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2012 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!

Note: ratings were recalculated in Oct 2011 using an improved smoothing algorithm; the prior algorithm was not optimized for non-uniform meshes. Typically scores changed by approximately 2 points.

The numbers, please!

Kennedy Trail
Soda Springs Road
Mount Hamilton Road
Quimby Road
Montebello Road
San Gregorio to West Alpine Summit
Morgan Territory Road
Hwy 9 from Boulder Creek


Kennedy scores at the top because of its extended steepness. It's also dirt, which adds real difficulty, but the rating fails to consider that. So I think it's safe to say it's earned it's #1 slot for the year!

Soda Springs gains a lot of altitude and a consistently steep grade. But it never gets super-steep. Riders shouldn't have an issue keeping their low gear moving on Soda Springs.

Mount Hamilton is all about the sheer magnitude. The grade is gradual, and the intermediate descents hurt its climb ratings, but from a sheer physical challenge this one is tough.

Quimby Road is substantially shorter. But it dishes out some serious steep stuff. That the steep stuff comes at the end perhaps increases the challenge, although the rating doesn't care if it's the beginning or end. Of the paved climbs this year, this is the toughest "steep climb".

Montebello is Montebello. Not super-steep, not super-long, a good mid-range climb. It's no coincidence we use this as our opener every year.

San Gregorio with West Alpine is a tough, long combination. But since the rating scheme focuses on the climb aspect, the slog up 84 doesn't contribute anything to the final rating. If you go out too hard here, however, you'll be a sad panda when you hit the upper portion of West Alpine Road.

Morgan Territory is short with steep sections. It's rated very close to Old La Honda Road (the standard for 100 points) with similar net statistcis but is a lot different in character. The gradual finish will be interesting.

Finally, West Highway 9. This is the most gradual climb on the schedule this year. But it's another one where endurance and pacing are going to be key factors.

The nitty-gritty

Okay, here's the dirty details.

First the profile was extracted, typically from Garmin data if available on-line from motionbased, Garmin Connect, or Strava (Strava extracted with Cosmo's Strava-to-TCX converter).

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! Simple, really.

Dan Connelly