So give a mathematician the data of 100 well trained timetriallists. Don't tell them where the data is from, and ask them to find a threshold.

Their answer will be (a) around 1 minute and (b) around 2:30 to 4 hours. There won't be a threshold between 30 and 70 minutes.

And AC has been caught out quoting a statement from a paper of which he is co author and yet he now says he did not agree with that statement - nice one Trev

I see that many of the respected physiologists do not take AC seriously, since he exited physiology academia many years ago.

On the weekend Cycling NZ's opinion was to award me a Services to Cycling Award to go with my two Coaches of the Year awards from 2009 and 2011.

Pardon my French, but WTF are you talking about? I am currently PI, co-PI, or co-I on four grants totaling ~$1.2M, have published 14 papers in the last 3 y, have two more in preparation, have a review article under consideration at ESSR, and just won an award for my research efforts from my school. Indeed, I have never been busier with real work (which is why I have stepped away from my hobbies, e.g., am no longer contributing to WKO4).

??

Nowhere in there did I say anything about a downward deflection in power at around the 1 h mark.

In fact, I have repeatedly pointed out that any such deflection is a statistical artifact (necessity) engendered by assuming the existence of an absolute plateau in power (e.g., the CP model).

ETA: Emphasis added to counter the Trev reality distortion field.

I made no such claim.

I said threshold can be determined from PD data (via various methods including use of mathematical models) and that it is clearly visible in physiological response data.

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 your WKO4 mathematical model estimates FTP, and can show mFTP on the power duration curve, you must be able to provide a rigorous mathematical definition of FTP.

Please can we have this definition.

Pt = FTP + (Pt*t - FTP)/t

So, there's one possible "mathematical definition" if you really need one.

This response is great.

Trev's and Steve's questions continue to confuse ways of estimating FTP with the concept of FTP, which is why I used quotation marks.

Just a simple observance over the years of various training concepts. If it is good it will stick around and if it is indeed snake oil people catch on and it fades. In the world of strength training I have seen many schemes come and go and most of the sound training principles continue. Does that mean that everyone trains correctly or uses the common training principles dead on the money per the research papers or by elite coaches? No! There are varying degrees of effectiveness and the common athlete reaps what they sow. I am certainly one of these and accept that the effectiveness of any training concept is hindered by life obligations. Having research paper purity in training is not functional or practical with home, work and life obligations and yet I am progressing.

If training formed around FTP was bad and people were not progressing with it, it would have faded long ago. Yet there are multitudes that base training around FTP (even if they do not completely understand it or have the exact concept from the founder) and are successful. When people are successful with it they do not take the skeptics, whatever their agenda might be, seriously. So for those who cry snake oil in regards to FTP and metrics based off of FTP it is going to be difficult to convince those who have already and are currently progressing with it to take your bait.

How can you estimate something using a mathematical model if you can't rigorously mathematically define the thing that you're trying to estimate?

Edit: As you have liked to point out in the past that the map is not the territory, I'll mention that a definition will be expressed in terms of the territory, whereas a method of estimation, such as the WKO4 model, operates on the map.

Any attempt to mathematically define FTP operates on the map, not the territory.

IOW, you continue to confuse the concept of FTP with ways of estimating it.

Trev specifically asked for a mathematical definition of mFTP a few posts up. Hence Andy's response.

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

Aahhh....the serenity.

PS You do realise that no one but an Australian would have any idea of what you are talking about?

Of course. It just seems so fitting.

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.

Makes sense.

Absolutely a great post by Alex. One would think his post would satisfy any sincere questions about FTP and threshold.

Operative word here being "sincere".