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Land surveys and maps

The art of making maps is a very old one. The ancient Egyptians and Babylonians made maps and plans, fragments of which have survived. The Greeks, having recognized the Earth as a sphere, applied astronomical observations to map-making: in fact in the third century BC, Eratosthenes estimated the circumference of the Earth with a degree of accuracy only surpassed in quite modern times. In the second century AD the Egyptian-born Greek Ptolomey was responsible for the production of a set of maps which remained standard works of reference for more than a thousand years. During the fourteenth, fifteenth and sixteenth centuries a series of seamen's maps, known as portolan charts, were produced covering the Mediterranean and neighbouring seas. In the sixteenth century Mercator invented the projection known by his name and still commonly used, especially in navigational charts for which it is convenient because compass bearings appear as straight lines. Mercator's maps also use the framework of latitude and longitude, which originated among the ancient Greeks.

A line of division between ancient and modern map-making may be taken as marked by three great achievements namely, the triangulation of France begun by Cassini de Thury in 1747 and finished by the French revolutionary government, the first accurate triangulation of the United Kingdom done by William Roy, and the connection by triangulation of the observatories of Greenwich and Paris carried out under the auspices of the British Royal Society. Triangulation became the basis of all modern mapping. It is only with the introduction of the Global Positioning System (GPS) and the use of artificial earth satellites to establish the positions of points on the surface of the earth that a significant alternative to triangulation has become available.

The techniques of land surveying are founded on five basic principles. The first is that of “working from the whole to the part” that is establishing an initial framework of control points that is then “broken down” into smaller networks with points closer together. The second principle is that of consistency in that once the higher order network has been established, it is possible to work to less rigorous standards in the lower orders without affecting the overall accuracy of the work. There has been no point in working to higher standards since in connecting the later work to the earlier, the higher order work is held fixed and hence the new survey cannot be better than the higher order control. The third and related principle is that of economy, namely that since higher accuracy in general costs more money the surveyor should seek no higher accuracy than is necessary and sufficient for the task in hand. The fourth principle is that of applying an independent check on the data wherever possible - for example by measuring all three angles of a triangle even though the third angle measurement is redundant. This has the effect of providing built-in quality control. Finally, as a matter of principle, since changes take place over time, mechanisms must be established to ensure that the survey is kept up to date if it is to be of continuing use. It is the latter principle that has not been adequately addressed in much of the world's mapping today.

The traditional means for establishing control is triangulation, the principle behind which is that of simple trigonometry, namely that if either two angles and one side length in a triangle are known, or all three side lengths are measured, then the precise size and shape of the triangle is known. Measurements of angles are made using a theodolite while distances which in the past had to be measured very laboriously with metal tapes are now recorded using electronic distance measuring devices. The fact that the Earth is a spheroid and not a plane surface means that no Euclidean straight lines can be measured on its surface. Lines so measured are not even arcs of a true sphere and this introduces complications in the measurements and calculations. It does not however detract from the simplicity of the principle and most modern maps have ultimately been based on a series of triangles originating from one or two base lines of known length and extended across the area covered by the map. This has formed a primary network of control points that in turn were used as the basis for determining a series of second order networks; these in turn were used to establish third order and fourth order points with local detail being fixed in relation to the overall network.

Triangulation using AB as a base line
The distance AB is measured precisely
Then C, D, E, F, G, H, I, J and K can be fixed by angular measurement only.

While triangulation techniques have been used to establish horizontal control, measurements of height have been obtained either by the measurement of vertical angles using a theodolite (and correcting the observed angles for the effects of curvature of the earth and refraction of the light through the atmosphere) or by levelling. The latter technique uses a spirit level and two graduated staves to obtain what can be very precise measures of the difference of height between successive points. Thus by starting at points of known height, the levels can be transferred successively until another known point is reached which can be used to check that no gross error has occurred.

Given an initial framework of horizontal control points, additional points can be established either by further triangulation, or by trilateration (that is measuring the sides rather than the angles of triangles), or by traversing. In addition, satellite position fixing methods or photogrammetric techniques can be used.

Traversing is a method frequently used for surveying perimeters, or for defining an area for subsequent more detailed survey, or for plotting the course of a road, railway, stream or other feature. The method starts at a known point from which there is a known direction - for example a point already established by triangulation from which another known point is visible to provide the necessary orientation. Traversing then proceeds by measuring the angle and linear distance to the next point on the traverse; from there the bearings can be oriented from the previous point and a further control point established in a forward direction. The traverse proceeds in this way until either it can be closed back on to the point from which it started, or preferably on to a different previously established control point thus providing the necessary independent check against any gross error in the measurements. The angles are normally measured with a theodolite although a prismatic compass or a plane table can be used for elementary surveys. Distances should either be measured by tape with a steel band, by optical distance methods such as the subtense bar, or by electronic distance measurement. The data are either recorded in field notebooks or else electronically for subsequent computation.

Traversing between known points A and B using known points C and D for orientation and fixing E, F, G and H by measuring angles and distances

Electronic surveying techniques have become standard in the more developed world. They include measurements using a “total station” that combines both the angular qualities of a traditional theodolite with electronic distance measurement and automatic data recording. The advantages of using such equipment include the speed with which surveys can be carried out compared with traditional methods, thus giving greater levels of productivity; the lower level of risk of making gross errors in the measurements; and the lower levels of manipulative skills that are needed to obtain much higher levels of precision and accuracy. The disadvantages of electronic methods include the much higher capital investment that is needed and the much higher cost of maintenance, both elements being a drain on hard currency for developing countries. Furthermore, if the equipment breaks down it may need to be sent to a foreign country for repair and the progress of any survey can be seriously delayed.

The price of much electronic equipment, especially computers, is still declining but on the other hand much information technology has a relatively short life before it is replaced by more powerful systems that are capable of even greater productivity. The prices, for example of Global Positioning System (GPS) receivers have been reduced significantly since they were first introduced, making their use an economically viable option. With GPS it is necessary to see four satellites in the sky, the signals from which are picked up by the GPS receiver. The signals are marked with pulses at known times so that the instant at which three signals are received provides information on how far away the satellites were at that time - measurement to a fourth satellite is needed to establish the difference in time between the clock in the GPS receiver and the time being recorded by the satellite system. The system overall allows the relative positions of nearby points on the ground to be determined to within a few centimetres in latitude, longitude and height. Since a good all-round view of the sky is necessary, the technique is not suitable for forest or jungle areas or within city centres where there are many high-rise buildings. In open countryside it is, however, extremely useful and cost effective for establishing dense networks of control points.

Global Positioning System (GPS) Receiver with signals from four satellites
15% Lateral Overlap 60% Fore & Aft Overlap


Strips of Aerial Photography

Photogrammetry is another method whereby large numbers of control points can be established over a restricted area - provided that suitable points on the ground can be seen clearly on the photographs. The positions of some ground points must be determined either from GPS, triangulation or traverse surveys. Measurements of the position of other points can then be made on aerial photographs and calculations performed in a process known as aerial triangulation to derive the equivalent ground positions of the points measured. Suitable overlapping aerial photography must be available to provide stereometric cover, that is, every part of the ground must appear on at least two adjoining photographs and some points must appear on three successive photographs in a strip of photography. The fore and aft overlap for photographs should be about 60 percent while the lateral overlap between strips should be around 15 percent. Having acquired such a block of photography and depending on its scale, the equipment used, the quality of the images of the coordinated points and the skill of the operators, then it is possible to measure the relative positions of points on the ground to within an accuracy of a few centimetres. Photogrammetry is essentially a mass production technique that becomes cost effective only when a sufficiently large number of points on the ground need to be fixed. The accuracy achievable with modern equipment is dependent on cost more than any other factor.

An additional benefit that comes from using photogrammetry is that the techniques can be used not only for fixing control points but also for plotting detail and contour lines. Ground survey techniques are less suited to topographic mapping other than for relatively small areas.

The trigonometrical data, however derived, refer to positions on the spheroid taken as the survey datum. A map is usually a flat sheet and to transfer the spheroidal data on to this requires a map projection. There are many kinds of projection all of which require changes to be made to the angles and distances measured on the surface of the Earth. Either the shape or the area (or both) of features mapped will inevitably to some extent be altered. Different projections give different results for different parts of the Earth's surface. Some projections have special advantages for particular purposes and the choice of projection in each case is therefore determined by the part of the Earth's surface to which it is to be applied, and the purpose for which the map has been prepared.

The scale of the map, that is the number of units of length on the ground represented by one similar unit on the map, is of great practical importance. Scales are best described by ratios (or fractions) in which the first figure (or numerator) relates to one unit of measurement on the map and the second (or denominator) to the equivalent number of the same units on the ground. It is obvious that the larger the scale of the map the greater the detail that can be plotted on it. It is equally obvious that a scale that is convenient for one purpose may be most inconvenient for another purpose. Thus a walker may find a map on a scale of 1:10,000 convenient but the same scale would be inconvenient for a motorist who would drive beyond the limits of the map sheet in a few minutes.

The scale of the basic maps produced from topographic survey data is of considerable importance, because, while it is in general practicable and convenient to produce small-scale maps from a large-scale map by omitting detail and adjusting the position and shape of some objects, it is not practicable to produce large-scale maps from a basic map on a smaller scale without much further field work. The scale chosen for displaying a map must depend on the topography and closeness of occupation of the country mapped and on the purposes to which any maps derived from the original maps are to be put. Generally speaking the scale chosen should be the scale which will show the detail required with the necessary degree of accuracy and clarity and give sufficient space for the entry of the descriptive matter required for particular purposes.

When the basic scale has been determined, the foundation of the map is constructed on the required projection from the trigonometrical and other data recorded. The printed map is then usually taken to the field for the entry of final detail, though if it is based on air photographs much of this work may be done in the office.

A feature of most national maps is the “grid”. This is a series of lines drawn parallel to and at right angles with a chosen meridian. The purpose of the grid is to enable the position of any place on the map to be located or described. This is done by numbering the squares of the original grid (and their subdivisions) in a recognized sequence. It should be observed that the only map projection on which the grid coincides with the “graticule”, that is the projected positions of the network of lines of latitude and longitude on which the map is based, is the simple cylindrical projection. This is never used for topographical maps because of the way that it distorts the shape of the ground. In general the graticule and grid only coincide along selected lines such as the central meridian in the Transverse Mercator which is the most commonly used map projection for topographic mapping. In practice, the grid as a whole never coincides with the graticule.

The most convenient scales for topographic maps for general use are those between 1:25,000 and 1:250,000. Common scales are 1:50,000 and 1:100,000 Even the largest of these maps, however, contains many features indicated by “conventional signs” and not drawn to scale. If real accuracy of topographical detail is required, a larger scale has to be used. Failure to realize the limitations of standard topographical maps has led to much confusion in the past in many countries, especially in the matter of mineral concessions.

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