If your map is in an Unprojected Lat/Long projection, the units that appear in the Scale dialog are in latitude and longitude. Therefore, the dialog X Scale 1.0 in. = n map units can be interpreted as 1.0 in. = n degrees longitude. Similarly, the Y Scale 1.0 in. = n map units can be interpreted as 1.0 in. = n degrees latitude. If you know your map scale in feet (i.e. 1 inch = 8000 feet), you need to determine the correlation between the scale in feet and the scale in latitude and longitude units.

You must first figure out how many feet are in a degree of latitude and longitude at the specified scale. Longitude distance is accurate at the selected latitude only. This description uses the US50LL.GSB file located in your SAMPLES folder.

Longitudinal distance depends on the latitude at which you are measuring distance since the lines of longitude get closer at the poles. This means that the scale of the map in the X direction (longitude) is true at the given latitude (Y). The further you are from that latitude the more distorted the scale. This is true no matter what the projection of your map. See scale bars for more information.

Converting Latitude and Longitude to Feet

To convert latitude longitude to feet:

1. First, we must figure out how many feet are in a degree of latitude:

1 degree of latitude = 68.71 miles

1 mile = 5280 feet

therefore, 1 degree of latitude = 362788.8 feet

2. Find the center latitude of the US50LL.GSB map. The center latitude is found by:

[( yMax - yMin/2) + yMin]

The center latitude of the US50LL.GSB file is 35.669.

3. If 1 degree of longitude = [69.17 miles/degree][ cos(latitude)] and there is 5280 feet in 1 mile,

1 degree of longitude = [365217.6 feet/°][cos(35.669°)].

1 degree of longitude = 296702.46 feet at 35.669 degrees latitude.

Using Latitude and Longitude in Map | Scale

Once you have figured out how many feet are in each degree of latitude and how many feet are in a degree of longitude at a given scale, you can use these numbers to determine a given scale in MapViewer.

For example, using a 1 inch to 16,000 feet scale:

From step one in previous section, we know that 1 degree of latitude (Y) = 362788.8 feet. We want a 16,000 scale, so we need to know how many degrees latitude in 16,000 feet. Using the information provided in the previous two sentences and some basic math, there are 0.0441028 degrees latitude in 16,000 feet.

(1° / 362788.8') = ( n ° / 16,000') = 0.0441028

From step three in the previous section, 1 degree of longitude (X) = 296702.46 feet at 35.669 degrees latitude. We want a 16,000 scale, so we need to know how many degrees longitude in 16,000 feet. Using the information provided in the previous two sentences and some basic math, there are 0.0512893 degrees longitude in 16,000 feet at 31.332488 degrees latitude.

(1° / 296702.46') = (n ° / 16,000') = 0.0512893

Click on the Map | Scale command and uncheck the Proportional XY Scaling check box. Enter 0.0441028 into Y Scale (1 in. =) and enter 0.0512893 into the X Scale box.

See Also

Using Scaling to Minimize Distortion on Latitude and Longitude Maps

Introduction to Map Projections