- 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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> - --- 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

Will this be on the course? I found some sections

> 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.

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@...

__________________________________________________

Do You Yahoo!?

Send instant messages & get email alerts with Yahoo! Messenger.

http://im.yahoo.com/ - 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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