Aerospace Toolbox

GenerateRunScript (Aero.FlightGearAnimation)

geoc2geod - Convert geocentric latitude to geodetic latitude

Syntax

gd = geoc2geod(gc, r) gd = geoc2geod(gc, r, model) gd = geoc2geod(gc, r, f, Re)

Description

gd = geoc2geod(gc, r) converts an array of m geocentric latitudes, gc, and an array of radii from the center of the planet, r, into an array of m geodetic latitudes, gd. Both gc and gd are in degrees. r is in meters.

gd = geoc2geod(gc, r, model) is an alternate method for converting from geocentric to geodetic latitude for a specific ellipsoid planet. Currently only 'WGS84' is supported for model.

gd = geoc2geod(gc, r, f, Re) is another alternate method for converting from geocentric to geodetic latitude for a custom ellipsoid planet defined by flattening, f, and the equatorial radius, Re, in meters.

Geometric relationships are used to calculate the geodetic latitude in this noniterative method.

Examples

Determine geodetic latitude given a geocentric latitude and radius:

gd = geoc2geod(45, 6379136)


gd =

   45.1921

Determine geodetic latitude at multiple geocentric latitudes, given a radius and specifying WGS84 ellipsoid model:

gd = geoc2geod([0 45 90], 6379136, 'WGS84')


gd =

         0   45.1921   90.0000

Determine geodetic latitude at multiple geocentric latitudes, given a radius and specifying custom ellipsoid model:

f = 1/196.877360;
Re = 3397000;
gd = geoc2geod([0 45 90], 6379136, f, Re)


gd =

         0   45.1550   90.0000

Assumptions and Limitations

This implementation generates a geodetic latitude that lies between ±90 degrees.

References

Jackson, E.B., Manual for a Workstation-based Generic Flight Simulation Program (LaRCsim) Version 1.4, NASA TM 110164, April, 1995

Hedgley, D. R., Jr., An Exact Transformation from Geocentric to Geodetic Coordinates for Nonzero Altitudes, NASA TR R-458, March, 1976

Clynch, J. R., Radius of the Earth — Radii Used in Geodesy, Naval Postgraduate School, 2002, http://www.oc.nps.navy.mil/oc2902w/geodesy/radiigeo.pdf

Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, NY, 1992

Edwards, C. H., and D. E. Penny, Calculus and Analytical Geometry, 2nd Edition, Prentice-Hall, Englewood Cliffs, NJ, 1986