Longitude
• North - South Meridians
base point of world system is
Greenwich, England
Iowa - approximately 930 West
Latitude
• Measured from the Equator
• Iowa - approximately 42 0 North
Great circle distances
(assume a round world)
• Along a longitudinal line the Radius of the
earth is approximately
•
R = 3959 miles or
•
R = 6371 kilometers
• Distance along 1 degree of longitude:
• L = R * theta
where theta is in radians
• L = 3959 * (1 deg/ 57.2958 deg/rad)
• L = 69.09 miles
Great circle distances
(assume a round world)
• Along a latitudinal line the Radius of the
earth about the poles is a function of the
latitude:
• Radius(at Lat. y) = Radius *cos(Latidude)
• Distance =( R at Lat Y) * theta
• At 420 , lat, R = 3959 miles * Cos (420)
•
=2942 miles
• In 1 deg, Dist = 2942 *1/57.29 =51.35 mi
Navigational GPS at ISU
• Records to nearest 0.001 minute
• ___________________
• A) What is the distance in feet for 0.001
minute change in the longitude at a
latitude of 420?
• What is the distance in feet for 0.001
minute change in the latitude of 420 (or any
other latitude)?
Bearings from flat-earth society
Spherical trigonometry is used to obtain precise assessment of
distance.
HOWEVER, over short distances, Eastings and Northings from
surveying will give good estimates:
Point 1: Latitude 42d 17.369’ N, Longitude: 93d 43.614’ W
Point 2
Latitude 42d 18.749’ N
Longitude: 93d 44.865’ W
Angular change
Delta North = 1.380’ (minutes) to north
Delta West = 1.251’ to west
Bearings from flat-earth society
Delta North = 1.380’ (minutes) to north Delta West = 1.251’ to west
Distance north: Radius = 3959 miles along meridian
L = R * theta where theta is the central angle
L = 3959 mi * 5280 ft/mi * 1.380’/ (60’/deg) / (57.2958d per radian)
L = 8391 feet
Distance West - consider using average latitude of the two points
Average latitude = 42d 18.059’
Radius = 3959 * cos (42d 18.059’) = 2928 miles
L = 2928 mi *5280 ft/mi * 1.251min/ (60’/deg) / (57.2958d per radian)
L = 5626 feet
Bearing of line
Dist north = 8391 feet
Dist. West = 5626 feet
Bearing = atan( 5626/ 8391)
or N 33d 50’ W
Total Distance = 10,103’
This estimate of distance is in error by less than 0.00002 feet
compared to spherical trigonometry.