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RE: [hr100] Re: Hardrock is only 90 miles!

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  • Herr, Dennis B.
    Another possibility could be that the total distance is right, but the total vertical is significantly underestimated. Dennis Herr
    Message 1 of 4 , May 10, 2000
      Another possibility could be that the total distance
      is right, but the total vertical is significantly underestimated.

      Dennis Herr

      > ----------
      > From: John Cappis[SMTP:cappis@...]
      > Reply To: hr100@egroups.com
      > Sent: Wednesday, May 10, 2000 9:53 AM
      > To: hr100@egroups.com
      > Subject: [hr100] Re: Hardrock is only 90 miles!
      >
      > 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...
      >
      >
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    • Curiel, Tyler
      It s a closed loop. Really doesn t matter how long it is. If you keep running long enough, eventually you ll get back home. /TC
      Message 2 of 4 , May 10, 2000
        It's a closed loop. Really doesn't matter how long it is. If you keep
        running long enough, eventually you'll get back home. /TC
      • Matt Mahoney
        ... Another factor that distorts the space-time metric is sleep deprivation. I found that after about 44 hours that all of the trails were twice as long and
        Message 3 of 4 , May 12, 2000
          --- Roger Wiegand <rwiegand@...> wrote:
          Another factor that distorts the space-time metric is
          sleep deprivation. I found that after about 44 hours
          that all of the trails were twice as long and twice as
          steep.

          Furthermore, there was no longer a linear mapping of
          the terrain to my map, resulting in my map becoming
          useless for navigational purposes, resulting in my
          getting completely lost, resulting in a 51 hour DNF
          two years ago.

          > 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.

          Will this be on the course? I found some sections
          around Grant-Swamp pass that are not quite on the
          course but are far more difficult than anything we
          would normally have to do. It would be interesting to
          explore these regions in a normal space-time continuum
          to see if they really are as vertical as they seemed
          at the time. Just to make sure we don't miss the
          start, I would recommend we get up about 15 hours
          early and bring ropes.


          =====
          -- Matt Mahoney, matmahoney@...

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        • Curiel, Tyler
          Roger, I read with great care your cogent arguments. However, have you also considered the gravitational effects of the mass of runners, not to mention their
          Message 4 of 4 , May 12, 2000
            Roger, I read with great care your cogent arguments. However, have you also
            considered the gravitational effects of the mass of runners, not to mention
            their equipment? I suggest you make that a 12 miler just to be safe. /TC

            -----Original Message-----
            From: Roger Wiegand [mailto:rwiegand@...]
            Sent: Friday, May 12, 2000 9:18 AM
            To: hr100@egroups.com
            Subject: Re: [hr100] Re: Hardrock is only 90 miles!


            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




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