What does it mean to burn a match?
You'll hear this a lot in cycling commentary but what is actually burning a match? Is it used up forever and do we all have the same number of matches?
Burning a match is what riders say about an effort that costs you something you can’t get back inside the same ride unless you really take it easy, and underneath the phrase is the critical power model. Basically you have some power number personally where if you go above it you'll start draining your anaerobic battery. That critical power (CP) is the wattage the power-duration curve flattens out toward, and W′ is a fixed number of joules you get to spend above CP at whatever rate you like. The thing that made it click for me is that W′ behaves less like a battery and more like a supercapacitor, since it dumps an enormous amount of power for a short time and then takes ages to charge back up. Riding 380W against a CP of 250W is 130 joules a second coming out of a tank of roughly twenty thousand. But riding at 300W is only 50 joules a second coming out of the tank. You'll hear often that "smooth is fast" - not spiking too high above your threshold is key, dumping a 900W effort for 10 seconds is a huge W' drain whereas if you can accomplish the same move at 400W for longer you'll end up burning fewer matches.
The animation is trying to show that the refill is way slower than the drain, and if you don't have the luxury of riding easier then it may not refill at all. Skiba’s W′bal model fits the recharge as an exponential whose time constant gets longer the closer your recovery wattage sits to CP, around 377 seconds when you’re soft pedaling at 20W and nearer 580 seconds when the recovery is still up in the heavy domain. So you're truly burning a match from a semi-fixed matchbook.
Where this comes from
The two-parameter model is Monod and Scherrer’s from 1965, and the modern version most people quote is Vanhatalo, Jones and Burnley. They put the typical W′ under 15 kJ for endurance-trained cyclists and over 25 kJ for sprint-trained ones, which is where the 15 to 25 kJ range you see everywhere comes from and why I put 20 kJ in the picture above. The recharge numbers are Skiba’s, reported by Jones. And CP is not FTP, they usually come out within a few percent of each other and they correlate strongly, but they are defined differently and the literature is fairly clear that the two shouldn’t be swapped in for one another.