Angles, Distances, and Trigonometry
Angles and Distances
Learning Objectives:
- Define and differentiate between azimuths, bearings, latitudes, departures, northings, and eastings.
- Learn measurement techniques for determining azimuths, bearings, latitudes, departures, northings, and eastings using surveying instruments such as theodolites, total stations, and compasses.
- Learn methods for calculating azimuths, bearings, latitudes, departures, northings, and eastings from field observations and measurements.
Azimuth:
Azimuth represents the horizontal angle measured clockwise from a reference direction, typically the north direction, to a point or line. In surveying, azimuth plays a crucial role in determining directions and bearings for mapping and construction projects. It is expressed in degrees, with 0° corresponding to the north direction, 90° to the east, 180° to the south, and 270° to the west. Azimuths can be measured using various surveying instruments such as theodolites, total stations, and compasses.
Bearings:
Bearings denote the direction of a line with respect to a reference direction, often the north direction. They are expressed in degrees, minutes, and seconds, or in the form of angles measured clockwise or counterclockwise from the north direction. Bearings play a critical role in surveying for determining directions of lines, property boundaries, and alignments of structures. Understanding bearings is essential for accurate mapping, land surveying, and civil engineering projects. Surveyors commonly use bearings alongside azimuths to describe the orientation of lines and features on the ground, facilitating precise measurements and calculations in construction and land development.
Latitudes and Departures:
In surveying, latitudes and departures are components used to represent the north-south and east-west distances, respectively, between consecutive points along a traverse or boundary line. Latitudes denote the north-south distances, while departures represent the east-west distances. They are calculated by measuring the differences in northing and easting coordinates between consecutive points. Latitudes and departures are fundamental in traverse calculations, aiding in the determination of closure errors, adjustments, and the overall accuracy of survey measurements.
Northings and Eastings:
Northings and eastings are coordinate values used in surveying to represent the position of a point on the Earth's surface within a specific coordinate system. Northings indicate the distance northward from a reference point or line, while eastings denote the distance eastward from the same reference. These coordinates are typically expressed in meters or feet and are crucial for accurately locating points on maps, plans, and survey drawings. Northings and eastings facilitate precise measurements, calculations, and spatial analysis in various civil engineering applications, including land surveying, construction layout, and geographic information systems (GIS).