1. Alternate coordinate systems: Solutions for large-scale maps+
X axis - +
(0,0)
Y axis -
Universal Transverse Mercator (UTM)
State Plane Coordinate System (SPCS)
US Public Land Survey (USPLS)

2. The Geographic Coordinate System:
Strengths:
One set of coordinates can describe an exact location anywhere on the globe
Based on the earth’s spherical shape
Issues:
Subdivision of degrees:
1° = 60’
1’ = 60”
1 degree = 60 minutes
1 minute = 60 seconds
The length of 1 ° longitude varies

3. UTM Grid System: Why it was developed
UTM = Universal Transverse Mercator
Developed shortly after World War II by US Army
Now, UTM system used widely for precise positioning

4. Mercator
Transverse Mercator
1 UTM zone:
6 degrees wide

5. Is divided into north-south columns known as zones (between 80°S and 84°N)
Zones are numbered 1 to 60 eastward from the Int’l Date Line

6. UTM Zones for the United States

7. Logic of the UTM Grid
Zone 12
500,000 m
Origin

8. Reading the UTM Grid
Easting is measured from the central meridian + 500,000 m
Northing is measured from the equator
Austin is:
621,161 m E,
3,349,894 m N,
Zone 14 N,
NAD 83

9. Some additional facts about UTM
Accuracy level of UTM --
Maximum error is:
1 m / 1000 m
(5 feet in a mile)

10. Designating location: GCS
Geographic Coordinate System
33° 40’ 12” North ° 55’ 30” West
Deg. Min. Sec. Hemisph. Deg. Min. Sec. Hemisph.
Universal Transverse Mercator
621,100 m E, 3349,800 m N, Zone 14 N, NAD 83
Easting, Northing, Zone, Datum
Or, on topo map:
m E, m N

11. Comparing coordinate systems
(0,0) + -
X axis
Y axis
The Geographic Coordinate System
Universal Transverse Mercator (UTM)
State Plane Coordinate System (SPCS)
US Public Land Survey (USPLS)

12. The Geographic Coordinate System: Longitude and latitude
33° 30’ 00” North, ° 00’ 00” West
Degrees, Minutes, Seconds N, Degrees, Minutes, Seconds W

13. The United States Public Land Survey: The National Picture

14. The United States Public Land Survey: Townships & Ranges
T 2 S, R 3 W, Gila and Salt River Meridian
Township, Range, Principal Meridian
Survey
Township
Townships
6 mi.
Ranges

15. Choosing a Coordinate System
Cartesian coordinate systems:
When precise measurements of distance & area are needed
Choose a system based on size & position
USPLS
UTM
Geographic Coordinate system:
Thematic maps – coordinates give general idea of location on globe

16. Use of Known Features
Size of known objects may be visible on the map—particularly true with aerial photographs

17. Map distance / real distance Simplify:
In real life:
Athletic field is 130 yards
Strategy:
Create a fraction:
Map distance / real distance
Simplify:
Numerator & denominator are in same units
numerator is “1”
On the photo:
Athletic field 7/8 inch
Photo scale =
Approx 1:5,350

18. Use of Latitude and Longitude
Strategy:
Create a fraction:
Map distance / real distance
Simplify:
Numerator & denominator are in same units
numerator is “1”
In real life:
1° latitude = km
10° latitude = 1,111.3 km
On the map:
10° latitude = 8.8 cm
Map scale =
approx
1:12,628,750

19. Using longitude instead:
If using longitude, remember they converge at the poles. Calculate the distance with the following formula:
Distance = cos(latitude) x km

20. Map Comparison
Use a map with a known scale and compare features on the map with unknown scale

21. 1. Measure the distance between same pair features on both maps
6 inches
5 inches
1:5200

22. 2. Calculate the real- world distance on the map with the known scale
6” = x” on ground?
6” = 5200” x 6
6” = 31,200” on ground
6 inches
5 inches
1:5200

23. 3. Calculate the ratio – as before – of the map with unknown scale
6” = x” on ground?
6” = 5200” x 6
6” = 31,200” on ground
5” = 31,200” on ground
1” = 31,200” / 5
1” = 6240” on ground
6 inches
5 inches
1:5200
1:6240

24. Scale and area 9 square inches, 1:5200 map:
9 sq in (map) = 46,800 sq in (ground) ?
NO! That would imply that, from McAllister to Palm Walk is 207 inches on the ground!
RFs are LINEAR scales, and can be used to measure lines but not areas (at least not directly) 2 3 1 4 5 6 9 7 8
1:5200

25. Scale and area To calculate AREA from a linear scale … 3” 3” 1:5200
3 inches on each (linear) side
3”map = 5200 x 3”ground
3”map = 15,600” ground
15,600” / 63,360in/mi = .246 mi
.246 mi x .246 mi =.064 mi2
To calculate AREA from a linear scale …
Strategy:
Measure width & height of area (on map):
Use RF to calculate the area’s width & height in real world
Convert to more convenient real-world units
Multiply real-world width x height 3” 3”
1:5200

26. New points about scale …
Two common RF’s:
1:63,360 1 inch represents 1 mile
1:100,000 1 cm represents 1 km
Use these two RFs to be able to visualize the meaning of other RF’s
Strategies for solving scale problems:
To calculate RF for a map of unknown scale
1. Create a fraction:
Map distance / real distance
2. Simplify:
Numerator & denominator are in same units
numerator is “1”
To calculate land area:
1. Find height and width in real-world units
2. Multiply these 2 values