Roads that are also inportnant latitudes or longitudes

"Dick Boyd" wrote in message
oups.com...

The legals are flat earth representations of a curved surface.
North-south lines on the surface of the earth converge. Longitude lines
get closer and closer until they all meet in one place at the poles. So
north-south roads laid out on legals, really don't run true
north-south. To compensate, north-south section line roads are offset
to correct for the convergence of meridians of longitude.

Fascinating; I never thought much of meridians from a global perspective!

So let's say you're standing on the North Pole and took a few steps south.
If one was to then walk to the east (or west), each step would be onto a
different meridian. Likewise, one would have to traverse long distances
between meridians at the equator. With that in mind, the distance between
the meridian is relative to where one is between the equator and one of the
earth's pole. If you're lucky enough, maybe you'd get to stand directly on
the poles and never take a step--however that's a privilege most don't have!

With that in mind, all meridians converge at one of the earth's poles. This
solves a riddle an algebra teacher gave me nine years ago, which was, "When
do parallel lines touch each other? Hint: Think of the earth's curvature."

....Here's an off-shoot to the discussion. In theory, let's say that our
ancestors created poles at two points on what we have been considering (for
centuries) the equator. Thus, the north and south poles would have never
received any polar nomenclature. Also, to remove confusion in this
discussion, what we know in reality as "west" and "east" is mentioned as "x"
and "y", respectively, while "north" and "south" is mentioned as "w" and
"z", respectively. The x pole would have lines which would spread and
re-converge at the y pole. Meanwhile "w" and "z" would consist of lines
running parallel to to the x and y poles.

Here are a couple questions that arise for this scenario:

Would it be appropriate to call those lines converging in and from the x and
y poles "meridians"? Would it be appropriate to label "lines of latitude"
as those lines which span out in w and z directions?

The objective for this question is to determine whether the terms "meridian"
or "line-of-latitude" are relative to our ancestors' perception & assignment
of the North and South Poles, or if the terms are relative to the poles'
location as assigned by the person(s) studying a spherical object.

Cheers,

Carl Rogers
-----------------
Calrog.com, Pictures of Highway Shields: http://hwy-shields.calrog.com
Calrog.com, Personal and Interpersonal Psychology page:
http://psychology.calrog.com
Highway Shield & Travel Literatu http://www.lulu.com/calrog-bookstore

"Carl Rogers" wrote...

...Here's an off-shoot to the discussion. In theory, let's say that
our
ancestors created poles at two points on what we have been
considering (for
centuries) the equator. Thus, the north and south poles would have
never
received any polar nomenclature. Also, to remove confusion in this
discussion, what we know in reality as "west" and "east" is
mentioned as "x"
and "y", respectively, while "north" and "south" is mentioned as
"w" and
"z", respectively. The x pole would have lines which would spread
and
re-converge at the y pole. Meanwhile "w" and "z" would consist of
lines
running parallel to to the x and y poles.

Here are a couple questions that arise for this scenario:

Would it be appropriate to call those lines converging in and from
the x and
y poles "meridians"? Would it be appropriate to label "lines of
latitude"
as those lines which span out in w and z directions?

The objective for this question is to determine whether the terms
"meridian"
or "line-of-latitude" are relative to our ancestors' perception &
assignment
of the North and South Poles, or if the terms are relative to the
poles'
location as assigned by the person(s) studying a spherical object.


Chances are, if such a polar system had been developed, the name
'meridian of longitude' would not have been used as the word
'meridian' comes from the latin root 'meridies', meaning 'midday' (the
sun is at its highest at the same time [midday] along a meridian of
longitude). On the other hand, the name 'parallel of latitude' would
be quite appropriate as long as the 'x' and 'y' poles are at opposite
points on the planet, since the planes through the planet along
parallels of latitude would still be parallel to each other.


Cheers,

Carl Rogers


--Andy
--------------------------------------------------
Andrew G. Tompkins
Software Engineer
Beaverton, OR
http://home.comcast.net/~andytom/Highways
--------------------------------------------------

Carl Rogers wrote:
"Dick Boyd" wrote in message
oups.com...

The legals are flat earth representations of a curved surface.
North-south lines on the surface of the earth converge. Longitude lines
get closer and closer until they all meet in one place at the poles. So
north-south roads laid out on legals, really don't run true
north-south. To compensate, north-south section line roads are offset
to correct for the convergence of meridians of longitude.

Fascinating; I never thought much of meridians from a global perspective!

So let's say you're standing on the North Pole and took a few steps south.
If one was to then walk to the east (or west), each step would be onto a
different meridian. Likewise, one would have to traverse long distances
between meridians at the equator. With that in mind, the distance between
the meridian is relative to where one is between the equator and one of the
earth's pole. If you're lucky enough, maybe you'd get to stand directly on
the poles and never take a step--however that's a privilege most don't have!

With that in mind, all meridians converge at one of the earth's poles. This
solves a riddle an algebra teacher gave me nine years ago, which was, "When
do parallel lines touch each other? Hint: Think of the earth's curvature."

...Here's an off-shoot to the discussion. In theory, let's say that our
ancestors created poles at two points on what we have been considering (for
centuries) the equator. Thus, the north and south poles would have never
received any polar nomenclature. Also, to remove confusion in this
discussion, what we know in reality as "west" and "east" is mentioned as "x"
and "y", respectively, while "north" and "south" is mentioned as "w" and
"z", respectively. The x pole would have lines which would spread and
re-converge at the y pole. Meanwhile "w" and "z" would consist of lines
running parallel to to the x and y poles.

Here are a couple questions that arise for this scenario:

Would it be appropriate to call those lines converging in and from the x and
y poles "meridians"? Would it be appropriate to label "lines of latitude"
as those lines which span out in w and z directions?

The objective for this question is to determine whether the terms "meridian"
or "line-of-latitude" are relative to our ancestors' perception & assignment
of the North and South Poles, or if the terms are relative to the poles'
location as assigned by the person(s) studying a spherical object.

Cheers,

Carl Rogers
-----------------
Calrog.com, Pictures of Highway Shields: http://hwy-shields.calrog.com
Calrog.com, Personal and Interpersonal Psychology page:
http://psychology.calrog.com
Highway Shield & Travel Literatu http://www.lulu.com/calrog-bookstore

I think it was Robin in Winnie the Pooh who searched for the East Pole.
Or was it the West Pole? In navigating over the poles, aircraft resort
to "grid navigation". The navigators invent a grid for the specific
flight and use gyro compasses to align to that grid. The equator and
meridians are great circles on the surface of a sphere. At the poles,
the meridians converge.

The shorter arc of a great circle is the shortest distance between two
points on the surface of a sphere. For long flights, the navigator
plots the shorter arc of the great circle. Except for going east or
west along the equator, or directly north or south, the desired arc of
a great circle will intersect latitudes and longitudes of earth
coordinates at changing angles.

Think of flying from New York to London. On a flat map with mercator
projection, the route is pretty much east. (Rhumb line) On a sphere the
flight starts out to the northeast, at mid point of the flight is
flying east and as it approaches London is flying south east.

Another factor with legals is the "closure". In surveying around a
circuit, the circuit must "close". Go around clockwise or
counterclockwise, the surveyor should arrive at the strating point. On
a flat surface, the angles of a triangle add to 180 degrees. Not so
with spherical triangles. to "close" the triangle, the surveyor adds or
subtracts corrections. For example, if the angles of his triangle added
to 183 degrees and the legs were all about the same length, he would
subtract one degree from each angle.

Surveying errors would accumulate and then be corrected out at the
border with a new datum. I think all the dog legs in roads in flat
lands due to closure errors have been corrected by now.

There is a riddle about walking one mile south, one mile east and one
mile north and coming back to the same place. You see a bear, what
color is the bear? What is the other place on the surface of the earth
that you could be and not see any animals?

Measuring angles gets even trickier in three dimensions. Trying to get
elevated highways to line up, for instance.

"Dick Boyd" wrote...

Carl Rogers wrote:

...Here's an off-shoot to the discussion. In theory, let's say
that our
ancestors created poles at two points on what we have been
considering (for
centuries) the equator. Thus, the north and south poles would
have never
received any polar nomenclature. Also, to remove confusion in
this
discussion, what we know in reality as "west" and "east" is
mentioned as "x"
and "y", respectively, while "north" and "south" is mentioned as
"w" and
"z", respectively. The x pole would have lines which would spread
and
re-converge at the y pole. Meanwhile "w" and "z" would consist of
lines
running parallel to to the x and y poles.

Here are a couple questions that arise for this scenario:

Would it be appropriate to call those lines converging in and from
the x and
y poles "meridians"? Would it be appropriate to label "lines of
latitude"
as those lines which span out in w and z directions?

The objective for this question is to determine whether the terms
"meridian"
or "line-of-latitude" are relative to our ancestors' perception &
assignment
of the North and South Poles, or if the terms are relative to the
poles'
location as assigned by the person(s) studying a spherical object.

Carl Rogers

I think it was Robin in Winnie the Pooh who searched for the East
Pole.
Or was it the West Pole? In navigating over the poles, aircraft
resort
to "grid navigation". The navigators invent a grid for the specific
flight and use gyro compasses to align to that grid. The equator and
meridians are great circles on the surface of a sphere. At the
poles,
the meridians converge.


I was going to mention this myself, having flown grid on a number of
occasions, in my last post but decided against it as I felt that it
was far enough off the asked question. Actually, there is usually a
pre-printed standard grid printed on aviation charts (usually the JNC
and GNC series charts) that allows you to convert from polar to grid
headings using a multiplication factor on the longitude. Regulations
specify that grid must be used north of 70N and south of 60S. I only
got into that range once but we practiced on a regular basis. Getting
in and out can be a real chore sometimes.


The shorter arc of a great circle is the shortest distance between
two
points on the surface of a sphere. For long flights, the navigator
plots the shorter arc of the great circle. Except for going east or
west along the equator, or directly north or south, the desired arc
of
a great circle will intersect latitudes and longitudes of earth
coordinates at changing angles.

Think of flying from New York to London. On a flat map with mercator
projection, the route is pretty much east. (Rhumb line) On a sphere
the
flight starts out to the northeast, at mid point of the flight is
flying east and as it approaches London is flying south east.


--Andy
--------------------------------------------------
Andrew G. Tompkins
Software Engineer
Beaverton, OR
http://home.comcast.net/~andytom/Highways
--------------------------------------------------

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