rmur17 said:

Andy is the leader for sure. Re diff. load measures: I have about three years worth of data split into indoor and outdoor rides and using load measures of: plain kJ, std. TSS(^2), linear.TSS (^2) and linear.TSS(^4).

I liked the linear.TSS(^2) porridge best of all. But perhaps it __is__ just down to taste. After doing 5-6 months of indoor training each year, those easy pedalling/coasting ride sections just beg to be cleaned up. Difference is typically 10-15% IIRC over the week.

It seems the conflict is to between getting proper credit for big efforts over threshold, versus losing adequate credit for long efforts below threshold.

One approach to this would be hyperbolic sine ( sinh(x) = (exp(x) - exp(-x) / 2), where the "power" in effect increases with increasing power above threshold. For example, you could say:

TSS = (100/hr) integral { [ K sinh(P/FTP) ]^2 dt }

Attractive, but unfortunately I looked at Andrew's lactate level data from:

http://www.midweekclub.ca/articles/coggan.pdf
and those data ARE really well fit by P^4, not sinh^2.

So it seems to me what one wants is to consider multiple sources of stress. There's one source of stress from blood lactate, another from doing work. At some point, it stops being easier to climb a hill slower. If I do a 1000 meter climb in 8 hours, it's no easier than doing it in 4 hours. Work is work. Of course, if I do it in 1 hour, that gets harder. Even w/o elevated lactate, I get muscular fatigue, more than if I were laying in bed reading.

So perhaps the best approach is neither ^1, ^2, ^3, or ^4 but a combination of P^4 proportional fatigue and good old fashioned kJ:

TSS(t + dt) = TSS(t) + (100/hr) [ a (P/FTP) + (1 - a) (P/FTP)^4 ]

for some a. For example, if a = 0.5:

TSS(t + dt) = TSS(t) + (50/hr) [ (P/FTP) + (P/FTP)^4 ]

Of course, you can still add in a term like I suggested before, for the effect of accumulated ride fatigue.

Dan