The dictionary defines the verb survey as, "To determine and delineate the form, extent, position, etc., of, as a tract of land, by taking linear and angular measurements, and by applying the principles of geometry and trigonometry." One of the functions of the science of geodesy was defined in the Introduction as the determination of the exact positions of points on the earth's surface. It was further explained that modern technology has brought with it a positioning problem insofar as long and intermediate range defensive weapons are involved. The operations to be discussed in this chapter are closely associated with the entire problem of How far? In what direction?, etc. Four traditional surveying techniques (1) astronomic positioning, (2) triangulation, (3) trilateration, and (4) traverse are in general use for determining the exact positions of points on the earth's surface. In recent years, modern technological developments have added several new methods utilizing artificial earth satellites. Other methods relevant to geodetic surveying are being developed and are discussed in Chapter VII. Another field of endeavor, Photogrammetry, has contributed to geodetic surveying for many years but is not discussed in this publication except for the observation of satellites by cameras which is included in Chapter VI.
Astronomic Position Determination
The position of a point can be obtained directly by observing the stars. Astronomic positioning is the oldest positioning method. It has been used for many years by mariners and, more recently, by airmen for navigational purposes. Explorers have often used the astronomic method to locate themselves in uncharted areas. Geodesists must use astronomic positions along with other types of survey data such as triangulation and trilateration to establish precise positions. Single astronomic positions not interconnected by geodetic surveys cannot be related to each other with sufficient accuracy for the computation of distance and direction between points.
As the name implies, astronomic positions are obtained by measuring the angles between the plumb line at the point and a star or series of stars and recording the precise time at which the measurements are made. After combining the data with information obtained from star catalogues, the direction of the plumb line (zenith direction) is computed.
While geodesists use elaborate and very precise techniques for determining astronomic latitude, the simplest method, in the northern hemisphere, is to measure the elevation of Polaris above the horizon of the observer. For the purposes of this publication, astronomic latitude is defined as the angle between the perpendicular to the geoid and the plane of the equator. Figure 6.
Astronomic longitude is the angle between the plane of the meridian at Greenwich (Prime Meridian) and the astronomic meridian of the point. Figure 6.
FIGURE 6 ASTRONOMIC COORDINATES
Actually, astronomic longitude is measured by determining the difference in time-the difference in hours, minutes, and seconds between the time a specific star is directly over the Greenwich meridian and the time the same star is directly over the meridian plane of the point. Shortwave radio equipment is used to obtain time signals which can be referred to Greenwich Mean Time while chronometers (very accurate clocks) are used to measure the time at the point. By referring to a star catalogue, the exact Greenwich Mean Time the star was over the Prime Meridian is obtained. The difference between the time at the point and the time at Greenwich is used to compute the astronomic longitude of the point. Since a point of the earth rotates through 360° in 24 hours, the difference in local time between two points can be easily converted into difference in longitude.
Another astronomic observation related to horizontal positioning is the astronomic azimuth. Very accurate azimuths are used in the controlling of the orientation of first-order triangulation which is the next topic to be discussed. Referring again to Figure 6 and to point P, the astronomic azimuth of some other point Q as seen from P is defined as the angle between the meridian plane of point P and the plane containing both Q and the perpendicular to the geoid at P. This angle is reckoned from north at P clockwise from O° to 360°.
Astronomic observations are made by optical instruments-theodolite, zenith camera, prismatic astrolabe-which all contain leveling devices. When properly adjusted, the vertical axis of the instrument coincides with the direction of gravity and is, therefore, perpendicular to the geoid. Thus, astronomic positions are referenced to the geoid. Since the geoid is an irregular, nonmathematical surface, astronomic positions are wholly independent of each other.
Triangulation
The most common type of geodetic survey is known as triangulation. It differs from the plane survey mentioned earlier in that more accurate instruments are used, instrumental errors are either removed or predetermined so that they can be compensated for in the computations and more rigorous procedures are employed to reduce observational errors. Another very important difference is that all of the positions established by triangulation are mathematically related to each other.
Basically, triangulation consists of the measurement of the angles of a series of triangles. The principle of triangulation is based on simple trigonometric procedures. If the distance along one side of a triangle and the angles at each end of the side are accurately measured, the other two sides and the remaining angle can be computed. Normally, all of the angles of every triangle are measured for the minimization of error and to furnish data for use in computing the precision of the measurements. Figures 7. Also, the latitude and longitude of one end of the measured side along with the length and direction (azimuth) of the side provide sufficient data to compute the latitude and longitude of the other end of the side.
The measured side of the base triangle is called a base line. Measurements are made as carefully and accurately as possible with specially calibrated tapes or wires of invar, an alloy highly resistant to changes in length resulting from changes in temperature. The tapes or wires are checked periodically against standard measures of length (at the Bureau of Standards in the United States and corresponding agencies in other countries). The geodimeter and tellurometer, operating on electro-optical and electronic principles respectively, have replaced the older methods of base measurement in the recent surveys. The work can be completed more rapidly and accurately than with wire or tape. The laser equipped geodimeter has proven to be the most accurate and it can measure much longer distances without losing accuracy.
To establish an arc of triangulation between two widely separated locations, a base line may be measured and longitude and latitude determined for the initial point at one end. The locations are then connected by a series of adjoining triangles forming quadrilaterals extending from each end. Figure 7. With the longitude, latitude, and azimuth of the initial points, similar data is computed for each vertex of the triangles thereby establishing triangulation stations or geodetic control stations. The coordinates of each of the stations are defined as geodetic coordinates. Figure 8.
FIGURE 7 A SIMPLE TRIANGULATION NET
FIGURE 8 GEODETIC COORDINATES
Triangulation is extended over large areas by connecting and extending series of arcs and forming a network or triangulation system. The network is adjusted in a manner which reduces the effect of observational errors to a minimum. A denser distribution of geodetic control is achieved in a system by subdividing or filling in with other surveys. Figure 9 serves to illustrate, in a general manner, the major triangulation networks which have been established.
FIGURE 9 FUNDAMENTAL GEODETIC NETWORKS (HORIZONTAL CONTROL)
There are four general orders of triangulation. First-Order (Primary Horizontal Control) is the most accurate triangulation. It is costly and time-consuming using the best instruments and rigorous computation methods. First-Order triangulation is usually used to provide the basic framework of horizontal control for a large area such as for a national network. It has also been used in preparation for metropolitan expansion and for scientific studies requiring exact geodetic data. Its accuracy should be at least one part in 100,000.
Second-Order, Class I (Secondary Horizontal Control) includes the area networks between the First-Order arcs and detailed surveys in very high value land areas. Surveys of this class strengthen the US National Horizontal Control Network and are adjusted as part of the network. Therefore, this class also includes the basic framework for further densification. The internal closures of Second-Order, Class I triangulation should indicate an accuracy of at least one part in 50,000. The demands for reliable horizontal control surveys in areas which are not in a high state of development or where no such development is anticipated in the near future justifies the need for a triangulation classified as Second-Order, Class II (Supplemental Horizontal Control). This class is used to establish control along the coastline, inland waterways and interstate highways. The control data contributes to the National Network and is published as part of the network. The minimum accuracy allowable in Class II of Second-Order is one part in 20,000.
Third-Order, Class I and Class II (Local Horizontal Control) is used to establish control for local improvements and developments, topographic and hydrographic surveys, or for such other projects for which they provide sufficient accuracy. This triangulation is carefully connected to the National Network. The work should be performed with sufficient accuracy to satisfy the standards of one part in 10,000 for Class I and one part in 5,000 for Class II. Spires, stacks, standpipes, flag poles and other identifiable objects located to this accuracy also have significant value for many surveying and engineering projects.
The sole accuracy requirement for Fourth-Order triangulation is that the positions be located without any appreciable errors on maps compiled on the basis of the control.
Normally, triangulation is carried out by parties of surveyors occupying preplanned locations (stations) along the arc and accomplishing all the measurements as they proceed. When distances between two points were too long for conventional methods, connections were sometimes made by a method known as flare triangulation. Stations were occupied on either side of the gap and magnesium flares were parachuted from aircraft or "shot" into the air from ships at suitable points between them. Intersections of lines were made simultaneously at all of the stations and reasonably accurate "bridges" established. A connection of this type was established between Norway and Denmark. However, satellite geodesy (Chapter VI) has solved the problem of bridging wide gaps.
Trilateration
Another surveying method that has been used involves the use of radar and aircraft. The SHORAN, HIRAN and SHIRAN electronic distance measuring systems have been applied to performing geodetic surveys by a technique known as trilateration. Figure 10. Since very long lines (to 500 miles) could be measured by these systems, geodetic triangulation networks have been extended over vast areas in comparatively short periods of time. In addition, the surveys of islands and even continents separated by extensive water barriers have been connected by the techniques. The Canadian SHORAN network connecting the sparsely populated northern coastal and island areas with the central part of the country and the North Atlantic HIRAN Network tying North America to Europe are examples of the application of the trilateration technique. Figure 11 shows these and several other trilateration networks (SHORAN and HIRAN) which have been established throughout the world. SHIRAN has been used in the interior of Brazil.
FIGURE 10 A TRILATERATION NET
FIGURE 11 MAJOR TRILATERATION SURVEYS SHORAN AND HIRAN
Only distances are measured in trilateration and each side is measured repeatedly to insure precision. The entire network is then adjusted to minimize the effects of the observations errors. The angles of the triangles are computed so the geodetic positions are obtained as in triangulation.
Traverse
The simplest method of extending control is called traverse. The system is similar to dead reckoning navigation where distances and directions are measured. In performing a traverse, the surveyor starts at a known position with a known azimuth (direction) to another point and measures angles and distances between a series of survey points. With the angular measurements, the direction of each line of the traverse can be computed; and with the measurements of the length of the lines, the position of each control point computed. If the traverse returns to the starting point or some other known position, it is a closed traverse, otherwise the traverse is said to be open. Figure 12.
FIGURE 12 AN OPEN TRAVERSE; A CLOSED TRAVERSE
Since electronic distance measuring equipment has become available, the accuracy of traverse surveys has increased significantly. The tellurometer (microwave) has been used in Australia to complete a network (Australian Geodetic Datum) covering that continent. The average loop length is about 900 miles; the average loop closure of this work is 2.2 parts per million. The laser equipped geodimeter has been used to produce internal accuracies better than one part per million in establishing the transcontinental traverse in the United States. The traverse consists of a series of high-precision length, angle and astronomic azimuth determinations running approximately east-west and north-south through the conterminous states, forming somewhat rectangular loops. Figure 13. This traverse will be the "backbone" of a re-adjustment of the horizontal control network in this country.
FIGURE 13 TRANSCONTINENTAL TRAVERSE
Celestial Techniques
Celestial methods in geodesy involves the determination of an observer's position from observations of the moon, stars and satellites. Celestial triangulation permits the extension of long arcs across oceans and inaccessible space terrain. Satellites also permit a determination of the shape of the earth and provide important knowledge of its gravitational field (discussion of satellite geodesy is reserved for Chapter VI). All of the celestial methods possess one common characteristic-observed data is not affected by the direction of the vertical at the observation point.
Geodetic experiments have been performed in the past with the solar eclipse, star occultation and moon-position camera methods, but for various reasons the experiments did not produce useful geodetic results. The three techniques have been replaced by the observation and tracking of artificial earth satellites.
Vertical surveying is the process of determining heights-elevations above the mean sea level surface. As noted earlier, the geoid corresponds to the mean level of the open sea. In geodetic surveys executed primarily for mapping purposes, there is no problem in the fact that geodetic positions are referred to an ellipsoid and the elevations of the positions are referred to the geoid. However, geodetic data for missiles requires an adjustment in the elevation information to compensate for the undulations of the geoid above and below the regular mathematical surface of the ellipsoid. The adjustment uses complex advanced geodetic techniques. One method based on Stokes' Theorem is mentioned in the discussion of physical geodesy (Chapter V).
Precise geodetic leveling is used to establish a basic network of vertical control points. From these, the height of other positions in the survey can be determined by supplementary methods. The mean sea level surface used as a reference (vertical datum) is determined by obtaining an average of the hourly water heights for a period of several years at tidal gauges.
There are three leveling techniques-differential, trigonometric, and barometric-which yield information of varying accuracy. Figure 14. Differential leveling is the most accurate of the three methods. With the instrument locked in position, readings are made on two calibrated staffs held in an upright position ahead of and behind the instrument. The difference between readings is the difference in elevation between the points.
FIGURE 14 METHODS OF ELEVATION DETERMINATION
The optical instrument used for leveling contains a bubble tube to adjust it in a position parallel to the geoid. When properly "set up" at a point, the telescope is locked in a perfectly horizontal (level) position so that it will rotate through a 360 arc. The exact elevation of at least one point in a leveling line must be known and the rest computed from it.
Trigonometric leveling involves measuring a vertical angle from a known distance with a theodolite and computing the elevation of the point. With this method, vertical measurements can be made at the same time horizontal angles are measured for triangulation. It is, therefore, a somewhat more economical method but less accurate than differential leveling. It is often the only practical method of establishing accurate elevation control in mountainous areas.
In barometric leveling, differences in height are determined by measuring the difference in atmospheric pressure at various elevations. Air pressure is measured by mercurial or aneroid barometers, or a boiling point thermometer. Although the degree of accuracy possible with this method is not as great as either of the other two, it is a method which obtains relative heights very rapidly at points which are fairly far apart. It is widely used in the reconnaissance and exploratory surveys where more exacting measurements will be made later or are not required.