This comes from a desire by some to know their cumulative TSS while riding.
But is the kJ read-out a valid proxy for TSS?
For those that use the newer ergomo power meter, they already have this feature built into their CPUs, so they have no need for using kJ as a proxy for TSS. However, for the rest of us, unless you do the same type of ride every time you head out the door or get on the trainer, it is unlikely that this linear relationship will hold true.
The Practical Example
While the mathematics shows this relationship to be a spurious one, there's nothing like real data to emphasise a point.
The above chart is a plot of kJ vs. TSS for 161 rides so far this season.
While the relationship is roughly linear, there are major differences in work performed for rides of a similar TSS, even rides with TSS around 100-130, the energy spread is greater than 1,000kJ or up to three times the difference for the same TSS!
So I won't be using the kJ display on my power meter as a proxy for TSS.
Besides, I'm better at estimating what TSS to expect per hour for certain types of rides. While you can do this by estimating the Intensity Factor (IF) of a given ride (or sections of ride), I simply know from experience what to expect since I have probably already done similar rides as a part of my regular training and racing.
Here's a quote from Andy Coggan on the matter to explain the maths:
"The relationship between TSS and total work not only varies with the individual, but also with the nature of the workout. That is evident by looking at the respective formulae:
Total work = duration x average power
TSS = duration x (normalized power/functional threshold power)^2
Thus, during long workouts the ratio of TSS to total work will tend to be lower, since normalized power and average power will tend to be closer together. Conversely, during shorter, higher intensity workouts (especially, e.g., with trackie style "go hard, puke, go home" level 6 intervals) the ratio of TSS to total work will tend to be higher, since normalized power will be much higher than average power. Of course, if practically all of your workouts are "middle of the road", then these differences won't be apparent and you may find a fairly high correlation between total work and TSS. As should be evident from the formulae given above, however, the two are not equivalent, i.e., such a correlation is simply spurious."
So until TSS, IF etc are incorporated into the CPUs of more brands of power meter, I guess most of us will just need to get to know our own data better....