Position Reference System using Latitude and Longitude
Requirement of Position Reference System
- Position Reference System to denote a place on earth without ambiguity
- It is similar to Cartesian co-ordinate system which uses X and Y axis
- Latitudes and longitudes are used in the position reference system
Great Circles
- Great circles are imaginary lines or circles drawn on the surface of earth
- The centre and radius of a Great Circle are the same as that of earth
- Plane of a great circle cuts earth into two equal halves
- Only one great circle can be drawn between any two points
- However, infinite number of great circles can be drawn between two diametrically opposite points
- Shorter arc of great circle is the shortest possible distance between two points
- Flying great circle tracks are important to airliners to save on time and fuel
The Equator
- Equator is a great circle whose plane is at perpendicular to the spin axis of earth
- Equator divides earth into two hemispheres called Northern and Southern hemispheres
- Equator is taken as datum for measurement of latitudes
- Therefore, Equator is called as zero-degree latitude
Meridians and Anti-Meridian
- Meridians are semi-great circles joining the poles
- Anti-meridians are the Meridians that are 180 degrees displaced from a Meridian
- Meridians indicate True North and South since they join they are drawn joining the poles
- All Meridians and Anti-meridians cut the equator at 90 degrees
Prime Meridian
- The meridian passing through Greenwich has been taken as the Prime meridian
- Prime meridian is taken as the datum for defining longitudes
- Therefore, Prime meridian is also called zero-degree longitude
Small Circles
- Small circles are also circles drawn on surface of earth
- The centre and radius of a small circle are not the same as that of earth
- Plane of the small circle divides the earth into two unequal halves
Parallels of Latitude
- Parallels of latitude are small circles parallel to the equator
- Since equator is perpendicular to the spin axis, parallels are also perpendicular to the spin axis
- All parallels of latitude indicate east or west direction
Special latitudes
- Some latitudes are called as special latitudes and are given a name
- Zero-degree latitude is referred to as the Equator
- Latitudes 66 ½ North and South are called as Arctic and Antarctic circles
- Latitudes at 23 ½ North and South are called Tropic of Cancer and Capricorn
Graticule in Position Reference System
- Graticule is a network formed by parallels of latitude and meridians of longitude
- Combination of latitudes and longitudes are used to refer a point unambiguously
- Latitudes are denoted as North or South of equator
- Longitudes are denoted as East or West of Prime Meridian
- Position is normally defined in degrees, minutes and seconds
- At times, seconds are replaced by decimals of minutes
- By convention, latitude of a place is given first, followed by its longitude
Measurement of Latitude
- Latitude is the smaller arc of a meridian between the equator and a point on the earth surface
- It is measured as an angular distance from the equator to the point
- Latitudes are expressed in degrees, minutes and seconds and indicated as north or south of equator
Geocentric Latitude
- Geocentric latitude is the angle between the line joining a point to the centre of the earth with the plane of equator
- Since earth is not a perfect sphere, geocentric latitude varies with curvature
Geodetic or Geographic Latitude
- Geodetic latitude is the angle measured between the normal to the meridian at a point with the plane of the equator
- Normal is the line drawn perpendicular to the tangent of the meridian
- Unlike Geocentric latitude, Geodetic latitude may not pass through the centre of earth
- The maximum difference between geocentric and geodetic latitudes is 11.6 min at 45° North and South latitudes
Measurement of Longitude
- Longitude is the shorter arc of the equator between the prime meridian and the meridian passing through the point
- They are measured from 0 to 180 degrees of arc at the centre of equatorial plane
- Longitudes are expressed as being east or west of the Prime meridian
Orientation of Longitudes
- Orientation of longitudes change while looking at the earth with Prime Meridian and Anti-meridian in the field of view
- If the Prime meridian in the field of view, easterly longitudes are to right and westerly longitudes are to the left
- If the 180 EW anti-meridian is in the field of view, easterly longitudes are left and westerly longitudes are to the right
Change in Latitude (Ch-lat)
- Change in latitude is the difference of latitude between two points
- Ch-Lat is measured along the meridian between the points and expressed in degrees, minutes and seconds
- Distance between two points on a great circle can be calculated using Ch-lat
- Ch-Lat of a point is expressed as north or south of the other point along the shorter great circle path
Change of Longitude (Ch-long)
- Change in Longitude is the difference in longitude between two points
- It is the smaller angular change in longitude along the equator measured in degrees, minutes and seconds
- Ch-long of a point is expressed as east or west of the other point
- Distance between two points on the equator can be calculated using Ch Long
- If Ch-long is greater than 180, then recalculate in the opposite direction to get the shorter arc
Accuracy of Graticule
- The accuracy of graticule can be increased depending on the purpose
- Latitudes and Longitudes are angular distances on earth that can be defined as accurately as required
- One degree of arc is the fundamental unit of angular measurement
- One degree is the angle corresponding to 1/360 th part of circumference of a circle
- Minutes of arc is equal to one sixtieth part of a degree ( ‘ )
- Seconds of arc is equal to one sixtieth part of a minute ( “ )
- En-route charts normally use degrees and minutes
- Instrument Let-down charts use degrees, minutes and seconds for higher accuracy
- Modern avionics like Flight Management System use decimals of minutes
- Precision aids like Instrument Landing System even use decimals of seconds for improving accuracy