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Geodetic to Geocentric Latitude

Convert geodetic latitude to geocentric latitude

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  • Geodetic to Geocentric Latitude block

Libraries:
Aerospace Blockset / Utilities / Axes Transformations

Description

The Geodetic to Geocentric Latitude block converts a geodetic latitude (μ) into geocentric latitude (λ) and optional radius from the center of the planet to the center of gravity (r) using geodetic latitude and ellipsoidal altitude. For more information on the geocentric latitude, see Algorithms.

Limitations

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

Ports

Input

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Geodetic 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

Ellipsoidal altitude, specified as a scalar.

Data Types: double

Output

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Contains the geocentric latitude, specified as a scalar, in degrees.

Data Types: double

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

Dependencies

To enable this port, select Output radius.

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).

Dependencies

Selecting the Custom option enables these parameters:

  • Flattening

  • Equatorial radius of planet

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

Select this check box to output the scalar distance radius from the equatorial radius to the center of the planet.

Dependencies

Select this check box to enable the r port.

Programmatic Use

Block Parameter: outputRadius
Type: character vector
Values: off | on
Default: 'off'

Algorithms

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

  • λ — Geocentric latitude

  • μ — Geodetic latitude

  • h — Height from the surface of the planet

  • f — Flattening

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

Given the geodetic latitude (μ) and the height from the surface of the planet (h), this block first calculates the geometric properties of the planet.

e2=f*(2−f)N=a1−e2sin(μ)2).

It then calculates the geocentric latitude from the point's distance from the polar axis (ρ) and distance from the equatorial axis (z).

ρ=(N+h)*cos(μ)z=(N(1−e2)+h)sin(μ)λ=tan−1(zρ).

References

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

Extended Capabilities

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

Version History

Introduced before R2006a

See Also

Topics