Local Area Augmentation System (LAAS) – A real-time DGPS correction system with a 20-30 mile radius
developed by the U.S. Federal Aviation Administration for landing aircraft at small to medium-sized airports. The
LAAS system is extremely accurate to within 1 meter are the horizontal and vertical plane.
Degrees, Minutes, Seconds & Mils
Navigation begins with a point and everything around that point. So the circle is a very important part of navigation.
The circle in navigation is subdivided into degrees, minutes, seconds and mils.
All of our navigation systems, formats and datums are based on this circle design.
The most common subdivision is the degree (o). There are 360o in a circle; 0 is the start, a 1/4th of a circle is 90o, 180o to
a ½, 270o to 3/4th and so on.
When working with degrees, in the case of adding & subtracting the values, it starts at 0o - 359o.
The degree’s subdivision is the minute, expressed by a tick mark (‘). There are 60’ to one degree ( o).
The minute’s subdivision is the second, expressed by two tick marks (“). There are 60” to one minute (‘)
When working with minutes & seconds, in the case of adding & subtracting the values, it starts at 0 – 59.
Various Examples Listed Below:
Working with minutes & seconds:
37” + 21” = 59” (almost one minute)
45” – 15” = 30” (half a minute)
46” + 33” = 73” = 1’ 13” (one minute & 13 seconds)
1’ 07” + 49” = 1” 56” (one minute & 56 seconds)
5’ 45” – 2’ 15” = 3’ 30” (three minutes & 30 seconds)
Working with degrees, minutes & seconds:
270o 15’ 45” + 10o 7’ 23” = 280o 23’ 08”
165o 23’ 17” – 42o 12’ 48” = 123o 11’ 31”
Converting Decimal Degrees to Degrees & Decimal Minutes
76.257o = 76o (.257 x 60’) = 15.42’ (remember 60 degrees to 1 degree)
Answer: 76o 15.42’
320.926o = 320o (.926 x 60’) = 55.56’
Answer: 320o 55.56’
* If you want to convert these values the opposite way, just divide 60, instead of multiplying
Converting Decimal Degrees to Degrees, Minutes & Seconds
Using the same examples above we can further break down the decimal minutes to seconds.
76.257o = 76o (.257 x 60’) = 15.42’ (remember 60 seconds to 1 minute)
= 76o 15.42’ (.42 x 60) = 25.2” exactly or rounded to 25”
Answer: 76o 15’ 25”
320.926o = 320o (.926 x 60’) = 55.56’
= 320o 55.56’ (.56 x 60) = 33.6” exactly or rounded to 34”
Answer: 320o 55’ 34”
* If you want to convert these values the opposite way, just divide 60, instead of multiplying
How to Find the Opposite Direction
Simply add or subtract 180o to your bearing.
74o 32’ 45” = 74o (+ 180o) = 254o
Answer: 254o 32’ 45”
315o 45’ 30” = 315o (- 180o) = 135o
Answer: 135o 45’ 30”
What is a Mil & How Does It Relate to Navigation?
A circle can also be subdivided into mils, instead of degrees, minutes & seconds. The cool thing about mils is there is
no subdivision of a mil, so there are no silly conversions! A full circle is made up of 6,400 mils and/or 1 mils is one
sixty-four hundredths (1/6400) of a circle.
Mils are best related when you know how to convert the two from one to another. Examples below:
1 mil = 360o / 6400 = .05625o
1o = 6400 mils / 360 = 17.778 mils
To convert degrees to mils, simply multiply the number of degrees by 17.778.
68o = 68o x 17.778 =
Answer: 1208.904 exactly or 1209 mils
* TO convert degrees, minutes & seconds, be sure to convert it to decimal degrees, then multiply by 17.778
To convert mils to degrees, simply multiply the number of mils by .05625.
4200 mils = 4200 x .05625 =
Answer: 236.25o
A few equivalent examples:
North (N) = 0o = 0 mils
East (E) = 90o = 1,600 mils
South (S) = 180o = 3,200 mils
West (W) = 270o = 4,800 mils
Post-Processing cont…
Consumer grade GPSr do not collect the necessary information to apply post-processing corrections
DGSP is highly accurate, but would be to expensive and bulky to take on the trail.
DGPS = 60+ land based sites in the U.S. & it’s provinces.
DGPS = The Coast Guard system requires an additional purchase of an antenna & a DPGS unit, WAAS is more
convenient to the outdoor enthusiast.
DGPS is also used to monitor dams, excellent way to control water levels and fill rates below the failure point of the
dam.
Reading Distance on a Paper Map
Yes, you can (to a certain extent) do this by knowing the distance between o (degrees), ‘ (minutes), “ (seconds) or
UTM’s meters, but the west way is:
Use the legend to interpret distance along with some sort of straight edge instrument.
Use a special ruler that is calibrated to read minutes & seconds on a 2.5’ x 2.5’ grid.
Use the ruler on your compass (make sure the scale on the map & the compass match)!
Draw a finer grid on your map (subdivide the map into smaller grids).
Make sure the grid lines are easy to interpret distance measurements and are easy to read.
When interpreting distance on a paper map, it takes some knowledge & practice to accurately interpret distance.
Latitude distance is consistent.
Longitude distance is not! If you remember from my bulleted information about longitude, as you move
north or south away from the equator, the distance between grid lines decreases. The only time both latitude &
longitude are the same is at the equator.
Additional Information on Declination & What It Means
You must know the declination of the area you are in, for example: declination around this area is roughly 11-12o W.
Since we are right of the Magnetic North line we add the declination difference to our compass to get to a certain point
on a paper map. (Remember East is Least, West is Best!)
Determining Your Declination – Expressed as either East or West Declination according to your present location of
the magnetic North Pole.
If your present location is right of the magnetic pole line it is considered West Declination.
If your present location is left of the magnetic pole line it is considered East Declination.
DISPLAY PICTURE OF US DECLINATION LINES.
East is Least, West is Best – Which means you subtract east declinations and add west declinations to your calculations
depending on which side of the magnetic pole line you stand on. The examples below show how this works.
Ex.1 – Location: Eastern PA
Origin: Doodle Hollow Road
Coordinates: 41o 13’ 50” N 74o 53’ 31” W (Start)
Destination: Dingmans Falls
Coordinates: 41o 13’ 51” N 74o 53’ 45” W (Finish)
Estimated Distance: .22 miles
Map Declination: 13o W (according to my map)
Maps Compass Bearing: 93o
Maps Compass Bearing + Declination: 93o + 13o W = 106 o (Magnetic North)
Correct Compass Bearing to Waterfalls: 106o (follow compass bearing in this direction to reach the falls
in .22 miles)
DISPLAY PICTURE OF WEST DECLINATION
Ex.2 – Location: Central MT PA
Origin: Neihart, MT
Coordinates: 46o 54’ 36” N 110o 43’ 52” W (Start)
Destination: Big Baldy Mt. Peak
Coordinates: 46o 57’ 05” N 110o 35’ 05” W (Finish)
Estimated Distance: 7.18 miles
Map Declination: 13o (according to my map)
Maps Compass Bearing: 64o
Maps Compass Bearing + Declination: 64o - 13.5o E = 50.5o (Magnetic North)
Correct Compass Bearing to Mt. Peak: 64o (follow compass bearing in this direction to reach the Mt. Peak in 7.18
miles)
DISPLAY PICTURE OF EAST DECLINATION

Most all maps will tell you the declination difference somewhere on the legend, the USGS Topo! software maps
declination is located in the lower right corner.
How Do I Know Which Datum & Format My Map or GPS Is In?
To figure out how your map has been setup look over the legend and look to the edges of the map. The USGS Topo!
software tells you the datum used in the upper right & lower right-hand corners. It can also generate maps in four
formats (3 lat. & long. & UTM). The format markings are along the outer edges of the map & would contain the
coordinates.
The USGS maps you would purchase at outfitters are 7.5’ topographic maps. You will find (9) 2.5’ blocks on each
map. 7.5’ is the distance it covers in both directions using the latitude & longitude grid system. It will also contain the
UTM grid system with markings every 1000 meters.
The map below would contain UTM marks from: 4584 – 4597 for northing (south to north) & 291 – 301 for eastings
Ex. Map Name: Cammel, PA
Northern Corners: 41o30’00” N. 77o30’00” W.
41o30’00” N. 77o22’30” W.
45
97 N.
45
84 N. 291 E.
Southern Corners: 41 22’30” N. 77 30’00” W.
o
o
3
01 E.
41o22’30” N. 77o22’30” W.
Midpoint of Map 41o26’15” N. 77o26’15”
Note: When using the National Geographic TOPO! software set the grid markings to:
450 seconds to see each USGS Quad Map on the screen when using latitude & longitude
150 seconds to see each 2.5’ quadrant when using latitude & longitude
Latitude & Longitude
Degrees, Minutes& Seconds: The map is divided by tick marks every 30” for both lat. & long.
Degrees & Decimal Minutes: The map is divided by tick marks every 500’ for both lat. & long.
Decimal Degrees: The map is divided by tick marks every .00833o for both lat. & long.
UTM
Eastings: The map is divided by tick marks every 805 meters (.5 miles).
Northings: The map is divided by tick marks every 805 meters (.5 miles).