Geocentric to Geodetic Latitude

Convert geocentric latitude to geodetic latitude

  • Library:
  • Aerospace Blockset / Utilities / Axes Transformations

Description

The Geocentric to Geodetic Latitude block converts a geocentric latitude (λ) into geodetic latitude (μ). A number of geometric relationships are used to calculate the geodetic latitude in this noniterative method. For more information, see Algorithms.

Limitations

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

Ports

Input

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Geocentric latitude, specified as a scalar, in degrees. Latitude values can be any value. However, values of +90 and -90 may return unexpected values because of singularity at the poles.

Data Types: double

Radius from center of the planet to the center of gravity, specified as a scalar.

Data Types: double

Output

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Geodetic latitude, specified as a scalar, in degrees.

Data Types: double

Parameters

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Parameter and output units:

Units

Radius from CG to Center of Planet

Equatorial Radius

Metric (MKS)

Meters

Meters

English

Feet

Feet

Programmatic Use

Block Parameter: units
Type: character vector
Values: 'Metric (MKS)' | 'English'
Default: 'Metric (MKS)'

Planet model to use, Custom or Earth (WGS84).

Programmatic Use

Block Parameter: ptype
Type: character vector
Values: 'Earth (WGS84)' | 'Custom'
Default: 'Earth (WGS84)'

Flattening of the planet, specified as a double scalar.

Dependencies

This parameter is enabled when Planet model is set to Custom.

Programmatic Use

Block Parameter: F
Type: character vector
Values: double scalar
Default: 1/298.257223563

Radius of the planet at its equator, in the same units as the Units parameter.

Dependencies

This parameter is enabled when Planet model is set to Custom.

Programmatic Use

Block Parameter: R
Type: character vector
Values: double scalar
Default: 6378137

Algorithms

The Geocentric to Geodetic Latitude block converts a geocentric latitude (λ) into geodetic latitude (μ), where:

  • λ — Geocentric latitude

  • μ — Geodetic latitude

  • r — Radius from the center of the planet

  • f — Flattening

  • a — Equatorial radius of the plant (semi-major axis)

Given geocentric latitude (λ) and the radius (r) from the center of the planet, this block first converts the desired points into the distance from the polar axis (ρ) and the distance from the equatorial axis (z).

ρ=r(cos(λ))z=r(sin(λ)).

It then calculates the geometric properties of the planet:

b=a(1f)e2=f(2f)e'2=e2(1e2).

And then uses the fixed-point iteration of Bowring's formula to calculate μ. This formula typically converges in three iterations.

β=tan1((1f)sin(μ)cos(μ))μ=tan1(z+be'2sin(β)3ρae2cos(β)3).

References

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

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

[3] Clynch, J. R. "Radius of the Earth - Radii Used in Geodesy." Naval Postgraduate School, Monterey, California, 2002.

[4] Stevens, B. L., and F. L. Lewis. Aircraft Control and Simulation, Hoboken, NJ: John Wiley & Sons, 1992.

[5] Edwards, C. H., and D. E. Penny. Calculus and Analytical Geometry 2nd Edition, Prentice-Hall, Englewood Cliffs, New Jersey, 1986.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Introduced before R2006a