Alternate coordinate systems:Solutions for large-scale maps

• Universal Transverse Mercator (UTM)• State Plane Coordinate System

(SPCS)

(0,0)

+

-

+- X axis

Y a

xis

• US Public Land Survey (USPLS)

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

1 degree = 60 minutes

1 minute = 60 seconds

The length of 1 ° longitude varies

Issues: Subdivision of degrees:

1° = 60’ 1’ = 60”

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

Mercator Transverse Mercator

1 UTM zone:6 degrees wide

• 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

UTM Zones for the United States

Origin

Logic of the UTM GridZone 12

500,000 m

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

Some additional facts about UTM

Accuracy level of UTM --

Maximum error is:

1 m / 1000 m(5 feet in a mile)

Designating location: GCS

• Geographic Coordinate System

33° 40’ 12” North 111° 55’ 30” WestDeg. Min. Sec. Hemisph. Deg. Min. Sec. Hemisph.

• Universal Transverse Mercator

621,100 m E, 3349,800 m N, Zone 14 N, NAD 83Easting, Northing, Zone, Datum

Or, on topo map:621100 m E, 3349800 m N

Comparing coordinate systems

• Universal Transverse Mercator (UTM)

• State Plane Coordinate System (SPCS)

(0,0)

+

-

+- X axis

Y a

xis

• US Public Land Survey (USPLS)

• The Geographic Coordinate System

The Geographic Coordinate System: Longitude and latitude

LongitudeLatitude

33° 30’ 00” North, 112° 00’ 00” WestDegrees, Minutes, Seconds N, Degrees, Minutes, Seconds W

The United States Public Land Survey: The National Picture

The United States Public Land Survey: Townships & Ranges

Tow

nshi

ps

Ranges

SurveyTownship

6 mi.

T 2 S, R 3 W, Gila and Salt River MeridianTownship, Range, Principal Meridian

T 2 S, R 3 W, Gila and Salt River MeridianTownship, Range, Principal Meridian

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

Use of Known Features

Size of known objects may be visible on the map—particularly true with aerial photographs

In real life:

Athletic field is 130 yards

On the photo:

Athletic field 7/8 inch

5349

1

875.04680

875.0875.0

4680

0.875

inches 36*130

inches 875.0

yards 130

inches 87

Photo scale =Approx 1:5,350

Strategy:

1. Create a fraction:

Map distance / real distance

2. Simplify:

• Numerator & denominator are in same units

• numerator is “1”

Strategy:

1. Create a fraction:

Map distance / real distance

2. Simplify:

• Numerator & denominator are in same units

• numerator is “1”

Use of Latitude and Longitude

750,628,12

1

8.8000,133,111

8.88.8

cm 100,000*1111.33

cm 8.8

km 1111.33

cm 8.8

In real life:

1° latitude = 111.13 km

10° latitude = 1,111.3 km

Strategy:

1. Create a fraction:

Map distance / real distance

2. Simplify: • Numerator & denominator are in

same units• numerator is “1”

Strategy:

1. Create a fraction:

Map distance / real distance

2. Simplify: • Numerator & denominator are in

same units• numerator is “1”

Map scale =approx

1:12,628,750

On the map:

10° latitude = 8.8 cm

Using longitude instead:

If using longitude, remember they converge at the poles. Calculate the distance with the following formula:

Distance = cos(latitude) x 111.113km

Map Comparison

Use a map with a known scale and compare features on the map with unknown scale

1:5200

6 inches 5 inches

1. Measure the distance between same pair features on both maps

1. Measure the distance between same pair features on both maps

1:5200

6 inches 5 inches

2. Calculate the real- world distance on the map with the known scale

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

1:5200

6 inches 5 inches

5” = 31,200” on ground

1” = 31,200” / 5

1” = 6240” on ground

3. Calculate the ratio – as before – of the map with unknown scale

3. Calculate the ratio – as before – of the map with unknown scale

1:6240

6” = x” on ground?

6” = 5200” x 6

6” = 31,200” on ground

Scale and area

RFs are LINEAR scales, and can be used to measure lines but not areas (at least not directly)

1:5200

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!

1 2 3

4 5 6

7 8 9

Scale and area

• To calculate AREA from a linear scale …

1:5200

3 inches on each (linear) side3”map = 5200 x 3”ground

3”map = 15,600” ground

15,600” / 63,360in/mi = .246 mi

.246 mi x .246 mi =.064 mi2

3”

3”

Strategy:

1. Measure width & height of area (on map):

2. Use RF to calculate the area’s width & height in real world • Convert to more convenient

real-world units

3. Multiply real-world width x height

Strategy:

1. Measure width & height of area (on map):

2. Use RF to calculate the area’s width & height in real world • Convert to more convenient

real-world units

3. Multiply real-world width x height

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 units2. Multiply these 2 values