## B. Global Two-D Position

### 1. Definition

2D position reference is not limited to a flat plane. Geographic coordinates,* latitude* and *longitude*, have been used for centuries as an absolute positioning system. Sea bound navigators used flat paper maps which were plotted using latitude and longitude.

Assuming the Earth is a sphere, geographic coordinates are angular values with their verticies at the Earth's center, Figure B-1

- Latitude is the angle in the observer's meridian from the equator to the observer's vertical line. It varies from 0° at the equator to 90°N at the north pole and 90°S at the south pole.
- Longitude is the angle in the equatorial plane from the Greenwich Meridian (GM) to the observer's meridian. It varies from 0° at the GM to 180°E in the east direction and 180°W in the west.

Figure B-1 Geographic Coordinates |

As long as the directional suffixes are included, geographic coordinates are non-ambiguous.

### 2. Drawbacks?

Geographic coordinates are simple, but they do have some disadvantages.

#### a. Spherical trigonometry

##### (1) Distances

Distances between points are arcs, Figure B-2. Their lengths are angular and must be determined using spherical trigonometry.

Figure B-2 Arc Distance |

Survey distances are measured in linear units so another computational layer is added to make them work with geographic coordinates

##### (2) Angle Conditions

Multi-sided figures have curved sides and the Σ (interior angles)=(n-2)x180° angle condition does not apply, For example, the interior angle sum of triangle CDE in Figure B-3 can exceed 180°00'00".

Figure B-3 Spherical Triangle |

The amount by which the angle condition is exceeded is called *spherical excess* and accumulates at approximately 0°00'01" per 70 square miles of enclosed area.

#### b. Meridian convergence

##### (1) Directions

Meridians are parallel at the equator and converge to a point at the poles, Figure B-4

Figure B-4 Convergence |

- Except for due east-west or north-south lines, forward and back directions are not exactly 180° degrees apart.
- Because they are perpendicular to meridians, east-west lines are curved not straight.
- A uniform angular difference between meridians is not uniform length. In Figure B-5, The longitude difference from G to F is the same as from K to J, but the arc distance GF is longer than KJ. This is true for any angle difference that is not along a meridian.

Figure B-5 Length Variation |

#### c. The earth isn't round

Geographic coordinates are based on a sphere. Unfortunately the Earth is not spherical. A different geometric model is needed which complicates things. We still use latitude and longitude positions, but their *geodetic* counterparts, not *geographic*. This may seem a trifling difference, but it isn't, and will be covered in a subsequent chapter.