GPS TrackMaker Reference Manual page 115

Area #1
Latitude Longitude
-3.5 -53.0
-3.5 -52.5
-3.0 -52.5
-3.0 -53.0
Being that the three areas are located in the same latitude and having the same angular dimension, we could
expect that it would have the same area. However, when we calculate the cartographic area in a UTM system, we
get the following results:
• Area #1 = 307290.1056 hectares
•
Area #2 = 307008.3940 hectares
• Area #3 = 307478.1052 hectares
Using UTM grid to calculate the cartographic area, we get values with considerable differences, even when the
three areas are equal! This doesn't happen if the calculation is done through topographical area:
•
Area #1 = 307271.4108 hectares
• Area #2 = 307271.3999 hectares
• Area #3 = 307271.4131 hectares
The small difference in the topographical area calculation happens because of internal rounding errors due to the
formula's complexity. The topographical area was calculated using the SAD69 Average datum, with an average
altitude of 200 meters. The altitude is provided by the GPS, that is to say, in relation to the Earth's ellipsoid.
NOTE: The file with this example is called area_topo.gtm and it is in the CD of GTM PRO® program or in the
home-page: www.trackmaker.com
Calculating Topographical Distance and Area at GTM PRO®
GTM PRO® calculates distances for topographical areas like it calculates distances for cartographic areas. The
difference is that the User will have to choose between the Tracklogs altitude or choose NA average altitude for
the calculation.
Certainly the best way to understand the difference between the local topographical
surface and the cartographic surface is with a practical example. The side picture
shows three-square areas with identical angular dimensions, located in the
extremities and in the center of the UTM 22M zone, in Para State/Brazil.
The three areas have sides with angular dimensions of 0.5 degree (SAD69) and they
are aligned in the same latitude, according to the table of dimensions below:
Area #2
Latitude Longitude
-3.5 -51.0
-3.5 -50.5
-3.0 -50.5
-3.0 -51.0
Area #3
Latitude
-3.5
-3.5
-3.0
-3.0
115
Longitude
-49.0
-48.5
-48.5
-49.0