts that can be performed in training before failure. This table from an Excel sheet shows how the CP, W’, wattage for the effort, the length of the effort in seconds, the wattage for recovery and length of recovery can all be used to determine how many repeats can happen before failure of the effort (W’ reaches 0 J). 

An example of how CP and W’ work together: A rider has a CP of 300W, a W’ of 20000J and is riding at 400W (100W above CP). So, 20000 (W’) divided by 100 (W above CP) = 200 seconds, the length at which the rider can theoretically sustain 400W. If then riding at 200W for 200s, the W’ should be replenished. 

As you can see, come effort number 5, the W’ should be depleted. Even after the recovery period, W’ is not replenished enough to complete the next effort fully

Having a high W’ is a trait commonly seen in successful CX and crit riders. If the battery is greater, then the rider can perform a greater number of short attacks or sustain a power above CP for longer. Additionally, they can do more repeated AC efforts, which is very useful in races where pace is variable. However, if a rider improves their CP through training, they may find their W’ value dropping. This isn’t necessarily a bad thing though, as a higher CP means that a higher wattage needs to be reached before the W’ starts to drain, and a higher power can be sustained while still recovering the W’.

CX is a discipline where a large W’ is particularly useful

However, W’ and CP do have their limitations. Firstly, a rider’s pain tolerance/threshold can make the 3min test difficult to conduct, as burying themselves that deep and subjecting themselves to pain like that so quickly can often lead to a rider backing off from the effort. In the same way, CP may be 300W but a rider would struggle massively to hold that for, say, 120 minutes. There are also other thresholds at play for both short term AC efforts and longer duration sustained ones. Heat, neuromuscular fatigue and substrate availability all affect a rider’s ability to perform and maintain/put out the theorised wattage that W’ and CP testing assumes possible. However, even with day-to-day variances in personal performance and variances in equipment measurements, W’ and CP still present a useful testing tool for athletes and coaches. The results can be used to programme training sessions that will benefit a rider by progressing them towards their chosen goals, whether that be improving race results, getting more out of club runs or moving up the local KOM rankings. 

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