Wednesday, July 21, 2010

Rating Climbs: summary

Okay, for the record, here's a summary of the three candidate methods:
  1. The Fiets/Summerson formula: net climbing² / net distance (each reference uses a different normalization factor to make the result unitless). This is good because it can be applied to an broad ensemble of riders. Nobody may agree on what's steep, but everyone agrees to some extent steeper deserves to be rated higher. This formula has the advantage of being trivial to calculate in your head, especially if you are given average grade and are willing to make the approximation that climbing / distance = average grade.
  2. My simple formula: net climbing × (1 + [ 12.5 × net climbing / distance ]²). Note during this series of blog posts I've upped the coefficient on climbing due to feedback I've received on the tradeoff between steepness and altitude gained in perceived difficulty of the Low-Key Hillclimbs. This formula is also fairly easy to calculate in your head.
  3. The method I described in the preceding blog post. This method was also tuned from my initial description. Forget about calculating this one in your head!

So, with each method, here's the ranking of the Low-Key Hillclimbs from 2008-2010, where I've sorted the climbs using the full-profile rating (rfull), but also listed the Fiets/Summerson formula (rfiets) and my "simple formula" (rsimple). In each case I've normalized to Old La Honda, to facilitate comparison. In general, the full-profile rating clearly gives a high weight to climbs with extended steep sections like Alba, Welch Creek, and Bohlman. However, a climb which is relatively steep but with a steady grade, like Soda Springs, fails to score higher with the full-profile rating.

rank climb                              rfiets   rsimple  rfull
1    Alba_Road                          2.16942  2.22745  2.35366
2    Mount_Diablo_(N)                   2.22693  2.29079  2.3154
3    Bohlman-Norton                     1.89235  1.98033  2.30907
4    Kennedy_Trail                      1.90262  1.95956  2.1915
5    Welch_Creek_Road                   1.81027  1.81975  2.15237
6    Hicks_-_Mt_Umunhum                 1.92388  2.00287  2.1223
7    Soda_Springs_Road                  2.11797  2.11073  2.07743
8    Mt_Hamilton_Road                   1.59271  2.00601  2.06048
9    Quimby_Road                        1.78158  1.82695  1.98761
10   Sierra_Road                        1.75709  1.77709  1.86811
11   Montebello_Road                    1.43379  1.44195  1.50318
12   Jamison_Creek_Road                 1.39096  1.45849  1.49202
13   Montevina_Road                     1.49401  1.49641  1.48992
14   Bonny_Doon_-_Pine_Flat_Rd.         1.34382  1.37818  1.48754
15   E._Dunne_Ave_(Henry_Coe)           1.25048  1.2993   1.47067
16   Portola_State_Park_-_W._Alpine_Rd. 1.34549  1.3489   1.36768
17   west_Alpine_Road                   1.30607  1.3182   1.36134
18   Metcalf_Road                       1.13607  1.20307  1.24131
19   west_El_Toyonal_-_Lomas_Cantadas   1.05474  1.05098  1.19332
20   Tunitas_-Star_Hill_-_Swett         1.06779  1.1033   1.15293
21   Kings_Mountain_Road                1.11102  1.1215   1.12563
22   Old_La_Honda_Road                  1        1        1
23   West_Bear_Gulch_Road               0.292306 0.354397 0.337179


Arjan said...

Dan, are you familiar with the Cotacol method? It's based on the forces that act on a cycling climber, and includes corrections for variations of slope during a climb, as well as road surface conditions. The guys that came up with this are from Belgium, so their method had to be applicable to the cobbled climbs in Flanders...

djconnel said...

Thanks for the comment! The closest thing I can find to a reference is here, from which I can approximate the look-up table as follows:

Pts=å pcc*(d+cr/d)

D = distance / km,
pcc = (1000/9) (h/d)²,
where (h/d) = net climbing / distance

I'm not sure how to calculate cr. Do you know?

In any case, this is the Fiets method with the addition of the "CR" term, which is zero for a uniform grade.

I like Fiets: it's a philosophical difference whether a 2% grade hill gaining 1000 meters should be rated twice as hard as a 1% hill gaining the same meters. The latter is actually harder to ride, but the former might be considered the "better" hill. In the idealized limit they take the same energy, so Cotacol isn't energy-based: if it were, then net climbing would be all that mattered.

Arjan said...

Actually, they take the slope for every 100m of the climb, calculate pcc for that 100m, and sum all the pcc-terms of the climb. I'll make a page with an explanation of their method, and the ideas behind it.

djconnel said...

Thanks! I still need to figure out what cr is, however.

BTW, I made a typo in my previous comment. It should have been:

pc = [(1000/9) (h/d)]²

I left off the brackets.