FTP test maths musings

I know in times of ML and AT FTP tests are out, but here goes anyway. While my brain was frantically looking for a way out of the self-inflicted 20 min hell, I realised that you should be able to calculate if the 20 min test is actually possible to finish if you have previous power data.

The thing with all short-form FTP tests is that you have to ride over FTP for at least some of the test time. If you ride over FTP, you are burning through your anaerobic capacity (FRC). If this isn’t enough to last you for the duration of the FTP test, you can’t finish, or at least you will fall somewhat short of your real FTP.

In the case of the 20-min test, this is fairly easy to calculate. The resulting FTP value is calculated as 95% of the average over over 20 minutes. Thus, you have to ride at just over 105% of you FTP to keep it at the same value (and obviously more if you want an FTP increase). Which means that you need to have an FRC (in kJ = 1000 Ws) of at least 5% of your FTP for 20 minutes, which is 1200 seconds. Or, in maths: FTP x 0.05 x (20 x 60)s 7 1000 = FTP(in W) x 0.06s. The factor 1/1000 comes in to convert from J to kJ.
For an FTP of 200W, this means an FRC of at least 12kJ, if your FTP is 300W, you already need 18kJ.

Similarly for the 8-minute test. Typically 90% of the average power are taken as the FTP, which means you need to ride 11% over FTP, but only for 480 seconds. Thus: FTP x 0.11 x 480s/1000. Interestingly this results in 10.56 kJ for a 200W FTP, and 15.84 kJ at 300W FTP.
The FRC needed is considerably less for the 8-minute test, which is likely why that test has a reputation for being unreliable (strong riders overtest), and variations wit “anaerobic blowouts” exist. However, for those with relatively low anaerobic capacity, it might actually be a good choice?

The ramp test is a bit more complicated because the percentage over FTP changes with every step, and the total FRC needed is a cumulative product, so I*ve made a table:


Min - is the minute step in the TR ramp test (might be off by one?)
Step %FTP - is the power of that step as a factor of FTP
result FTP% - the resulting FTP (as factor of current FTP), if only that minute is completed
factor t - the multiplicand to calculate work over FTP
cFRC (200W) and cFRC (300W) are examples of the cumulative FRC needed to complete that step, for example FTPs of 200W and 300W

As you can see, the FRC needed to complete the magic 19.5 minute is roughly similar to that of the 20 minute test (coincidence, or by design?). However, with the ramp test, each extra minute needs progressively more work over FTP. With the 20 minute test, each extra minute takes exactly the same amount of energy. This is probably why the ramp test seems to give more anaerobic riders too high an FTP, and those with less FRC can’t seem to reach their actual FTP. We knew that beforehand obviously, but I found it interesting to work out some numbers which you can use to get an estimate of what you should be able to do.

I do think that there is more that is going on, and more that is needed to complete a successful FTP test. For example, some sort of aerobic capability and muscular endurance is needed, otherwise you won’t make it to those last minutes. And track sprinters would have amazing FTPs.

…how we spend our Friday nights, eh…


Aaaah! Interesting observation.

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I switched to KM baseline test. For some reason, I find it way easier mentally. I even could say that I enjoy it as a workout.

I usually do 40-45 minutes before I call it quits.


Yep, I would usually do that to. But I needed a 20min number.

I couldn’t quite bring myself to work out what impact it has if you save your FRC for a final ramp up (how long?) in a KM-style test. Someone else can do that, lol.

Personally, I never try to game the KM test with an all out effort at the end. By the end, I know that I’m over my threshold. I’d rather have a solid, conservative number.

Your ability to do mental math / deeper thinking under pressure is impressive. I’m usually trying to figure out when I can celebrate having 1/7 th left or some such.

Thanks for the ramp test math, I was too lazy to do it but have done the math for other efforts.

The best way to find your ftp, in my humble opinion, is to actually go out and find it by riding at ftp. Short tests over threshold are just rough approximations, and influenced by anaerobic capacity and ability to pace. And the 95% multiplier isn’t a fixed multiplier, it was originally given as an example. FasCat Coaching uses a 90-95% multiplier on the 20-min test, depending on your anaerobic abilities.


Impressive that you did all this math during an FTP test :rofl:

I reduce the result of the ramp test by 5%. And even with that number, my TTE is probably not a whole lot more than 30 mins. Definitely nowhere near 60 mins. My physiology is very skewed towards sprinter vs endurance athlete.

Very interesting mental excercise, isn’t it quite similar to the Skiba model?

My dumb brain always needs an analogy and the one I came up with is boiling water in a kettle. The size of the kettle is your VO2max. Water is your anaerobic capacity. Temperature is work. Below the boiling point the water volume will not change much, once you get close to it the water starts to evaporate quickly. When the kettle is empty it burns.

The rate of evaporation at different temperatures is basically the CP - the warmer, the faster it evaporates but only above the boiling point the depletion speeds up dramatically.

Now the problem with all kinds of FTP estimation methods is that we know the evaporation rate of water at different temperatures, but each rider’s kettle size is different and is an estimate and on top of that we’re never sure how much water is in it. So that’s an equation with 3 variables, 2 of which are estimates.

Of course, there isn’t anything original in my model. I just worked out how big a kettle you need to complete each type of test. Or, wirh the ramp test, how far it gets you.

The interesting thing to me is that if you know your FRC (the size of the kettle), from maybe intervals.icu, or Golden Cheetah or WKO (anything that models the power durarion curve), you can estimate if you are likely to over- or undertest on any of the short-form FTP tests.

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And nu design you should first do an “all-out” 5’ effort

Nice math for all the tests, I enjoyed this :+1: do you mean by “if the test can be completed”, can you hold a certain W for that time?

Still some noticeable differences between the 8 and 20min test, right? 18 vs 15.8 at 300W.

I think the FRC can be estimated (WKO?), how are those estimates done and are they robust?

I think if you run out of FRC during the 20 min test (for example), you can’t continue to ride over FTP, and have to drop to FTP or below. As the test takes 95% of your average, riding at FTP for it means the new FTP will be lower. (Also running out of FRC for me is the crack point, and it takes an emormous amount if willpower to not just give up completely.)

Yes. Which is why riders with more power likely over-estimate using the 8-min test. A lot of the 8min test protocols also have you do some sort of high-intensity “blowout” before, to reduce the available FRC. However I think if you have below-average FRC (a pure TTer, for example, or just somebody weaker), using that test might be better, as you can actually ride above FTP for that duration. (Or use the long-form KM test, where you don’t have to ride over FTP at all).

Worth noting that FTP and FRC are not neccessarily linked, but I think average riders with a high FTP also tend to have a higher FRC. These 12kJ at 200W and 18kJ at 300W seem not unreasonable to me, from the little data I have seen. If someone is a strong sprinter type, they will have higher FRC, a strong diesel type, lower FRC.

AFAIK it is one of the fitting parameters for the power-duration curve. Better data in your curve makes for a better estimate? Pretty sure that the estimate is often a bit on the low side, at least I manage to dip into negative W’ on intervals.icu now and then. (I actually think that FRC balances with FTP, and if one estimate is too high, the other is too low, but I haven’t actually looked at the model parameters to see if that is true)

So bigger frc, bigger ftp. I think you’re on the cusp of an epiphany

I’ve found the ramp test over-estimates more than the 20 min test.

In your analysis for the 20 min test, did you account for the above-threshold intervals before the main test?

No, I didn’t pick a specific 20-min test like the TR test. Just the 20 min interval. Same for the 8-min test, I mention that there.

I don’t think its quite as easy to do this if there are above-threshold intervals before the main block. You could calculate how much FRC that uses, but then there’s recovery in between, and the recovery kinetics are more complicated I think.

Think you’re right about the ramp test overestimating more than the 20-min test. I think maybe because lasting an extra minute makes quite a difference, whereas if you punch out a high-power last minute in the 20-min test, the impact on FTP is quite small.

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The Hunter Allen (?) protocol a 5-minute blowout effort followed by a maximum 20 minute effort, right?

What I don’t understand is why not just add a 30-40 minute break between the 5 and 20 minute max efforts and use that to estimate CP and be done with it.

But the calculation on how fast it replenishes is fuzzy at best.

Hunter Allen’s words:

”Now the real test begins.

  1. Ride 5 minutes all out. Punch it and hold it! Start at a high pace, but not so high that you die at the end. You should have a little energy held in reserve to kick it toward the finish line in the last minute.

The goal of this first part of the effort is twofold: first, to open up the legs for the rest of the test, and second, to measure your ability to produce watts in the VO2max power zone. This initial 5-minute effort also helps to dispense the “freshness” that always exists at the beginning of a ride; your next effort will produce power that is more likely to be truly representative of your FTP. “

If you are strong enough to do 5 and 20 min TTs at near maximal, in the same test, then sure those would be two good data points for CP estimate. Or take a longer rest between, even if that pushes the second test out a couple days.

That is literally the second part of the sentence you quoted :laughing:

Its interesting though. I feel like even if you allow enough time for “full” recovery, a hard “blow-out” before the main work has an impact. It’s not in the model though.

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