The Nature of Geographic Information

6. Measuring Angles


Angles can be measured with a magnetic compass, of course. Unfortunately, the Earth's magnetic field does not yield the most reliable measurements. The magnetic poles are not aligned with the planet's axis of rotation (an effect called magnetic declination), and they tend to change location over time. Local magnetic anomalies caused by magnetized rocks in the Earth's crust and other geomagnetic fields make matters worse.

For these reasons, land surveyors rely on transits (or their more modern equivalents, called theodolites) to measure angles. A transit consists of a telescope for seeing distant target objects, two measurement wheels that work like protractors for reading horizontal and vertical angles, and bubble levels to ensure that the angles are true. A theodolite is essentially the same instrument, except that some mechanical parts are replaced with electronics.

A transit which looks like a telescope on a tripod.
Figure 5.7.1 Transit.
Credit: Raisz, 1948. Used by permission.

Surveyors express angles in several ways. When specifying directions, as is done in the preparation of a property survey, angles may be specified as bearings or azimuths. A bearing is an angle less than 90° within a quadrant defined by the cardinal directions. An azimuth is an angle between 0° and 360° measured clockwise from North. "South 45° East" and "135°" are the same direction expressed as a bearing and as an azimuth. An interior angle, by contrast, is an angle measured between two lines of sight, or between two legs of a traverse (described later in this chapter).

Diagrams of Azimuths (degrees) and Bearings (Cardinal Directions)
Figure 5.7.2 Azimuths and bearings.

In the U.S., professional organizations like the American Congress on Surveying and Mapping, the American Land Title Association, the National Society of Professional Surveyors, and others, recommend minimum accuracy standards for angle and distance measurements. For example, as Steve Henderson (personal communication, Fall 2000, updated July 2010) points out, the Alabama Society of Professional Land Surveyors recommends that errors in angle measurements in "commercial/high risk" surveys be no greater than 15 seconds times the square root of the number of angles measured.

To achieve this level of accuracy, surveyors must overcome errors caused by faulty instrument calibration; wind, temperature, and soft ground; and human errors, including misplacing the instrument and misreading the measurement wheels. In practice, surveyors produce accurate data by taking repeated measurements and averaging the results.