*** GPS to Map Conversions ***

Wed Jan 18 01:09:53 1995
Message : #20962833    From: Ronald D. Wong
Address : rwong@cello.gina.calstate.edu
Group   : Usenet.rec.backcountry
Subject : GPS and Map Questions
 
Org.  : Physics Instructor

Last December Tom Vervaeke wrote:

>Santa brought the new GPS I had asked for. Now I have used it for a day
>or so and have a few questions on inputting lat and long. data into it.
>My problem is what's the best method to take a point
>on the map and get it's exact latitude and longitude?

His GPS happened to be a Garmin 40.

There were a number of responses, but they didn't seem to offer a
"simple" solution.

Hopefully, the following info will prove useful to those using GPS in
their backpacking activities.


1. GPS was *not* developed with the backpacker in mind

     This system was developed for a number of reasons one of which was
to help professional navigators. Certain terms which they use have a
different meaning from ours. The most important one here is the
measurement of distance in miles. They use the *nautical* mile (n.m.) for
their work instead of the statute mile (where 1 mile = 5280 ft). Your
Garmin probably can be set for either but I!m quite sure it comes
pre-configured to measure distances in nautical miles (where 1 mile =
6076 ft). This can be very useful as you!ll soon see.


2. One minute of Latitude = one nautical mile

     This is how the nautical mile is arrived at. As a result, you can
determine the distance between any two points on a map (called !charts!
in the navigation trade) in n.m. by simply comparing the distance between
the two points to the latitude scale along the left or right hand margins
of the map. Each minute of latitude represents one n.m. *no matter what
the scale of the map is*. If the distance is 48! of latitude than the
distance is 48 miles (understood as n.m.). Because of this, there is no
need to have a mileage scale as you do with topo maps. It!s very handy.
In your case, involving 7.5! topo!s, 2.5! of latitude is about 19.3 cm
(yep, metric) - more precisely, 19.2913 cm/7.595 in. This means that 1!
of latitude represents about 7.7 cm (more precisely, 7.71652 cm/3.038
in). If you measure 7.7 cm along the scale for distances in ft that
you'll find at the bottom of your topo map you!ll see that it is about
6080 ft. Measure any distance between two points on your map in cm and
divide by 7.7 and you!ll have the distance in n.m. (or measure in inches
and divide by 3 to get the same result).


3. Only at the equator is one minute of longitude = 1 n.m.

     If you look at a globe you!ll see that a difference of 15 degrees of
latitude is the same size arc whether you are near the equator or at the
poles whereas, 15 degrees of longitude gets smaller and smaller until it
is  reduced to zero at the poles. Thus one minute of longitude will
usually represent less than one n.m.
     An interesting relationship exists between a measurement of distance
measured in an east-west direction and the corresponding difference in
longitude. *For the scale of maps you are using*, multiplying the
east-west distance in n.m. by the cosine (cos) of the latitude of your
map will give you the corresponding difference in minutes of longitude.
Technically, you should use the cosine of the mid-latitude. This would be
the latitude of a point midway between the top and bottom of the map but,
on the scale you are working at, this probably isn!t important.


4. Getting Lat & Long of a point on a topo map

     Method 1 - Using the information given above
        Get a calculator and find the cosine of the mid-latitude of your
topo map and divide it by 7.7. Store the result in the calculator!s
memory. For the United States, the use of the lat. & long. at the lower
right hand corner works best as a point of reference. Find a way of
establishing a perpendicular line from the right hand margin to the point
of interest (if you have a T-square, the simplest way would be to lay the
right hand edge of the map along the edge of a table and lay the T-square
so that it!s upper edge runs through the point of interest when the "T"
end is butted up against the table. Parallels work fine using the top and
bottom margins, and you can get rulers with a roller built in that
achieves the same purpose. A single large triangle with a right angle
will work also. etc,.etc.). The important point is to make a tick mark
where this line meets the right hand margin. You *don!t* have to draw the
line in.
     Measure the horizontal distance from the point of interest to the
tick mark in cm. Multiplying this number by the number stored in memory
will give you the number of minutes of longitude you must add to the
long. of the lower right hand corner to get the longitude of the point of
interest. Measuring the vertical distance from the tick mark down to the
lower right hand corner in cm and dividing this value by 7.7 will give
you the number of minutes to add to the latitude of the lower right hand
corner to get the lat. of the point of interest. Getting the lat & long
of any point on your map by this method should take very little of your
time once you!ve got the hang of it.

     Method 2 - Taking advantage of your GPS
        I!m offering this 2nd method because I think it will be of more
use to you both at home, while planning the trip, and in the field, when
you are actually are on the trip.
     You mentioned that the Garmin gives the lat & long when you give it
the course (known as "direction") and distance from a known position.
This is a very useful feature. I!m assuming the Garmin works in such a
way that you enter the initial lat & long and follow this up by entering
the course and distance to each of a series of way points. As each course
and distance is entered, the Garmin gives you the lat & long of the way
point.
     If that is the case, all you need to do is draw a series of linked
arrows. The chain starts from a known position on the margin of your topo
map and runs through each of the points of interest you have in mind. The
arrows! directions are those which you would follow as if you were to
move from the margin and travel from one point to another. Number each of
the arrows in order starting from the starting point at the margin.
     Make a table with four columns and as many rows as legs/arrows.
Label the columns: Leg, Course (or direction), Distance, Position.
Measure the length of each of the numbered arrows in cm/in and divide by
7.7/3.  This is the distance traveled in n.m. and should be entered in
the appropriate row under "Distance".
     The easiest way to determine the course is to use a !Silva-type!
compass. One which is transparent and is mounted on a rectangular,
plastic base with the N-S line parallel to the length of the card. If the
compass has the ability to correct for declination, zero the correction
out. You will be using the compass as a protractor. If the sides of the
card are kept oriented so that the N-S line is always parallel to the
left and right hand margins of the map (suggestions in method 1 are
useful here) than the direction of an individual arrow can be found by
maneuvering the compass so that a section of the line runs through the
center of the compass. The line will cross the azimuth circle (the ring
of numbers that run around the edge of the compass) at two places. The
correct value for the direction is the one on the ring which is on the
same side of the ring as the arrowhead of the line. Mind you, you *don't*
have to carefully place the center of the compass at the beginning or end
of the arrow. Just as long as the line runs through the center of the
compass you'll get the correct value for the direction (or course) when
you pick the value on the side of the line where the arrowhead is. Do
this for each of the arrows and enter them in your table.
     By entering into your GPS the lat. & Long. of the initial position
followed by the series of courses and distances, you will get the
information you seek.
     Since the compass is being used as a protractor there is no magnetic
corrections like "deviation" or "variation" (the latter is called
"magnetic North declination" on a topo map. The provisional 7.5' maps
give the value of the declination in a listing in the lower left hand
corner of the map. Other topo's show it on an abbreviated compass rose
showing true north and the angle the magnetic north makes with true
north.). What you have is the "true" direction or "course". If your GPS
asks for any magnetic corrections, just enter zero as the correction.
     Actually, if you understand these directions for getting the course,
 you'll see that an ordinary protractor and T-square/parallels/large
right triangle will also work just as well as the compass. Just remember
that the compass rose increases from 0 to 360 degrees clockwise from true
north.

5. What I would probably do with a GPS

     I'm not sure why you would want the position of major features on
your map. If I had GPS, I'd use it to plan my cross country ventures.
     I'd use "method 1" to determine the location of the point on the
trail where I would begin the cross country trek. On the map, I would lay
out my trip using "method 2" starting from the point where I would leave
the trail. and drawing the arrows along the planned route. The lat. &
long I would be interested in are the major points on the route (a
mountain pass, a lake, a saddle, a trail crossing, etc).
     Before setting out on the trip I'd store the mag. declination for
the area I was hiking into the GPS if that were possible. I'd also take
the table with me and, at any waypoint, I'd use the GPS to check my
position. If it didn't agree with that in my table I'd update the present
position and use my table to update the next waypoint using "method 2".
     If, during the hike, I got lost I'd whip out my GPS *not* to get my
present lat & long (not very useful) but to use another feature of a GPS
- getting the "desired Track". In one or two key strokes I'd have the
magnetic direction to my next waypoint and its distance (probably in
n.m.). Laying out the desired Track on the map from the waypoint back
towards my position will give me some idea of the terrain I would have to
cover and, if I measure off the distance from the waypoint, I'd know my
actual position - all pretty useful stuff.

Have fun with your GPS. I'd be interested in your experiences with this
new technology.

Ron

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