There are already all sorts of ways of *estimating* FTP; I'm not sure why you think the world needs another one.

I'm asking for a rigorous definition of it, not another way of estimating it. I've looked back at your posts in this thread and can't see a rigorous definition of FTP. Your post about changes in time for changes in power suggested you saw those sorts of relationships as defining the concept, but if they don't define it, what does define it (rigorously)?

As I have said many times before, I consider FTP akin to a population variance, i.e., ultimately unknowable, yet estimable with reasonable precision.

Because FTP is ultimately unknowable (due to biological and technological variability), calls such as yours for a "rigorous definition" are IMO misguided.

(Quoting myself from 2002 or so: "probably the easiest and most direct way of estimating a rider’s functional threshold power is therefore to simply measure their average power during a ~40 km (50-70 min) TT. This highly pragmatic approach is justified by laboratory research showing that the power a cyclist can generate for 60 min correlates very highly with, but is slightly greater than, their power at LT (defined as a 1 mmol/L increase in blood lactate over exercise baseline) (2). The precise value obtained for threshold power using this approach may vary slightly depending on the exact distance/duration of the TT, the terrain, the athlete’s level of motivation and ability to pace themselves properly, etc. However, such variability is likely to be small relative to the breadth of the defined training levels and the somewhat arbitrary division between them. Furthermore, the simplicity of the approach means that the test (which doubles as a level 4 training session) can readily be repeated if the data obtained are considered suspect, or if there is reason to believe that the athlete’s fitness has changed significantly. If for some reason (e.g., phase of training) it is considered undesirable to have the athlete perform a full 40 km TT, data from a shorter TT can be used instead, although
this may require slight adjustment of the exact percentages of threshold power for each level and/or application of an appropriate correction factor (e.g., threshold power = average power during a 20 km TT multiplied by 0.93). Again, however, given the breadth of the specified power levels, day-to-day variability in performance, and individual differences in the precise shape of the power-duration curve, the real effect of employing such a correction factor may simply be to convey a false sense of precision. ")

All you have to do is look at how the plethora of "rigorous definitions" of LT to see how trying to paint things that are really grey only in shades of black and white fails to further insight and understanding.

The same can be said when you widen your perspective to consider other physiological responses at "threshold". That is, it really doesn't help to rigorously define, say, MLSS and the NIRS breakpoint using exact criteria, when they only agree on average, and not exactly in every individual.

I've read this thread and have no idea what ftp is supposed to be, still only what it isn't. The mental masturbation of academics makes it way more complicated than it needs to be.

I hate to be the bearer of bad news, but life is complicated.

Why do we need certainty?

Use power number(s) to train and race to.

Ultimately if you cannot hold a given number of watts over a given duration, it doesn’t matter if you have the formula right. Maybe you didn’t physically have it, mentally have it or your PM malfunctioned on the day.

On another note, there is no guarantee that you will respond the same way to training at a % of FTP as the average person. Maybe you respond better or worse.

Train at different levels of power, some lower for longer and some higher for shorter. Overtime you will get to train faster and race faster.

I think the more you train and study training the less certainty you require.

JFT

...steps off soapbox

[quote

Alternatively, you could just ask yourself, "how long can CP be maintained?", and realize that the answer to that question (i.e., 30 to 70 min, and longer in trained than in untrained subjects) also matches up with FTP.[/quote]

That's an interesting point, as the literature has not shown much (anything?) in the way of CP tolerance >40mins; hence I had always considered CP to be a touch higher than FTP.

Of course, you are at the mercy of error of determination in the first place when training to nail such a threshold (i.e. get it slightly too high and tolerance plummets).

I am also interested in your position of FTP being more a notion, than having a fixed definition. Maybe we should call it "HP" (hour-power)!? Presumably your reluctance to nail FTP as average hour power is due to inter-individual variation in the ability to sustain MLSS/Dmax/VT2 (particularly in relation to training status)?

If I can probe your opinions further, I am also interested where you stand on the "3min all-out" test?

Well that is all i do, it’s a number i plug in to trainer road to set up training paces.

I just find it a bit funny that Andy can always define what ftp isn’t pretty clearly, but can’t clearly define what it actually is, it’s just an abstract concept.

So do we need a new term for 95% of a 20min test ? Then we can say ftp is dead, or change the name to functional test power.

Up to 60 min, with an average of 43 +/- 4 min, but in recreationally-active, not trained, subjects:

https://www.ncbi.nlm.nih.gov/pubmed/9923729

"Hour power" is what Ed went to after I left UT-Austin:

https://www.ncbi.nlm.nih.gov/pubmed/1997818

Before that, we used time-to-fatigue at ~90% of VO2max, which for the top 5 or 6 subjects, was maintained long enough to consider it to be FTP:

https://www.ncbi.nlm.nih.gov/pubmed/3403447

As you say, though, the problem with defining FTP as exactly 60.000............ min power is that it ignores the fact that time-to-fatigue is variable.

The very first time I heard about the all-out 3 min test, I knew that it would often overestimate CP in trained cyclists, and said as much on the wattage list. Experiments have since shown this to be true, e.g.:

https://www.ncbi.nlm.nih.gov/pubmed/24022575

Why? On average, it provides an accurate estimate of FTP.

I think you guys are missing the entire point. Your FTP, your own, may actually be a precise number. It could even be precisely 95% of your 20-minute power on a given day. But because of all the individual variability, as very thoroughly and repeatedly explained by Dr. Coggan, it is impossible to pin it to a given formula precisely for everybody. Your FTP is not the same concept as Everybody In The World's FTP, in other words.

That's why, when pressed, Dr. Coggan keeps going back to "well, you can estimate it", and that doesn't mean that IT is imprecisely defined, it just means that FTP is a complex concept representing so many factors that it's a bit fuzzy for populations of sizes greater than one: so yes, you're right, it IS an abstract concept. And that is OK, and it doesn't matter if everybody switched to 20-minute TT power, either: for the exact same reasons it would be a bit squishy. Some people would be able to hold 102% of CP20, others 107%, for an hour, and it would therefore be just as imprecise as FTP. I mean, seriously, do a 20-minute all-out test once a month for a year and tell me that your very own results reflect any kind of consistency or repeatability to the degree you are demanding come from FTP (the concept)......

Does that clear it up a bit?

-Eric

This thread started with Trev saying he can't see a threshold in people's power duration curves. You then showed some curves and said they exhibit a threshold because of the relationship they show between time and power, but when asked to make the statement of the relationship rigorous, you're unwilling to do so. So it's easy to see why Trev might struggle to see something in the curves if what he's looking for cannot be defined for him to satisfy himself whether the curves show it or not. Population variance has a rigorous definition.

In terms of the relationship you stated, where you said that reducing 60 minute power by 5% gives a power that can be sustained for around 2 hours, whereas adding 5% to 60 minute power gives a power that can only be sustained for around 20 minutes, I disagree with that. 5% less power being sustainable for 2 hours sounds roughly correct, but I can manage significantly more than 5% more power for 20 minutes, and given that you've said the average relationship is 20 minute power = 0.93x 60 minute power, I'd say many other people can as well. If I had to guess at how long I could sustain 5% more than my 60 minute power for, I'd guess at around 30 mins, i.e. the relationship seems approximately symmetrical, with a 5% increase in power dividing TTE by 2, and a 5% reduction in power multiplying TTE by 2, rather than the asymmetrical relationship that you described.

Coggan has explained that on average those numbers are a good rough guide, he didn't say that you or anybody you know were a perfect example of average.
I don't get why you are trying to pin down an average of tested population to be your own.
It might be,it might not be.
In a really crude statistical analysis, half the people will be too high and half will be too low.
Why do you keep asking for precision of averages to apply to individual persons?

My own figures do match the average he has given of 0.93 * 20 minute power for 60 minute power. The problem is this doesn't match his statement that if you increase 60 minute power by 5%, you reduce TTE to 20 mins. The latter statement implies a ratio of 0.952x not 0.93x.

The reason this matters is that Trev started this thread with a post that included this statement:
"But after approximately 60 minutes, when power has dropped below FTP, wattage continues to fall at approximately the same rate as it did from approximately 20 minutes to approximately 60 minutes"

If the ratio is 0.93x, it supports Trev's claim. If it's 0.952x, it supports Andy's claim. Andy has said it's 0.93x in several places over the years.

How did you get from '~' and 'a couple' to calculating ratios to the third decimal point?

Never mind, the mere fact that you made that cosmic leap demonstrates the problem with your thinking.

"a 5% increase in power dividing TTE by 2, and a 5% reduction in power multiplying TTE by 2"

Plot these X,Y pairs, then show your work:

0.5 1.05
1.0 1.0
2.0 0.95

(Hint: you won't get a straight line.)

I was responding to your statement:
"Not necessarily obvious from the figure, but going just ~5% over FTP means that fatigue will occur after only 20 min (hence Hunter's way of *estimating* FTP).
In contrast, a power output that is just ~5% under FTP can be maintained for a couple of hours."

I thought what you were saying is that one multiplies TTE by 2, and the other divides it by 3, and the fact that these two numbers are different is the reason why it can be regarded as a threshold. So I was saying the 0.93x ratio you've stated suggests the numbers aren't so different. But as you won't rigorously define what constitutes a threshold in the power duration curve, it's hard to know exactly what you're claiming.

Hey, Andy...

Welcome back to Slowtwitch. We've missed you. Mostly. I think. :)

It helps to start with what the concept of "Threshold" is. We can get to the Functional and Power bits later.

Threshold is the maximal exercise intensity sustainable such that various (relevant) physiological responses firstly attain and can maintain a quasi steady state. One example of such a physiological response is blood lactate concentration but there are others such as tissue oxygenation levels.

Naturally these physiological responses will also attain/maintain a quasi steady state at exercise intensities below threshold.

However once the exercise intensity exceeds threshold these physiological responses no longer maintain a quasi steady state. That's because the energy demand is increasingly supplemented by non-sustainable capacity-limited energy supply sources (e.g. via anaerobic metabolism) and these supplemental metabolic processes result in more rapid changes in physiological markers (e.g. blood lactate utilisation/clearance can no longer keep up with production and so BL levels rise rapidly).

Hence the term "Threshold".

Essentially it's a conceptual expression of an intrinsic physiological capability, the maximal sustainable exercise intensity before non-sustainable physiological/metabolic processes begin to manifest themselves in a significant manner.

FTP expresses this threshold intensity in terms of Power output at the bicycle cranks.

The "Functional" part is simply to emphasise it's purpose is to be a practically useful marker of this intrinsic physiological capability. So rather than be bogged down with all the underlying physiological/biological/metabolic complexity, we can express this intrinsic physiological capability in one relatively simple and useful term - FTP.

The functionality is of course enhanced by the relatively straightforward ability by just about anyone to measure one's power output on a bicycle, whereas the various physiological responses typically measured in labs are somewhat less practical for the regular athlete to measure. FTP has the added advantage of being an integral of all of the underlying physiological factors that determine this "threshold".

So that's FTP.

There are of course various ways in which one can arrive at an estimate of FTP, some more reliable than others and these are often discussed.

---

http://www.cyclecoach.com
http://www.aerocoach.com.au

+1 - this is the proper explanation of what I was trying to say.

Its been shown on wattage (and not disputed) that the threshold is not identifiable from power data in the region 20 to 120 minutes. Which is all that Trev is saying.

How that makes him a troll is beyond me.

To calculate the threshold you need a model which proposes its existence and uses short duration efforts to find it. i.e. even though it exists usually between 45 and 60 minutes, and you have data from 20 to 120 minutes, that would not be sufficient to calculate it, you need maximal data from 1 minute to 20 minutes also

There is absolutely no way that a mathematician could take the high quality maximal power data of a well trained cyclist and identify a threshold without input from physiological models which create the concept of threshold. The shape of the power curve does not look at all like a threshold, it is a continuously reducing gradient from 5 minutes to way beyond 2 hours. In terms of pure data, it simply is not there, it does not exist.

They would find a threshold around the point where glycogen runs out, in well trained cyclists, that turnpoint doesn't happen until between 02:30:00 and 03:30:00

So yes, its just a concept in physiology - an attempt to identify where LT is. Apart from that, it doesn't look like a threshold, it doesn't feel like a threshold, its not visually identifiable as a threshold, its not mathematically identifiable as a threshold. But apparently, its still a threshold.

So I think its time to stop banging on about the shape of the power curve which supposedly looks like a threshold. That happens because:

(a) when you take the log of the x axis, a turnpoint is created. That is just a mathematical coincidence with no relevance to physiology
(b) a lot of riders don't have maximal efforts beyond one hour, so the turnpoint is amplified

So you recognise that threshold is referring to physiological responses to exercise intensity. That's good. LT is but one of them but good that you see we are talking about physiological threshold.


Well I suppose that's a matter of opinion. When I ride at that level it most certainly feels like I'm riding on that edge. I'm not alone in that sensation but I suppose that's subjective.


Well all of those are, frankly, wrong. I guess you've never looked at a chart plotting various physiological responses to sustained exercise intensity. Such a change from quasi steady state to non steady state physiological responses is most definitely visually identifiable, and it's also mathematically identifiable from physiological response data.


It's a threshold because it's the maximal intensity level at which physiological responses can maintain a quasi steady state, and above that intensity they no longer do.


No, this was not shown on wattage.

To reasonably estimate the intensity associated with this threshold all one needs is one decent data point in that range, i.e. a mean maximal effort of about an hour's duration. That will, for all intents and purposes represent a very good estimate of one's power at threshold.

That's because the duration maximally sustainable for various physiological thresholds is typically of that order. This has been shown repeatedly in the literature.

What such a data set (20-min to 120-min) does not necessarily reliably enable one to do is to use some mathematical models to identify threshold power. If you want to use such a model to tease out a threshold power value, it requires data from shorter durations.

But as I pointed out above, use of mathematical models is but one method of estimating threshold power. Do a 40km TT and you'll have a very good estimate.


There is no need to propose its existence. It's a very well documented physiological phenomenon. It's established science. To propose otherwise would require an extraordinary amount of counter evidence.

Threshold exists, and there is an intensity level associated with it and it can be expressed as a power output.


Short duration efforts are required if you propose to use a mathematical model in order to quantify each the various fundamental physiological capabilities, including threshold. One does not however need to use a mathematical model in order to ascertain a value for threshold power.


I'm not sure you'll take this in but really I'm doing this for the benefit of others.

The power we can sustain for any given duration is an integral of various physiological capabilities.

Some of these capabilities are sustainable for a very long time and are fuelled via an essentially limitless aerobic metabolism. While this power supply is not capacity limited it is somewhat rate limited - IOW this "threshold" capability can only provide so much power.

To go harder, this threshold level capability is supplemented by other non-sustainable but far less rate limited metabolic processes. These are significantly anaerobic in nature but it's a bit more complex than that, so let's just consider them capacity-limited capabilities which are far less rate limited - IOW they can supply significant additional power but only for relatively short durations. A little like a battery - it can discharge very quickly but there's only so much energy available. And also like a battery the rate at which it is discharged can vary - use it up quickly to service a very high power demand, or it can be made to last longer at lower (but still supra threshold) power.

So in order to ascertain this base level "threshold" capability via a mathematical model of the power-duration curve, you need data that provides enough information about how much these capacity-limited metabolic processes are contributing to the total power output. If your data set only includes points at which such capacity-limited metabolic processes represent a small proportion of the total energy supply then you risk introducing error in estimates. Keep in mind that such models also provide more than an estimate of threshold power, they also inform about one's capacity limited energy supply.

With a good model and with good input data over a suitable range of durations, it is a very good way to parse out each of the fundamental physiological capabilities - in particular the sustainable component, threshold, and the non sustainable capacity limited component.

This parsing out is reliably done with mean maximal power data starting from a few minutes duration as in general for most people it represents a minimum duration one can fully expend their non-sustainable capacity - to drain that supplemental battery if you like.


Once again, threshold is a very well established physiological phenomenon. I'm not really sure why you dispute either its existence or the fact that one can ascertain the intensity at which it occurs via power data.

That you can't "see" it in an MMP plot is neither here nor there. Threshold exists and the intensity at which it occurs is most definitely ascertainable via power data (provided you have good input data and use an appropriate method).

---

http://www.cyclecoach.com
http://www.aerocoach.com.au

This post should be enshrined at the top of every page that mentions FTP.

And no way of establishing how reliable the estimate is, nor which method is any more reliable than any other -- since FTP is purely conceptual.

Now if you say FTP *is* power at MLSS a study could check quite simply.

I was providing a verbal description of the quantitative relationship that exists. If you plot the values that I suggested, it might be clearer to you.