Archive:
Ride Smart / Not Hard
Today's Topic: Save It for the Hills
By Peter Jensen
In the last edition of "Ride Smart, Not Hard," (archive) we looked at human efficiency and improved performance through thoughtful coordination of the pedal stroke. Through the correct mental focus, we can ride faster without working harder. Today's topic is similar, as are all of the topics in this column, which focuses on the brain's ability to squeeze more juice from a lemon, more toothpicks from a tree, and more speed from you and your bike.
Today's topic, "Save It for the Hills," is a common saying amongst roadies, the implication being that your efforts accomplish more when climbing hills. Take a look at the Tour de France, for example. It always begins with several flat stages in which the giant pack remains one giant multi-colored blob, and the sprinters always rush to lead the blob across the finish line. Everyone's time is the same, except maybe those with the flu or who flatted in the final couple of miles, and everyone except the sprinters thinks "Well gosh, what was the point of that, anyway?" But then come the hills, leaders emerge and leave the pack far behind, and the sprinters abandon the race while complaining of imagined gastro-intestinal disorders contracted from a previously unknown species of carbon-fiber-boring titanium tick.
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Actually, "Save It for the Hills" is a study of wind resistance versus gravity. When climbing a steep hill, your speed is limited primarily by gravity, and when riding across flat ground, your speed is limited by wind resistance. In each case, if you work harder, you can go faster. But as we'll soon discover, all is not equal.
When climbing a steep hill, if wind effects are nil, then your speed is proportional to your effort. In other words, if you work twice as hard, you will go twice as fast. This proportionality arises from the force you are working against — gravity — that is constant and is not affected by your speed. (Note for the purists: we're assuming that the cyclist's speed is far below the speed of light, that relativistic effects can be ignored, and that Vulcan tractor-beams are not present.)
When you're riding fast on flat ground, things are different. You slice through the air, and the faster you go, the more turbulent the air becomes. No doubt you've noticed this on windy days or during fast descents, when it's impossible to carry on a conversation simply because the wind noise is too loud. Significantly, the force arising from this turbulence is not constant. Nor does it increase in step with your velocity. Instead, assuming fully developed turbulent flow, the force increases as the square of your velocity.
Wow. So what does this mean? Well, if you double your speed, then the force increases by a factor of 4. If you triple your speed, then it increases by a factor of 9.
But the story doesn't end there. Your work rate is defined as the force multiplied by velocity. For the mathematician, this can be written as a simple multiplication equation.
 Work Rate = F * V
But because we've noted that the force is proportional to the velocity squared, this equation can be rewritten as
Work Rate = k * V2 * V
Or
Work Rate = k * V3
If you don't have an eye for equations, never fear. What all of this means is that when the wind is turbulent and noisy in your ears, then to double your speed you must work 8 times as hard. To triple your speed you must work 27 times as hard.
Comparing flatlands with the hills, if you work twice as hard on level ground, your speed will increase only by 25%. But if you work twice as hard on a hill, your speed will double. So if there's a choice to make, save it for the hills. From all of this complex math the old saying is vindicated, and now you know more than ever how to ride smart, not hard.
"Ride Smart / Not Hard" is a regular column in the Eastern Idaho Bike Magazine. Can you think of a topic for
the next issue? Let Us Know!
Peter Jensen has resided in Eastern Idaho for 19 years. He is an avid cyclist, though a "non-racer" because
of his low melting temperature (above 75 degrees you'll find him frying up some beef liver and gummi bears on
the road). He is an Internet programmer and engineer, and like all true engineers is constantly thinking of
simple ways to make things easier.
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Road Riding at Night!
Actually it's not as insane
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