LLA to Flat Earth | Engee Documentation

Description

The LLA to Flat Earth block converts geodetic coordinates - latitude ( ), longitude ( ), and elevation ( ) - into a 3-by-1 vector of positions in a planar coordinate system ( ). Latitude and longitude can take any values, but latitude values +90° and −90° (poles) may return incorrect results due to peculiarities of calculations.

Algorithms

The local tangent plane coordinate system assumes a positive downward direction of the Z axis. The calculation begins by defining small changes in latitude and longitude as the difference between the final and initial values of latitude and longitude.

The algorithm uses to convert geodetic latitude and longitude to north/east coordinates:

where

- is the equatorial radius of the planet;
- the compression of the planet.

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

When converting north/east coordinates to and coordinates of a plane coordinate system, a transformation of the form is used:

where is the clockwise angle (in degrees) between the axis and the north direction.

The value of coordinate in the local tangent plane coordinate system is calculated as:

Ports

Input

# 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

# 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

# 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

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 the planet defined 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 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.