Power/Duration Curve

RapDaddyo said:

Does anybody know of any empirical data on power/duration curves for a large sample of trained cyclists?

When power is expressed as a percentage of functional threshold power, there is relatively little variation between riders, at least over the portion of the power-duration curve that would cover most events (e.g., ~1 to ~5 h). At both shorter and longer durations, the variation between individuals will tend to increase somewhat, due to abilities/adaptations specific to such performance. Specifically, the duration that you can maintain a power that is significantly greater than your functional threshold/critical power will depend in part upon your anaerobic work capacity, whereas the duration that you can maintain a power that is significantly less than your functional threshold/critical power will depend upon your "specific endurace" (for want of a better word). Nonetheless, the variation is still sufficiently small that 1) you can describe/prescribe level 5 intervals as a percentage of functional threshold/critical power, and 2) the majority of people racing an ultra-endurance event such as an Ironman distance triathlon will still complete the cycling leg at a fairly constant percentage of their functional threshold/critical power. OTOH, if you attempt to exercise for a very short time at a power well in excess of your functional threshold/critical power, or for a very long time at a power way, way below it, then other factors become so important that the variation between individuals can be great (which is why level 6 intervals are simply specified as being >120% of functional thresholdcritical power and level 7 intervals aren't based on functional threshold/critical power at all, or why somebody who has a very high functional threshold/critical still may not do all that well in a 12+ h race).

Back to your question, and your specific reason for asking it: I would suggest using the mid-point of each of the training levels and the durations that those can be maintained as representing what the average cyclist can maintain for a particular period of time. That is, after all, the very question that I faced when developing the classification scheme in the first place.

acoggan said:

Back to your question, and your specific reason for asking it: I would suggest using the mid-point of each of the training levels and the durations that those can be maintained as representing what the average cyclist can maintain for a particular period of time. That is, after all, the very question that I faced when developing the classification scheme in the first place.

Cool. Yes, that is what I'm looking for, as a 2nd constraint of optimal VPP strategies (the 1st constraint being NP=FT for the event duration).

acoggan said:

At both shorter and longer durations, the variation between individuals will tend to increase somewhat, due to abilities/adaptations specific to such performance. Specifically, the duration that you can maintain a power that is significantly greater than your functional threshold/critical power will depend in part upon your anaerobic work capacity, whereas the duration that you can maintain a power that is significantly less than your functional threshold/critical power will depend upon your "specific endurace" (for want of a better word).

I'd like to add some data points..
Makes sense to me, all the weight training and 300-400 m dashes I did as a track athlete have given me good anaerobic power, a 5 minute power around 475 w (possibly erroneous, I'm testing using a precor stationary bike but after emailing them for power error margins on their equipment it seems to be so). Mind you before I started heavy cycling training I had difficuly maintaining 350 w for 5 minutes. My 1 hr TT power (estimated, using analyticcycling.com, based on Cda and rolling resistance and 40 km time) is about 320 watts, so my 5 minute power is 148% of my 1 hr power. At durations greater then 4 hrs, my power drops to around 175 watts, and over 6 hrs to 150 watts. Greater than that, and my muscles basically seize up. However, I haven't adapted to durations greater than 4 hrs, as I've done maybe 3 efforts of 4 hrs or more this year.

-Bikeguy

acoggan said:

Back to your question, and your specific reason for asking it: I would suggest using the mid-point of each of the training levels and the durations that those can be maintained as representing what the average cyclist can maintain for a particular period of time. That is, after all, the very question that I faced when developing the classification scheme in the first place.

Andy, do you have or have you published additional data points on the power/duration curve?

RapDaddyo said:

Andy, do you have or have you published additional data points on the power/duration curve?

I'm not exactly sure what you mean...between 1 and 5 min and/or between 5 and 60 min, perhaps? (There wouldn't seem to be any need to durations longer than that, since presumably any course would be broken into numerous short segments for analysis.)

Thinking about it a bit more, I'd say that if you're trying to develop a generic constraint, then I'd suggest using the critical power approach to estimate maximal power at durations <60 min (as asgelle suggests), using a default AWC of 250 kJ/kg for men and 200 kJ/kg for women.

acoggan said:

I'm not exactly sure what you mean...between 1 and 5 min and/or between 5 and 60 min, perhaps? (There wouldn't seem to be any need to durations longer than that, since presumably any course would be broken into numerous short segments for analysis.)

Thinking about it a bit more, I'd say that if you're trying to develop a generic constraint, then I'd suggest using the critical power approach to estimate maximal power at durations <60 min (as asgelle suggests), using a default AWC of 250 kJ/kg for men and 200 kJ/kg for women.

Thanks, Andy. Yes, I meant between 1 and 5 min and between 5 and 60 min. I can use the critical power approach as suggested by asgelle, but was looking for empirical data if available. For example, a typical TT is an out/back course with a net elevation change. Unconstrained, an optimization model will produce a pacing strategy that pushes the envelope on the net upgrade segment (e.g., 107%FT for 38 min). Most of the shorter push opportunities are self-limiting due to the high NP cost. Obviously, if one has a complete power/duration curve, that is the constraint relationship of choice. But, I also want a default, generic relationship. BTW, I have a document I want to send you, but don't know how. If you can send me a PM and let me know how, I'd appreciate it. Thanks.