17
Jun 2008
by mark

The Question of Hills

Updated August 23rd, 2008. See corrected math and discussion in the comments.

Kurt climbing out of Brownsville I was recently asked: “How can get around town by bike without going up and down so many hills?”

Avoiding hills is often not an option, so I have to re-frame the question in order to answer it: “How I can be comfortable riding in hilly terrain?”.

For a cyclist used to driving, there may be an adjustment about what to expect. A car may (unnaturally) travel the same speed up a hill, across the ridge line and back down it.


Still, I sometimes ask myself “Am I going extra slow up this hill?”.

I think about how fast I might descend the same hill. Say I’ve averaging 12 mph on trip and find myself going 3 mph up a big hill. That’s a difference of 9 mile per hour. 12 plus 9 is 21. Could I descend the hill at 21 mph? If so, then I could continue to inch up the hill at 3 miles per hour and continue to average 12 for the trip, assuming I get to zoom down the hill at some point.

There’s a related mental trick that we can play on ourselves because the average speed is calculated over distance not over time. In the example above, it would take me seven times longer to climb the hill to descend it, but both parts contribute equally to the average speed, because going up and down the hill are both the same distance.

The result is that on a given bike trip, I can speed a lot of time riding slowly up hills, even though my average speed is much faster because I’m zooming down hills is so fast.

Enough of the math games.

Here’s my basic tips for climbing hills as a bike commuter.

I keep up a moderate effort until I feel the hill start to push back at me. If I have some momentum, this may be part way up the hill. For small short hills, I like to gear down to create a high cadence and sprint to the top.

Sprinting to the top works if I’m able to crest the hill quickly, say in 30 seconds of effort of less. In these cases, my speed may actually /increase/ as I go up the hill. I do this when I’m crossing the Richmond Avenue bridge from east to west. If there’s one place to put in a little extra effort on a bike ride, it’s on short hills.

With practice, this habit has become reflexive for me. I recall being tired on mile 60 of a loaded bike tour, and watching myself shift down and spin over a small hill, almost as an out of body experience. Rationally, I was tired and just intended to keep turning the pedals around. Because I had practiced it so may times intentionally, it happened automatically when I was tired and not “trying”. Spooky. At this point small hills “don’t count” because they are conquered with hardly a dip below average speed.

For longer climbs, I also use a low enough gear so I can pedal comfortably– no pain and no gasping for air. On a perfect climb of a steadily increasing hill, my speed should continue to remain steady or drop as I go up the hill.

Part of my current speed is effort I’m putting into it and part of it is momentum. It’s noticeably harder to increase speed going up hill than it is to keep it, because of the principle of inertia.

A recipe for getting burned out on a hill is to put in a burst of energy to speed up, only need to a rest before I reach the top, and then work extra hard to build up my speed again.

If the speed gets down to 3 miles per hour and I’m straining, it’s time to realize that walking is now a competitively fast option, and it may be a better idea to get off walk the bike. Unless a hill is cruelly steep or the bike lacks sufficiently low gears, this should rarely happen.

I try to only pick up my pace on a long hill if I’m close to crest and feel like I can keep up my speed all the way there without needing a rest.

The other day I went out to the hill on Niewoehner Road near Richmond, Indiana to practice riding up a steeper hill. The first time I climbed it at a steady, comfortable pace. Then I zoomed down it (at about 45 mph!), and tried it again. This time I pushed harder and went up it faster, but started to get out of breath. Although my speed going into the hill was faster, I nearly had to stop and catch my breath. If that had happened, I would have had to work extra hard to accelerate on the hill, and the slower, steady approach to ascending hill would have surely been the fastest time to the top.

With knowing personal limits, steady, comfortable effort is the safe bet for hill climbs.

It may seem odd to intentionally choose hilly routes to ride, but by intentionally practicing on them when I have a choice, I’m better prepared for all the hills I can’t avoid.

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  • http://justenoughcraig.blogspot.com Craig

    The math in this post is incorrect. Average speed is not the average of your climbing and descending speeds but is instead the total distance (climbing and descending) divided by total time. This difference will give you a radically different average speed but one that is correct.
    For example, if you climb a hill for X miles at a pace of 3 MPH, then it is impossible to achieve an average speed for both climbing and descending of 6 MPH or greater. This is because even if you descend at the speed of light — not recommended on most bikes! — you merely double your total distance traveled to 2X, and doubling the distance merely doubles the average speed.
    In the example in the post, climbing a hill for X miles at 3 MPH and descending at 21 MPH yields the following:
    T = D / V (velocity)
    D-up = X miles (given)
    V-up = 3 MPH (given)
    T-up = X miles / 3 MPH
    D-down = X miles (given)
    V-down = 21 MPH (given)
    T-down = X miles / 21 MPH
    T-total = (X miles / 3 MPH) + (X miles / 21 MPH)
    D-total = 2X miles (given)
    V-total = D-total / T-total
    V-total = 2X miles / ((X miles / 3 MPH) + (X miles / 21 MPH))
    V-total = 5.25 MPH
    So in the above example, going up a hill at 3 MPH and down at 21 MPH gives an average speed of 5.25 MPH. This is not as encouraging of a result — sorry!
    Two comments:
    (1) Try this for yourself. Go up a hill at 3 MPH and down at 21 MPH. Measure how far you went in total up and down the hill as well as how much time elapsed. Then find a flat stretch the same distance and go 5.25 MPH. You should find that it takes the same time.
    (2) An intuitive way to understand the math is that you spend a lot of time going up the hill slowly but zip down the hill quickly. Therefore, the uphill portion penalizes your average speed much more than the downhill.

  • http://mark.stosberg.com/ Mark Stosberg

    Craig, Thanks for the reply. I double checked the math and you are right.
    However, my experience remains that going up hills doesn’t lower my overall average speed as much as I expect it to. This could perhaps be because the momentum of the downhill has a greater affect than any additional recovery required once I’ve reached the crest after an uphill.
    For example, Consider a course that is one mile uphill followed one mile downhill and then one mile of flat. For some distance on the flats I’ll be able to continue to put the downhill momentum to work as my speed tapers back town a “normal” speed for flat ground.
    In the rolling hills of Indiana, that also means that some amount of the downhill momentum is going into making climbing the raise immediately following it easier.
    Of course, I’m using intuition again and you are using physics equations, so I’m prepared to be wrong about the reality again.

  • http://www.PortlandBikeCommuting.org/ JohnB

    Regarding your statement about walking becoming a competitive option, I would say that’s true only if you are not carrying a heavy load, especially in a trailer. In that case, as I have experienced several times in the last few months with over 50 pounds of freight, I may be standing on the pedals in granny gear to climb the hill with the load, but if I get off and try pushing it uphill instead, it’s much harder still. I guess from a physics point of view you could say that at least in a heavy load-bearing situation, your gears really are doing a lot of work for you. Which is encouraging!