I’m having a hard time figuring out how TSS is calculated. The only thing that resembles a formula I can find on the Internet is this:
TSS = (t * NP * IF) / (FTP * 3600) * 100
where t is the ride duration in seconds.
That looks awfully complicated. For one thing, why measure t in seconds only to divide by 3600? Why not just measure it in hours (1 hour = 3600 seconds)? For another, isn’t IF just NP / FTP?
So the formula simplifies to this:
TSS = t * IF * IF * 100
where t is the ride duration in hours.
But why IF twice? A ride of the same length, but half as intense, yields a TSS only a quarter as much? What’s the reasoning behind this?
NP represents a nonlinear physiological response to hard work. If my FTP is 300W, riding at 400W is significantly more difficult than 200W. The physiological cost of that 400W effort is much more than double the 200W effort. TSS maintains that nonlinear response.
Worth noting that a lot of the mathematics here is just to get ballpark figures that make some sense and roughly correspond to what we think happens in the body. Coggan took power to the fourth order in the NP calculation because, meh, he thought it was a good fit. The following calculations like TSS and so on are similarly arbitrary.
According to this chapter, the TSS equation was modeled on Banister’s TRIMP calculation. The 4th order weighting in the NP algorithm came from analyzing lactate data from a large number of cyclists.