D. Latitudes and Departures
1. Definition; Equations
Latitude is the north-south component of a line; departure the east-west. North latitudes are positive, South are negative; similarly East departures are positive, West are negative.
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| Figure D-1 Latitudes and Departures |
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Latitude (Lat) and Departure (Dep) are computed from:
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Equations D-1 and D-2 |
Dir can be either a bearing angle, Figure D-2(a), or azimuth angle, Figure D-2(b).
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| Figure D-2 Bearings or Azimuths |
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Because a bearing angle never exceeds 90°, the Lat and Dep equations will always return positive values.
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Sin(0°) to Sin(90°) ranges from 0 to +1.0 Cos(0°) to Cos(90°) ranges from +1.0 to 0 The correct mathematical sign for the Lat and Dep come from the bearing quadrant. A bearing of S 47°35' E has a negative Lat (South) and a positive Dep (East). |
| Figure D-3 Quadrants |
An azimuth angle ranges from 0° to 360°, so the sine and cosine return the correct signs on the Lat and Dep.
Examples
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| Figure D-4 NE Azimuth |
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| Figure D-5 SW Azimuth |
Reversing a line direction results in the same magnitude Lat and Dep but reversed signs:
| Line A to B | Line B to A |
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| Figure D-6 Reverse Latitude and Departure |
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