I agree that the power has a significance. I just think people over-interpret the time point (TTE) corresponding to FTP.
I’ve scrolled through the WKO document but I find the papers with actual formulas more interesting 
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I’m sorry, I think we’re getting lost with not-so-productive stuff. Both you and I know how to guess and work with our FTP.
Because FTP is closely related to the point where blood lactate accumulates more rapidly. Physiologically, above FTP the working muscles can’t use all the lactate that is being produced anymore, and start offloading it into the bloodstream. That state can’t be kept up for very long. Below FTP this doesn’t happen. Look at a lactate curve to see the change in gradient. (Sorry I’m on my phone and can’t link a nice on easily.)
I’m sorry I expressed myself in a confusing way. I didn’t mean FTP not to be something physiological. My problem is the inflection point - there is no physiological inflection point, it is just an artifact of the model or a consequence of having a limited number of all-out tests.
I wouldn’t be too sure of that - there is a reason all advanced modelling has an inflection point there, and I doubt it’s because everybody introduces artifacts into their PD curve by only ever doing 2x20.
Anyway, as an experimental physicist, its sound like you volunteered yourself to do the series of “just above” and “just below” all-out tests 
Haha. Theoretical mathematicians don’t like to get their hands dirty 
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Just look at the formulas. The lack of differentiability at TCPmax is just a consequence of the piecewise definition…
[Puchowicz, Baker, Clarke, OD PD model]
Damn I really shoud get back to my actual work, but I like this modelling stuff .
I’ve never understood why the WKO model shows a smooth downward deflection. versus the abrupt transition you see with models like this. Any idea?
My understanding is the inflection point is where you go past MLSS (maximal lactate steady state). Below MLSS, your body can clear lactate, above it accumulates.
Hmm I don’t think the WKO PD curve model is smooth?! (look at stevemz’s graphic above).
It seems to be pretty similar to the formula I posted. Above TTE the decrease in power is essentially linear in log t.
This is the region I meant. The transition looks pretty smooth to me.
No, I don’t think so. The above formula should yield about this. (Of course it’s continuous - there is no “jump”, but it’s not smoother than that.)
Here’s the graph corresponding to the PD model of the formula I posted above. It’s not an abrupt transition but you can guess the “inflection point” (I really don’t like this name XD).
WKO model (red) with 90-days / 82 rides of actual data (yellow), I put the cursor at the time duration of my modeled FTP:
A lot of hard group rides and hard semi-structured workouts. Given that I’d say the model was well fed and I had some long TT like efforts to correlate against the model. I purchased WKO about a year after that time period.
re: piecewise, I vaguely recall Coggan stating on a webinar that he rejected doing a piecewise linear model. Believe it was the webinar that introduced the new PDC (WKO4 era).
This would be a fun topic for a video meeting, trying to do it in a thread is somewhat problematic. As STEM major with a lot of modeling background it has been really fun to play around with my data in WKO. This topic really deserves a separate thread.
I have that dip in my PDC because I don’t want to do the effort to seed the model! Currently WKO is recommending a test at 52 minutes @ 90% of my FTP. I’m sure I can easily do it. I’ve even been training in that zone lately but it’s been things like 2x20, 3x15. I’m progressing out farther so once I get to 3x20, I might do a 1x60 to fill out the model as part of my training progression.
I just got started with WKO this last year. Even though I’m only using a small smidgen of the software at this point I’m enjoying it. I really like the modeled FTP. I can do a Kolie Moore Baseline FTP test and WKO will pick it up and update my mFTP. It’s so easy.
Thanks for the screenshot - that’s a nice example where there is no inflection point around FTP in the actual data. It only shows up in the modeled line in red.
Obviously you can’t tell for sure by visual inspection, but to me the aerobic part of the WKO PD curve (green dashed line) looks very much like something log-linear past FTP.
Also, there are some people working in this field who have compared the “secret” WKO model with the (published) Peronnet and Thibault model, and the differences, if they exist, are negligible: https://veloclinic.com/peronnet-and-thibault-the-source-model-under-the-hood-of-wko4-wko5/
For awhile I followed the modeling side, and I have the math and programming chops to do it myself (have even hacked GoldenCheetah code and recompiled), but why bother? WKO has so many handy tools, a scripting language for customization, and customizable charts.
and one where it does. We could go back and forth for days, with examples and counter examples. All I can say is that the WKO model works well when fed good data, and I’ve got a complete set of (customizable) tools to analyze my data.
Right, that’s what I’m getting at. Other attempts show a distinct transition point, whereas the WKO modeled P-D curve is smooth, or at least smoother - why?
ETA. Here’s another example. Note how smooth the red curve is compared to the sharp kink in the modified P & T model.
As I understand it (from a Tim Cusick post), there are a family of PD curves. The algorithm maps your 90-day MMP to one of those curves.
Now I’m really confused - I thought that was how ICU did things?
I don’t think that the WKO model is very different from other models (I don’t have the expertise to judge this myself but the creators of those other models claim this), see the link already mentioned above Peronnet and Thibault; the source model under the hood of WKO4 WKO5 - veloclinic
If WKO really is this model then the “sharpness of the inflection” just depends on the parameters you choose to use (i.e. the data).
What models do you have in mind with a sharper “turn” at FTP? (Edit: Just saw your addition.)
