AMC 2512: LAND SURVEYING General Principles of land surveying The main principles to be observed in surveying are to "work from the whole to the part (Control Network)", and to use methods which are accurate enough for the object in view but which, since increased accuracy means greater labour and cost, are no more accurate than the necessity of the case demands. AMC 2512: LAND SURVEYING Control Network A control network is the framework of survey stations whose coordinates have been precisely determined and are often considered definitive The stations are the reference monuments, to which other survey work of a lesser quality is related Other survey works that may use the control will usually be less precise but of greater quantity AMC 2512: LAND SURVEYING By its nature, a control survey needs to be precise, complete and reliable This is done by using equipment of proven precision, with methods that satisfy the principles and data processing that not only computes the correct values but gives numerical measures of their precision and reliability The practice of using a control framework as a basis for further survey operations is often called ‘working from the whole to the part’. AMC 2512: LAND SURVEYING In control network, the first thing that is done is the establishment of a number of fairly widely separated points fixed with the most refined apparatus and methods Next, the wide gaps between these primary points are filled in with a number of secondary points at much closer intervals than the primary points, and surveyed by methods which are rigorous and accurate, but not so rigorous or so accurate as those used in fixing the positions of the primary points. AMC 2512: LAND SURVEYING This still leaves rather wide gaps between fixed points, so a number of tertiary points are fixed to fill in the gaps The positions of these tertiary points not being so accurately surveyed as are those of the secondary and primary points The result is a network of points, fairly thickly spaced, which can be used by the ordinary surveyor to do a detailed surveying on the ground AMC 2512: LAND SURVEYING It must be noted however that, all survey work, even the most refined, is subject to error, and errors are very quickly propagated and generally very much magnified as the work proceeds Hence, if the primary work were not of the utmost possible accuracy, and the secondary work only slightly less so, very small errors at the beginning would soon become very large errors as the work was extended over a large area. AMC 2512: LAND SURVEYING Thus, the primary points control the secondary, the secondary the tertiary, and the tertiary the detail survey Errors in the primary can lead to large errors in the secondary, and errors in the secondary can equally lead to large errors in the tertiary, and so on Much the same principle is observed even in simple surveys Thus, in a chain survey of a small estate, lines are first run round the perimeter, with a number of clear cross lines between, or else the outer perimeter is surveyed with a theodolite traverse, and lines are then run across the interior AMC 2512: LAND SURVEYING These lines are fairly accurately measured and are the first to be plotted to see that they all fit in properly Minor chain lines, which may be of lesser accuracy, are then run between the main lines until the area is split up into convenient blocks for the survey of the detail In none of these cases do we start with the survey of detail and build up from block to block or from detail to tertiary points and then to primary points AMC 2512: LAND SURVEYING In all cases, the points first laid down are the most accurately surveyed and serve as a skeleton on which to hang the later work, all of which is adjusted to them. AMC 2512: LAND SURVEYING Methods used in Surveying Nearly every operation in surveying is based ultimately on fixing on a horizontal plane the position of one or more points with relation to the position of one or more others, or/and determining the elevation or vertical height of one or more points above a definite horizontal datum plane, which is very often taken as Mean Sea Level AMC 2512: LAND SURVEYING There are four main methods used in fixing the position of a point on the horizontal plane. I. By triangulation from two points whose positions are already fixed and known II. By bearing and distance from a single fixed point III. By offset from a chain line IV. By resection AMC 2512: LAND SURVEYING Triangulation AMC 2512: LAND SURVEYING In the figure in previous slide, A and B are two points whose positions are known. This means that we know (or can compute) the distance between the two points, and the direction of one from the other. C is a point whose position is required If now (a) two of the angles of the triangle ABC are observed, or (b) the distances AC and BC are measured, the size and shape of the triangle can be fully determined, either by drawing or by computation, and hence the position of C with relation to both A and B can be found AMC 2613: LAND SURVEYING When the position of C is fixed, we know the direction and length of the side BC, and hence, from this side, using similar methods to those already employed, we can fix a fourth point D, and after it a fifth point E, and so on. In practical triangulation involving angular observations, the three angles of every triangle are measured wherever possible, as this not only acts as a check, but it also serves to add considerably to accuracy AMC 2613: LAND SURVEYING If the angles BAC and ABC only in ‘fig. triangulation’ are observed, the point C is said to be fixed by intersection AMC 2613: LAND SURVEYING Bearing and distance from a single fixed point AMC 2613: LAND SURVEYING In fixing a point by bearing and distance, we measure the distance AB (fig. in previous slide), where A is the fixed point and B the point to be fixed, and also measure the bearing or direction of the line AB For certain purposes, when very great accuracy is not needed, we can measure bearings or directions directly by means of a magnetic compass AMC 2613: LAND SURVEYING This will give the bearing or direction of the line with reference to a fixed direction known as magnetic north, which is shown as the line AC in the figure For more accurate work, the bearing must be obtained by sextant or theodolite by observing the angle DAB between a fixed point, say D, whose bearing or direction from A is known, and the point B AMC 2613: LAND SURVEYING When this angle is known, we can compute the bearing of AB and this, combined with the measured distance, enables us to fix the position of B AMC 2613: LAND SURVEYING This principle is used in traversing, a process also extensively used in surveying AMC 2613: LAND SURVEYING Traversing AMC 2613: LAND SURVEYING A traverse consists of a series of zigzag lines whose bearings and distances are measured Thus, in fig. in previous slide, starting from the fixed point B we measure the distances BC, CD, DE, EF and FG, and also either the bearings of BC, CD, DE, EF, FG or else the angles ABC, BCD, CDE, DBF, EFG, where in the latter case the bearing or direction of the point A from B is known, and the bearing of BC is obtained by calculation from it and the measured angle ABC AMC 2613: LAND SURVEYING Then, knowing the bearing and distance BC, we can fix the position of C, and after that, knowing the bearing and distance CD, we can fix the position of D, and so on, the bearing of CD, if not observed directly from compass observations, being obtained from the bearing of BC, which we have already found, and the observed angle BCD. AMC 2613: LAND SURVEYING Offset from a chain line AMC 2613: LAND SURVEYING The term offset in surveying is applied to a line laid out at right angles to a chain line to fix some point of detail In fig. in previous slide, AB is part of a chain line and c is a point on it whose distance from A, the beginning of the line, is noted and recorded, d is a point of detail whose position is to be plotted The point c is chosen so that the line cd is perpendicular to the line AB, and the distance cd is measured AMC 2613: LAND SURVEYING When the line AB is plotted on paper, and the line cd laid out the correct distance from the plotted position of c, so that dc is perpendicular to AB, the position of the point d is at once plotted It will be seen that an offset is really a special case of fixing by bearing and distance. AMC 2613: LAND SURVEYING Resection AMC 2613: LAND SURVEYING The method of fixing the position of a point by observations to three fixed points is known as resection Thus, in fig. of previous slide, A, B and C are three points whose exact positions are known or are plotted on a plan. Then the position of the point O can be fixed if the angles AOB and BOG are measured. AMC 2613: LAND SURVEYING Alternatively, if the work is being done by plane-table, there is a method which, by suitable pointings of the alidade or sight rule in the directions of A, B and C, enables the position of to be determined graphically in the field. AMC 2613: LAND SURVEYING Errors in Surveying All survey operations are subject to errors of observation, but certain types of error are more serious than others 1. Gross error or mistake This means a serious mistake in reading an instrument: for instance, reading 150 instead of 105 when reading the circle of a theodolite, or booking a reading of 80 on a chain when it is really 60 Every care must be taken to avoid making mistakes of this kind, since the results may naturally be very serious. AMC 2613: LAND SURVEYING 2. Constant error Has the same value and sign for every single observation Sometimes constant errors cancel out Suppose the first graduation on a level staff is marked 1 ft. instead of zero, then every single sight taken on the staff will be one foot longer than it should be, and hence the apparent reading will be one foot too high AMC 2613: LAND SURVEYING But, since a level is used to measure differences of elevation, and these differences are obtained by subtracting one staff reading from another, the error will cancel out and the true difference of elevation will be obtained Nevertheless, constant errors are to be avoided as much as possible AMC 2613: LAND SURVEYING 3. Systematic error Is an error which has always the same sign, not necessarily always the same magnitude, at every observation Thus, a chain may be uniformly stretched so that the error in apparent length of any part of it is proportional to the length. AMC 2613: LAND SURVEYING If we knew the amounts and signs of constant or systematic errors we could allow for them by applying calculated corrections This is often done, but sometimes, although systematic error is suspected, neither its magnitude nor its sign is known, and consequently no correction is possible AMC 2613: LAND SURVEYING 4. Accidental errors Accidental errors of observation are the small errors of observation that vary in magnitude and in sign with every single observation Their occurrence depends on the laws of chance and, their magnitudes and signs being unknown, their effects cannot be calculated and allowed for. AMC 2613: LAND SURVEYING Small errors are more likely to occur than large ones The small errors in reading a levelling staff due to "shimmer " in the atmosphere or to temperature changes, small errors in reading an angle, etc., are of this type AMC 2613: LAND SURVEYING It should be noted that, in the case of systematic error, the total error in a measurement which is dependent on the sum of a series of repeated readings of the same quantity, is directly proportional to the total measurement, but, in the case of accidental errors of observation, the total error is proportional to the square root of the total measurement, or rather to the square root of the number of repetitions of readings AMC 2613: LAND SURVEYING Thus, if there is a systematic error of k units per unit length in the reading of a chain, the total error from this cause in the length L of a line measured with that chain will be k X L On the other hand, errors of ordinary levelling tend on the whole to be of the accidental type, so that the total error in the measurement of a difference of elevation between two points L units of length apart will be K× L, where K is the "probable" accidental error per unit length of line AMC 2613: LAND SURVEYING Hence, since the effects of systematic and constant errors tend to be propagated according to a linear law, and the effects of accidental errors according to a square root law, it is more important to reduce or eliminate constant and systematic errors than it is to reduce or eliminate the small purely accidental errors In many cases, but not in all, constant and systematic errors can be reduced or eliminated by using suitable methods of observation
