civil engineering
surveying
Surveying is a method of making relatively large-scale, precise measurements of the Earth's surfaces. It entails determining measurement data, reducing and interpreting the data to usable form, and, conversely, establishing relative position and size in accordance with given measurement requirements. Thus, surveying serves two similar but opposing purposes: (1) determining existing relative horizontal and vertical position, such as that used in the mapping process, and (2) establishing marks to control construction or indicate land boundaries.
Surveying has been such an important part of the evolution of the human environment for so many centuries that its significance is often overlooked. It is a must in the planning and execution of nearly every type of construction. Surveying was critical at the beginning of history, and some of the most significant scientific discoveries would not have been realised without the contribution of surveying. Its primary modern applications are in transportation, construction, land apportionment, and communications.
Except for minor technical differences and the use of one or two minor hand-held instruments, surveying is essentially the same all over the world. The methods are a reflection of the instruments, which are mostly made in Switzerland, Austria, the United Kingdom, the United States, Japan, and Germany. Japanese instruments are similar to those made in the West.
History
Surveying is very likely to have originated in ancient Egypt. The Great Pyramid of Khufu at Giza was constructed around 2700 BCE and stands 755 feet (230 metres) tall and 481 feet (147 metres) long. Its nearly perfect squareness and north-south orientation attest to the ancient Egyptians' surveying prowess.
Evidence of boundary surveying dating back to 1400 BCE has been discovered in the fertile valleys and plains of the Tigris, Euphrates, and Nile rivers. Sumerian clay tablets contain records of land measurement as well as plans of cities and surrounding agricultural areas. Land plot boundary stones have been preserved. On the wall of a tomb in Thebes (1400 BCE), there is a representation of land measurement showing head and rear chainmen measuring a grainfield with what appears to be a rope with knots or marks at uniform intervals. Other people are shown. According to their clothing, two are of high estate, most likely a land overseer and a boundary stone inspector.
There is some evidence that the Egyptians used wooden rods for distance measurement in addition to a marked cord. There is no record of any angle-measuring instruments from that era, but there was a level made of a vertical wooden A-frame with a plumb bob supported at the A's peak so that its cord hung past an indicator, or index, on the horizontal bar. By standing the device on two supports at roughly the same elevation, marking the position of the cord, reversing the A, and making a similar mark, the index could be properly placed. The index should be placed halfway between the two marks. Thus, the ancient Egyptians were able to measure land areas, replace property corners lost when the Nile covered the markers with silt during floods, and build the massive pyramids to exact dimensions using simple devices.
During their slow voyages from the Indus to the Persian Gulf around 325 BCE, the Greeks used a type of log line to record distances run from point to point along the coast. In the 12th century CE, Arab traders brought the magnetic compass to the West. In the second century BCE, the Greeks invented the astrolabe. A graduated arc suspended from a hand-held cord was used to measure the altitudes of stars, or their angle of elevation above the horizon. The star was pointed by a pivoted pointer that moved over the graduations. For several centuries, the instrument was only used for scientific purposes, remaining a scientific aid.
The Greeks may have invented the groma, a device used to establish right angles, but Roman surveyors popularised it. It was constructed from a horizontal wooden cross that was pivoted in the middle and supported from above. A plumb bob hung from the ends of each of the four arms. The correct angle could be determined by sighting along each pair of plumb bob cords in turn. By observing the same angle after turning the device approximately 90°, the device could be adjusted to a precise right angle. A perfect right angle would be obtained by shifting one of the cords to take up half of the error.
Vitruvius, a Roman architect and engineer, mounted a large wheel of known circumference in a small frame, much like the wheel on a wheelbarrow; when pushed along the ground by hand, it automatically dropped a pebble into a container at each revolution, giving a measure of the distance travelled. In effect, it was the first odometer.
The water level was either a trough or a tube with the ends turned upward and filled with water. There was a sight made of crossed horizontal and vertical slits at each end. The sights determined a level line accurate enough to establish the grades of the Roman aqueducts when these were lined up just above the water level. The Romans are said to have used the plane table to plan their vast road system. It consists of a drawing board mounted on a tripod or other stable support, as well as a straightedge with sights for accurate aim (the alidade) to the objects to be mapped, along which lines are drawn. It was the first device that could record or establish angles. Magnetic compasses were added to later versions of the plane table.
Surveyors used plane tables in the 16th century, and the principle of graphic triangulation and intersection was practised. Willebrord Snell, a Dutch mathematician, used instrumental triangulation to measure an arc of meridian in 1615. Edmund Gunter, an English mathematician, invented a surveying chain in 1620, which was only surpassed by the steel tape in the late nineteenth century.
The study of astronomy resulted in the development of angle-reading devices based on large arcs, making such instruments too large for field use. Portable angle-measuring instruments became popular with the publication of logarithmic tables in 1620. They were known as topographic instruments, or theodolites. They had pivoted arms for sighting and could be used to measure both horizontal and vertical angles. Some may have had magnetic compasses.
By around 1720, theodolites had incorporated the vernier, an auxiliary scale that allowed for more accurate readings (1631), the micrometre microscope (1638), telescopic sights (1669), and spirit levels (around 1700). James Watt was the first to use Stadia hairs in 1771. The invention of the circle-dividing engine around 1775, a device for accurately dividing a circle into degrees, was one of the most significant advances in surveying methods, allowing angle measurements to be made with portable instruments far more accurately than had previously been possible.
Modern surveying can be traced back to the late 18th century. One of the most notable early feats of surveyors was the measurement of the meridian from Barcelona, Spain, to Dunkirk, France, in the 1790s by two French engineers, Jean Delambre and Pierre Méchain, to establish the basic unit of measurement for the metric system.
All of the basic surveying instruments have undergone numerous improvements and refinements. These have resulted in increased accuracy and speed of operations, as well as opportunities for improved field methods. In addition to modifying existing instruments, two revolutionary changes in mapping and surveying were introduced: photogrammetry, or mapping from aerial photographs (around 1920), and electronic distance measurement, which included the use of the laser for this purpose as well as for alignment (in the 1960s). Beginning in the late twentieth century, significant technological developments included the use of satellites as reference points for geodetic surveys and the use of electronic computers to speed the processing and recording of survey data.
Modern surveying
Basic control surveys
Geodetic surveys cover such large areas that the curvature of the Earth must be taken into account. To begin computations, baseline measurements for classical triangulation (the basic survey method that consists of accurately measuring a base line and computing other locations by angle measurement) are reduced to sea-level length, and angular determinations are corrected for spherical excess. The accuracy of geodetic operations is classified into four "orders," with first-order surveys having the smallest permissible error. To ensure first-order accuracy, primary triangulation is performed under strict specifications.
Efforts are now being made to extend and connect existing continental networks using satellite triangulation in order to facilitate the adjustment of all major geodetic surveys into a single world datum and determine the size and shape of the Earth spheroid with far greater accuracy than has previously been obtained. Simultaneously, existing national networks will be strengthened, while the amount of work remaining may be reduced slightly. Satellite triangulation became operational in the United States in 1963, thanks to observations made by the Rebound A-13 satellite, which was launched that year, as well as previous work using the Echo 1 and Echo 2 passive reflecting satellites. Pageos 1, the first satellite specifically designed for geodetic work, was launched in 1966.
An adequate pattern of horizontal and vertical control points is a first requirement for topographic mapping of a given area, and an initial step is the compilation of all such existing information. This consists of descriptions of points for which latitude and longitude positions and elevations above mean sea level have been determined. They are occasionally located some distance from the immediate project, necessitating an expansion from the existing work. Depending on the length of the circuits involved, this is usually done on second- or third-order standards.
Survey measurement accuracy can be improved almost indefinitely, but only at a cost. As a result, control surveys are used, which consist of a relatively few accurate measurements that cover the project area and from which short, less accurate measurements to the objects to be located are made. The traverse is the most basic form of horizontal control, consisting of a series of marked stations connected by measured courses and the measured angles between them. When a series of distances and angles returns to its starting point or begins and ends at stations of superior (more accurate) control, the small errors of measurement can be adjusted for mathematical consistency. The rectangular coordinates of all the stations can be computed by assuming or measuring the direction of one of the courses and rectangular coordinates of one of the stations.
A triangle system typically provides superior horizontal control. The triangulation system's angles and at least one side (the base) are all measured. Though several arrangements can be used, the quadrangle or a chain of quadrangles is one of the best. With four sides and two diagonals, each quadrangle provides eight angles to be measured. Angles must satisfy three angle equations and one side equation to be geometrically consistent. That is, the three angles of each set of adjacent triangles within the quadrangles yields the same values for any side. The quadrangles should ideally be parallelograms. If the system is linked to previously determined stations, the new system must conform to the existing measurements.
When the survey area is large enough for the curvature of the Earth to be a factor, an imaginary mathematical representation of the Earth must be used as a reference surface. The geoid is a level surface at mean sea level that is thought to represent the Earth's size and shape. The geoid is irregular due to gravity anomalies; however, it is very close to the surface generated by an ellipse rotating on its minor axis—that is, an ellipsoid slightly flattened at the ends, or oblate. A spheroid is a figure like this. Several have been computed by various authorities; the one that English-speaking nations usually use as a reference surface is (Alexander Ross) Clarke's Spheroid of 1866. This oblate spheroid has a polar diameter that is about 27 miles (43 kilometres) smaller than its Equatorial diameter.
Because gravity's directions converge towards the geoid, any length of Earth's surface measured above the geoid must be reduced to its sea-level equivalent—that is, to the geoid. These lengths are assumed to be the distances measured on the spheroid from the ends of the measured lengths on the actual surface of the Earth. The survey stations' positions on the Earth's surface are given in spherical coordinates.
The vertical controls of surveying are bench marks, or marked points on the Earth's surface connected by precise levelling. Bench mark elevations are given in terms of their heights above a selected level surface known as a datum. The geoid is the most commonly used datum in large-scale surveys. The height of mean sea level determined by a series of observations at various points along the seashore taken continuously for at least 19 years is used as the reference datum. Because mean sea level is not exactly the same as the geoid, most likely due to ocean currents, all heights determined for mean sea level have been held at zero elevation in adjusting the level grid for the United States and Canada.
Because the level surfaces determined by levelling are slightly distorted in the area towards the Earth's poles (due to a decrease in centrifugal force and an increase in gravity at higher latitudes), the distances between the surfaces and the geoid do not exactly represent the heights of the surfaces from the geoid. Orthometric corrections must be applied to long lines of levels at high altitudes with a north-south trend to correct these distortions.
When accurate elevations are unavailable or the elevations of inaccessible points must be determined, trigonometric levelling is frequently required. Triangulation is used to find the horizontal position of an unknown point from two points of known position and elevation, and vertical angles from the known points are measured. The elevation differences between the known points and the unknown point can be calculated trigonometrically.
In recent years, the National Ocean Service has hoped to increase the density of horizontal control to the point where no location in the United States will be more than 50 miles (80 kilometres) from a primary point, and advances in analytic phototriangulation suggest that the envisioned density of control may soon suffice in terms of topographic mapping. Control densities in the United Kingdom and much of Western Europe are already adequate for mapping and cadastral surveys.
Global positioning
The techniques used to determine the positions of reference points within a mapped area are similar to those used in navigation. However, greater accuracy is required in surveying, which is possible because the observer and the instrument are stationary on the ground rather than in a ship or aircraft that is not only moving but also subject to accelerations, making it impossible to use a spirit level to accurately measure star elevations.
The method of locating oneself by observing celestial objects is rapidly becoming obsolete. In practise, the surveyor uses a theodolite with a spirit level to accurately measure the elevations of the Sun at various times of the day or of several known stars in various directions. Each observation defines a line on the Earth's surface along which the observer must be located; a series of such lines provides a fix, the accuracy of which is indicated by how closely these lines intersect in a point. It is also necessary to record the Greenwich Mean Time of each observation for longitude. Since 1884, this has been accomplished by using an accurate chronometer that is checked at least once a day against time signals transmitted telegraphically over land lines and submarine cables, or broadcast via radio.
A more recent method of global positioning relies on satellites, the precise location of which is known at any given time due to continuous observation from a network of stations located all over the world. These stations' coordinates were determined using very large scale triangulation based on a combination of radar distance observations and measurements of the directions of special balloons or flashing satellites obtained by photographing them at known instants of time against the background of fixed stars.
The primary method of using satellites for precise positioning is based on the Doppler effect. The satellite transmits a radio signal at a constant frequency, but a stationary observer detects a higher frequency as the satellite approaches and a lower frequency as it recedes. The speed of the frequency drop is proportional to the observer's distance from the satellite's track, so determining this speed provides a measure of that distance. The observed frequency is the same as the transmitted frequency at the moment of the satellite's closest approach, so the observer must be located somewhere along the line at right angles to the satellite's track at that time. Because the observer's position on the Earth's surface is always known, these data define the observer's position.
Establishing the framework
Most surveying frameworks are built by measuring the angles and lengths of the sides of a chain of triangles connected by global positioning points. The positions of ground features are then determined in relation to these triangles using less precise and thus less expensive methods. The framework is established to ensure that detail surveys conducted at different times or by different surveyors fit together without overlaps or gaps.
For centuries, the corners of these triangles have been located on hilltops, each visible from at least two others, and the angles between the lines connecting them have been measured; this is known as triangulation. The lengths of one or two of these lines, known as bases, are meticulously measured; all other lengths are derived from them and the angles via trigonometric calculations. The accuracy is checked quickly by measuring all three angles of each triangle, which must add up to 180 degrees.
Working at large scales in small flat areas, it may be easier to measure the lengths of all the sides, rather than the angles between them; this procedure, known as trilateration, was impractical over large or hilly areas until the invention of electromagnetic distance measurement (EDM) in the mid-20th century. By electronically timing the passage of radiation over the distance to be measured, this procedure has made it possible to measure distances as accurately and easily as angles; microwaves, which penetrate atmospheric haze, are used for long distances and light or infrared radiation for short distances. EDM devices emit either light (from a laser or an electric lamp) or an ultrahigh-frequency radio beam. The radio beam can penetrate fog, haze, heavy rain, dust, sandstorms, and some foliage, whereas the light beam requires a clear line of sight. At one survey station, both types have a transmitter and a receiver. The light type includes a set of corner mirrors at the remote station, whereas the high-frequency type includes a retransmitter (requiring an operator) that is identical to the transmitter-receiver at the original station. A corner mirror is shaped like the inside of a cube's corner; it returns light from whatever angle it is received, within reasonable limits. A retransmitter must be directed at the transmitter-receiver pair.
The distance is determined in both types of instruments by the time it takes the radio or light beam to travel to and from the target. The phase shift of a modulating signal superimposed on the carrier beam determines the elapsed time. This phase shift is detected by electronic circuitry and converted to time units; the use of more than one modulating frequency eliminates ambiguities that could arise if only one frequency was used.
EDM has greatly simplified an alternative technique for establishing a framework known as traversing. The surveyor measures a series of distances and angles between them while traversing, usually along a travelled route or a stream. Traversing was previously used only in flat or forested areas where triangulation was impossible. Measuring all distances with tape or chain was tedious and time-consuming, especially if great accuracy was required, and no check was available until the traverse closed, either on itself or between two points already fixed by triangulation or astronomical observations.
The slope of each measured line must be allowed for in both triangulation and traversing so that the map can be reduced to the horizontal and referred to sea level. A measuring tape can be stretched along the ground or suspended between two tripods; in precise work, corrections for sag, tension, and temperature must be applied if they differ from the values at which the tape was standardised. Geodetic work of the highest order requires errors to be kept to one millimetre per kilometre, or one part in 1,000,000.
The theodolite
Though a compass or graphic techniques can be used to measure angles on sketch maps, only a theodolite can ensure the accuracy required in the framework required for precise mapping. The theodolite is a telescope that pivots around horizontal and vertical axes to measure both horizontal and vertical angles. Angles are read from circles with degrees and smaller intervals of 10 or 20 minutes. The exact position of the index mark (indicating the direction of the line of sight) between two of these graduations is measured with a vernier or a micrometre on both sides of the circle. Modern first-order or geodetic instruments with five-inch glass circles have an accuracy of about one second of arc, or 1/3,600 of a degree. At a distance of two kilometres, such an instrument can detect a one-centimetre sideways movement of the target. Horizontal angles can be measured more precisely by repeating the measurement up to 16 times and averaging the results; in geodetic surveying, measurements of all three angles of a triangle are expected to give a sum of 180 degrees within one second of arc.
Signaling lamps or heliographs reflecting the Sun are used as targets for the theodolite in the most precise long-distance work. Smaller theodolites with simpler reading systems can be used for less demanding work and work over shorter distances; targets are commonly striped poles or ranging rods held vertical by an assistant.
An extensive set of these measurements creates a network of points on the map, where their positions are plotted by their coordinates, and on the ground, where they are marked by pillars, concrete ground marks, bolts inserted into the pavement, or wooden pegs of varying cost and permanence, depending on the importance and accuracy of the framework and the maps that will be based on it. Once this framework is established, the surveyor moves on to detail mapping, beginning with these ground marks and knowing that their accuracy ensures that the data obtained fits precisely with similar details obtained elsewhere in the framework.
Detail surveying
The actual depiction of the map's features can be done on the ground or, since the invention of photography, aviation, and rocketry, by interpreting aerial photographs and satellite images. On the ground, the framework is dissected into even smaller areas as the surveyor moves from one point to the next, fixing additional points on the features from each position using a combination of angle and distance measurement, and finally freehand sketching the features between them. In difficult terrain, this operation can be slow and inaccurate, as evidenced by comparing maps created on the ground with those created later from aerial photographs.
Ground survey is still required for some purposes, such as in areas where aerial photographs are difficult to obtain; under the canopy of a forest, where the shape of the ground—rather than the shape of the treetops—is required; in very large scale work or close contouring; or if the features to be mapped are not easily identifiable on aerial photographs, such as property boundaries or zones of transition between different types of soil or vegetation. One of the two fundamental differences between ground and air surveys is that ground surveys, as previously stated, interpolate, or sketch, between fixed points, whereas air surveys, using semiautomatic instruments, can trace the features continuously once the positions of the photographs are known. One effect is that features are shown in uniform detail rather than along short stretches between fixed points in a ground survey.
The second distinction is that different techniques and accuracies may be used in ground survey for horizontal and vertical measurements, with the latter typically being more precise. Accurate height determinations are required for engineering and planning maps, such as railway gradients or, more specifically, irrigation or drainage networks, because water in open channels does not flow uphill.
The methods used to fix locations within the horizontal detail framework are similar to, but less precise than, those used in the primary framework. Angles can be measured with a prismatic compass or graphically with a plane table, or they can be estimated as right angles in the case of points offset by short distances from straight lines already fixed. Detail points can be found by measuring their distances from two fixed points or by measuring their distance and bearing from only one.
The surveyor can take measurements in the field and plot them later on a sketch board or in the office, but if the country is open and hilly, or even mountainous, the plane table is the best way to record the data. Because plane-table work cannot be checked in the office, it necessitates greater intelligence and integrity on the part of the surveyor. The plane table saw its most efficient use in the Survey of India, which began in 1800 and involved dedicated Indian surveyors mapping large areas with it. It is made up of a flat board mounted on a tripod and can be fixed or rotated around a vertical axis. It is positioned horizontally over a framework point or one end of a measured baseline, with its surface (covered with paper or other drawing medium) horizontal. It is turned until the line connecting its location to another framework point or the opposite end of the baseline is parallel to the line drawn on the paper. This alignment is done with the help of an alidade, or sight rule, which is a straightedge with simple sights. The alidade is then directed towards fixed-point features, and pencil rays are drawn along the sight rule towards them. The procedure is repeated at the other framework point or at the other end of the baseline; the points on the table where the rays intersect will be the map positions of the features.
More sophisticated instruments are used in engineering surveying to maximise accuracy. Distances, for example, can be measured using EDM or tachymetry, a geometric technique in which the vertical distance on a graduated vertical staff, as seen between two stadia hairs in the theodolite eyepiece, is a measure of the horizontal distance between the theodolite and the staff—typically 100 times the difference between the two readings. This method necessitates the use of at least one assistant to move the staff from one location to another. A theodolite, EDM equipment, and a computer record all observations and calculate height differences obtained by measuring vertical angles in modern surveying instruments.
Aerial surveying
Detail mapping of features visible from the air has been revolutionised by aviation and photography. An aerial photograph, on the other hand, is not a map. When the House of Parliament and Westminster Bridge in London are mapped, the tops of the towers coincide with the corners of the foundations. They would not, however, in an aerial photograph because they are radially displaced from the centre. An important feature of vertical aerial photographs is that angles are correctly represented only at their centres. Photographs of hilly terrain exhibit similar distortions. This issue can be addressed in two ways, depending on the relative scales of the map and the photographs, as well as whether contours are required on the map. The older method, which was adequate for planimetric maps at scales smaller than photographs, was widely used during and after WWII to map large areas of desert and sparsely populated country; mountainous areas could be sketched in, but the relief was inaccurately shown.
A framework of identified points, similar to a ground survey, is required before detailed mapping can be carried out from the air. Ordinarily, the photographs are taken with a vertically aligned camera in a series of strips (see Figure 1), with each picture overlapping about 60% of the one before it; adjacent strips overlap only slightly. The overlaps allow for the construction of a low-order framework or control system based on small, recognisable features that appear in multiple photographs. In its most basic form, each photograph is replaced by a transparent template on which rays are drawn (or slots are cut) from the centre of the image to the desired features. The angles between these rays or slots are correct, and slotted templates can be fitted together by inserting studs representing the features into the appropriate slots and sliding the templates so that each stud engages the slots in all of the pictures depicting the corresponding feature. This operation ensures that the image centres and the selected features are in the proper relationship. As long as the studs remain engaged in the slots and the array of overlapping photographs can be expanded or contracted by sliding them around on the work surface, the assemblage can be positioned, oriented, and scaled by fitting it to at least two—preferably several—ground-control points identified on different photographs.
This technique can be improved by adding two more cameras, one on each side, aimed at right angles to the flight path and 30 degrees below horizontal. The photographs taken by the side cameras overlap those taken by the vertical camera and also include the horizon, resulting in a wider strip of ground covered and thus less flying required. To connect the adjacent flight paths, points in the backgrounds of the oblique photographs can be incorporated into the overlapping array as before. This technique has been rendered obsolete by photography from high-flying jet aircraft and satellites, but prior to those advancements, it greatly aided in the mapping of underdeveloped areas.
A more sophisticated approach is required for the production of maps with accurate contours at scales five or six times that of the photographs. The ground-survey effort must be expanded to provide the heights and positions of all features used to establish the framework.
The details within each segment of the map are based on the overlap between two successive photographs in the same strip, starting with the positions and heights of features in the corners of each area. By viewing each pair of consecutive photographs in a stereoscope, a three-dimensional model can be created; by manipulating a specially designed plotting instrument, the overlapping area can be correctly positioned, scaled, and oriented, and elevations of points within it can be derived from those of the four corner points. These photogrammetric plotting instruments come in a variety of shapes and sizes. Photographs are projected in different colours onto a table in projection instruments, so that each eye sees only one image and the operator sees a three-dimensional model of the ground through spectacles with complementary colour lenses. A table or platen with a lighted spot in the centre can be moved around the model and raised or lowered so that the spot appears to touch the ground while the operator scans any feature, even one on a steep hillside. A pencil is then placed directly beneath the spot to trace the exact shape and location of the feature on the map. For contouring, the platen is set at the desired height (at a scale appropriate for the model), and the spot is free to touch the model surface wherever it pleases; the contour is then drawn with a pencil.
Rays of light reaching the aircraft taking the two photographs are represented by rods meeting at a point that represents the position of the feature of the model being viewed in more complex mechanical devices. As with projection instruments, the operator sees a spot that can be moved anywhere in the overlap and up or down to touch the model surface using a complicated system of prisms and lenses. A mechanical or electronic system positions a pencil on a plotting table to which the map manuscript is attached.
Light rays reaching the aircraft taking the two photographs are represented by rods meeting at a point that represents the position of the feature of the model being viewed in more complex mechanical devices. As with projection instruments, the operator sees a spot that can be moved anywhere in the overlap and up or down to touch the model surface. A mechanical or electronic system moves a pencil to the corresponding position on a plotting table to which the map manuscript is attached.
All of these methods generate a line or drawn map; some also generate a data file on disc or tape that contains the coordinates of all the lines and other features on the map. Aerial photographs, on the other hand, can be combined and printed directly to create a photomap. This operation requires simply cutting and pasting the photographs together into a mosaic for flat areas. The centres of the photographs can be aligned more precisely by using slotted templates as described above to create a photomap known as a controlled mosaic.
An orthophotoscope is used in a much more precise technique. This device uses overlapping photographs in the same way that the stereoscopic plotter does, but instead of manually tracing the features and contours, the instrument scans the overlap and produces an orthophotograph by dividing the area into small sections, each of which is correctly scaled. This procedure works best in low-relief areas without tall buildings; the resulting maps can then be used in place of line maps in rural areas, where they are especially useful in planning resettlement in agricultural projects. Because there is no need for a fair drawing, the final printed map can be produced much more quickly and cheaply than would otherwise be possible.
Hydrographic surveying, or surveying of underwater features, used to require techniques very different from ground surveying for two reasons: the surveyor was usually moving rather than stationary, and the surface being mapped could not be seen. The first issue, which made establishing a framework difficult except near land or in shoal areas, was solved by dead reckoning between points established by astronomical fixes. A traverse would be run in effect, with the ship's bearing measured by compass and distances obtained either by measuring speed and time or by a modern log that directly records distances. These must be checked on a regular basis because, no matter how accurate the log, airspeed indicator, and compass are, a ship's or aircraft's track is not the same as its course. Crosscurrents or winds constantly push the craft off course, and those along the path influence the speed and distance travelled over the ground beneath.
Before underwater echo sounding and television, the only way a hydrographer could chart the seabed was to cast overboard at intervals a sounding line with a lead weight at the end and measure the length of the line paid out when the weight hit the bottom. The line was measured in fathoms, which are one-thousandth of a nautical mile, or about six feet (1.8 metres).
The introduction of echo sounding in the early twentieth century marked a significant improvement over lead line sounding, which is obviously very slow, especially in deep waters. It was made possible by the development of electronic devices for measuring short time intervals. Timing the lapse between the transmission of a short loud noise or pulse and its return from the target—in this case, the bottom of the sea or lake—is essential for echo sounding. Sound travels about 5,000 feet (1,500 metres) per second in water, so measuring time intervals with an accuracy of a few milliseconds gives depths within a few feet.
The speed at which sound waves travel through water is affected by its temperature and density, and allowances must be made for variations in these properties. The reflected signals are captured several times per second on a moving strip of paper, allowing the depth beneath the ship's track to be scaled. The echoes may also reveal other objects, such as schools of fish, or the dual nature of the bottom, where soft mud may overlie rock. Initially, only the depth directly beneath the ship's tracks was measured, leaving gaps between the ship's tracks. Later inventions, such as sideways-directed sonar and television cameras, have enabled these gaps to be filled. While depth measurements away from the ship's track are less precise, the images reveal any dangerous objects, such as rock pinnacles or wrecks, and the survey vessel can then be diverted to survey them in detail.
Modern radar position-fixing techniques have simplified the entire process, as the ship's location is now known continuously with reference to fixed stations on shore or satellite tracks. Another modern technique is to use images taken from aircraft or satellites to indicate the presence and shape of shoal areas and to help plan their detailed survey.
Inertial guidance systems can be used instead of radar or satellite signals to continuously and automatically record a ship's position. These military-grade devices detect every acceleration involved in the motion of a craft from its known starting point and convert it, along with the elapsed time, into a continuous record of the distance and direction travelled.
The bottom of the sounding lead was hollowed out to hold a charge of grease to pick up a sample from the seabed for detailed study. Television cameras can now be lowered to transmit images back to the survey ship, though their range is limited by the amount of light that can penetrate the water, which is frequently murky. Ordinary cameras are also used in pairs to create stereoscopic images of underwater structures such as drilling rigs or ancient shipwrecks.
Height determination
Surface feature heights above sea level are determined in four ways: by spirit levelling, measuring vertical angles and distances, measuring differences in atmospheric pressure, and, since the late twentieth century, by using three-dimensional satellite or inertial systems. The first is the most accurate; the second is next in accuracy but faster; and the third is the least accurate but can be the fastest if heights are measured at well-separated points. The last two techniques necessitate sophisticated equipment that is still prohibitively expensive.
For centuries, surveyors have used a surveying level, which consists of a horizontal telescope fitted with cross hairs, rotating around a vertical axis on a tripod, with a very sensitive spirit level attached to it; the instrument is adjusted until the bubble is precisely centred. Through the telescope, the reading on a graduated vertical staff is observed. If such staffs are placed on successive ground points and the telescope is truly level, the difference in readings at the cross hairs equals the difference in point heights. Differences in height can be accurately measured over long horizontal distances by moving the level and the staffs alternately along a path or road and repeating this procedure.
Over a distance of 100 kilometres, the most precise work can keep the error to less than a centimetre. To achieve this level of precision, great care must be taken. The instrument must include a high-magnification telescope and a very sensitive bubble, as well as a graduated scale on the staff made of an Invar strip (an alloy with a very small coefficient of thermal expansion). Furthermore, the staffs must be placed on pegs or special heavy steel plates, and the distance between them and the level must always be the same to cancel out the effects of light aerial refraction.
A single wooden staff can be used for less precise work; for detailed levelling of a small area, the staff is moved from one point to another without moving the level, allowing heights to be measured within a radius of about 100 metres. The distances between these points and the instrument can be measured with tape or, more commonly, by recording not only the reading at the central cross hair in the telescope's field of view but also those at the stadia hairs, as described above by tachymetry. Each point's bearing is observed using a compass or on the horizontal circle of the level so that it can be plotted or drawn on a map.
Since the 1950s, levels have been introduced that automatically level the line of sight by passing it through a system of prisms in a pendulum, eliminating the need to check the bubble. The disadvantage of spirit levelling is that the instrument must be moved and realigned numerous times, especially on steep hills; it is used primarily along practically flat stretches of ground.
Trigonometric height determination is used for faster work in hilly areas where lower accuracies are usually acceptable, using a theodolite to measure vertical angles and measuring or calculating distances by triangulation. This method is especially useful for obtaining heights along a major framework of triangulation or traverse where the majority of the points are on hilltops. To improve precision, observations are made simultaneously in both directions to eliminate aerial refraction; this is best done around noon, when the air is well mixed.
The third method of determining height is based on atmospheric pressure differences measured with a sensitive aneroid barometer, which can respond to pressure differences as small as a foot or two (0.3 to 0.6 metre) in height. However, because air pressure changes constantly, it is necessary to use at least two barometers; one at a known height reference point is read at regular intervals while the surveyor moves around the area, recording locations, times, and barometer readings. The height differences are then determined by comparing readings taken at the same time.
An alternative to a barometer for measuring pressure is a device for measuring the boiling point of a liquid, because this temperature is affected by atmospheric pressure. This method was used by early explorers to determine heights, but the results were very rough; this method was not accurate enough for surveyors until sensitive methods for temperature measurement were developed. The airborne profile recorder is a refined apparatus combined with a radar altimeter to measure the distance to the ground beneath an aircraft.
The analysis of signals received simultaneously from multiple satellites yields heights as well as positions. This method of determining heights is useful in previously unmapped areas as a check on results obtained by faster relative methods, but it is not accurate enough for mapping developed areas or engineering projects. Inertial systems accurate enough to provide approximate heights suitable for aerial surveys of large areas within a framework of points established more precisely by spirit levelling can be carried by all-terrain vehicles or helicopters.
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