Latitude and longitude notations often include six decimals of precision, but how close does that get us? Starting with the nautical mile helps relate lat/lon coordinates to everyday distances. HowStuffWorks.com explains
“The length of a nautical mile is based on the circumference of the planet Earth. If you were to cut the Earth in half at the equator, you could pick up one of the halves and look at the equator as a circle. Then divide that circle, or arc, into 360 degrees and divide each degree into 60 minutes. A minute of arc on the planet Earth is 1 nautical mile. This unit of measurement is used by all nations for air and sea travel.”
Most of us don’t normally pilot ships or airplanes though and commonly use other linear distances like kilometers and miles. For the conversion examples that follow, let’s use the coordinates of the USGS office in Menlo Park located at latitude and longitude
37° 27′ 22.86″ N, 122° 10′ 15.6714″ W
37.456350 , -122.17102
The notation degrees° minutes′ seconds″ converts to decimal notation as shown here and then we can calculate typical distances corresponding with each position in the notation:
37 + 27/60 + 22.86/3600 = 37.456350 37° 27' 22.86" | | | | | | | +- 1/100 of an arcsecond = 1.0127 feet | | +---- One arcsecond = 1 nautical mile / 60 = 101.27 feet | +------------ One arcminute = 1 nautical mile = 1.15077945 statute miles +----------------- One (arc) degree = 60 nautical miles = 69 statute miles
In the decimal notation of the same latitude, each position corresponds to the following north/south travel distances:
37.456350 | |||||| | |||||+--- 0.00006 naut mi. = 0.3646 feet = 4.3748 or 4-3/8" inches = 11.112 cm | ||||+---- 0.0006 naut. mi. = 3.646 feet = 1.1112 m | |||+----- 0.006 nautical mi= 36.46 feet = 11.112 m | ||+------ 0.06 nautical mi.= 364.6 feet = 111.12 m | |+------- 0.6 nautical mi. = 0.69 statute miles= 1.1112 km | +-------- 6 nautical miles = 6.9 statute miles = 11.112 km +--------- 60 nautical miles = 69 statute miles = 111.12 km
Longitude lines. Traveling N/S along one changes your latitude.
(For reference, 1 nautical mile is defined as exactly 1.852 km and is about equal to 1.1508 statute miles.)
Moving one arcdegree of latitude north or south by traveling along a longitude line represents the same distance anywhere on earth.
One degree of E/W travel requires different distance at different latitudes.
Moving one arcdegree of longitude east or west by traveling along a latitude line, however, represents different distances depending on the cosine of the latitude’s degrees north or south. At higher latitudes, traveling one arcdegree east or west covers a smaller distance because circles of latitude are smaller at higher latitudes.
For example, in Caracas at 10 degrees north latitude, traveling one arcdegree along that latitude line represents east/west travel of:
1 arcdegree = 1 naut. mi. * cos(10 deg) = 0.985 nautical miles = 1.333 statute miles
but at 37.45635 degrees north, 1 arcdegree of east/west travel represents just:
1 arcdegree = 1 naut mi. * cos(37.45635 deg) = 0.7938 nautical miles = 0.9135 statute miles
These calculations are close to correct, however, the Earth is not quite a perfect sphere and so professional geodetic measurements use a mathematical model of those imperfections called a datum. For more conversions, and pointers to the nuances introduced by geodetic systems, see http://transition.fcc.gov/mb/audio/bickel/DDDMMSS-decimal.html .
Without access to professional surveying equipment and geodetic correction software, five decimals or 1/10 of an arc second, representing around 1m of accuracy, is about as accurate as a consumer GPS is likely to measure. Go hiking and enjoy!
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