The WattPlan Podcast · Episode 28 · 9 min
What is W prime, and why do I crack twenty watts over threshold?
Next episodes: How should you pace a hilly race? · Durability: what your FTP can't tell you about hour five · Why is my power lower indoors?
Read the transcript
James. Hello, this is the WattPlan Podcast, and I'm James. Dad, day job, the occasional podium, building WattPlan in the gaps, and a reading habit in sports science that my family would describe as a problem. Here's one I've lived. You're on a long climb, just a little over threshold, it feels fine, and ten minutes later the legs simply stop. What is W prime, and why does twenty watts over still finish me? Lyra, our AI research voice, is here, and every study is linked in the show notes.
Lyra. Because twenty watts over is still over. There's a line called critical power, the highest power you can hold without steadily running down a reserve. Above it you're spending from a fixed tank of work called W prime. It doesn't matter how small the overspend is. The tank drains, and when it's empty you slow down whether you like it or not.
James. Critical power. Is that just FTP with a lab coat on?
Lyra. Close enough for everyday riding. Critical power usually sits near FTP, often a touch above it, and you can treat them as the same line. The difference is what comes with it. FTP is one number. The critical power model gives you two, the line and the tank above it.
James. And how big is the tank?
Lyra. Small, which is the surprise. For most riders W prime is somewhere between 10 and 30 kilojoules. Think of critical power as an engine that runs as long as you feed it, and W prime as a battery that only covers what the engine can't. Every second above the line draws on the battery. Every second below puts a little back.
James. Where does this come from? It sounds very tidy.
Lyra. It's old and it's tidy. The first source is a 1965 paper in Ergonomics by Monod and Scherrer. They plotted the power a muscle group could sustain against how long it could sustain it, and got a curve that flattens towards a floor. The floor is critical power. The bend above it is W prime. [1]
James. Right, but nobody rides at one steady power. I'm surging, freewheeling, sprinting for signs.
Lyra. Which is exactly why the next paper matters. The second source is Skiba and colleagues, 2012, in Medicine and Science in Sports and Exercise. Seven people rode one minute hard, thirty seconds easier, over and over until they couldn't. From that they built a way to track the tank second by second. Above critical power it drains, below it refills along a curve, and the refill was faster the further below critical power they eased off. [2]
James. So soft pedalling refills it quicker than just backing off to tempo.
Lyra. Much quicker. And refilling is always slower than spending. You can empty a big chunk in a minute and need several minutes to get it back. That's the bit riders feel but rarely put a number on.
James. Does the model actually work outside a lab though? Really?
Lyra. That was the next test. The third source is a 2014 field study in the International Journal of Sports Physiology and Performance, the same group again. They took power meter files from eight trained triathletes. In the rides where riders said they'd cracked, the modelled tank was all but empty, about half a kilojoule left. [3]
James. And when they didn't crack?
Lyra. The tank never got that low. Even on hard sessions they finished, the lowest point stayed a few kilojoules clear of empty. That's what makes the gauge worth watching. When the model says you're near zero, riders really are near the end.
James. Okay, do my climb for me. Twenty watts over.
Lyra. Take a rider with a critical power of 250 watts and a 20 kilojoule tank. Twenty watts over costs twenty joules a second, so the tank lasts about sixteen and a half minutes. On a short climb, that's fine. On a climb that takes twenty five minutes, it's empty with eight still to go, and the legs make the decision for you.
James. And if that same rider attacks properly?
Lyra. A hundred watts over and the same tank is gone in three minutes and twenty seconds. The time to empty is just what's left in the tank divided by how far over the line you are.
James. Oh, that's brutal. So it's not that I'm weak on long climbs, I'm just overdrawn.
Lyra. Overdrawn is a lovely way to put it. Small gaps take a long time to bite. They still bite.
James. So the answer is never go over threshold on a climb?
Lyra. No, that's the wrong lesson. Spending the tank is what it's for. The aim on a long climb is to reach the top with it nearly empty, rather than to empty it near the bottom. If your time to empty is longer than the climb that's left, you can afford to hold on. If it's shorter, you're over budget, and easing off a little now costs far less than grinding to a halt later.
James. And where can I actually see the tank?
Lyra. In WattPlan's workout player there's a reserve gauge that turns up the first time you go above critical power. It shows what's left as a percentage, and above the line it counts down your time to empty. It also projects where you'll be in two minutes if you hold that power, so you can see the cliff before you reach it.
James. What does it use for my numbers? I've never measured W prime in my life.
Lyra. Your FTP stands in for critical power until you set one, and W prime starts at a middle-of-the-road 20 kilojoules. After a hard ride in the player with efforts above threshold, the app can estimate both from your best efforts between one and twenty minutes, and asks before it applies them. They drive the gauge, the match count and the reserve warnings in Route analysis. Your zones and your plan stay on FTP.
James. Matches. Go on, that's the bit racers love.
Lyra. A match is a distinct dip in the tank. If you race, that's the language for it. In the Premium ride review, an effort above critical power counts as a match if it lasts at least ten seconds and costs at least half a kilojoule. Shorter spikes are pooled together, because lots of little surges add up without any one of them looking like much.
James. And for a racer in the moment, what's the gauge actually telling them?
Lyra. When the next surge is affordable. Sit in at 200 watts instead of 240 and you buy back far more of the tank per minute. Watching it climb between attacks is a better guide than feel, because feel lags behind.
James. What about someone who's new to this and just wants to get up a climb without blowing?
Lyra. If you're new to structured training, keep one idea. A little over your limit isn't solid ground, it's a slow leak. On a long climb, settle in just under what feels sustainable at the bottom, and save anything extra for the top when you can see it.
James. Where does the model let you down?
Lyra. The refill rate is a population average, fitted on a handful of people. Real riders vary a lot, and well trained ones often refill faster than the formula. Heat, low fuel and yesterday's ride all shift it. And at very high power, well above critical power, riders tend to fail sooner than the maths says, because the limit is in the muscle and nerves rather than the tank. Treat it as a guide, not an oracle.
James. Fair. So what's worth doing before my next hard ride?
Lyra. If you train with power, go to Metrics in the app and find W prime and critical power. Untick Keep critical power equal to FTP, tap Estimate from rides, then Use this, then Save W prime settings. It needs hard efforts somewhere between one and twenty minutes in the last ninety days. Then, on your next long climb, watch the time to empty and see how it compares with the climb you've got left.
James. So the engine keeps going, the battery doesn't, and I've been riding up hills overdrawn.
Lyra. And it works for intervals too. Note where the gauge sits at the start of each rep. If it starts lower every time, the rest between reps is too short for the target you've set.
Lyra. The full article and every study we mentioned are on the WattPlan blog, linked in the show notes. And if you've enjoyed this, follow the WattPlan Podcast wherever you're listening, so you don't miss the next one.
James. And if you want a plan built around the time you've actually got, get WattPlan on the App Store or Google Play. Thanks for listening.
Voices produced with ElevenLabs. James's voice is a clone of his own, Lyra is an AI voice, and James reviews every episode.
Most riders have cracked on a climb while holding a power that looked sustainable on paper. Twenty watts over threshold does not feel reckless. Ten minutes later the legs go anyway. The number that accounts for this is W', pronounced "W prime". It is the second half of a two-part model of what a rider can do, and once you can see it, a lot of hard riding stops being a mystery.
Two numbers, one curve
The first number is critical power, or CP. It is the highest power you can hold without steadily running down a reserve. Below it you can keep going for a long time. Above it a clock starts. For most riders CP sits close to FTP, often a little above it, and for everyday purposes you can treat the two as the same line.
The second number is W'. It is the finite amount of work you can do above CP before you have to slow down or stop. It is measured in kilojoules, and for most riders it sits somewhere between 10 and 30 kJ. Newer riders tend to be at the lower end. Punchy riders and experienced racers tend to be at the upper end.
The easiest way to hold both in your head is as an engine and a battery. CP is the engine, and it runs for as long as you feed it. W' is the battery, and it only covers the part above what the engine can manage. Every second above CP draws on it. Every second below CP puts a little back.
W' is often called anaerobic capacity. That is a working name rather than a precise one. It reflects phosphocreatine stores, glycolytic capacity and how much metabolic by-product the muscle can carry, with oxygen kinetics in the mix as well. The label matters less than the behaviour.
Where the idea came from
Monod and Scherrer described the relationship in 1965. They found that when you plot the power a muscle group can sustain against how long it can sustain it, you get a hyperbola. The curve flattens towards a floor, and that floor is CP. The bend in the curve is W'. Written out, total work equals CP multiplied by time, plus W'. Two parameters describe the whole curve, and every best effort you have ever ridden sits somewhere on it.
The balance model
The original model only worked for steady efforts. Real riding is nothing like steady. In 2012 Philip Skiba published a way to track the reserve second by second through variable riding, and called it W' balance, or W'bal. The idea is plain. When power is above CP, W'bal falls by the difference each second. When power is below CP, W'bal recovers towards full along an exponential curve. Field testing in 2014 found that when riders reached exhaustion, the modelled balance sat close to zero. That is the finding that makes the gauge worth watching.
What drains W' and what refills it?
Draining is linear and easy to count. If your CP is 250 W and you ride at 350 W, you spend 100 joules every second. Ride at 270 W and you spend 20 joules a second. The cost is always the gap between your power and your CP, and nothing else.
Refilling is slower and depends on how far below CP you drop. Soft pedalling at 150 W refills faster than tempo at 240 W. The first part of recovery comes quickly, then it tails off, which is why the model uses a curve rather than a straight line. In practice, recovery is always slower than depletion. You can empty a large chunk of W' in a minute and need several minutes to get it back.
Why can twenty watts over threshold still finish you?
Take a rider with a CP of 250 W and a W' of 20 kJ. On a climb at 270 W the gap is only 20 W. That costs 20 joules a second, and 20,000 divided by 20 is 1,000 seconds. Call it sixteen and a half minutes. On a twelve-minute climb that is fine. On a 25-minute climb the reserve is gone with eight minutes still to ride, and the choice is to slow down or to stop.
The same rider attacking at 350 W has 200 seconds, or three minutes and twenty seconds. That is the general rule. Time to exhaustion is W'bal divided by the gap to CP. Small gaps take a long time to bite. They still bite.
Matches
Coaches have talked about "burning a match" for decades, and W'bal gives the phrase a number. A match is a distinct, deep dip in W'bal. In WattPlan's ride review, a match is an effort above CP that lasts at least ten seconds and costs at least half a kilojoule. Brief spikes of a few seconds are pooled as micro-efforts rather than counted one by one, because a dozen four-second surges can add up to several kilojoules without any of them looking like much on its own.
As a rough guide, matches come in sizes. A small one costs 1.5 to 3 kJ and you recover quickly. A medium one costs 3 to 6 kJ. A large one costs 6 to 10 kJ and you feel it for a while. Anything over 10 kJ is most of the tank. The total W' expended across a ride is the real metric. Matches are the picture that makes it readable.
Pacing with the gauge
On a long climb, as in any paced effort, the aim is to reach the top with the battery nearly empty rather than to empty it near the bottom. If the time-to-exhaustion reading is shorter than the climb you have left, you are over budget and need to ease off. If the number is falling slowly and the top is in sight, hold what you have.
For repeated attacks, each surge is a match, and the refill rate tells you when the next one is affordable. Sitting in at 200 W buys back far more per minute than sitting in at 240 W. Watching the balance climb between efforts is a better guide to when you can go again than how you feel, because feel usually lags.
For interval workouts, note where W'bal sits at the start of each rep. If it starts lower every time, the rest between reps is too short for the target you have set.
Where the model falls short
The recovery rate in the model is a population average. Individual riders vary a good deal, and well-trained riders often refill faster than the standard formula says. Heat, low glycogen, a hard ride yesterday and the state of your legs on the day all shift it. At very high intensities, well over 150% of CP, riders tend to fail earlier than the maths predicts, because the limit is neuromuscular rather than metabolic.
So treat W'bal as a guide and not an oracle. Calibrate CP and W' with proper efforts when you can, ideally a three-minute and a twelve-minute all-out ride, or let WattPlan estimate them from your rides. Then watch how your own balance behaves over a few hard rides. Once you know your own refill pattern, the gauge stops being the textbook's and becomes yours.
How WattPlan handles this
The workout player shows W'bal as a percentage with a colour band, a time to exhaustion when you are above threshold, and a time to recover to 80% when you are below it. A two-minute projection on the gauge shows where the balance is heading if you hold your current power. After the ride, the ride review lists each match with the energy it cost. The live gauge in the player is free. The match analysis in the ride review is part of Premium.
Sources
- The Work Capacity of a Synergic Muscular Group, Ergonomics
- Modeling the Expenditure and Reconstitution of Work Capacity above Critical Power, Medicine & Science in Sports & Exercise
- Validation of a Novel Intermittent W' Model for Cycling Using Field Data, International Journal of Sports Physiology and Performance
- The Reliability of 4-Minute and 20-Minute Time Trials and Their Relationships to Functional Threshold Power in Trained Cyclists, International Journal of Sports Physiology and Performance