Surveying and navigation often rely on the measurement of two phenomena in order to determine position, those of distance (already covered in lectures) and direction or bearing. These lecture notes will introduce the concept of bearings and cover the instrumentation that has been developed over the centuries to facilitate the determination of relative and absolute 'bearing'. In order to start, we will look at the definition of some terms specific to the determination of direction.

1. Definitions:

Directions: - Simply that, a direction (over there).

Bearings: - A direction relative to a datum

Whole-circle bearings: The direction of survey lines is generally expressed as an angle measured from a reference meridian, generally north, commencing from 0 degrees (0°) and increasing clockwise to 360 degrees (359°59'60"). Bearings are never expressed as "North, X degrees East".

Angles: - The arithmetic difference between two directions or bearings.

Reference meridians:

True north (through the geographic poles about which the Earth rotates)

Magnetic north (through which lines of magnetic flux pass)

Grid north - An arbitrary meridian (one adopted for a particular project) - a mathematically determined value

Magnetic meridian: - The direction of the earth's magnetic lines of force. This varies with date, time and locality.

Magnetic declination - The angle between the magnetic and true meridians.

Angle measurement is a fundamental part of surveying field observations, as the combination of a direction and a distance gives a polar vector to a point and hence a unique location of that point in space. The instruments that have been developed to facilitate angle (or direction) measurement are the magnetic compass , the sextant and the theodolite.

2. The Magnetic Compass

The Magnetic Compass is an instrument which indicates the whole circle bearing from the magnetic meridian to a particular line of sight. It consists of a needle or disc magnetised so that it will align itself with the direction of the Earth's magnetic flux, and some type of index scale so that numeric values for the bearing can be determined. See diagram below.

The magnetic bearing is related to true bearings as follows:

d = Magnetic declination (positive when clockwise) qt = True bearing qm = Magnetic bearing

qt = q m + d

3. Variations in Declination

The geophysical phenomena that generate the Earth's magnetic flux are still not fully understood. It is known that magnetic north moves quite considerably over time, and has even reversed polarity in prehistory. Some of the phenomena that effect the direction of magnetic flux (and hence magnetic north) are known as variations in declination and are as follows:

4. Local Attraction

The needle of the compass can also be 'attracted' by metallic objects close to the point of observation. These objects cause local aberrations in the direction of magnetic flux, and give rise to an effect known as local attraction. These local disturbances in the Earth's magnetic field are often due to large iron masses, electric cables, fences, cars and so on. They tend to occur locally, and if detected can sometimes be compensated for in survey procedures. Magnetic anomalies caused by underground minerals are a problem for surveyors, but form the basis of many mineral exploration techniques so the news is not all bad.

Where a closed traverse consisting of compass bearings and distances has been performed around a parcel of land (see later) it is possible to compensate for the effects of local attraction and to distribute 'angular misclosure'.

This will be covered in more detail later but in summary the procedure consists of:

1. measuring forward and back bearing of each line

2. computing angles and angle misclosure

3. (misclosure = [180°(n - 2)] - S angles) {¹(n-2) - S angles} )

4. adjusting each angle by adding to each

5. recomputing bearings from adjusted angles. (The bearing of one line must be known or assumed).
   

The presence or otherwise of local attraction can be determined from the difference between a 'forward' bearing and a 'reverse' bearing observed from, and to, a station. If I was to measure from Point A to Point B, and then from Point B back to Point A the difference in the bearings should be 180°. Any variation in this in excess of what would be expected from random error would be most likely due to local attraction. Needless to say both forward and reverse bearings are always observed when using a compass for traversing.

5. Compasses:

There are two main types of magnetic compasses used in the field by surveyors navigators and orienteers: the Sunnto type and the prismatic type, as well as compass-theodolites. There are others like the gyro-compass which are used in inertial navigation systems, however they will not be addressed here.

Both the Sunnto type and the Prismatic type are held in the hand for use, and are therefor subject to poor centring and an unstable platform. The effects of this are reduced over long sight lines, which, when combined with the vagaries of the magnetic meridian, combine to make the compass a reconnaissance or inventory tool only. Neither the instruments nor the basis upon which they work are sufficiently stable for any sort of precision work.

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