The Physics of Bicycle Climbing (oh, and a few words about a stupid bicycle climb)

Last night, when I got home, my wife asked me if I'd read Eldon's blog. A quick look showed that he was trash talking about today's ride. Me, I don't need to trash talk or work to psych anybody out, because I'm confident in my climbing skills. So confident, in fact, that I thought I was a virtual lock to make it to the top of the hill, and even pick up some time over my previous ascent.

Despite the fact that I run, and unlike Eldon, I'm not a particularly gifted climber. I'm learning how to suffer (more on that later), but my physique is not suited to be first up the hill.

The sport of bicycling has lot of variables. Wind and aerodynamics play a huge part, as does drafting. But when you get to the steep hills - unless you're talented to ride up them at meaningful speeds - it's mostly about power/weight ratio. I was thinking about this a few days ago, and dusted off some disused physics expertise.

First, we need to figure out my potential energy at the top of the hill. For that, we'll use the following formula:

PE (Joules) = mgh

My bike and I weigh pretty close to 200 pounds (a few pounds less, but that doesn't matter) = 200 / 2.204 kg = 91 kg. That's the m.
Zoo hill is 1200 feet = 1200 * 12 inches = 1200 * 12 / 39.3 meters = 366 meters. That's the h.
Finally, g stands for gravity, and for the earth, it's 9.81 m/sec^2

So, that gives me:

PE = 91 * 9.81 * 366 = 330000 Joules (if I mess up on the significant digits, my wife will kill me.)

All that is left is to convert that to Watts. Conveniently, 1 Watt = 1 Joule / sec. I climb the zoo in 25:30, so

Climbing Power = 330000 / 1530 = 220 Watts

There's some additional sources of resistance, but they probably aren't that big for the Zoo, especially at the speeds I ride.

Eldon wrote that he did the Zoo last week in about 21 minutes (lets say 21:30). That's a ratio of 0.84 to my time. To match that, I either need to up my power output to 220 / 0.84 = 262 watts, or I need to reduce my weight by the same factor to 180 * 0.84 = 151.2. I did weigh that much in high school, but I had less upper body muscle than I do now (hard to believe, I know).

So, class, what did I prove? Well, I proved that there was no way I was going to beat Eldon. But maybe there was another way. For the climb, I wrote up a few guidelines and printed them out, along with a map. Here's what they said:

  • It’s tough to get lost. Just keep going up. When you get to the stop sign, turn left. When there’s a green gate on you’re right, you’re at the top, and it’s all downhill from there.

  • On the descent, turn left at the stop sign.

  • This is an unsupported ride, so if you stop, you will fall over.

  • Limit your speed on the first pitch. In fact, you should probably stay behind me the whole ride, just to be safe.

  • Those who reach the top may choose to coast back down to ride up with those who haven’t made it up yet. Those who haven’t made it up yet may choose to whack those who have made it with their pumps.

  • The organizers request that any riders who pass out attempt to do so that their bodies will roll onto the shoulder.

  • Those with something to prove should ride the inside of the hairpin. Those with a lick of sense should ride a more rational line.

I then handed Eldon a sheet and asked him to read them out loud, with the excuse that I didn't want him to be the only guy who got to be funny.


What he didn't know was that his sheet was special. All the other ones had an additional guideline which said:

  • (This guideline isn’t on Eldon’s sheet, so don’t ruin it). $20 to the top finishing rider who beats Eldon to the top. I’m not kidding on this one – I have the cash with me.

Yes, if I can't beat Eldon myself, perhaps I can pay somebody to do it. Eldon claims that that is evil. Hmm. What did I read yesterday? Oh, yeah, "I will pay other people to interfere with my boss's boss". Yeah.

So, anyway, we did the ride, and I displayed my mad climbing skillz. I bumped my average heart rate up about 5 points, and got up in a time virtually indistinguishable from last time. And I wasn't last to the top, though I should note that of the two guys arriving after me, one started 10 minutes behind me, and the second was about 5" taller than I am.

But I am learning to suffer better.


Comments (11)

  1. Sam says:

    Eric, just a funny question (I cant find your other post about the climb): what was your average heart rate this time?

  2. ericgu says:


    I don’t usually talk about heart rate because it’s doesn’t really transfer from person to person, and my polar software only gives me averages for the whole workout, not the climb.

    But, just for you, I pulled the info out and put it into Excel. My average heart rate for the climb was 166. I could have pushed a little more – I was okay at 171 – but that pushed me more to the limit of my muscle strength on the middle of the climb. I went and looked at my last ascent, and I averaged about 161.

    Right now, while watching football on the couch (and with the Seahawks leading 34-12), my resting heart rate is 42.

  3. Chris says:

    Though unsolicited I will offer up my own information. As I rode the Zoo my heart-rate hovered between 180 and 184. 184 is the absolute highest I have ever seen for me on a bike. My resting heart rate is roughly 56. Out of curiosity…. can anyone explain what it means that I have a higher resting heart rate and apparently a higher max heartrae than Eric. I realize that everyone is unique but are there trends or generalizations that can be pulled from this information?

    Chris (The shorter of the two in the Tazo jersey.)

  4. Abed Husseini says:

    I was the last to make it up the Zoo Hill climb on Saturday (tall guy, MS Jersey), and my heart rate got to a suprisingly "low" 180…I say low because I have gotten my heart rate up well past 190 in the not so distant past over shorter climbs. Anyway, it was a fun ride, I was thoroughly pooped, and FatCyclist was thoroughly insane to climb it again right after reaching the top. I am planning on going at it again this next weekend…anybody else interested?

  5. Mark Wan says:

    There is still a way to catch Eldon and it should be three pronged:

    1. decrease the weight of your bike by buying yet another climbing daemon that weighs less than 14 lbs. Hey, nobody is going to weigh your bike I think.

    2. increase your power output by about 8%. around 237 W

    3. decrease your weight by about 8%. So aim for 165lb.

    If you do that you should be able to climb at 20.4 minutes.

    🙂 I know this is easily said than done. I am in the same boat as you are.


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