Geodetic to Geocentric Latitude

R2026b

Convert geodetic latitude to geocentric latitude

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Geodetic to Geocentric Latitude block

To add a block to a model, double-click the canvas and start typing the block name. Then, select the block from the list.

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

μ — Geodetic latitude

scalar

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

h — Ellipsoidal altitude

scalar

Ellipsoidal altitude, specified as a scalar.

Data Types: double

Output

λ — Geocentric latitude

scalar

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

Data Types: double

r — Radius

scalar

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

Units — Units

Metric (MKS) (default) | English

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 — Planet model

Earth (WGS84) (default) | Custom

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 — Flattening

1/298.257223563 (default) | scalar

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

Equatorial radius of planet — Radius

6378137.0 (default) | scalar

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

Output radius — Enable output of radius

off (default) | on

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'

Programmatic Use: Add Block

To add the block programmatically, use the add_block function with one of these library block paths as the source.

"aerolibtransform2/Geodetic to  Geocentric Latitude"

Example: add_block("aerolibtransform2/Geodetic to Geocentric Latitude","myModel/myBlock",MakeNameUnique="on")

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 (semimajor 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.

$$\begin{array}{l}{e}^2=f*\left(2-f\right)\\ N=\frac{a}{\sqrt{1-e^2\sin {(\mu )}^2})}.\end{array}$$

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

$$\begin{array}{l}\rho =(N+h)*\cos (\mu )\\ z=(N(1-e^2)+h)\sin (\mu )\\ \lambda ={\tan }^{-1}\left(\frac{z}{\rho }\right).\end{array}$$

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