This is not a question. It's something I find interesting which I found while playing with the formula to calculate TSS. You may or may not find it interesting, but I don't really care.😉 I'm just sharing in case any of you find it interesting.
All of you here would probably recognize the algorithm below that's copied from Dr. Coggan's "Training and racing using a power meter: an introduction" paper written in 2003. I added my comments bracketted in []:
1) starting at 30 s, calculate a 30 second rolling average for power
2) raise the values obtained in step 1 to the 4th power
3) take the average of all the values obtained in step 2
4) take the 4th root of the number obtained in step 3
[which is Normalized Power, or NP]
5) divide the normalized power obtained in step 4 by the individual’s power at LT – the resulting decimal value is the IF
[IF = NP / FTP]
6) multiply the normalized power by the duration of the effort (in s) to obtain the normalized work performed (in J)
[Normalized Work = NP * T]
7) multiply the normalized work by the IF (step 5) to derive the “raw” TSS
[raw TSS = NW * IF = NP * T * NP / FTP = NP^2 / FTP * T]
8) divide the “raw” TSS by the amount of work that could be performed in one hour at threshold power (i.e., threshold power x 3600 s) and multiply by 100 to obtain the final TSS
[final TSS = raw TSS / (FTP * 3600) * 100
= NP^2 / FTP * T / (FTP * 3600) * 100
= NP^2 / FTP^2 * T / 3600 * 100
= IF^2 * t * 100
where t is the work duration measured in hours; i.e. t = T/3600]
So, in simplified form, TSS is really IF^2 * training duration in hours * 100.
What this means is, it makes the training stress levels at intensity higher than FT look "quadratically more expensive" while doing the exact opposite to those at intensity lower than FT. While I'm not sure if the quadratic function is the best match to the actuall stress levels of training at various intensity levels, I'm sure it's much better than linear.
Also, the simplified formula above makes it much simpler (well, for me, anyway) to estimate rough TSS of any given training session beforehand. You don't even need to know your own FTP to do this.
TSS_L = 0
TSS_H = 0
For each training level (L1-L7)
TSS_L = TSS_L + (the lower bound %FTP of the level in fraction)^2 * (duration you aim to work in that level) * 100
TSS_H = TSS_H + (the upper bound %FTP of the level in fraction)^2 * (duration you aim to work in that level) * 100
TSS_L will be the lower bound of TSS roughly estimated for your training session, and TSS_H the upper bound.
By "%FTP of the level in fraction", I mean, for instance, if your target level is L3 (76-90%FTP), the upper and lower "fractions" will be 0.76 and 0.90. So, for instance you target to work for an hour at L3, your TSS for that particular part of session will fall in the range of 57-81 (0.76^2 * 1.0 * 100, and 0.90^2 * 1.0 * 100, respectively).
Of course it's way too simplified calculation of TSS (for one thing, variable power is not considered at all), but when I try to do tempo work for an hour, I usually end up with TSS somewhere between upper 60s and upper 70s so it's a good estimate I presume.
Cheers,