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6 EngineeringSurveying

T J M Kennie BSc, MAppSci (Glasgow),ARICS, MInstCESLecturer in Engineering Surveying,University of Surrey

Contents

6.1 Introduction 6/36.1.1 Branches of surveying 6/36.1.2 Principles of surveying 6/36.1.3 Errors in surveying 6/3

6.2 Surveying instrumentation 6/46.2.1 Angular measurement using the

theodolite 6/46.2.2 Distance measurement 6/86.2.3 Height measurement using the level 6/12

6.3 Surveying methods 6/156.3.1 Horizontal control surveys 6/156.3.2 Detail surveys 6/176.3.3 Vertical control surveys 6/186.3.4 Deformation monitoring surveys 6/21

6.4 Computers in surveying 6/266.4.1 Digital mapping and ground modelling

systems 6/266.4.2 Land information systems 6/28

6.5 Acknowledgements 6/28

References 6/28

Bibliography 6/29

6.1 IntroductionThe work of the land surveyor can be classified into three mainareas of responsibility. Firstly, he is concerned with the record-ing of measurements which allow the size and shape of the Earthto be determined. Secondly, and primarily, he is involved in thecollection, processing and presentation of the informationnecessary to produce maps and plans. Thirdly, he may berequired to locate on the surface of the Earth the exact positionsto be taken up by new roads, dams or other civil engineeringworks.

As a consequence of the diverse nature of the land surveyor'sduties, several distinct branches of the subject have evolved.

6.1.1 Branches of surveying

Geodetic surveys are carried out on a national or internationalbasis in order to locate points large distances apart. This type ofsurvey acts as a framework for 'lower order' surveys. In order toensure high accuracy, the effect of factors such as the curvatureof the Earth on observations must be considered and thenecessary corrections applied.

Topographic surveys are concerned with the small-scale rep-resentation of the physical features of the Earth's surface.Frequently, the data necessary for such an operation will beprovided by the use of aerial photography. The science of takingmeasurements from photography in order to produce maps isknown as photogrammetry. Topographic surveys are often theresponsibility of a national organization such as, for example,the Ordnance Survey in the UK.

Hydrographic surveys, in contrast, involve the representationof the surface of the seabed. The end-product is normally anavigational chart. In recent years this branch has becomeincreasingly important with the development of the offshore oilindustry. In this case, in addition to the production of charts,the surveyor may be required to position large structures such asoil production platforms. This type of operation would nor-mally necessitate the use of ground and satellite electronicposition-fixing equipment.

Cadastral surveys relate to the location and fixing of landboundaries. In many countries in the world, e.g. Australia, theinformation supplied by the cadastral surveyor may be anintegral part of a land registration system.

Finally, engineering surveys are required for the preparationof design drawings relating to civil engineering works such asroads, dams or airports. The surveys are normally at a largescale, 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 thischapter will be to discuss: (1) those aspects of the subject whichare required in order to carry out simple surveys for engineeringprojects; (2) the processes involved in carrying out precisesurveys for deformation monitoring projects; and (3) the use ofcomputers in surveying for digital mapping and ground model-ling.

6.1.2 Principles of surveying

In spite of the diverse nature of land surveying, it is possible todefine certain basic principles which are common to all branchesof the subject. These principles have proved over the years to bevital if accurate surveys are to be conducted.

The first and most important principle is the provision of aninitial framework before observing and fixing the detail of asurvey. This process is ofteri known as providing control. It isessential to ensure that the positions of the control points areknown to a higher order of accuracy than those of the sub-sidiary points. By satisfying this principle it is possible to ensurethat errors, which inevitably occur, do not accumulate but arecontained within the control framework.

A second and perhaps more obvious principle is that ofplanning. All too often it is tempting to rush into a surveywithout consideration for an overall plan. Of particular import-ance is the need to define a job specification. This is indispens-able since the relationship between cost and accuracy is notlinear and an increase in accuracy may have a disproportionateeffect on cost. For example, if a distance of 50Om is to bedetermined to an accuracy of either 5 or 0.5 mm, the cost ratioof the respective accuracies may be of the order of 1:300. It isimportant, therefore, to choose techniques and instrumentsappropriate to the survey specification. Of equal importance isthe need to plan the reconnaissance stage. Before starting a taskit is essential to examine the area carefully, considering all thepossible ways of doing the survey and then selecting the mostsuitable method. Remember, 'time spent on reconnaissance andplanning is never wasted'.

A third principle is the need to ensure that sufficient indepen-dent checks are incorporated into the survey to eliminate orminimize errors. It is important that the checking system isincluded at all stages of the survey from fieldwork and computa-tions to the final plotting. In addition, the checking systemshould be independent and not solely a repeat of the initialmeasurement. 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 isequally important at all stages of the survey, and refers to theprocess of ensuring that the survey results can be replicated ifaccidental, or other, damage occurs to the survey markers orfield observations. Thus, it is important when constructingpermanent survey markers to take 'witness or reference meas-urements' to points of prominent detail in the vicinity of thepoint. Linear measurements of this type enable the point to berelocated if it is damaged, or alternatively if it is difficult to find.The latter situation can often occur with road projects. In manyinstances there may be a gap of many years between initialsurvey and final setting-out. During this time the permanentsurvey markers may become overgrown with vegetation andhence difficult to locate. The use of witness marks and measure-ments can often be of crucial importance if the permanentmarks are to be relocated.

Safeguarding of field observations is also of paramountimportance. Thus, it is considered good practice to produceabstract sheets from the surveyor's fieldbook at the end of eachday. These abstract sheets should summarize the major resultsfrom the fieldbook (e.g. rounds of angles, mean distance etc.)and should be carefully filed in the survey office. By such aprocess the possibility of several days' work being lost if thefieldbook is damaged or misplaced can be eliminated.

6.1.3 Errors in surveying

It is an unfortunate and often misunderstood fact that allmeasurements are affected by errors. So often, when confrontedwith the question: 'How accurate do you want the survey to

be?', or 'How accurately do you want this point located?', theglib answer 'Exactly!', or 'Spot on!', is given as the reply by aprospective client. If, in addition, the question of errors is raised,it is quickly dispensed with the comment: 'Errors don't occur ifyou do it properly.' The answer is correct in one respect, i.e. inrelation to mistakes, or, more correctly, gross errors. Theseshould not occur if a survey is carried out according to the basicprinciples of surveying. However, other types of errors do occurwhich can be much more difficult to handle.

Systematic errors, as the name suggests, are errors whichfollow a pattern or system. Errors of this type are normallyrelated to the variations in physical conditions which can occurwhen a measurement is made. For example, a steel tape isnormally known to be a certain length at some standardtemperature. If the temperature under which a measurement ismade varies from this standard, a systematic error will occur. Byknowing the coefficient of linear expansion a value for theexpansion of the tape can be determined and a correctionapplied. Systematic errors whose effect can be modelled mathe-matically are, hence, eliminated.

Random errors, in contrast, do not follow a standard patternand are entirely based on the laws of probability. These errors,or rather variations in measurement, will occur after gross andsystematic errors have been eliminated. The measurement of adistance by taping can again be taken as an example. It is oftennot appreciated that the same distance measurement madeunder the same physical conditions with the same tape willproduce different answers. Since it is assumed that the measure-ments will follow a normal distribution they can be examinedusing standard statistical techniques.

The following formula can therefore be applied to the analy-sis of random errors:

arithmetic mean = Jc = —- „ ,,n (6.1)

where /= 1, 2, . . . , n are the observed values and n denotes thenumber of observed values.

The arithmetic mean is significant because it is often taken tobe the closest approximation to the 'true' value and as such isknown as the most probable value (m.p.v.). The differencebetween the m.p.v. and the observed value is known as aresidual (v).

A term often used in order to estimate the precision of a seriesof measurements is the standard error, where standard error of asingle observation is:

0-±(ZV*\ '«°'-±\i^l) (6.2)

and standard error of the arithmetic mean is:

Table 6.1 Characteristics of some modern theodolites

°M~±\n^) (6.3)

For surveying purposes, the terms 'standard error', 'standarddeviation' and 'root mean square (r.m.s.) error' are synony-mous. All such terms are used to give an indication of theprecision of the result, i.e. the degree of agreement betweensuccessive measurements. High precision may not be indicativeof high accuracy, since accuracy is related to the proximity ofthe measurement to the true value. If, however, all the effects ofthe bias caused by systematic errors have been eliminated, theseindices of precision may also be used as indices of accuracy.

For example, suppose an angle has been measured 9 timesand the subsequent error analysis indicates that CT^ = 3" andaw = 0.81". What does this information tell us? Firstly, it indi-cates that the angle has been measured to a high precision.Secondly, it indicates that, statistically, there is a 68% chance orprobability of the standard error of a single measurement beingless than 3". Furthermore, if one extends the confidence limit toa value 3 times the standard error, or 9", then statistically theprobability that the error will be less than 9" is now 99.7% withonly a 0.3% chance of the error being greater than 9". Thisconfidence limit is often applied as a rejection criterion to agroup of observations. Any observation with a residual greaterthan 3 times the standard error may then be rejected, on thebasis that it is highly unlikely that the variation is solely aconsequence of random effects. Similar reasoning would applyto the standard error of the arithmetic mean. Further informa-tion on errors and their treatment can be found in Cooper' andMikhail and Grade.2

6.2 Surveying instrumentation

Surveying is essentially concerned with the direct measurementof three fundamental quantities: (1) the angle subtended at apoint; (2) the distance between two points; and (3) the height ofa point above some datum, normally mean sea-level. From themeasurement of these three quantities, it is then possible tocompute the three-dimensional positions of points.

With the exception of electronic methods of determiningdistance, the instruments used by the surveyor have not radi-cally changed in principle for 40 to 50 years. The advances intechnology may have reduced the size and increased the ef-ficiency of the instruments, but the fundamental principlesremain unchanged.

6.2.1 Angular measurement using the theodolite

The theodolite is used for the measurement of horizontal andvertical angles. In simple terms, a theodolite consists of a

Type of theodolite:Typical example:Country of manufacture:

Direct reading toBy estimation toTelescope magnificationTelescope aperture (mm)Sensitivity of plateLevel per 2 mm runWeight of instrument (kg)

1" PreciseKern DKM 2A-ESwitzerland

1"0.1"32 x40

20"6.2

20" EngineersSokkisha TM20ESJapan

20"5"28 x45

30"4.2

10' BuildersZeiss(Ober.)TH51W. Germany

10'r2Ox30

45"2.2

CompassWild TOSwitzerland

r30"2Ox28

8'2.9

ElectronicKern E-2Switzerland

1"

32 x45

8.7

telescope mounted on a platform which may be levelled to forma horizontal plane by means of a simple spirit bubble. Anglesare measured by pointing the telescope at targets and establish-ing the difference between readings on a circular protractormounted on the level platform.

There is a bewildering choice of theodolites available. Table6.1 lists the characteristics of a selection of commonly availablemodern theodolites. The broad distinction can be made betweenthose instruments which measure angles and those such ascompass and gyro theodolites which measure bearings, relativeto magnetic north and to true north respectively.

6.2.1.1 General construction of the theodolite

There are certain fundamental relationships and componentswhich are common to all theodolites. Before examining thedetailed construction of a modern glass arc theodolite, it isimportant to appreciate the geometrical arrangement of the axesof a theodolite, as illustrated in Figure 6.1.

Figure 6.1 Theodolite axes

In this ideal arrangement the vertical axis is vertical, thetrunnion axis is perpendicular to it and hence horizontal, andthe line of collimation is perpendicular to the trunnion axis.Unfortunately, it is not possible during the manufacturingprocess to ensure that these orthogonal relationships occurexactly. Similarly, during use over a period of years, wear mayoccur which may also alter these conditions. The extent to whicha theodolite fails to satisfy them can be measured by a series ofinstrument 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 aspecialist instrument technician for adjustment. Details of thefield tests and methods of adjustment may be found in Cooper.3

If, however, a modern theodolite is treated with care, and asuitable observational technique is employed, regular servicingshould be all that is required in order to obtain good results.

The detailed construction of a modern 1 s precise theodolite isshown in Figures 6.2 and 6.3. Examination of these figuresillustrates that the theodolite consists essentially of three distinctparts:

(1) Base. This consists of two main components: the tribrachand the horizontal circle. The tribrach can be screwedsecurely to the tripod and, by means of three footscrews, theinstrument may be levelled. The circle is made of glass withphotographically etched graduations. It is normally gra-duated in a clockwise manner. A circle-setting screw is alsousually provided and the base will generally house an

Figure 6.3 Construction of a theodolite

optical plummet. This consists of a small eyepiece with a lineof sight which is deviated by 90° in order to point verticallydown. By this process it is possible to centre the instrumentprecisely over a ground point. In some cases the opticalplummet may be housed in the alidade.

(2) Alidade. This rotatable upper part of the theodolite mayalso be known as the upper plate. The alidade rotates aboutthe vertical axis. Mounted on the alidade is the plate-levelbubble which indicates whether the instrument is level. By

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

Telescopeobjective

Trunnion axis

Telescope eyepiece

Plate level

Footscrew

Standing axis

StandardUpper plate (alidade)

Horizontal circle

Tribrach

Trivet stage

means of clamps and slow-motion screws it is possible torotate and clamp the alidade relative to the base.

(3) Telescope. Attached to the trunnion axis of the theodoliteis the telescope. The telescope magnifies the object and, bythe use of cross-hairs, allows the exact bisection of thetarget. Focusing of the object and the cross-hairs is carriedout using separate focusing screws. A further clamp andslow-motion screw allow precise pointing of the telescope ina vertical plane.

Angles of elevation or depression are measured using avertical circle also attached to the trunnion axis. Prior tomeasuring a vertical angle it may be necessary to set thealtitude bubble. However, most modern theodolites employan automatic compensating mechanism. In these casesvertical angles may be recorded after the plate level has beenset, without recourse to an additional bubble setting.

When the vertical circle is to the left of the telescope, thetheodolite is in what is conventionally called the face left(FL) position. Conversely, when the vertical circle is to theright of the telescope as it views an object, the theodolite isin the face right (FR) position.

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 horizontaland vertical circles.

In order to resolve a direction to a higher precision than thatto which the circle has been graduated, an optical micrometer isemployed. Optical micrometers are the modern equivalent ofverniers. The principle of operation involves the use of a planeparallel-sided block of glass as shown in Figure 6.4. When theglass is in the normal position, as shown by position (a), lightpassing through will be uninterrupted. Rotation of the block ofglass, however, produces a lateral shift of the incident beam asshown by position (b). This rotation is controlled by the

micrometer screw of the theodolite. Movement of this screwenables the observer to read, on an auxiliary scale, the lateralshift required in order to bring the image of the main-scaledegree graduations into coincidence with the index marks whichare built into the optical path. Using this technique it is possibleto resolve directly to 20" of arc if the micrometer is reading fromone side of the circle. Resolution direct to 1" is possible if amean-reading optical micrometer is used. In this case, readingsfrom two points diametrically opposite are meaned in order toeliminate the effects of any circle eccentricity.

Figures 6.5 and 6.6 illustrate two typical examples of the circlereading systems for both the single- and mean-reading opticalmicrometers.

Uninterrupted light path

Parallel platemicrometer

Circle graduations

Refracted light path

Figure 6.5 Single reading optical micrometer: circle reading WildT-1A 05° 13' 30" (Wild Heerbrugg)

Figure 6.6 Mean reading optical micrometer: circle reading WildT-2 94° 12' 44.3" (Wild Heerbrugg)

6.2.1.3 Field procedure

Potentially the theodolite is a very precise instrument. It is,however, necessary to follow a strict procedure both in setting-Figure 6.4 Parallel plate micrometer

up the instrument and in observing if this potential is to berealized. Incorrect use of a theodolite will undoubtedly result inpoor results, regardless Of how precise the instrument may be.

Setting-up. Setting-up a theodolite prior to observations beingtaken consists of three separate operations: centring, levellingand focusing.

Centring involves positioning the instrument exactly over aground point. This may be achieved by means of either a plumbbob suspended from the instrument or a centring rod or anoptical plummet. The process of centring and levelling should beconsidered as iterative in nature, becoming increasingly moreprecise after each operation.

Levelling the theodolite carefully is a necessary prerequisitefor precise measurements. The following sequence of operationsmust be carried out in order to level a theodolite:

(1) Approximately level the instrument using the small circularbubble.

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

(3) Rotate the alidade until the bubble is now approximatelyperpendicular to the initial position, as shown in Figure6.7(b). Using footscrew C only, centralize the bubble.

(4) Return to the initial position and again centralize the bubbleusing footscrews A and B. Repeat (2) and (3) until thebubble is central in both positions.

(5) Rotate the alidade through 180° until the position shown byFigure 6.7(c) is achieved. If the bubble does not remain in acentral position, move the bubble until it is in a positionmidway between a central position and its initial position.

(6) Rotate the alidade until the position illustrated by Figure6.7(d) is achieved. Using footscrew C, move the bubble intothe same position as in Figure 6.7(c). The bubble shouldthen remain in the same off-centre position for any align-ment of the alidade.

The final step before observations begin is to focus both thecross-hairs and the object to which observations will be made. Itis important to ensure that both images appear clear and sharp.In addition, it is critical that parallax does not exist. Parallaxrefers to the apparent movement of the cross-hairs and objectsrelative to each other when the observer moves his head. It iscaused by the image of the object not lying in the same verticalplane as the cross-hairs. If this occurs, the focusing operationmust be repeated until it is eliminated.

Observational procedure. A strict observational procedure isessential if both human and instrumental errors are to bereduced to a minimum. Consider the problem of measuring theangle shown in Figure 6.8.

Figure 6.8 Angle measurement

The observational procedure which should be adopted is asfollows. A booking procedure is illustrated by Table 6.2.

(1) Point with telescope in the FL position to the target at Xand 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

Round 1

Round 2

Level footscrews

Level bubble

Station YHeight of Inst:

Observer.Booker ..

.Date

.Weather.

TO FL FR MEAN ANGLE COMMENTS

X 90 20 30 270 20 40 90 20 35 4nZ 130 25 40 310 25 50 130 25 45 U ^ 1U

X 135 30 15 315 30 25 135 30 20Z 175 35 30 355 35 40 175 35 35 U ^ ^

Mean angle: 40° 05'13"

(3) Change face to FR and point to target Z and record circlereading 310° 25' 50".

(4) Point on FR to target X and record direction 270° 20' 40".

In order to reduce the effect of instrument maladjustments toa minimum, the mean of the FL and FR minutes and secondsreadings to the same point is averaged and the value entered inthe mean column. The difference between the mean circlereadings is then derived and entered in the angle column.

This constitutes one round of angles. The base setting screwshould then be adjusted and the process repeated in order toincrease the precision of the angle measurement. A minimum oftwo rounds is necessary for the least precise measurements; upto sixteen rounds may be required for very precise operations.

6.2.2 Distance measurement

The second fundamental quantity which it is necessary tomeasure is distance.

A wide variety of techniques can be used for the determi-nation of distance. The general distinction can, however, bemade between direct, optical and electronic methods. All of thetechniques discussed are capable of varying levels of precisiondepending on the degree of sophistication of the instrumen-tation and the observational techniques adopted.

6.2.2.7 Direct distance measurement (DDM)

The simplest method of measuring distance is that of physicallymeasuring the distance with a tape. In the past invar tapes wereused for the precise measurement of baselines for triangulationnetworks. Nowadays, DDM is generally confined to either theprecise measurement of short distances for setting-out or con-trol purposes or the less precise measurement of the detaileddimensions of a building or land parcel.

There are basically two types of tape in common use. Fibre-glass measuring tapes are manufactured from multiple strandsof fibreglass coated with PVC. They are waterproof and nor-mally either 30 or 50 m in length. Fibreglass tapes are generallyused for detail measurements and have largely superseded thelinen tapes which were available previously. For more precisemeasurements it is necessary to use steel bands. These aretypically either 30, 50 or 10Om in length.

In order to obtain high precision with either type of tape, it isessential that it is periodically checked against a standardreference tape, the length of which is known to a higher order ofaccuracy than that of the tape being checked. If a significantvariation exists, a standardization correction should be applied.In addition, it is vital that suitable attention is paid to the effectof variations in slope, temperature and tension which maynecessitate appropriate corrections being applied to the mea-sured distance. The corrections (C1, C2 and C3 respectively) are:

Slope:

C1= -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:

C2=±aL(/m-g (6.5)

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

Tension:

C3= ± L(Tn-TJAE

where Tm = measured tension, Ts = standard tension, A = cross-sectional 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 achievedwith steel tapes.

6.2.2.2 Optical distance measurement (ODM)

As an alternative to the direct method of measuring distance, itis also possible to measure distance indirectly by opticalmethods.

The development of ODM began over two centuries ago.James Watt is recorded as having used this approach in hissurvey of the West of Scotland in 1774. Although manyinstruments and improvements have been introduced since then,they all essentially involve the solution of the same geometricalproblem.

All methods of ODM are based on the solution of an isoscelestriangle, as shown in Figure 6.9. The triangle consists of threeimportant 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 knowingthe relationship between the three components, the horizontaldistance D between two points can be determined.

Figure 6.9 Optical distance measurement (ODM)

Two methods of solution are possible: either an instrumentwith a fixed parallactic angle is used and the variable base B ismeasured (Figure 6.10) or a base of fixed length is set up and thevariable 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 andvariable quantities it is therefore possible to determine thehorizontal distance.

Tacheometry. The first approach described above (fixed angle,variable base) is commonly known as tacheometry or morecorrectly as vertical staff stadia tacheometry. It is normally usedfor the measurement of distance where a proportional error ofbetween 1/500 and 1/1000 is acceptable, e.g. in picking-upsurvey detail points.

All modern theodolites have a diaphragm consisting of amain horizontal cross-hair and two horizontal stadia lines

Figure 6.11 ODM: fixed base, variable angle

spaced either side of it. These stadia lines define the fixedparallactic angle. If the theodolite telescope is sighted on to alevelling staff and the readings of the outer lines noted, thedifference in the readings, the staff intercept (s), will be directlyproportional to the horizontal distance between the instrumentand the staff. Generally, the distance between the stadia lines isdesigned in such a manner that the horizontal distance Z>Hbetween the instrument and staff is given by:

DH=lOQs (6.7)

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

/)s= 100(5 cos O) (6.8)

where D5=slope distance, and 6—vertical angle measured bythe 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 ofinstrument (trunnion axis to ground), m = middle hair reading,and V= difference in height between middle-hair reading andtrunnion axis = 505 sin 29 (6.11)

Several self-reducing tacheometers have also been designed.The main advantage of these instruments is their ability tocompensate for the effect of the inclination of the theodolitetelescope and, hence, allow the direct determination of horizon-tal distance without additional computation.

Two notable examples of this type of instrument are the WildRDS vertical staff self-reducing tacheometer and the Kern DK-RT horizontal bar double-image self-reducing tacheometer.Details of the construction and use of these instruments may befound in Hodges and Greenwood,5 and Smith.6 In recent years,the manufacture of these precise optical devices has ceased, theirplace being taken by low-cost electronic measuring devices.

Subtense bar. The second approach (fixed base, variable angle)is commonly known as the subtense or horizontal subtense barmethod. The method is normally confined to the measurementof distance for control purposes. Using this approach, distancesmay 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 theWild T2. The bar has targets mounted at each end of an invarstrip. The strip is protected by a surrounding aluminium strip inorder to ensure that, for all practical purposes, the length of thebar remains constant at 2 m. The bar is set up and oriented atright angles to the line of sight of the theodolite, as shown inFigure 6.13.

Figure 6.10 ODM: fixed angle, variable base

Figure 6.12 Stadia tacheometry: inclined sights

The horizontal parallactic angle a is measured with thetheodolite. Irrespective of the vertical angle to the bar, thehorizontal distance is given by:

Z>H = ifccot(a/2) (6.12)

with b = 2m

/>H = cot(a/2) (6.13)

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

Figure 6.13 Subtense bar

Subtense methods are also tending to be superseded by low-cost electronic methods. Nevertheless, many organizations stillpossess this type of equipment and for many projects it is a verysuitable technique to adopt.

6.2.2.3 Electronic distance measurement (EDM)

Development. The first generation of EDM instruments wasdeveloped in the early 1950s. Typical of the early meters werethe Swedish Geodimeter (GEOdetic Distance METER) and theSouth African Tellurometer instrument. The former, an electro-optical instrument, used visible light measurement, whilst thelatter used high-frequency microwaves. Both instruments wereprimarily developed for military geodetic survey purposes andhad the ability to measure long distances, up to 80 km in thecase of the Tellurometer, to a precision of a few centimetres.They were also, however, bulky, heavy and expensive in com-parison to their modern-day equivalents.

During the late 1960s, developments in microelectronics andlow-power light-emitting diodes led to the emergence of asecond generation of EDM instruments. These electro-opticalinstruments utilized infra-red radiation as the measuring signaland were developed for the short range (<5km) market. Inaddition, they were considerably smaller, lighter and less expen-sive than their predecessors. Probably the best-known exampleis the Wild DI-IO Distomat.

The introduction of microprocessors into the survey world inthe early 1970s led to the introduction of a third series of EDMinstruments. With this group it became possible, not only todetermine slope distance, but also to carry out simple computa-tional tasks in the field. For example, the facility becameavailable to compute automatically the corrected horizontaldistance and difference in height between two points by manualinput of the vertical angle read from the theodolite. Electronicdistance measurement instruments of this type had also beenreduced in size to the extent that the EDM unit could betheodolite-mounted. The Wild DI-3 is a typical example of thistype of instrument.

The most recent short-range EDM instruments are similar tothe previous group, but have several additional features worthyof mention. Firstly, the technology now exists to sense automa-tically the inclination of the EDM unit and therefore to be ableto compute automatically the horizontal distance between twopoints. The Geodimeter 220 (Figure 6.14) has this facility. Thisinstrument also has the ability to measure to a moving target, ortrack, a useful feature for setting-out purposes. By using anadditional unit it is also possible to have one-way speechcommunication between the instrument and target positions,again valuable when setting-out. This instrument can also beconnected to a Geodat 126 hand-held data collector (Figure6.14), which is able to store automatically distance informationfrom the EDM unit. Other relevant information (numeric oralphanumeric) can be input manually via the keyboard. TheGeodimeter 220 has a range of 1.6km with one prism and2.4km 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 isthe electronic tacheometer or 'total station'. The former term ismore appropriate in view of the different interpretations, by theinstrument manufacturers, of the term total station. In essence,an electronic tacheometer is an instrument which combines anEDM unit with an electronic theodolite. Hence, such instru-ments are capable of measuring, automatically, horizontal andvertical angles and also slope and/or horizontal distance. Themajority also have the facility to derive other quantities such asheights or coordinates and store this data in a data collector.Two designs of instrument have evolved during the last 5 years.

Figure 6.14 (a) Geodimeter 220; (b) Geodat 126 data collector(Geotronics)

The first, the integrated design, consists of one unit which,generally, houses the electronic circle-reading mechanism andthe EDM unit. The Wild TCI Tachymat and the Geodimeter140 (Figure 6.15) are representative of this range of instrument.The second design approach is the modular concept. In thiscase, the EDM instrument and the electronic theodolite areseparate units which can be operated independently. This ap-proach tends to be more flexible and enables units to beexchanged and upgraded as developments occur; it may also bea more cost effective solution for many organizations. The KernE-2 and Wild T-2000 Systems (Figure 6.16) are representative ofthis design of electronic tacheometer.

Finally, mention should be made of high-precision EDMinstruments. These instruments have been designed for projectssuch as dam deformation or foundation monitoring whereextremely high precision is necessary. Instruments which are

Figure 6.16 Electronic tacheometer, modular design: Wild T-2000,with DI4

representative of this design include the Tellurometer MA-IOOJaakola,7 the Kern ME-3000 Mekometer (see Froome,8 Meir-Hirmer,9 and Murname10) and the Comrad Geomensor 204DME (Figure 6.17). The latter instrument has a range of up to

Figure 6.17 High-precision EDM: Comrad Geomensor 204DME

10km with a standard error of ±0.1 mm±0.5p.p.m. Furtherup-to-date technical information on many modern EDM instru-ments can be found in Burnside."

Principle of measurement. Although there is a wide variety ofEDM instruments on the market, they all measure distanceusing the same basic principle. This can be most clearly illus-trated by means of the flow diagram (Figure 6.18), which relatesspecifically to electro-optical instruments.

An electromagnetic (EM) signal of wavelength equal to either560 nm (visible light), 680 nm (HeNe laser) or 910 nm (infra-red)is generated. This signal is subsequently amplitude-modulatedbefore being transmitted through the optical system of theinstrument towards a retro-reflector mounted at the end of theline to be measured. The signal is then retro-reflected, orredirected through 180°, by a precisely ground glass corner cube.Cheaper acrylic corner cubes may also be used.12'13 This reflectedsignal is consequently directed towards the receiving opticalsystem. On entering the optical system of the instrument, thesignal is converted by means of a photomultiplier into anelectrical signal.

The next stage involves the measurement of the phase differ-ence between the transmitted and received signals and theconversion of this information into distance. Figure 6.19 showsthe path taken by an EM signal radiated by an EDM instrumenttogether with the instantaneous phase of the signal. It isapparent that the distance X-Y-X travelled by the EM signal isequivalent to twice the distance to be measured. Also, thisdistance can be seen to be related to the modulation wavelength(A) and the fraction of the wavelength (/4A) by the followingrelationship:

Figure 6.15 Electronic tacheometer, integrated design:Geodimeter 140

Figure 6.19 Double path measurement using EDM

2D = >d + A A (6.14)

where n is an unknown integer number of wavelengths. Thedetermination of the distance therefore involves resolving bothAX and n. Phase detectors are used to determine AX whicheffectively measures the phase difference between the transmit-ted and received signal and, hence, allows the fractional part ofthe distance less than one full wavelength to be determined. Thevalue of n can be determined by using two or more EM signalsof slightly varying wavelengths. For example, assume 2D = 25.5,A1 = 2.5 m and A2 = 2.4 m then:

ID = 2.5«, +0.5 (6.15)

and

2£> = 2.4«2+1.5 (6.16)

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

«=10 (6.17)

Substituting in Equations (6.15) or (6.16)

D= 12.75m (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 isnecessary to apply several corrections to the measured slopedistance in order to determine the corrected horizontal distance.The first correction to be applied is the atmospheric or refractiveindex correction. Just as a steel tape varies in length withvariations in temperature and pressure so, too, does the modula-tion wavelength of an EDM instrument. It is therefore necessaryto measure the temperature, pressure and, in some cases,relative humidity during measurements. A correction is thenapplied to compensate for the variation in modulation wave-length caused by variations in atmospheric conditions.

Many instruments have the facility to compute automaticallyand apply this correction to observations directly in the field.Temperature, pressure and relative humidity readings are takenand the appropriate reading to be set on the refractive indexcorrection dial is read from a nomogram.

A second important correction is the additive zero or prismconstant. This correction represents the difference between theelectro-optically determined distance and the correct length ofline. It is a combination of the errors due to prism offset and thevariation in the physical and electrical centres of the EDMinstrument. Many manufacturers design their corner cube re-flectors in order to eliminate this correction totally. However, ifseveral different types of corner cube are being used, it isessential that a full field calibration be undertaken in order todetermine the correction. (See Schwendener,14 Ashkenazi andDodson,15 and Sprent and Zwart16 for further details of theprocedure for instrument calibration.) The slope correction isthe same as for DDM. For distances measured above or belowmean sea-level (MSL) a correction is necessary in order toreduce the distance to its equivalent at MSL. The correction (C4)is given by:

C4 = (-LHJ/R (6.19)

where Hm is the mean height of the instrument and reflectorabove MSL and R is the radius of the Earth (6370 km). Finally,if the distance is to be used for computation of coordinates onthe national grid, the horizontal distance at MSL must bemultiplied by the local scale factor. For the Transverse Mer-cator projection, the local scale factor (F) may be approximatelycalculated 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 theline 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 alevel.

Electromagnetic ^ Transmittingsignal optic

>Retro-reflector

ReceivingPhase measurement •* ootic

I Slope distance I CorrectionsAtmosphericAdditiveconstant

•* SlopeHeightabove MSLScale

I factor

Datta Corrected

uT"!—Y^

Figure 6.18 Principle of operation: electro-optical distancemeasurement

EDMInstrument Retro-reflector

The fundamental principle of the level is illustrated by Figures6.20 and 6.21. Figure 6.20 represents the situation which nor-mally exists when the level is initially set up. In this case, thestanding 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 axiswhen the instrument has been levelled using the procedureoutlined in 'Setting up' in section 6.2. L3. It can be seen thatcompletion of this procedure ensures that, firstly, the standingand vertical axes are made coincident and, secondly, if the

Figure 6.23 Level construction: tilting level

Prior to recording an observation, the instrument is approxi-mately levelled. This is normally achieved by means of a 'ball-and-socket' arrangement and a small circular bubble. In orderto set the standing axis exactly vertical, the tilting screw isturned and the main bubble altered until a coincident position(Figure 6.24), as viewed through a small auxiliary eyepiece, isachieved.

If the telescope is now rotated horizontally to sight a secondor subsequent point, it is important to relevel the main bubbleby means of the tilting screw.

Before levelling After levelling(a) (b)

Figure 6.24 Coincidence bubble-reading system

6.2.3.1 Dumpy level

The dumpy level was so named because of the rather shorttelescopes which were used with early versions of this instru-ment.

The construction of a typical dumpy level is shown in Figure6.22. The most distinctive feature of this type of level is that theaxis of the telescope is fixed rigidly to the standing axis of theinstrument. In order to satisfy the condition that both thevertical and standing axes are coincident, the standard levellingprocedure outlined in section 6.2.1.3 is carried out. Rotation ofthe telescope will now define a horizontal plane.

In the past, this type of level was very popular for generalengineering work. It has, however, been replaced in recent yearsby the automatic level.

6.2.3.2 Tilting level

The tilting level is a more precise instrument than the dumpylevel. Figure 6.23 illustrates the main features. In contrast to thedumpy level, the telescope is not rigidly attached to the standingaxis but is able to be tilted in a vertical plane about a pivot pointX, by means of a tilting screw.

Objective

TelescopeLevellingscrews

Spirit bubble Bubble-adjusting screw

Eyepiece

- Line ofcollimation

•Tilting screw

Trivet stage

Standing axis

Pivot X

Spirit bubble

Horizontal line of sight

Line of collimation of level

VerticalStanding axisof level

Figure 6.20 Geometry of the level axes: before levelling

Spirit bubbleHorizontal line of sight

Line of collimation of level

Vertical

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 engineerinsurvey purposes: (1) the dumpy level; (2) the tilting level; and (3the automatic level.

Spirit bubble Bubble-adjustingscrew

Line ofcollimation

Eyepiece

Tribrach

Telescope

Objective

Trivet stage

Levelling screws

Standing axisFigure 6.22 Level construction: dumpy level

Figure 6.25 Level construction: automatic level

For high-precision levelling, e.g. in order to detect the settle-ment of a building, a parallel plate micrometer (PPM), attachedto the front of the objective of the telescope normally forms partof the construction of the level. Almost all precise levels in usenowadays are of the automatic design and, ideally, should bedesigned so that the PPM forms an integral part of the instru-ment, rather than being an 'add-on' attachment. One suchinstrument is the Zeiss (Jena) Ni 007 (Figure 6.26). Thisparticular instrument also has an unusual compensatingmechanism which results in the 'periscope'-type appearance ofthe instrument. The PPM operates by deflecting the line of sightto the nearest whole staff graduation, the amount of displace-ment which is required being measured by a micrometer. Thisvalue is then added to the staff reading to give the final staffreading. This is illustrated in Figure 6.27. Clearly in an opera-tion such as precise levelling it is important to minimize theeffects of systematic errors. This is partially overcome by asuitable field procedure,17 and partially by ensuring that the staffis maintained at a constant length. In order to achieve this, aninvar staff with stabilizing arms and a level bubble attachment isnormally used.

6.2.3 A Laser level

Lasers are monochromatic, coherent and highly collimated lightsources, initially developed in the 1940s. Until relatively

Figure 6.27 Operation of a parallel plate micrometer for preciselevelling

recently, their use has tended to be restricted to the field of purescientific research. Nowadays, however, the laser is a widelyused tool in land surveying for distance measurement, align-ment,18 and levelling purposes.

There are essentially two types of laser in use in civil engineer-ing: (1) the fixed-beam; and (2) the rotating beam laser. Thefixed-beam laser projects a single highly collimated light beamto a single point. This design is particularly suited to alignmentproblems. The rotating-beam laser, in contrast, takes the fixed-beam source and rotates it at high speed, so forming a plane(either in the horizontal or vertical sense), of laser light. Thisdesign is more appropriate for levelling or grading purposes.

The Spectra-Physics EL-I shown in Figure 6.28 is a typicalexample of the laser levels currently in use. The laser beam in

Figure 6.26 Zeiss (Jena) Ni 007 automatic precise level

Undeflected line of sight

Parallel Plate MicrometerDeflectedline of sight

Reading = 1.61 +A

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 majorsource of human error, that of setting the bubble, is replaced byan automatic compensating system. In common with the tiltinglevel, approximate levelling is still necessary. The tedious anderror-prone bubble-setting process, however, is eliminated. Aswith the dumpy level, the instrument defines a horizontal planewhen rotated. The automatic level therefore combines the speedof operation of the dumpy level with the precision of the tiltinglevel.

Figure 6.25 illustrates the main components of this type oflevel. The essential feature of the instrument is the incorporationof an automatic optical-mechanical compensating mechanism.The use of such a system ensures that the line of collimation asdefined by the centre cross-hair will trace out a horizontal planeirrespective of the fact that the optical axis of the instrumentmay not be exactly horizontal. It is, however, necessary to levelthe instrument approximately in order to ensure that the line ofsight is within range of the compensating mechanism.

Optical-mechanicalcompensatorObjective

Eyepiece

Line ofcollimation

Circular spirit levelTribrach

Telescope

Levelling screwsTrivet stage

Standing axis

Figure 6.28 Spectra-Physics EL-1 (Spectra-Physics)

this case forms a 360° horizontal plane which is detected by aportable sensing device also shown in Figure 6.28. The laser unitautomatically 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 rangeof 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 axisof the level has been set truly vertical, then the line of collima-tion will be horizontal. This may not always be the case.

If this condition does not occur, then a collimation error issaid to exist. This is illustrated in Figure 6.29. If accuratelevelling is to be achieved, it is essential that a regular testingprocedure is established in order to check the magnitude of anycollimation error that may exist.

Figure 6.30 Two-peg test

the difference between the two readings calculated. Thisvalue represents the true difference in height between A andB. Any collimation error which exists will have an equaleffect on both readings and, hence, will not affect thedifference between the readings. In this case the difference inheight is 1.415-0.932 = 0.483m.

(3) The instrument is now moved to a point C close to the staffat B (about 3 to 5 m away), as in Figure 6.30(b). The readingon staff B is recorded (1.301). If no collimation error exists,the reading on staff A should be equal to the reading on staffB ± 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 der-ived previously in (3) indicates the magnitude and directionof any collimation error. For example, in this case, the errorwould be 1.794- 1.784= 10mm per 50m.

An error of up to 2 to 3 mm over this distance would beacceptable. If, however, the error is greater than this, theinstrument should be adjusted. Unlike theodolite adjustments,this type of adjustment can normally be performed without anygreat difficulty by the engineer and the procedure is as follows.

For the dumpy and automatic level: alter the position of thecross-hairs until the centre cross-hair is reading the value whichshould have been observed from step (3) above. This is achievedby loosening the small screws around the eyepiece which controlthe position of the cross-hairs.

For the tilting level: again alter the position of the centrecross-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-adjustingscrew.

6.3 Surveying methods

6.3.1 Horizontal control surveys

Any engineering survey or setting-out project, regardless of itssize, requires a control framework of known co-ordinatedpoints. Several different control methods are available as des-

Figure 6.29 Collimation error

A common field procedure which can be used to test a level isknown as the 'two-peg test'. The procedure is as follows:

(1) Set out two points A and B approximately 50m apart, asshown in Figure 6.30(a). The level is set up at the mid-pointof 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

Line of collimationHorizontal plane

Collimation error