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2014 Low-Key Hillclimbs
Climb Ratings

Here are the special "Low-Key Climb Ratings" for the climbs in this year's series. The rating is in Old La Honda equivalents, where Old La Honda is by definition 100. Of course, everyone has their own idea of how steep compares with long, or with steady compares with variable, so don't associate any sort of precision to these numbers. But you can be fairly sure the climbs with the highest numbers will be challenging!

One thing to note: the climb rating formula is for individual climbs, not multiple climbs, so multi-climb weeks (4, 8) get rated according to their highest-rated climb.

The numbers, please!

16Hicks - Mt Umunhum (white line)249
23Welch Creek Road213
39Mt Hamilton209
42Sierra Road188
74LKHC Berkeley Hills100
88Marin Headlands: Miwok + Marincello74
97Mount San Bruno (W)73

The nitty-gritty

Okay, here's the dirty details.

First the profile was extracted, typically from Garmin data if available on-line from Strava. Cosmo's Strava-to-TCX converter can be used to extract data.

Then the data were smoothed with a Gaussian of sigma 50 meters and interpolated onto a grid of 10 meter spacing. The smoothing is to correct for the "noise" present in the measurements: the Garmin-reported altitude tends to vary somewhat for a given position.

Next data were transformed to a function of time, as opposed to a function of distance. For GPS ride data, time are already available. However, the rating of a route shouldn't depend on how a given rider on a given day rode the hill, so these time data were ignored. Instead an empirical differential equation was used to product a "typical" riding rate:

dt / ds = [ 1 + ln | 1 + exp( 50 g ) ] | / vmax,

where t is time, s is distance, g is the rate of altitude change with respect to distance, and vmax = 14 m/s. Don't sweat this formula too much; it has very little effect on the final rating.

Then g was further smoothed with respect to time with a Gaussian smoothing function with standard deviation 15 seconds, representing the ability of neuromuscular power and inertia to effectively smooth out very short, steep grades. The idea is if it takes more than 15 seconds to climb a steep segment, your legs really start to feel the true grade.

Now the data were ready for calculating the rating. For each 10 meter segment of road, add to a parameter f as follows:

df = exp(g / g0) ds,

where ds is the length of the segment (10 meters in this case) and g0 = 8%, sort of the grade at which climb segments start to become especially hard.

To get the raw rating, I do the following:

rraw = f z / s,
where rraw is the raw rating, z is the net climbing of the hill, and s is the net distance.

The result is a raw rating with units of distance. To get the number reported here, the rating for Old La Honda was calculated, and the result divided by that and multiplied by 100. So no matter what the details (smoothing, vmax, g0), Old La Honda scores 100:

r = 100 rraw / rraw,OLH,

where rraw,OLH is the raw score for Old La Honda.

That's it!

Dan Connelly