Power/Duration Curve

I don't think you'd be able to use that chart because the values don't represent a single rider (or group of riders) across the different time periods. IOW, Andy says that the short duration World Class figures are from the top trackies, whereas the longer duration WC figures would come from the TT specialists.

If you're looking for where you are stronger vs. weaker than the populace, then wouldn't you use Andy's system described here: cyclingpeakssoftware.comprofile.htmlOpen ↗

and compare your shape vs. the different 'rider types'?

frenchyge said:

I don't think you'd be able to use that chart because the values don't represent a single rider (or group of riders) across the different time periods. IOW, Andy says that the short duration World Class figures are from the top trackies, whereas the longer duration WC figures would come from the TT specialists.

If you're looking for where you are stronger vs. weaker than the populace, then wouldn't you use Andy's system described here: cyclingpeakssoftware.comprofile.htmlOpen ↗

and compare your shape vs. the different 'rider types'?

Well, Andy's chart is definitely a good starting point for what I'm looking for. Have you ever studied the chart with the data converted to power as % of FT power? Attached is a chart of the horizontal values at 4 FTs: 4.71, 4.03, 3.35 and 2.67. I focused on these because I think they capture a large percentage of the non-elite, non-recreational cycling population. For me, these represent approximately 200w, 250w, 300w and 350w. This chart suggests that as one's FT increases, the power/duration chart flattens out at the short (duration) end. But, at 5 min, everybody is at ~120%FT, regardless of FT. Interesting. Basically, I'm interested in more points on the curve, especially between 5 mins and FT, and whether the curve is essentially the same for a wide range of FTs. So, if I know FT, is 20min power predictable to a high degree of accuracy?

BTW, I checked my 5min MP as % of FT and it was 123%. Cool.

Have you looked into the Monod Critical Power model? There's a good layman's sumary at http://www.velo-fit.com/articles/critical-power.pdf The gist of it is that for times greater than about 5 minutes, the points along the power-duration curve are not independent but depend on only two parameters - critical power and anaerobic work capacity. If these two values are known, all points on the curve can be filled in.

RapDaddyo said:

This chart suggests that as one's FT increases, the power/duration chart flattens out at the short (duration) end.

I have to disagree with that conclusion. You've chosen the horizontal values, but remember that that doesn't represent a single rider or group across that horizontal row. Individuals will typically have a slanted profile across the columns.

What your bar graph shows is that there's somewhat less power variation between Sprinters and TT-ers (expressed as a %of FT) amongst the better riders than there is in the less gifted riders. I'm not sure what that information could be used for, but it doesn't seem surprising.

asgelle said:

Have you looked into the Monod Critical Power model? There's a good layman's sumary at velo-fit.comcritical power.pdfOpen ↗ The gist of it is that for times greater than about 5 minutes, the points along the power-duration curve are not independent but depend on only two parameters - critical power and anaerobic work capacity. If these two values are known, all points on the curve can be filled in.

No, I had not seen that document. That's pretty cool. Thanks for the link. I wonder what the std dev (predicted vs. actual) is at different durations?

frenchyge said:

I have to disagree with that conclusion. You've chosen the horizontal values, but remember that that doesn't represent a single rider or group across that horizontal row. Individuals will typically have a slanted profile across the columns.

What your bar graph shows is that there's somewhat less power variation between Sprinters and TT-ers (expressed as a %of FT) amongst the better riders than there is in the less gifted riders. I'm not sure what that information could be used for, but it doesn't seem surprising.

Actually, quoting Andy, "the vast majority of non-elite athletes will likely show a generally horizontal power profile." Again, I'm much more interested in the points on the curve between 5mins and FT (and even beyond FT), where this chart suggests there is a lot of commonality between riders.

It might be helpful if I clarify why I am interested in this relationship. No surprise to regulars, it's related to VPP. Specifically, I'm interested in the interrelationship between NP, FT and the power/duration curve as it affects VPP strategies. For example, a very common 40K TT is an out/back course with a net altitude change in one direction (e.g., +2% outbound, -2% inbound). Such a course is an ideal opportunity for a VPP strategy. But, what are the practical limits of the push power on the upgrade leg? Let's say one's FT is 275w and the optimal pacing strategy is 295w on the +2% leg and 230w on the -2% leg. But, the +2% leg would be ~38 minutes. Is 107%FT at 38 minutes reasonable? IOW, is the cyclist working against two constraints in VPP -- NP=FT and the power/duration curve?

RapDaddyo said:

Actually, quoting Andy, "the vast majority of non-elite athletes will likely show a generally horizontal power profile."

Don't forget the sentence that precedes your quote: "Given the fact that only specialists will likely truly excel at the extreme durations, very few individuals will show this pattern and still fall at the upper end of each range." The 4.71 and possibly 4.03 FT rows fall into that category.

frenchyge said:

Don't forget the sentence that precedes your quote: "Given the fact that only specialists will likely truly excel at the extreme durations, very few individuals will show this pattern and still fall at the upper end of each range." The 4.71 and possibly 4.03 FT rows fall into that category.

Oh, you figure I cooked the books? No problem. Just for you, frenchy, here are the horizontal power profiles from the center row in the range.😄 I'm not sure it changes anything.

This is where I think the Monod paradigm can be useful. The way I look at it is critical power (CP) is a baseline of power that can be maintained over the entire TT. Anaerobic work content (AWC) is a stack of chips that can be spent to give a boost over CP. In the simplest model, AWC is fixed for the ride: what you start with is all you have. Then the stack can be spent at an even rate throughout the TT (constant power pacing) or spent more at some times than others (VPP). The optimization is fairly simple as it comes down to optimizing how to spend your AWC chips.

A more complicated model is where AWC is allowed to increase during periods of lower power. Then your AWC is increasing as power drops below CP and there is no fixed value for AWC. In other words during periods of low power, you're storing work to be used later and AWC for the TT depends of the total pacing of the ride. I don't know how the rate of increase of AWC corresponds to power relative to CP. I think if this were known, then deriving an optimum VPP strategy could be handled.

RapDaddyo said:

Just for you, frenchy, here are the horizontal power profiles from the center row in the range.😄

Ah Ha! See there?!? :p

RapDaddyo said:

IOW, is the cyclist working against two constraints in VPP -- NP=FT and the power/duration curve?

That's certainly the case. The best they can do is to increase power at a point within a few km of the turnaround, and recover after the turn.

asgelle said:

This is where I think the Monod paradigm can be useful. The way I look at it is critical power (CP) is a baseline of power that can be maintained over the entire TT. Anaerobic work content (AWC) is a stack of chips that can be spent to give a boost over CP. In the simplest model, AWC is fixed for the ride: what you start with is all you have. Then the stack can be spent at an even rate throughout the TT (constant power pacing) or spent more at some times than others (VPP). The optimization is fairly simple as it comes down to optimizing how to spend your AWC chips.

A more complicated model is where AWC is allowed to increase during periods of lower power. Then your AWC is increasing as power drops below CP and there is no fixed value for AWC. In other words during periods of low power, you're storing work to be used later and AWC for the TT depends of the total pacing of the ride. I don't know how the rate of increase of AWC corresponds to power relative to CP. I think if this were known, then deriving an optimum VPP strategy could be handled.

I'm working toward a somewhat different model, perhaps with the same end objective. I view the overall constraint for a given duration as NP=FT=CP. Physics creates the incentives to deviate from a CP strategy, but using power >FT has a further limit, perhaps defined by the power/duration curve (which, in turn, may be approximated by the CP algorithm). So, it's an LP problem, with two sets of constraints (NP=FT and the P/D curve).

frenchyge said:

That's certainly the case. The best they can do is to increase power at a point within a few km of the turnaround, and recover after the turn.

Or, ride the entire +2% leg at their max power for that duration (e.g., 105%FT).

RapDaddyo said:

Or, ride the entire +2% leg at their max power for that duration (e.g., 105%FT).

Sure. Even better.

frenchyge said:

Sure. Even better.

Actually, all this VPP stuff is getting too complicated. I think I'll just develop ~400w of sustainable power and ride at CP. Forget all this math. Power rules!😄

I'm pretty sure I remember Lonnie Utah posting a link in the Training Forum where you could enter data points and have it generate a P/D curve for you. The site had a German sounding name to it. You might search his posts to find it.

Edit: Post #24 -
cyclingforums.comshowthread.phpOpen ↗

frenchyge said:

I'm pretty sure I remember Lonnie Utah posting a link in the Training Forum where you could enter data points and have it generate a P/D curve for you. The site had a German sounding name to it. You might search his posts to find it.

Edit: Post #24 -
cyclingforums.comshowthread.phpOpen ↗

It appears that what Lonnie did is to use the kreuzotter site to estimate his MP numbers at several durations and then created his personal power/duration curve. But, I don't think the kreuzotter site does what the Critical Power model does, generate a power/duration curve given a few data points.

RapDaddyo said:

It appears that what Lonnie did is to use the kreuzotter site to estimate his MP numbers at several durations and then created his personal power/duration curve. But, I don't think the kreuzotter site does what the Critical Power model does, generate a power/duration curve given a few data points.

😕 Isn't that the same thing? Enter in a couple points and have it fill in the rest for you?

frenchyge said:

😕 Isn't that the same thing? Enter in a couple points and have it fill in the rest for you?

No. The only thing Lonnie used the kreuzotter site for was to compute his power at a few durations. He used the kreuzotter site because he doesn't have a PM. He then ran a least squares regression on his power/duration data points to arrive at his power/duration curve. The kreuzotter site had nothing to do with the power/duration curve and it's not based on a population or study. The curve is Lonnie's curve, not a generalized curve. IOW, he took a back door approach to arrive at what you and I have with the CP software (mean maximal power curve). I can do that too, from a handful of my max power data points at different durations, but in the end all I would have is my personal power/duration curve. I am looking for a generalization of the power/duration curve for a population of trained cyclists.