W Prime or W’
W Prime (Work Prime/W’), often referred to as the Anaerobic Capacity/Battery/Reserve, is the amount of work you are able to do above your Critical Power (CP) and is measured in joules (J) or kilojoules (KJ). It can be used as a template on which to base how long a certain wattage above CP can be sustained for, and how long it takes (in theory) for the battery to be recharged, when using the W’bal model.
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 (>35min) durations. Theoretically it can be sustained indefinitely but many other thresholds come into play during this (neuromuscular, substrate utilisation and heat for example).
In practice CP is sustainable for 35-60min depending on the athlete and conditions. It is also used to refer to the transition point between Heavy and Severe Domains of exercise intensity using the 3 or 4 Domain Model (D1 – Moderate up to LT, D2 – Heavy LT up to CP, D3 – Severe Above CP, D4 – Extreme such as sprints).
There are two common ways of determining someone’s Work Prime, with both methods requiring CP testing.
The first is the 3 minute all-out 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 Prime by the 2 minute 30 second mark. At that point, the theory is that you cannot sustain power above CP since the W Prime is drained, 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 or KJ) above CP is determined as your W Prime. This test can be tricky to do reliably and requires the athlete to fully empty the tank early in the effort, more often than not athletes will pace themselves a bit and have a small reserve for the final 30 sec of the test.
Another method of testing Critical Power and W Prime is using multiple maximal power tests (usually 2-3 efforts) over durations generally between 3 to 20 minutes to create a PD curve. The 3 and 12 minute power test is a commonly used variant and has been shown in literature to be accurate.
This test 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, so unable to surge at the end. Between each effort is 40 minutes of very low intensity to fully recharge the W Prime.
Using these results and a couple of formula to determine the power curve, CP can be derived as well as the W Prime. An example graph below shows the W Prime in the shaded area – note how the volume of the blocks is the same with the duration inversely linked to the power.
So with a 3min power of 400 W, a 12min of 325 W, we get a CP of 300 and a W’ of 18000 J. This means that for 5min the athlete can theoretically sustain 360 W. This is because 1 W = 1 J/s, so at 60 W above CP it takes 300s (5min) to drain that 18000 J. Likewise for 20min (1800s), power is 315 W (18000/15 = 1200).
The reason W Prime can be useful for both athletes and coaches is that it provides not only a way of measuring improvement in proposed repeated efforts capacity or predicting PD for shorter, sharper 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 Prime reaches 0 J). This is the W’bal model and can be useful for prescribing say 40/20 intervals to suit each individual rider.
An example of how CP and W Prime work together using the W’bal model for interval prescription: 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.
However, it should be considered that the W’bal model becomes less accurate the more repeated efforts there are, or after higher workloads are completed. This is because the fatigue generated by repeated efforts or higher workloads can reduce the CP and W Prime thus altering the model significantly.
Having a high W Prime 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 short, sharp efforts, which is very useful in races where pace is variable. It can also be useful for a rider who may not see an increase in CP, but an increase in W’ may mean they can sustain higher power outputs for durations up to 35min, which depending on their target events, may be more beneficial.
Additionally, 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’.
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, 60 minutes. In fact some studies have found that CP is only sustainable for ~35 minutes in the majority of athletes.
There are also other thresholds at play for both short term glycolytic or phosphocreatine efforts, and longer duration sustained ones. Heat, psychological toll, central and peripheral 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.
For those wanting to know their Critical Power and Watts Prime, we do testing for that for both our coached athletes and anyone just wanting to accurately determine their own power zones and physiological boundaries. You can find out more here.
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