Flat Earth to LLA | Engee Documentation

Description

Block Flat Earth to LLA transforms the coordinates of the local tangent plane ( ) in latitude ( ), longitude ( ) and height ( ).

Algorithms

The coordinate system of the local tangent plane assumes a positive direction of the axis down. The transformation begins with the recalculation of the plane coordinates and to the coordinates of the north and east. This transformation has the form:

Where — this is the angle (in degrees) clockwise between the axis and heading north.

To convert the coordinates of the north and east to geodetic latitude and longitude, the algorithm uses:

Where

— this is the equatorial radius of the planet;
— planet compression.

Small changes in latitude and longitude are approximated through small changes in the coordinates of the north and east by the formulas:

The output latitude and longitude values are calculated as the sum of the initial latitude/longitude values and their small increments:

The height is calculated as the negative value of the coordinate the local tangent plane minus the reference height ( ):

Ports

Input

# X_e (m) — position in the coordinate system of the local tangent plane
`vector 3 by 1

Details

The position in the coordinate system of the local tangent plane, returned as a vector.

Data types	`Float64`.
Complex numbers support	No

# h_ref (m) — reference height
scalar

Details

The reference height from the Earth’s surface to the coordinate system of the local tangent plane.

Data types	`Float64`.
Complex numbers support	No

Output

# μ l (deg) — geodetic latitude and longitude
`vector 2 by 1

Details

Geodetic latitude and longitude given as a vector in degrees.

Data types	`Float64`.
Complex numbers support	No

# h (m) — altitude above sea level
scalar

Details

The height above the input reference height given by a scalar quantity.

Data types	`Float64`.
Complex numbers support	No

Parameters

# Planet model — planet
Earth (WGS84) | Custom

Details

The planet model used.

Values	`Earth (WGS84)` \| `Custom`
Default value	`Earth (WGS84)`
Program usage name	`planet_model`
Tunable	No
Evaluatable	Yes

# Flattening — planetary contraction

Details

The compression of a planet, given as a scalar.

Dependencies

To use this parameter, set the parameter Planet model to Custom.

Default value	`0.0033528106647474805`
Program usage name	`flat`
Tunable	No
Evaluatable	Yes

# Equatorial radius of planet — equatorial radius of the planet

Details

The equatorial radius of the planet, given as a scalar.

Dependencies

To use this parameter, set the parameter Planet model to Custom.

Default value	`6378137`
Program usage name	`radius`
Tunable	No
Evaluatable	Yes

# Reference geodetic latitude and longitude (deg) — initial geodetic latitude and longitude (deg)

Details

Initial geodetic latitude and longitude (in degrees) given as a vector.

Default value	`[0, 10]`
Program usage name	`ref_pos`
Tunable	No
Evaluatable	Yes

# Direction of flat Earth x-axis (degrees clockwise from north) — direction of the local tangent plane along the x-axis (in degrees clockwise from north)

Details

Angle to convert the local tangent plane coordinates and to north and east (geodetic) coordinates, specified as a scalar, in degrees.

Default value	`0.0`
Program usage name	`ref_rot`
Tunable	No
Evaluatable	Yes

Literature

Stevens, B. L., and F. L. Lewis. Aircraft Control and Simulation, Hoboken, NJ: John Wiley & Sons, 2003.
Etkin, B. Dynamics of Atmospheric Flight, Hoboken, NJ: John Wiley & Sons, 1972.