Chapter 4 Angles and Directions

Azimuths and Bearings

Types of Vertical Angles

  • Vertical Angles: Angles associated with the observer's horizon.

    • Zenith Angles: Angles measured above the observer.

  • Nadir Angles: Angles measured below the observer.

Vertical Angles, Slope and Elevation

  • If the Height of the Instrument = Height of the Prism

  • If the Height of the Instrument ≠ Height of the Prism

Types of Horizontal Angles

  • Interior Angles: Angles formed inside a polygon.

  • Exterior Angles: Angles formed outside a polygon.

  • Deflection Angles: Angles related to the change in direction of a line.

Alternate Angles and Supplementary Angles

Closed Traverse

  • Definition: A traversal where the start and endpoint connect to form a closed loop.

  • Sum of Interior Angles:

    • Formula: =(n−2)180°=(n-2)180\degree

    • Where ( n ) = number of sides.

Open Traverse

  • Definition: A traversal that does not close back onto the start point.

  • Example measures:

Directions: Azimuth

Directions: Bearings

Finding Azimuths & Bearings

Reverse Bearings & Azimuths

Converting Azimuth to Bearings

To Convert Azimuth to Bearing:

  • NE Quadrant: Bearing = Azimuth.

  • SE Quadrant: Bearing = 180° - Azimuth.

  • SW Quadrant: Bearing = Azimuth - 180°.

  • NW Quadrant: Bearing = 360° - Azimuth.

Converting Bearing to Azimuth

  • NE Quadrant: Azimuth = Bearing

  • SE Quadrant: Azimuth = 180 - Bearing

  • SW Quadrant: Azimuth = 180 + Bearing

  • NW Quadrant: Azimuth = 360 - Bearing

Meridians as a Reference for Angles

  • Types of Meridians:

    • Geographic Meridian

    • Magnetic Meridian

    • Grid Meridian

    • Coordinate Grid

  • Geographic: Reference lines used for understanding longitudes. The Central Meridian is critical in defining the geographic landscape.

Magnetic Declination

  • Magnetic Declination: The angle that indicates the difference between magnetic north (measured by a compass) and true north (geodetic north).

  • Isogonic Map: Shows variations in magnetic declination globally.

    • Isogonic Lines: Lines reflecting changes in declination over time.

Setting up a Total Station

  • Total Station: Instrument used in surveying that combines an electronic theodolite with an electronic distance measuring device. It is crucial for making precise measurements in surveying tasks. Procedural setup involves calibration to ensure accuracy.