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Re: Is TSS a useful parameter? (Warning: Includes Maths) [vps]
vps wrote:
We recently had a discussion about TSS (Training Stress Score). My criticism was that it seemed a random parameter to me. Why should half an hour at FTP equal two hours at 50%, stress-wise? In my opinion the half hour at 100% FTP is way more taxing, however one could argue that the higher volume induces some stress on other levels.

However, when taking a closer look at the formula, I realized how awfully random TSS really is:

When I ride at FTP for an hour, then at 50% for another hour, that gives me a TSS of 145.8.
Now when I ride at FTP for an hour that gives me a TSS of 100. Riding for an hour at 50% gives me 25.
That means, the overall TSS (145.8 vs 125) is quite significantly different for the same session, depending on whether or not I stop and start my bike computer mid-ride. What am I missing?

My calculation:

The formula for TSS is TSS = [(s x NP x IF) / (FTP x 3,600)] x 100, where s is the time in seconds, NP is the normalized power, FTP is the functional threshold power and IF=NP/FTP.
(Side note: I don't know why they over-complicate it like that. The above formula is equivalent to
TSS = IF² x t/h x 100, with t/h the time in hours. Seems easier to me.)

NP is basically the 4-norm (p-norm for p=4) (the 30 s average is negligible here) and therefore the overall NP of the session is NP=((a^4+b^4)/2)^(1/4), where a = 100% x FTP is the power for the first hour and b = 50% x FTP the power in the second hour.
--> NP=(1+0.5^4)^(1/4) x FTP=0.8537 x FTP
--> IF = NP/FTP = 0.8537
--> TSS = 0.8537² x 2 x 100 = 145.8

The second case (two seperate files) is easy to calculate: An hour at FTP gives TSS=1 x 1 x 100=100 by definition and for 50%, IF=0.5 and therefore TSS=0.5² x 1 x 100=25.


Well, at first glance, you are doing your math wrong. NP should be ((1+1+.5^4)/3)^(1/4)xFTP = .91058xFTP

And then, TSS = (5400*.91058*FTP*.91058)/(FTP*3600)x100 = 124.37
TSS = (sec x NP® x IF®)/(FTP x 3600) x 100

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Ed O'Malley
www.VeloVetta.com
Founder of VeloVetta Cycling Shoes
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Last edited by: RowToTri: Mar 3, 19 17:24

Edit Log:

  • Post edited by RowToTri (Dawson Saddle) on Mar 3, 19 17:21
  • Post edited by RowToTri (Dawson Saddle) on Mar 3, 19 17:24