The Math of Misery: A Digression

Here’s an unhappy calculation about riding in hilly areas.

Let’s say you are cycling somewhere that is mainly hills, and they are symmetrical (same length up as down).  For sake of argument, let’s say you have a 6 mile long climb followed by a 6 mile long descent, just to keep the math simple.  I am a pretty aggressive climber (right Jenn and Frank?) and can go about 6 mph up with my loaded bike.  On the descent, 24 mph is easy without even peddling. That means the ascent would take 1 hour, whereas the descent would take 15 minutes. So, out of the 1 hr 15 min period you traveled that hill, 80% of the time you’d be climbing.  Ouch!

Also, no matter how fast you ride down,  you can never do better than doubling the uphill rate as an average speed for the hill.  Thus, in the previous example, if you came down the hill at the speed of light, you’d have covered 12 miles in one hour, twice your uphill rate. Any realistic downhill speed gives you a slightly slower average.  Moral: Climb quickly.

I still like hills.  In the Tour de France, I would be the guy with the polka dot jersey, the King of the Mountains.

King-of-The-Mountains

(Photo credit: Tour de France)

King-of-The-Mountains doctored

(Photo credit: Jenn Langheld)

2 thoughts on “The Math of Misery: A Digression

  1. Jenn's avatarJenn

    It amuses me to no end to know that this is what spins through your head while you’re powering up hills that seem to stretch on and up forever. I can assure you that at no time on our ride was I doing math or formulating equations while struggling up the hills. Instead I was more likely inventing ever new and colorful curse words, and arranging them into increasingly creative and salty combinations. It’s probably just as well that you never managed to get our two-way headsets working. 🙉 😉

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  2. Frank Shelp's avatarFrank Shelp

    There is another rather obvious solution!!! Slow the descent! If you apply the breaks and descend at 6 mph then you will spend 1 hour descending and 1 hour climbing. If you slow in more, say 4 mph you can move half your time going downhill !!! 🙂 In fact, if you get off and walk your bike downhill at say 2 mph you can spend 75% of your time going downhill !! Yay!!

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