6

Engineering Surveying T J M Kennie BSc, MAppSci (Glasgow), ARICS, MInstCES Lecturer in Engineering Surveying, University of Surrey Contents 6.1

Introduction 6.1.1 Branches of surveying 6.1.2 Principles of surveying 6.1.3 Errors in surveying

6/3 6/3 6/3 6/3

6.2

Surveying instrumentation 6.2.1 Angular measurement using the theodolite 6.2.2 Distance measurement 6.2.3 Height measurement using the level

6/4 6/4 6/8 6/12

6.3

Surveying methods 6.3.1 Horizontal control surveys 6.3.2 Detail surveys 6.3.3 Vertical control surveys 6.3.4 Deformation monitoring surveys

6/15 6/15 6/17 6/18 6/21

6.4

Computers in surveying 6.4.1 Digital mapping and ground modelling systems 6.4.2 Land information systems

6/26 6/26 6/28

Acknowledgements

6/28

6.5

References

6/28

Bibliography

6/29

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6.1 Introduction The work of the land surveyor can be classified into three main areas of responsibility. Firstly, he is concerned with the recording of measurements which allow the size and shape of the Earth to be determined. Secondly, and primarily, he is involved in the collection, processing and presentation of the information necessary to produce maps and plans. Thirdly, he may be required to locate on the surface of the Earth the exact positions to be taken up by new roads, dams or other civil engineering works. As a consequence of the diverse nature of the land surveyor's duties, several distinct branches of the subject have evolved. 6.1.1 Branches of surveying Geodetic surveys are carried out on a national or international basis in order to locate points large distances apart. This type of survey acts as a framework for 'lower order' surveys. In order to ensure high accuracy, the effect of factors such as the curvature of the Earth on observations must be considered and the necessary corrections applied. Topographic surveys are concerned with the small-scale representation of the physical features of the Earth's surface. Frequently, the data necessary for such an operation will be provided by the use of aerial photography. The science of taking measurements from photography in order to produce maps is known as photogrammetry. Topographic surveys are often the responsibility of a national organization such as, for example, the Ordnance Survey in the UK. Hydrographic surveys, in contrast, involve the representation of the surface of the seabed. The end-product is normally a navigational chart. In recent years this branch has become increasingly important with the development of the offshore oil industry. In this case, in addition to the production of charts, the surveyor may be required to position large structures such as oil production platforms. This type of operation would normally necessitate the use of ground and satellite electronic position-fixing equipment. Cadastral surveys relate to the location and fixing of land boundaries. In many countries in the world, e.g. Australia, the information supplied by the cadastral surveyor may be an integral part of a land registration system. Finally, engineering surveys are required for the preparation of design drawings relating to civil engineering works such as roads, dams or airports. The surveys are normally at a large scale, with scales of 1:500 and 1:1000 being most common. Many of these branches require highly specialized knowledge, beyond the scope of this chapter. In view of this, the aim in this chapter will be to discuss: (1) those aspects of the subject which are required in order to carry out simple surveys for engineering projects; (2) the processes involved in carrying out precise surveys for deformation monitoring projects; and (3) the use of computers in surveying for digital mapping and ground modelling. 6.1.2 Principles of surveying In spite of the diverse nature of land surveying, it is possible to define certain basic principles which are common to all branches of the subject. These principles have proved over the years to be vital if accurate surveys are to be conducted. The first and most important principle is the provision of an initial framework before observing and fixing the detail of a survey. This process is ofteri known as providing control. It is essential to ensure that the positions of the control points are known to a higher order of accuracy than those of the subsidiary points. By satisfying this principle it is possible to ensure that errors, which inevitably occur, do not accumulate but are contained within the control framework.

A second and perhaps more obvious principle is that of planning. All too often it is tempting to rush into a survey without consideration for an overall plan. Of particular importance is the need to define a job specification. This is indispensable since the relationship between cost and accuracy is not linear and an increase in accuracy may have a disproportionate effect on cost. For example, if a distance of 50Om is to be determined to an accuracy of either 5 or 0.5 mm, the cost ratio of the respective accuracies may be of the order of 1:300. It is important, therefore, to choose techniques and instruments appropriate to the survey specification. Of equal importance is the need to plan the reconnaissance stage. Before starting a task it is essential to examine the area carefully, considering all the possible ways of doing the survey and then selecting the most suitable method. Remember, 'time spent on reconnaissance and planning is never wasted'. A third principle is the need to ensure that sufficient independent checks are incorporated into the survey to eliminate or minimize errors. It is important that the checking system is included at all stages of the survey from fieldwork and computations to the final plotting. In addition, the checking system should be independent and not solely a repeat of the initial measurement. Examples of independent checks are: Fieldwork: • measure both diagonals of a quadrilateral • measure distances in both directions • measure angles using different parts of the theodolite circle Computations: • use the summation check on angle observations of geometric figures, e.g. sum of interior angles (2«-4) x 90° • levelling booking cross-checks Plotting: • plot positions of important points by using angles and distance and also using coordinates. The final principle is that of safeguarding. Safeguarding is equally important at all stages of the survey, and refers to the process of ensuring that the survey results can be replicated if accidental, or other, damage occurs to the survey markers or field observations. Thus, it is important when constructing permanent survey markers to take 'witness or reference measurements' to points of prominent detail in the vicinity of the point. Linear measurements of this type enable the point to be relocated if it is damaged, or alternatively if it is difficult to find. The latter situation can often occur with road projects. In many instances there may be a gap of many years between initial survey and final setting-out. During this time the permanent survey markers may become overgrown with vegetation and hence difficult to locate. The use of witness marks and measurements can often be of crucial importance if the permanent marks are to be relocated. Safeguarding of field observations is also of paramount importance. Thus, it is considered good practice to produce abstract sheets from the surveyor's fieldbook at the end of each day. These abstract sheets should summarize the major results from the fieldbook (e.g. rounds of angles, mean distance etc.) and should be carefully filed in the survey office. By such a process the possibility of several days' work being lost if the fieldbook is damaged or misplaced can be eliminated. 6.1.3 Errors in surveying It is an unfortunate and often misunderstood fact that all measurements are affected by errors. So often, when confronted with the question: 'How accurate do you want the survey to

be?', or 'How accurately do you want this point located?', the glib answer 'Exactly!', or 'Spot on!', is given as the reply by a prospective client. If, in addition, the question of errors is raised, it is quickly dispensed with the comment: 'Errors don't occur if you do it properly.' The answer is correct in one respect, i.e. in relation to mistakes, or, more correctly, gross errors. These should not occur if a survey is carried out according to the basic principles of surveying. However, other types of errors do occur which can be much more difficult to handle. Systematic errors, as the name suggests, are errors which follow a pattern or system. Errors of this type are normally related to the variations in physical conditions which can occur when a measurement is made. For example, a steel tape is normally known to be a certain length at some standard temperature. If the temperature under which a measurement is made varies from this standard, a systematic error will occur. By knowing the coefficient of linear expansion a value for the expansion of the tape can be determined and a correction applied. Systematic errors whose effect can be modelled mathematically are, hence, eliminated. Random errors, in contrast, do not follow a standard pattern and are entirely based on the laws of probability. These errors, or rather variations in measurement, will occur after gross and systematic errors have been eliminated. The measurement of a distance by taping can again be taken as an example. It is often not appreciated that the same distance measurement made under the same physical conditions with the same tape will produce different answers. Since it is assumed that the measurements will follow a normal distribution they can be examined using standard statistical techniques. The following formula can therefore be applied to the analysis of random errors:

°M~±\n^)

(6.3)

For surveying purposes, the terms 'standard error', 'standard deviation' and 'root mean square (r.m.s.) error' are synonymous. All such terms are used to give an indication of the precision of the result, i.e. the degree of agreement between successive measurements. High precision may not be indicative of high accuracy, since accuracy is related to the proximity of the measurement to the true value. If, however, all the effects of the bias caused by systematic errors have been eliminated, these indices of precision may also be used as indices of accuracy. For example, suppose an angle has been measured 9 times and the subsequent error analysis indicates that CT^ = 3" and aw = 0.81". What does this information tell us? Firstly, it indicates that the angle has been measured to a high precision. Secondly, it indicates that, statistically, there is a 68% chance or probability of the standard error of a single measurement being less than 3". Furthermore, if one extends the confidence limit to a value 3 times the standard error, or 9", then statistically the probability that the error will be less than 9" is now 99.7% with only a 0.3% chance of the error being greater than 9". This confidence limit is often applied as a rejection criterion to a group of observations. Any observation with a residual greater than 3 times the standard error may then be rejected, on the basis that it is highly unlikely that the variation is solely a consequence of random effects. Similar reasoning would apply to the standard error of the arithmetic mean. Further information on errors and their treatment can be found in Cooper' and Mikhail and Grade.2

6.2 Surveying instrumentation arithmetic mean = Jc = —n

„ ,, (6.1)

where /= 1, 2, . . . , n are the observed values and n denotes the number of observed values. The arithmetic mean is significant because it is often taken to be the closest approximation to the 'true' value and as such is known as the most probable value (m.p.v.). The difference between the m.p.v. and the observed value is known as a residual (v). A term often used in order to estimate the precision of a series of measurements is the standard error, where standard error of a single observation is: ZV 0-±( *\ '« °'-±\i^l)

(6.2)

and standard error of the arithmetic mean is:

Surveying is essentially concerned with the direct measurement of three fundamental quantities: (1) the angle subtended at a point; (2) the distance between two points; and (3) the height of a point above some datum, normally mean sea-level. From the measurement of these three quantities, it is then possible to compute the three-dimensional positions of points. With the exception of electronic methods of determining distance, the instruments used by the surveyor have not radically changed in principle for 40 to 50 years. The advances in technology may have reduced the size and increased the efficiency of the instruments, but the fundamental principles remain unchanged. 6.2.1 Angular measurement using the theodolite The theodolite is used for the measurement of horizontal and vertical angles. In simple terms, a theodolite consists of a

Table 6.1 Characteristics of some modern theodolites Type of theodolite: Typical example: Country of manufacture:

1" Precise Kern DKM 2A-E Switzerland

20" Engineers Sokkisha TM20ES Japan

10' Builders Zeiss(Ober.)TH51 W. Germany

Direct reading to By estimation to Telescope magnification Telescope aperture (mm) Sensitivity of plate Level per 2 mm run Weight of instrument (kg)

1" 0.1" 32 x 40

20" 5" 28 x 45

20" 6.2

30" 4.2

Compass Wild TO Switzerland

Electronic Kern E-2 Switzerland

10'

r

r

1"

2Ox 30

30" 2Ox 28

32 x 45

45" 2.2

8' 2.9

8.7

telescope mounted on a platform which may be levelled to form a horizontal plane by means of a simple spirit bubble. Angles are measured by pointing the telescope at targets and establishing the difference between readings on a circular protractor mounted on the level platform. There is a bewildering choice of theodolites available. Table 6.1 lists the characteristics of a selection of commonly available modern theodolites. The broad distinction can be made between those instruments which measure angles and those such as compass and gyro theodolites which measure bearings, relative to magnetic north and to true north respectively. 6.2.1.1 General construction of the theodolite There are certain fundamental relationships and components which are common to all theodolites. Before examining the detailed construction of a modern glass arc theodolite, it is important to appreciate the geometrical arrangement of the axes of a theodolite, as illustrated in Figure 6.1.

Figure 6.2 Wild T-2 one second theodolite (Wild Heerbrugg)

Telescope objective

Figure 6.1 Theodolite axes In this ideal arrangement the vertical axis is vertical, the trunnion axis is perpendicular to it and hence horizontal, and the line of collimation is perpendicular to the trunnion axis. Unfortunately, it is not possible during the manufacturing process to ensure that these orthogonal relationships occur exactly. Similarly, during use over a period of years, wear may occur which may also alter these conditions. The extent to which a theodolite fails to satisfy them can be measured by a series of instrument tests which may be carried out in the field. If, subsequently, the instrument is found to be out of adjustment, the instrument should be returned to the manufacturer or a specialist instrument technician for adjustment. Details of the field tests and methods of adjustment may be found in Cooper.3 If, however, a modern theodolite is treated with care, and a suitable observational technique is employed, regular servicing should be all that is required in order to obtain good results. The detailed construction of a modern 1 s precise theodolite is shown in Figures 6.2 and 6.3. Examination of these figures illustrates that the theodolite consists essentially of three distinct parts: (1) Base. This consists of two main components: the tribrach and the horizontal circle. The tribrach can be screwed securely to the tripod and, by means of three footscrews, the instrument may be levelled. The circle is made of glass with photographically etched graduations. It is normally graduated in a clockwise manner. A circle-setting screw is also usually provided and the base will generally house an

Trunnion axis Telescope eyepiece

Standard Upper plate (alidade)

Plate level

Horizontal circle Tribrach

Footscrew

Trivet stage

Standing axis Figure 6.3 Construction of a theodolite optical plummet. This consists of a small eyepiece with a line of sight which is deviated by 90° in order to point vertically down. By this process it is possible to centre the instrument precisely over a ground point. In some cases the optical plummet may be housed in the alidade. (2) Alidade. This rotatable upper part of the theodolite may also be known as the upper plate. The alidade rotates about the vertical axis. Mounted on the alidade is the plate-level bubble which indicates whether the instrument is level. By

means of clamps and slow-motion screws it is possible to rotate and clamp the alidade relative to the base. (3) Telescope. Attached to the trunnion axis of the theodolite is the telescope. The telescope magnifies the object and, by the use of cross-hairs, allows the exact bisection of the target. Focusing of the object and the cross-hairs is carried out using separate focusing screws. A further clamp and slow-motion screw allow precise pointing of the telescope in a vertical plane. Angles of elevation or depression are measured using a vertical circle also attached to the trunnion axis. Prior to measuring a vertical angle it may be necessary to set the altitude bubble. However, most modern theodolites employ an automatic compensating mechanism. In these cases vertical angles may be recorded after the plate level has been set, without recourse to an additional bubble setting. When the vertical circle is to the left of the telescope, the theodolite is in what is conventionally called the face left (FL) position. Conversely, when the vertical circle is to the right of the telescope as it views an object, the theodolite is in the face right (FR) position.

micrometer screw of the theodolite. Movement of this screw enables the observer to read, on an auxiliary scale, the lateral shift required in order to bring the image of the main-scale degree graduations into coincidence with the index marks which are built into the optical path. Using this technique it is possible to resolve directly to 20" of arc if the micrometer is reading from one side of the circle. Resolution direct to 1" is possible if a mean-reading optical micrometer is used. In this case, readings from two points diametrically opposite are meaned in order to eliminate the effects of any circle eccentricity. Figures 6.5 and 6.6 illustrate two typical examples of the circle reading systems for both the single- and mean-reading optical micrometers.

6.2.1.2 Circle reading By projecting daylight through the standards of the theodolite, it is possible to illuminate the glass scale of both the horizontal and vertical circles. In order to resolve a direction to a higher precision than that to which the circle has been graduated, an optical micrometer is employed. Optical micrometers are the modern equivalent of verniers. The principle of operation involves the use of a plane parallel-sided block of glass as shown in Figure 6.4. When the glass is in the normal position, as shown by position (a), light passing through will be uninterrupted. Rotation of the block of glass, however, produces a lateral shift of the incident beam as shown by position (b). This rotation is controlled by the

Figure 6.5 Single reading optical micrometer: circle reading Wild T-1A 05° 13' 30" (Wild Heerbrugg)

Uninterrupted light path Parallel plate micrometer

Circle graduations Refracted light path

Figure 6.6 Mean reading optical micrometer: circle reading Wild T-2 94° 12' 44.3" (Wild Heerbrugg)

6.2.1.3 Field procedure

Figure 6.4 Parallel plate micrometer

Potentially the theodolite is a very precise instrument. It is, however, necessary to follow a strict procedure both in setting-

(3) Rotate the alidade until the bubble is now approximately perpendicular to the initial position, as shown in Figure 6.7(b). Using footscrew C only, centralize the bubble. (4) Return to the initial position and again centralize the bubble using footscrews A and B. Repeat (2) and (3) until the bubble is central in both positions. (5) Rotate the alidade through 180° until the position shown by Figure 6.7(c) is achieved. If the bubble does not remain in a central position, move the bubble until it is in a position midway between a central position and its initial position. (6) Rotate the alidade until the position illustrated by Figure 6.7(d) is achieved. Using footscrew C, move the bubble into the same position as in Figure 6.7(c). The bubble should then remain in the same off-centre position for any alignment of the alidade.

up the instrument and in observing if this potential is to be realized. Incorrect use of a theodolite will undoubtedly result in poor results, regardless Of how precise the instrument may be. Setting-up. Setting-up a theodolite prior to observations being taken consists of three separate operations: centring, levelling and focusing. Centring involves positioning the instrument exactly over a ground point. This may be achieved by means of either a plumb bob suspended from the instrument or a centring rod or an optical plummet. The process of centring and levelling should be considered as iterative in nature, becoming increasingly more precise after each operation. Levelling the theodolite carefully is a necessary prerequisite for precise measurements. The following sequence of operations must be carried out in order to level a theodolite:

The final step before observations begin is to focus both the cross-hairs and the object to which observations will be made. It is important to ensure that both images appear clear and sharp. In addition, it is critical that parallax does not exist. Parallax refers to the apparent movement of the cross-hairs and objects relative to each other when the observer moves his head. It is caused by the image of the object not lying in the same vertical plane as the cross-hairs. If this occurs, the focusing operation must be repeated until it is eliminated.

(1) Approximately level the instrument using the small circular bubble. (2) Set the plate-level bubble parallel to any two footscrews, such as A and B in Figure 6.7(a). Rotate both footscrews together or apart until the bubble is in a central position.

Observational procedure. A strict observational procedure is essential if both human and instrumental errors are to be reduced to a minimum. Consider the problem of measuring the angle shown in Figure 6.8.

Level bubble

Level footscrews Figure 6.8 Angle measurement The observational procedure which should be adopted is as follows. A booking procedure is illustrated by Table 6.2. (1) Point with telescope in the FL position to the target at X and record the horizontal circle reading, e.g. 90° 20' 30". (2) Point on FL to target Z and record, e.g. 130° 25'40".

Figure 6.7 Levelling the theodolite Table 6.2 Booking and reduction of theodolite readings Station Y Height of Inst: TO Round 1 Round 2

Observer .Booker ..

FL

FR

.Date .Weather. MEAN

ANGLE

X Z

90 20 130 25

30 40

270 20 310 25

40 50

90 20 130 25

35 45

4n U

X Z

135 30 175 35

15 30

315 30 355 35

25 40

135 30 175 35

20 35

U

Mean angle: 40° 05'13"

COMMENTS

^

1U

^

^

(3) Change face to FR and point to target Z and record circle reading 310° 25' 50". (4) Point on FR to target X and record direction 270° 20' 40".

where /m = measured temperature in the field, /s = temperature at which the tape was standardized, usually 2O0C, and a = coefficient of linear expansion (0.000011 2 for steel bands)

In order to reduce the effect of instrument maladjustments to a minimum, the mean of the FL and FR minutes and seconds readings to the same point is averaged and the value entered in the mean column. The difference between the mean circle readings is then derived and entered in the angle column. This constitutes one round of angles. The base setting screw should then be adjusted and the process repeated in order to increase the precision of the angle measurement. A minimum of two rounds is necessary for the least precise measurements; up to sixteen rounds may be required for very precise operations.

Tension:

6.2.2 Distance measurement The second fundamental quantity which it is necessary to measure is distance. A wide variety of techniques can be used for the determination of distance. The general distinction can, however, be made between direct, optical and electronic methods. All of the techniques discussed are capable of varying levels of precision depending on the degree of sophistication of the instrumentation and the observational techniques adopted. 6.2.2.7 Direct distance measurement (DDM) The simplest method of measuring distance is that of physically measuring the distance with a tape. In the past invar tapes were used for the precise measurement of baselines for triangulation networks. Nowadays, DDM is generally confined to either the precise measurement of short distances for setting-out or control purposes or the less precise measurement of the detailed dimensions of a building or land parcel. There are basically two types of tape in common use. Fibreglass measuring tapes are manufactured from multiple strands of fibreglass coated with PVC. They are waterproof and normally either 30 or 50 m in length. Fibreglass tapes are generally used for detail measurements and have largely superseded the linen tapes which were available previously. For more precise measurements it is necessary to use steel bands. These are typically either 30, 50 or 10Om in length. In order to obtain high precision with either type of tape, it is essential that it is periodically checked against a standard reference tape, the length of which is known to a higher order of accuracy than that of the tape being checked. If a significant variation exists, a standardization correction should be applied. In addition, it is vital that suitable attention is paid to the effect of variations in slope, temperature and tension which may necessitate appropriate corrections being applied to the measured distance. The corrections (C1, C2 and C3 respectively) are: Slope: C 1 = -L(I -cos 0)

(6.4)

where 9 — slope angle, and L = measured slope distance or:

C,= -Atf/2L where Ah = height difference between end-points Temperature: C 2 =±aL(/ m -g

(6.5)

C3= ± L(Tn-TJAE where Tm = measured tension, Ts = standard tension, A = crosssectional area of tape, and E= Young's modulus for the tape, typically 200 kN/mm2 = 200 000 N/mm2 Miller4 details the typical accuracy levels which can be achieved with steel tapes. 6.2.2.2 Optical distance measurement (ODM) As an alternative to the direct method of measuring distance, it is also possible to measure distance indirectly by optical methods. The development of ODM began over two centuries ago. James Watt is recorded as having used this approach in his survey of the West of Scotland in 1774. Although many instruments and improvements have been introduced since then, they all essentially involve the solution of the same geometrical problem. All methods of ODM are based on the solution of an isosceles triangle, as shown in Figure 6.9. The triangle consists of three important components: the parallactic angle a, the base length B (which may be either in a horizontal or vertical plane), and Z), the horizontal bisector of the base of the triangle. By knowing the relationship between the three components, the horizontal distance D between two points can be determined.

Figure 6.9 Optical distance measurement (ODM) Two methods of solution are possible: either an instrument with a fixed parallactic angle is used and the variable base B is measured (Figure 6.10) or a base of fixed length is set up and the variable parallactic angle is measured (Fig. 6.11). In both cases, the variable quantity is proportional to the horizontal distance. By defining the mathematical relationship between the fixed and variable quantities it is therefore possible to determine the horizontal distance. Tacheometry. The first approach described above (fixed angle, variable base) is commonly known as tacheometry or more correctly as vertical staff stadia tacheometry. It is normally used for the measurement of distance where a proportional error of between 1/500 and 1/1000 is acceptable, e.g. in picking-up survey detail points. All modern theodolites have a diaphragm consisting of a main horizontal cross-hair and two horizontal stadia lines

where D5=slope distance, and 6—vertical angle measured by the theodolite. Therefore: £> H = 1005 cos2 O

(6.9)

Ah^ = H1+ V- m

(6.10)

where zl/iAB = difference in height between A and B, H1 = height of instrument (trunnion axis to ground), m = middle hair reading, and V= difference in height between middle-hair reading and trunnion axis = 505 sin 29 (6.11)

Figure 6.10 ODM: fixed angle, variable base

Several self-reducing tacheometers have also been designed. The main advantage of these instruments is their ability to compensate for the effect of the inclination of the theodolite telescope and, hence, allow the direct determination of horizontal distance without additional computation. Two notable examples of this type of instrument are the Wild RDS vertical staff self-reducing tacheometer and the Kern DKRT horizontal bar double-image self-reducing tacheometer. Details of the construction and use of these instruments may be found in Hodges and Greenwood,5 and Smith.6 In recent years, the manufacture of these precise optical devices has ceased, their place being taken by low-cost electronic measuring devices.

Figure 6.11 ODM: fixed base, variable angle spaced either side of it. These stadia lines define the fixed parallactic angle. If the theodolite telescope is sighted on to a levelling staff and the readings of the outer lines noted, the difference in the readings, the staff intercept (s), will be directly proportional to the horizontal distance between the instrument and the staff. Generally, the distance between the stadia lines is designed in such a manner that the horizontal distance Z>H between the instrument and staff is given by: DH=lOQs

Subtense bar. The second approach (fixed base, variable angle) is commonly known as the subtense or horizontal subtense bar method. The method is normally confined to the measurement of distance for control purposes. Using this approach, distances may be determined with a proportional error of up to 1/10 000. The instrumentation required consists of a subtense bar, normally 2m long, and a one-second theodolite, such as the Wild T2. The bar has targets mounted at each end of an invar strip. The strip is protected by a surrounding aluminium strip in order to ensure that, for all practical purposes, the length of the bar remains constant at 2 m. The bar is set up and oriented at right angles to the line of sight of the theodolite, as shown in Figure 6.13.

(6.7)

For inclined sights the geometry is as shown in Figure 6.12. Hence:

/)s= 100(5 cos O)

(6.8)

Figure 6.13 Subtense bar The horizontal parallactic angle a is measured with the theodolite. Irrespective of the vertical angle to the bar, the horizontal distance is given by: Z>H = ifccot(a/2)

(6.12)

with b = 2m />H = cot(a/2)

Figure 6.12 Stadia tacheometry: inclined sights

(6.13)

For distances greater than 10Om it is advisable to subdivide the distance to be measured or, alternatively, to use the auxiliary base method (Hodges and Greenwood,5 and Smith.6).

Subtense methods are also tending to be superseded by lowcost electronic methods. Nevertheless, many organizations still possess this type of equipment and for many projects it is a very suitable technique to adopt. 6.2.2.3 Electronic distance measurement (EDM) Development. The first generation of EDM instruments was developed in the early 1950s. Typical of the early meters were the Swedish Geodimeter (GEOdetic Distance METER) and the South African Tellurometer instrument. The former, an electrooptical instrument, used visible light measurement, whilst the latter used high-frequency microwaves. Both instruments were primarily developed for military geodetic survey purposes and had the ability to measure long distances, up to 80 km in the case of the Tellurometer, to a precision of a few centimetres. They were also, however, bulky, heavy and expensive in comparison to their modern-day equivalents. During the late 1960s, developments in microelectronics and low-power light-emitting diodes led to the emergence of a second generation of EDM instruments. These electro-optical instruments utilized infra-red radiation as the measuring signal and were developed for the short range ( < 5 k m ) market. In addition, they were considerably smaller, lighter and less expensive than their predecessors. Probably the best-known example is the Wild DI-IO Distomat. The introduction of microprocessors into the survey world in the early 1970s led to the introduction of a third series of EDM instruments. With this group it became possible, not only to determine slope distance, but also to carry out simple computational tasks in the field. For example, the facility became available to compute automatically the corrected horizontal distance and difference in height between two points by manual input of the vertical angle read from the theodolite. Electronic distance measurement instruments of this type had also been reduced in size to the extent that the EDM unit could be theodolite-mounted. The Wild DI-3 is a typical example of this type of instrument. The most recent short-range EDM instruments are similar to the previous group, but have several additional features worthy of mention. Firstly, the technology now exists to sense automatically the inclination of the EDM unit and therefore to be able to compute automatically the horizontal distance between two points. The Geodimeter 220 (Figure 6.14) has this facility. This instrument also has the ability to measure to a moving target, or track, a useful feature for setting-out purposes. By using an additional unit it is also possible to have one-way speech communication between the instrument and target positions, again valuable when setting-out. This instrument can also be connected to a Geodat 126 hand-held data collector (Figure 6.14), which is able to store automatically distance information from the EDM unit. Other relevant information (numeric or alphanumeric) can be input manually via the keyboard. The Geodimeter 220 has a range of 1.6km with one prism and 2.4km with three prisms determined to a standard error of ± 5 mm± 5 parts per million (p.p.m.) of the distance. The last development in the field of EDM instrumentation is the electronic tacheometer or 'total station'. The former term is more appropriate in view of the different interpretations, by the instrument manufacturers, of the term total station. In essence, an electronic tacheometer is an instrument which combines an EDM unit with an electronic theodolite. Hence, such instruments are capable of measuring, automatically, horizontal and vertical angles and also slope and/or horizontal distance. The majority also have the facility to derive other quantities such as heights or coordinates and store this data in a data collector. Two designs of instrument have evolved during the last 5 years.

Figure 6.14 (Geotronics)

(a) Geodimeter 220; (b) Geodat 126 data collector

The first, the integrated design, consists of one unit which, generally, houses the electronic circle-reading mechanism and the EDM unit. The Wild TCI Tachymat and the Geodimeter 140 (Figure 6.15) are representative of this range of instrument. The second design approach is the modular concept. In this case, the EDM instrument and the electronic theodolite are separate units which can be operated independently. This approach tends to be more flexible and enables units to be exchanged and upgraded as developments occur; it may also be a more cost effective solution for many organizations. The Kern E-2 and Wild T-2000 Systems (Figure 6.16) are representative of this design of electronic tacheometer. Finally, mention should be made of high-precision EDM instruments. These instruments have been designed for projects such as dam deformation or foundation monitoring where extremely high precision is necessary. Instruments which are

Figure 6.15 Electronic tacheometer, integrated design: Geodimeter 140

Figure 6.17 High-precision EDM: Comrad Geomensor 204DME 10km with a standard error of ±0.1 mm±0.5p.p.m. Further up-to-date technical information on many modern EDM instruments can be found in Burnside."

Figure 6.16 Electronic tacheometer, modular design: Wild T-2000, with DI4 representative of this design include the Tellurometer MA-IOO Jaakola,7 the Kern ME-3000 Mekometer (see Froome,8 MeirHirmer,9 and Murname10) and the Comrad Geomensor 204 DME (Figure 6.17). The latter instrument has a range of up to

Principle of measurement. Although there is a wide variety of EDM instruments on the market, they all measure distance using the same basic principle. This can be most clearly illustrated by means of the flow diagram (Figure 6.18), which relates specifically to electro-optical instruments. An electromagnetic (EM) signal of wavelength equal to either 560 nm (visible light), 680 nm (HeNe laser) or 910 nm (infra-red) is generated. This signal is subsequently amplitude-modulated before being transmitted through the optical system of the instrument towards a retro-reflector mounted at the end of the line to be measured. The signal is then retro-reflected, or redirected through 180°, by a precisely ground glass corner cube. Cheaper acrylic corner cubes may also be used.12'13 This reflected signal is consequently directed towards the receiving optical system. On entering the optical system of the instrument, the signal is converted by means of a photomultiplier into an electrical signal. The next stage involves the measurement of the phase difference between the transmitted and received signals and the conversion of this information into distance. Figure 6.19 shows the path taken by an EM signal radiated by an EDM instrument together with the instantaneous phase of the signal. It is apparent that the distance X-Y-X travelled by the EM signal is equivalent to twice the distance to be measured. Also, this distance can be seen to be related to the modulation wavelength (A) and the fraction of the wavelength (/4A) by the following relationship:

Electromagnetic signal

and

^ Transmitting optic

Phase measurement •*

>

2£> = 2.4« 2 +1.5

Retroreflector

Assuming «, =« 2 for short distances, solving for n leads to «=10

Receiving ootic

Slope distance •*

I

Corrections Atmospheric Additive constant Slope Height above MSL Scale I factor

Corrected uT"!—Y^ Figure 6.18 Principle of operation: electro-optical distance measurement

Retro-reflector

C4 = (-LHJ/R

Figure 6.19 Double path measurement using EDM 2D = >d + A A

(6.14)

where n is an unknown integer number of wavelengths. The determination of the distance therefore involves resolving both AX and n. Phase detectors are used to determine AX which effectively measures the phase difference between the transmitted and received signal and, hence, allows the fractional part of the distance less than one full wavelength to be determined. The value of n can be determined by using two or more EM signals of slightly varying wavelengths. For example, assume 2D = 25.5, A1 = 2.5 m and A2 = 2.4 m then: ID = 2.5«, +0.5

(6.18)

This entire process is fully automatic in modern instruments, taking approximately 10 to 20 s to complete. As with any other method of distance measurement, it is necessary to apply several corrections to the measured slope distance in order to determine the corrected horizontal distance. The first correction to be applied is the atmospheric or refractive index correction. Just as a steel tape varies in length with variations in temperature and pressure so, too, does the modulation wavelength of an EDM instrument. It is therefore necessary to measure the temperature, pressure and, in some cases, relative humidity during measurements. A correction is then applied to compensate for the variation in modulation wavelength caused by variations in atmospheric conditions. Many instruments have the facility to compute automatically and apply this correction to observations directly in the field. Temperature, pressure and relative humidity readings are taken and the appropriate reading to be set on the refractive index correction dial is read from a nomogram. A second important correction is the additive zero or prism constant. This correction represents the difference between the electro-optically determined distance and the correct length of line. It is a combination of the errors due to prism offset and the variation in the physical and electrical centres of the EDM instrument. Many manufacturers design their corner cube reflectors in order to eliminate this correction totally. However, if several different types of corner cube are being used, it is essential that a full field calibration be undertaken in order to determine the correction. (See Schwendener,14 Ashkenazi and Dodson,15 and Sprent and Zwart16 for further details of the procedure for instrument calibration.) The slope correction is the same as for DDM. For distances measured above or below mean sea-level (MSL) a correction is necessary in order to reduce the distance to its equivalent at MSL. The correction (C4) is given by:

Dat a t

EDM Instrument

(6.17)

Substituting in Equations (6.15) or (6.16) D= 12.75m

I

(6.16)

(6.15)

(6.19)

where Hm is the mean height of the instrument and reflector above MSL and R is the radius of the Earth (6370 km). Finally, if the distance is to be used for computation of coordinates on the national grid, the horizontal distance at MSL must be multiplied by the local scale factor. For the Transverse Mercator projection, the local scale factor (F) may be approximately calculated from: F= 0.999 601 27 + [1.228 x 10~ 14 x (E- 400 00O)2]

(6.20)

where E is the mean local national grid easting in metres of the line to be measured. 6.2.3 Height measurement using the level The third and final quantity which is measured is height or, more correctly, height difference. This is achieved by means of a level.

The fundamental principle of the level is illustrated by Figures 6.20 and 6.21. Figure 6.20 represents the situation which normally exists when the level is initially set up. In this case, the standing axis of the level and the vertical do not coincide. Hence, the line of collimation of the level will not be horizontal. Figure 6.21 represents the geometrical arrangement of the axis when the instrument has been levelled using the procedure outlined in 'Setting up' in section 6.2. L3. It can be seen that completion of this procedure ensures that, firstly, the standing and vertical axes are made coincident and, secondly, if the

Spirit bubble Horizontal line of sight

6.2.3.1 Dumpy level The dumpy level was so named because of the rather short telescopes which were used with early versions of this instrument. The construction of a typical dumpy level is shown in Figure 6.22. The most distinctive feature of this type of level is that the axis of the telescope is fixed rigidly to the standing axis of the instrument. In order to satisfy the condition that both the vertical and standing axes are coincident, the standard levelling procedure outlined in section 6.2.1.3 is carried out. Rotation of the telescope will now define a horizontal plane. In the past, this type of level was very popular for general engineering work. It has, however, been replaced in recent years by the automatic level. 6.2.3.2 Tilting level The tilting level is a more precise instrument than the dumpy level. Figure 6.23 illustrates the main features. In contrast to the dumpy level, the telescope is not rigidly attached to the standing axis but is able to be tilted in a vertical plane about a pivot point X, by means of a tilting screw.

Line of collimation of level

Vertical

Standing axis of level Figure 6.20 Geometry of the level axes: before levelling Objective

Horizontal line of sight

Eyepiece - Line of collimation

Telescope Levelling screws

Figure 6.21 Geometry of the level axes: after levelling instrument is in perfect adjustment, the line of collimation of th< level is coincident with a horizontal line of sight. Three distinct types of level are available for engineerin survey purposes: (1) the dumpy level; (2) the tilting level; and (3 the automatic level.

Spirit bubble

Pivot X •Tilting screw Trivet stage Standing axis

Figure 6.23 Level construction: tilting level

Vertical

Telescope

Bubble-adjusting screw

Spirit bubble

Line of collimation of level

Objective

Spirit bubble

Bubble-adjusting screw Line of collimation

Prior to recording an observation, the instrument is approximately levelled. This is normally achieved by means of a 'balland-socket' arrangement and a small circular bubble. In order to set the standing axis exactly vertical, the tilting screw is turned and the main bubble altered until a coincident position (Figure 6.24), as viewed through a small auxiliary eyepiece, is achieved. If the telescope is now rotated horizontally to sight a second or subsequent point, it is important to relevel the main bubble by means of the tilting screw.

Eyepiece Tribrach

Levelling screws Trivet stage Standing axis Figure 6.22 Level construction: dumpy level

Before levelling After levelling (a) (b) Figure 6.24 Coincidence bubble-reading system

6.2.3.3 Automatic level This type of level is not, as the name suggests, totally automatic. Human intervention is still necessary. However, one major source of human error, that of setting the bubble, is replaced by an automatic compensating system. In common with the tilting level, approximate levelling is still necessary. The tedious and error-prone bubble-setting process, however, is eliminated. As with the dumpy level, the instrument defines a horizontal plane when rotated. The automatic level therefore combines the speed of operation of the dumpy level with the precision of the tilting level. Figure 6.25 illustrates the main components of this type of level. The essential feature of the instrument is the incorporation of an automatic optical-mechanical compensating mechanism. The use of such a system ensures that the line of collimation as defined by the centre cross-hair will trace out a horizontal plane irrespective of the fact that the optical axis of the instrument may not be exactly horizontal. It is, however, necessary to level the instrument approximately in order to ensure that the line of sight is within range of the compensating mechanism.

Objective

Telescope

Optical-mechanical compensator Eyepiece Line of collimation Circular spirit level Tribrach

Levelling screws

Figure 6.26 Zeiss (Jena) Ni 007 automatic precise level

Trivet stage Standing axis Figure 6.25 Level construction: automatic level Undeflected line of sight For high-precision levelling, e.g. in order to detect the settlement of a building, a parallel plate micrometer (PPM), attached to the front of the objective of the telescope normally forms part of the construction of the level. Almost all precise levels in use nowadays are of the automatic design and, ideally, should be designed so that the PPM forms an integral part of the instrument, rather than being an 'add-on' attachment. One such instrument is the Zeiss (Jena) Ni 007 (Figure 6.26). This particular instrument also has an unusual compensating mechanism which results in the 'periscope'-type appearance of the instrument. The PPM operates by deflecting the line of sight to the nearest whole staff graduation, the amount of displacement which is required being measured by a micrometer. This value is then added to the staff reading to give the final staff reading. This is illustrated in Figure 6.27. Clearly in an operation such as precise levelling it is important to minimize the effects of systematic errors. This is partially overcome by a suitable field procedure,17 and partially by ensuring that the staff is maintained at a constant length. In order to achieve this, an invar staff with stabilizing arms and a level bubble attachment is normally used. 6.2.3 A Laser level Lasers are monochromatic, coherent and highly collimated light sources, initially developed in the 1940s. Until relatively

Parallel Plate Micrometer Deflected line of sight Reading = 1.61 +A Figure 6.27 Operation of a parallel plate micrometer for precise levelling recently, their use has tended to be restricted to the field of pure scientific research. Nowadays, however, the laser is a widely used tool in land surveying for distance measurement, alignment,18 and levelling purposes. There are essentially two types of laser in use in civil engineering: (1) the fixed-beam; and (2) the rotating beam laser. The fixed-beam laser projects a single highly collimated light beam to a single point. This design is particularly suited to alignment problems. The rotating-beam laser, in contrast, takes the fixedbeam source and rotates it at high speed, so forming a plane (either in the horizontal or vertical sense), of laser light. This design is more appropriate for levelling or grading purposes. The Spectra-Physics EL-I shown in Figure 6.28 is a typical example of the laser levels currently in use. The laser beam in

Figure 6.30 Two-peg test

Figure 6.28 Spectra-Physics EL-1 (Spectra-Physics) this case forms a 360° horizontal plane which is detected by a portable sensing device also shown in Figure 6.28. The laser unit automatically corrects for any error in level of the instrument, providing it has been roughly levelled to within 8° of the vertical. An accuracy of ± 5 to 6 mm per 100 m up to a maximum range of 300 m can be achieved with this type of instrument. 6.2.3.5 Collimation error So far the assumption has been made that once the standing axis of the level has been set truly vertical, then the line of collimation will be horizontal. This may not always be the case. If this condition does not occur, then a collimation error is said to exist. This is illustrated in Figure 6.29. If accurate levelling is to be achieved, it is essential that a regular testing procedure is established in order to check the magnitude of any collimation error that may exist.

Line of collimation Horizontal plane

Collimation error

Figure 6.29 Collimation error A common field procedure which can be used to test a level is known as the 'two-peg test'. The procedure is as follows: (1) Set out two points A and B approximately 50m apart, as shown in Figure 6.30(a). The level is set up at the mid-point of AB and levelled as in section 6.2.1.3. (2) A reading is taken on to a staff held at points A and B and

the difference between the two readings calculated. This value represents the true difference in height between A and B. Any collimation error which exists will have an equal effect on both readings and, hence, will not affect the difference between the readings. In this case the difference in height is 1.415-0.932 = 0.483m. (3) The instrument is now moved to a point C close to the staff at B (about 3 to 5 m away), as in Figure 6.30(b). The reading on staff B is recorded (1.301). If no collimation error exists, the reading on staff A should be equal to the reading on staff B ± the true difference in height as established in (2), i.e. 1.301+0.483= 1.784m. (4) The actual observed reading on staff A is now recorded (1.794). Any discrepancy between this value and that derived previously in (3) indicates the magnitude and direction of any collimation error. For example, in this case, the error would be 1.794- 1.784= 10mm per 50m. An error of up to 2 to 3 mm over this distance would be acceptable. If, however, the error is greater than this, the instrument should be adjusted. Unlike theodolite adjustments, this type of adjustment can normally be performed without any great difficulty by the engineer and the procedure is as follows. For the dumpy and automatic level: alter the position of the cross-hairs until the centre cross-hair is reading the value which should have been observed from step (3) above. This is achieved by loosening the small screws around the eyepiece which control the position of the cross-hairs. For the tilting level: again alter the position of the centre cross-hair until it is reading the value previously determined in (3), in this case by tilting the telescope using the tilting-screw. Unfortunately, this will displace the bubble. The bubble must, therefore, be centralized by means of the bubble-adjusting screw.

6.3 Surveying methods 6.3.1 Horizontal control surveys Any engineering survey or setting-out project, regardless of its size, requires a control framework of known co-ordinated points. Several different control methods are available as des-