Formula for adapting a number for cross reference As a keen cyclist I'm trying to use the Allen Coggan Relative Power table that then relates your Relative Power 'score' to what category rider you are.
My question is that given rides/segments/hill climbs are rarely exactly 5 seconds/1 minutes/5 minutes or an hour long, what formula is required to adapt a known relative power reading to each of these 'time-frames' for comparision?
For example:
I have a hill that took 8 minutes and 15 seconds to ride up and have a relative power reading of 3.23 w/kg for that effort. What would this reading be for 5 seconds, 1 minute, 5 minutes and 1 hour of effort?
Hopefully someone could help out :)
 A: Okay, I'm assuming you're referring to Table 4.1, the "Power Profile Chart" in the Allen and Coggan Book.  Reproduced below is a small portion of that table.

The first column corresponds to 5 seconds, the second to 60 seconds, the third to 300 seconds, the fourth to 3600 seconds.  You're interested in 495 seconds (your time up the hill), so you need an interpolating curve.  At http://zunzun.com/ I tried many, many different curves until I found one that fit each row of the data nicely.  The one that works for me is the Hocket-Sherby 2D curve, namely $y=b-(b-a)e^{-cx^d}$.  It fits all four data points cleanly, for each row, and looks like a reasonable interpolation.
The row starting with 13.93 has solution below, and gives 3.26 for 495 seconds.

a =  1.8360717445421550E+01
      b =  3.0199240417066466E+00
      c =  1.4200281786390395E-01
      d =  5.4399940156084914E-01  

Next best is the next row, starting with 13.63, which gives 3.16 for 495 seconds.  I would estimate your performance as between those two rows, closer to the first one.
