Thursday, January 26, 2012

rating New Zealand climbs

I've described a decent number of climb profiles from my trip to New Zealand, with profile data collected from a Garmin Edge 500 or, in the case of Haylocks, by Strava using topological data in conjunction with positions recorded by the Strava Android app. It's then obvious to ask: how do the climbs compare? Which was the toughest?

Good question.

First, some data. I plot here the altitude gained versus the climbing distance for each of the climbs. I define "the climb" as the portion of road which maximizes my climb rating, which I've described in this blog before. Here's the result, where I normalize each by the number associated with Old La Honda road:

vertical vs. distance

What makes a climb tough? To me, it's continuous time spent at a big grade, with a lot of altitude gained.

click on image for expanded view

Haylocks profile
profile of Haylocks from Maori church. Ignore wiggles, a mapping artifact; climb is continuously up. Click on image for larger view.

Using an objective combination of grade, continuity, and meters of elevation difference I'd have to rank Long Bay Road as the toughest. Haylocks Road was definitely the steepest: it was an effort just to keep the bike moving on that one, but it was fairly short. I did have the advantage on Haylock of having not climbed it continuously: I stopped at the junction with Hamiltons, went up Hamiltons, then descended back to the junction and did the portion of Haylocks from there. But even accounting for that I felt Long Bay was the greater endurance challenge.

click on image for expanded view

click on image for expanded view

You can see from the first plot that both sides of Crown Range Road gained more vertical than Long Bay. But the east side of Crown Range is gradual, only a few percent, for a considerable distance. Long kilometers on the road can be difficult and tiring, but the difficulty I'm talking about here isn't about hours in the saddle, it's about the portion of the difficulty due to the climbing itself. The western slope of Crown Range is far steeper. However, there is considerable recovery provided: approximately 5 km where the grade barely touches 7%, including descending. These kilometers dilute the rest of the climb, where the grade sustains between 10.1% and 12.6% by my determination. Long Bay Road also has recovery sections, but they are much shorter: 500 meters and 200 meters, approximately, most of the rest of the climb hovering about the 12-13% range.

So which is harder? A short grunt of a climb (Haylocks) flirting continuously with the nasty side of 20%, or a much longer climb (Long Bay) which tends to hang out in the 12-13% range? The answer depends, of course, on what gears relative to your strength-to-weight ratio.

My climb rating formula includes an exponential difficulty factor proportional to the exponent of the ratio of the grade to 8%: when the grade gets much over 8% difficulty per unit altitude change increases rapidly. With this assumption, the difference between a given amount of climbing at 12% and at 20%, sustained, is around a factor of e, or around 271%. This pays off big-time for Haylocks.

So here's a plot of the derived ratings, where I applied a 100 meter dual-sided exponential smoothing function to the Haylocks profile to get rid of those anomalous wiggles before applying the formula:

rating vs. vertical

Haylocks, despite being the least total climbing of any of the climbs I plotted, wins on the difficulty scale. Hmm... I still disagree, from my perception, but with different perceptions (for example, had I been stuck with a 39-23 low gear instead of a 34-26) it might have been an undisputable conclusion.

Here's a summary of the numbers, all of which have been normalized to Old La Honda Road (5.55 km, 393 meters, rating formula = 1005.5 meters):

Pigeon Bay Rd, Banks Peninsula
Dyers Pass Rd (S), Governors Bay
Crown Range Pass (E), South Island
Okains Bay Rd, Banks Peninsula
Arthurs Pass, Westland, South Island
Crown Range Pass (W), South Island
Long Bay Rd, Akaroa
Spur Rd - Haylocks Rd, Onuku


Shane Mc Quillan said...

Hi, can you have a look at Lighthouse Road, Akaroa. That is a lot harder than Longbay and likely one of the toughest climbs in NZ.

djconnel said...

I believe you. In this post I reported on my ride in the Onuku hills. My original goal had been Lighthouse, but I was with Cara and her bike wasn't set up to handle what Lighthouse clearly had to hand out. As it was we got our dose of steep stuff. But Lighthouse would have been a fun challenge. If I return I'll definitely give it a go. My memories of that trip are 100% positive. Indeed I was further reminded of it while watching the America's Cup in San Francisco Bay, but that's another subject...