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Can a hilly out and back course be faster than a flat course

  1. Jul 2, 2009 #1
    There is a scientific word/explanation for the phenomenon that a out and back course in a cycling time trial race can actually be faster than a flat course. For example, in Cherokee Park in Louisville, there is a 10 kilometer course that starts on the flats, then has a pretty good downgrade where speeds of over 30 mph are attained. When the upgrade is reached the momentum more than assists that climb only to be followed by another down grade. The only part of the course that bogs down is on the return trip climbing that final hill which was the first downhill on the outbound leg. I proposed to a physics instructor at the University of Florida two years ago, that the course was actually faster than had the course been totally flat. He gave me a name for the phenomenon, and I can't recall what it was having never previously heard that term. Can anyone help me with this through either an explanation and/or the name of the term? Thanks
     
  2. jcsd
  3. Jul 2, 2009 #2

    Danger

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    Welcome to PF, Peddlemasher.
    I know little about weather, and even less about bikes, but my best guess is that you're catching updraughts and/or tailwinds due to the alteration of airflow by the landscape.
     
  4. Jul 2, 2009 #3
    Perhaps my example was misleading. I'm really not talking about this instance - I only use it as an example. It has nothing to do with up and down drafts. There is a phenomenon, which has a name, that describes the physics behind the fact that in some instances a hilly out and back course can be faster than a flat course (normally not the case) when a cyclist traverses the course as fast as he or she can in a race situation. You can assume zero wind.
     
  5. Jul 2, 2009 #4
    Right. If there is a sudden downhill grade right at the start and you stay at low altitude until the finish, then you get a sudden burst of acceleration at the start and keep that high speed over the course, so it can be faster than a flat terrain. Don't know any name for that, though.
     
  6. Jul 2, 2009 #5
    Right, but understand this is an out and back course, so for every downhill on the outbound leg, the same stretch of roadway now has to be negotiated as an uphill grade. What I am stating is that there is some combination of road gradient that even negotiated in both directions is faster due to the way and steepness of the gradients encountered. I am searching for the information, which I know to exists, that discusses this interesting phenomenon.
     
  7. Jul 2, 2009 #6

    Danger

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    I'm easily misled. Sorry that I can't be of assistance in this case. :redface:
     
  8. Jul 2, 2009 #7
    Isaac Newton was given a problem, called the Brachistochrone Problem, about 1696 or '97. No other mathematician could solve it, nor could Isaac, so he invented calculus of variations, and solved the problem in (I'm told) one day. The problem is to find the fastest (total elapsed time) trajectory of a frictionless bead sliding on a wire from a point x1, y1 to a lower point x2, y2. Here is his solution:
    http://mathworld.wolfram.com/BrachistochroneProblem.html
     
  9. Jul 2, 2009 #8

    DaveC426913

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    I would point out that a factor that cannot be ignored is the human rider. This element of the total system may well work more efficiently in a cyclic pattern than a constant output pattern.
     
  10. Jul 3, 2009 #9
    I think its pretty unlikely that a hilly course could be faster than a flat one. You have to remember that the increase in air resistance is not proportional to speed but rather to the speed squared (roughly speaking), and overcoming air resistance is where most of the work is done in a cycling race. Say you have 2 (rather slow) cyclists doing a 2 mile race. Cyclist A rides at 15mph the whole way. Assuming air resistance varies with velocity2, the work done by him against air resistance in arbitrary units over 2 miles is 2x152=450. Cyclist B rides the first mile at 12mph then the second at 20mph so he finishes in the same time, but the work he does against air resistance is 1x122 +1x202=544, so he uses about 21% more energy to do the same course in the same time. Secondly, you also have to consider the physical demands of the race. Looking at the split times from Boardman's http://www.wolfgang-menn.de/hourrec.htm" [Broken], for example, shows very even pacing and it is generally acknowledged that this is the fastest strategy in athletics as well, where air resistance is less of an issue. Riding one part of a race producing more power than in another (apart from the sprint at the end) is inefficient and is hard to avoid in a hilly race.
     
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