Rating Climbs: summary
Okay, for the record, here's a summary of the three candidate methods:
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.
- 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.
- 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.
- 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
Comments
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.
BTW, I made a typo in my previous comment. It should have been:
pc = [(1000/9) (h/d)]²
I left off the brackets.