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Hardrock is only 90 miles!

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  • Matt Mahoney
    I just got my Hardrock entry booklet today. Very nicely done, But on page 2 of the course description, item 6, it says: All mileage used were obtained by map
    Message 1 of 4 , May 6 1:30 PM
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      I just got my Hardrock entry booklet today. Very nicely done, But on page 2
      of the course description, item 6, it says:

      "All mileage used were obtained by map measurement with on the ground wheel
      measurement verifications for over half the course. To correct for vertical
      changes on the map measurements, the vertical distances are added directly
      to horizontal distances to obtain the totals"

      If we subtract the vertical distance (66,000 ft. = 12.5 miles) from the
      total distance (101.7 miles), we obtain a horizontal component of 89.2
      miles. Then applying Pythagoras' theorem, which is the correct method of
      combining horizontal and vertical distances (assuming a constant grade), we
      have

      sqrt(89.2^2 + 12.5^2) = 90.1 miles.

      So this course is really not has hard as everyone says it is :-)

      Also, a couple of minor errata:

      1. Carl Yates is listed as -27 years old (a lingering Y2K bug maybe, or did
      we make an exception to the minimum age requirements?)

      2. At the absolute bottom of the all time finishers results (sorted by
      time), Fred Vance and I (with * by our names) are listed as finishing
      unofficially in 51:08 in '98. Our actual time was 51:38:34 (a blistering
      34:23/mile pace, and I had the blisters to prove it).

      -- Matt Mahoney, matmahoney@...
    • John Cappis
      Matt: Your point on the methodology used to obtain the distances for the Hardrock is well taken. It is done very deliberately for the following reason. Over
      Message 2 of 4 , May 10 6:53 AM
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        Matt:

        Your point on the methodology used to obtain the distances for the
        Hardrock is well taken. It is done very deliberately for the
        following
        reason.

        Over the years, Charlie and I have measured between 150 and 200 miles
        of trail in Colorado and New Mexico by pushing a bike wheel fitted
        with a Jones counter. In 1992 and 93 Rick Trujillo measured about
        half of the Hardrock course using this wheel.

        All the courses were then laid out and measured on the map using the
        Pythagorean theorem as you suggest. Correlation with the in field
        measurements was poor and systematically biased low. We have assumed
        the in field measurements are the more accurate numbers. The best fit
        of the map to field turned out to be the the vertical distances are
        added directly to horizontal distances to obtain the totals.

        John Cappis

        --- In hr100@egroups.com, "Matt Mahoney" <matmahoney@y...> wrote:
        > I just got my Hardrock entry booklet today. Very nicely done, But
        on page 2
        > of the course description, item 6, it says:
        >
        > "All mileage used were obtained by map measurement with on the
        ground wheel
        > measurement verifications for over half the course. To correct for
        vertical
        > changes on the map measurements, the vertical distances are added
        directly
        > to horizontal distances to obtain the totals"
        >
        > If we subtract the vertical distance (66,000 ft. = 12.5 miles) from
        the
        > total distance (101.7 miles), we obtain a horizontal component of
        89.2
        > miles. Then applying Pythagoras' theorem, which is the correct
        method of
        > combining horizontal and vertical distances (assuming a constant
        grade), we
        > have
        >
        > sqrt(89.2^2 + 12.5^2) = 90.1 miles.
        >
        > So this course is really not has hard as everyone says it is :-)
        >
        > Also, a couple of minor errata:
        >
        > 1. Carl Yates is listed as -27 years old (a lingering Y2K bug
        maybe,
        or did
        > we make an exception to the minimum age requirements?)
        >
        > 2. At the absolute bottom of the all time finishers results (sorted
        by
        > time), Fred Vance and I (with * by our names) are listed as
        finishing
        > unofficially in 51:08 in '98. Our actual time was 51:38:34 (a
        blistering
        > 34:23/mile pace, and I had the blisters to prove it).
        >
        > -- Matt Mahoney, matmahoney@y...
      • Roger Wiegand
        Dear Hardrockers, I have read with amusement the discussions on the length of the Hardrock course. Clearly a mathematician s input is needed. Of course we
        Message 3 of 4 , May 12 7:17 AM
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          Dear Hardrockers,

          I have read with amusement the discussions on the length of the Hardrock
          course. Clearly a mathematician's input is needed. Of course we live in
          a three-dimensional space, but for simplicity, let's just use x for
          horizontal displacement and y for vertical displacement. The usual
          Euclidean metric gives the total displacement as
          d = (x^2 + y^2)^{1/2} (the Pythagorean Theorem). In mathematical jargon
          this might be referred to as the L^2 metric. John and Charlie are using
          the L^1 metric: d = |x| + |y|. In fact, there is a whole continuum of
          L^p metrics, for 1 <= p <= infinity: d = (|x|^p + |y|^p)^{1/p} in the
          L^p metric. (For p = infinity, the limiting case,
          d = max{|x|,|y|}.)

          So what does this mean for us Hardrockers? While parapsychology is a bit
          outside my realm of expertise, it seems clear that a gathering of 100
          deranged minds in one location has the potential to distort space, thereby
          changing the metric. In fact, once the runners get spread out along the
          course, it is likely that the space surrounding one clump of runners will
          have drastically different geometry from the space surrounding runners on
          a different part of the course. This is the real reason that
          most of the runners finished ahead of me. They were working
          with a different metric, more favorable to the runner.

          I am virtually certain that I ran at least 100 miles last year. (Look how
          long it took me, if you have any doubts!) But just to be sure, I will get
          up early the morning of the race and take a ten-mile run before the
          start. I invite any other runners with geometric anxiety to join me.

          Roger


          Roger A. Wiegand
          http://www.math.unl.edu/~rwiegand
        • Michael A. Farris
          Roger wrote: ... I think Mulder and Scully are entered, undercover, to investigate just this phenomenon. Scully will be the one running in heels, so
          Message 4 of 4 , May 12 8:18 AM
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            Roger wrote:
            <snip>
            >So what does this mean for us Hardrockers? While parapsychology is a bit
            >outside my realm of expertise, it seems clear that a gathering of 100
            >deranged minds in one location has the potential to distort space, thereby
            >changing the metric.

            I think Mulder and Scully are entered, undercover, to investigate
            just this phenomenon. Scully will be the one running in heels, so
            she'll be EZ to pick out.

            The truth is out there.

            Mike

            ________________________________________________________________
            Dr. Mike Farris mfarris@...
            Associate Professor of Biology http://www.hamline.edu/~mfarris
            Hamline University, St. Paul, MN 55014
            ________________________________________________________________
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