GE 282 Large Scale Surveying Lecture Notes

GE 282 Large Scale Surveying Lecture Notes

Syllabus:

(i)Distance measurements – direct and indirect distance measurements-taping, optical (tacheometric, substance bar), EDM;

(ii)Angular measurements;

(iii)Traverse computations (reduction of forward bearings, L-D computation, computation of coordinates), and adjustments;

(iv)Area computations and subdivision of plots;

(v)Spirit and trigonometrical levelling;

(vi)Introduction to triangulation, trilateration, resection, intersection and radiation as methods for provision of controls.

Reference:

1) Wolf, P. R. and Brinker, R. C., 1994, Elementary Surveying (9th Ed.),HarperCollinsCollege Publishers, U.S.A., ISBN 0-06-500399-3;

2) Moffitt F. H. and Bouchard H., 1992, Surveying (9th Ed.),HarperCollinsCollege Publishers, U.S.A., ISBN 0-06-500059-5;

3) Bannister, A. and Raymond S., 1992, Surveying, Longman Group UK Ltd, ISBN 0-582-274532;

4) Uren, J. and Price, W. F., 1994, Surveying for Engineers (2nd Ed.), Macmillan Press Ltd., London, UK, ISBN 0-333-37081-3

Lecturer:Dr Isaac Dadzie

Geomatic Engineering Department

KNUST

Kumasi

1 Introduction to Surveying

1.1 Definition of Surveying

Surveying may be defined as the science, art, and technology of determining the relative positions of natural and man-made features above, on, or beneath the earth’s surface and the representation of this information either graphically or numerically.

To majority of Engineers, surveying is the process of measuring distances, height differences and angles on site either for the preparation of large-scale plans or in order that engineering works can be located in their correct positions on the ground.

Surveying, in a more general sense, can be regarded as that discipline which encompasses all methods for measuring, processing, and disseminating information about the physical earth and our environment. Surveying practice therefore involves:

(i)Determination of the shape of the earth and measurement of all facts needed to determine the size, position, shape, and contour of any part of the earth’s surface, and the provisions of plans, maps, files and charts recording these facts;

(ii)Positioning of objects in space, and positioning of physical features, structures, and engineering works on, above, or below the surface of the earth;

(iii)Determination of the positions of boundaries of public or private land, including national and international boundaries, and the registration of those lands with appropriate authorities;

(iv)Design, establishment, and administration of land and geographic information systems, collection and the storage of data within those systems, and analysis and manipulation of that data to produce maps, files, charts and reports for use in the planning and design processes;

(v)Planning of the use, development, and re-development of property, and management of that property, whether urban or rural, and whether land or buildings, including determination of values, estimation of costs, and the economic application of resources such as money, labour, and materials taking into account relevant legal, economic, environmental and social factors;

(vi)Study of the natural and social environment, measurement of land and marine resources, and the use of this data in planning and development in urban, rural and regional areas.

1.2 Basic SurveyingField Measurements and Deliverables

Basically,fieldoperations in surveying involve measuringdistances, height differences and angles, using ground-based or space-based instruments and techniques. The measured quantities are processed:

(i)to determine horizontal positions of arbitrary points on the earth’s surface;

(ii)to determine elevations or heights of arbitrary points above or below a reference datum, such as mean sea level;

(iii)to determine the configuration of the ground;

(iv)to determine the lengths and directions of lines;

(v)to determine the areas of tracts bounded by given lines.

To transfer designed drawings from paper onto the ground, distances, angles and grade lines are set-out (or laid off) to locate construction lines for buildings, bridges, highways and other engineering works, and to establish the positions of boundary lines on the ground.

1.3 Geodetic and Plane Surveys

With respect to the assumptions on which the survey computations are based as well as the orders of accuracies required, surveying may be divided principally into Plane and Geodetic Surveying.In geodetic surveying, the curved surface of the earth is considered by performing the computations on an ellipsoid (a curved mathematical figure used to approximate the size and shape of the earth).

Geodetic methods are employed to determine relative positions of widely spaced monuments and to compute lengths and directions of the long lines between them. These monuments serve as the basis for referencing other subordinate surveys of lesser extent.All height measurements in geodetic surveys are referenced tothe surface of the ellipsoid, and are termed ellipsoidal or geodetic heights.

In plane surveying, relatively small areas of the earth are involved and the surface of the earth is considered to be a horizontal plane or flat surface. The direction of a plumb line (and thus gravity) is considered parallel throughout the survey region, and all measured angles are presumed to be plane angles. All height measurements are referenced to mean sea Level or the geoid, and are termed orthometric heights.

Field measurements for geodetic surveys are usually performed to a higher order of accuracy (using special precise instruments and rigorous procedures) than those for plane surveys.

1.4 Classes of Surveys

The classes of land surveying are:

• Topographic Surveys:These are surveys conducted to determine the configuration of the ground as well as the location of the natural and man-made features of the earth including hills, valleys, railways etc.

• Cadastral Surveys:These are surveys conducted for legal purposes such as deed plans showing and defining legal property boundaries and the calculation of area(s) involved.

• Hydrographic Surveys:These are surveys conducted to determine the position of the survey vessel, depth of water and to investigate the nature of the sea bed.

• Photogrammetric Surveying: It is the science of making precise measurement and creating detailed maps from aerial images or photographs.

• Mining Surveys:These are surveys executed to establish location and boundaries of mining claims. It also involves the establishment of underground workings horizontally, vertically and lay out shaft connections.

• Engineering Surveying:Surveys executed to locate or lay out engineering or building works such as roads, railways, tunnels, dams etc.

• Global Positioning System (GPS) Surveys:Positioning in which the coordinates X, Y, and Z of survey stations are determined by the reception and analysis of NAVSTAR Satellite signals.

1.5 Questions

1. Distinguish between plane and geodetic surveying.

2. List and discuss four main classes of land surveying.

2Distance Measurements

Measurement of distance between two points on the surface of the earth is one of the basic operations in surveying. Distances can be measured and set out either directly using tapes or indirectly using optical theodolites through tacheometric techniques or by using electronicdistance meters(EDMs) or Total Stations.

2.1 Types of Distance Measurement

Depending on the relative positions and elevations of the two points involved, the measured distance could be a horizontal distance, slope distance or vertical distance.

In a 3-D coordinate system,

(i)a horizontal distance is obtained if the two points have the same Z-value;

(ii)a slope distance is obtained if the two points have different values for all X, Y, and Z coordinates;

(iii)a vertical distance is obtained if the two points have the same X and Y coordinates but different Z coordinate.

In plane surveying, the distance between two points at different elevations is reduced to its equivalent horizontal distance either by the procedure used to make the measurement or by computing the horizontal distance from a measured slope distance. Horizontal and vertical distances are used in survey drawings, setting out plans, and engineering design works. Slope distances and vertical distances are used on site during the setting out of designed points.

Note: Distances are corrected for mean sea level and local scale factor corrections only when the survey is based on the National Grid System.

2.2 Taping: Direct Distance Measurement

Taping is a direct means of determining the straight-line distance between two points using a tape. The tape may be made of steel, fiberglass or plastic, and may be of length 20 m, 50 m or 100 m. Taping is performed in six steps:

(i)lining in (through ranging);

(ii)applying tension;

(iii)plumbing;

(iv)marking tape length;

(v)reading the tape; and

(vi)recording the distance.

When the length to be measured is less than that of the tape, measurements are carried out by unwinding and laying the tape along the straight line between the points. The zero of the tape (or some convenient graduation) is held against one point, the tape is straightened, pulled taut and the distance read directly on the tape at the other point.

2.2.1 Ranging

When the length of a line between the two points exceeds that of a tape, some form of alignment is necessary to ensure that the tape is positioned along the straight line required. This is known as ranging and is achieved using ranging poles (or rods) and marking pins (or arrows). Ranging a line between two points A and B requires two people, identified as the leader (or surveyor) and the follower (or assistant), and the procedure is as follows:

(i)Ranging poles are erected as vertical as possible at the points A and B and, for a measure in the direction of A to B, the zero point of the tape is set against A by the follower;

(ii)The leader, carrying a third ranging pole, unwinds the tape and walks towards point B, stopping just short of a tape length, at which point the ranging pole is held vertical;

(iii)The follower steps a few paces behind the ranging pole at point A, and using hand signals, lines up the ranging pole held by the leader with bottom part of the ranging pole at A and with the pole at B. This lining-in should be done by the follower sighting as low as possible on the poles;

(iv)The tape is now straightened and laid against the pole held by the leader, pulled taut and the tape length marked by placing an arrow on line;

(v)For the next tape length, the leader and the follower move ahead simultaneously with the tape unwound, the procedure being repeated but with the follower now at the first marking arrow;

(vi)As measurements proceeds, the follower picks up each arrow and, on completion, the number of arrows held by the follower indicates the number of whole tape lengths measured. This number of tape lengths plus the section at the end less than a tape length gives the total length of the line.

2.2.2 Step-Chaining: Horizontal Distance Measurements on Sloping Ground

Step-chaining is a field procedure fordirectly obtaining horizontal distance between two points on sloping ground without using angle-measuring or levelling instruments. Two men, a surveyor (leader) and an assistant (follower), are required, and with reference to Fig. 2.2, the procedure is as follows:

(i)To measure D1, the zero end of the tape is held at A and the tape then held horizontally and on line towards B against a previously lined-in ranging pole;

(ii)At some convenient tape graduation (preferably a whole metre mark), the horizontal distance is transferred to ground level using a plumb line (i. e. a string line with a weight attached), a marking arrow or a ranging pole;

(iii)The leader notes the length of the first step in his book, and the tape is now moved forward and the process is repeated to measure D2and D3 in a similar manner; and

(iv)The sum of the steps D1, D2 and D3gives the requiredhorizontal distance between A and B.

The length of steps which can be adopted is limited by the gradient. At no time should the tape be above the surveyor’s eye level, because plumbing becomes very difficult. As the gradient increases the length of step must therefore decrease.

2.2.3 Slope Measurements

In measuring the horizontal distance between two points on a steep slope, rather than break tape every few metres, it may be desirable to tape along the slope and compute the horizontal distance. This requires measurement also of either the angle of inclination (θ) or the difference in elevation (d) as indicated in Fig. 2.1.The slope angle can be measured using a hand-held device called an Abney Level (see Fig. 2.3) but where better accuracy is required, a theodolite is used to measure the slope angle.

Fig 2.3 Abney level

To use an Abney level, an observer first distinctly marks his eye height (h in Fig. 2.4) on a ranging pole which is then placed at point B. Standing at point A and looking down the sighting tube, the cross-wire is seen and is set against the mark on the ranging pole at B. The observer’s line of sight will be A'B', which is parallel to AB.

Fig 2.4 Measuring slope angle with Abney level

To record the slope angleθ, the milled wheel is turned until the image of the bubble appears centrally against the cross-wire when viewed through the sighting tube. A fine adjustment is provided by the slow motion screw. A simple vernier, attached to the milled wheel, is then read with the aid of a small reading glass against the scale attached to the sighting tube. This gives a measure of θ to within 10 minutes of arc.

Worked Example 1:

Calculate the plan length for a measurement of 126.300 m along a gradient of 2° 34′.

Solution 1:

Let θ be the inclination (or slope) angle = 2º 34'

Plan (or Horizontal length) = slope length X cos θ

= 126.300 X cos 2º 34'

= 126.173 m

Worked Example 2:

Calculate the plan length where a distance has been measured along a slope of 1 in 3 and found to be 149.500 m.

Solution 2:

Let θ be the inclination (or slope) angle

For a slope of 1 in 3,

Plan length = slope length=

Questions

1.A horizontal distance of 745.000 m is to be established along a line that slopes at a vertical angle of 5º 10'. What slope distance should be measured off?

2.A distance of 3236.86 ft was measured along a smooth slope. The slope angle was measured and found to be 3º 22'. What is the horizontal distance?

2.2.4 Reduction of Slope Measurements by Difference in Elevation

Measurements made on the slope (L) can be reduced to their corresponding horizontal distances (H) using Pythagoras theorem if the differences in elevation between the two ends of the tape (d) have been measured by levelling.

Worked Example 3:

A distance of 290.430 m was measured along a smooth slope from A to B. The elevations of A and B were measured and found to be 865.2 and 891.4 m, respectively. What is the horizontal distance from A to B?

Solution 3:

Slope distance, L = 290.430 m

Elevation difference, d = 891.4 – 865.2 = 26.2 m

From Pythagoras theorem,

Horizontal distance,

Question

A line measures 1446.25 m along a constant slope. The difference in elevation between the two ends of the line is 57.24 m. Calculate the horizontal length of the line.

2.2.5 Errors in Making Measurements

An error is the difference between a measured value for a quantity and its true value. That is,

, where is the error in a measurement, the measured value, and its true value.

It can be unconditionally stated that:

(i)no measurement is exact;

(ii)every measurement contains errors;

(iii)the true value of a measurement is never known; and therefore

(iv)the exact error present is always unknown

Note that mistakes are observer blunders and are usually caused by a misunderstanding of the problem, carelessness, fatigue, missed communication, or poor judgement. Examples are transposition of numbers such as recording 73.96 as 79.36; failure to include a full tape length. Mistakes can be detected by systematic checking of all work, and eliminated by redoing part of the job or even all of it.

2.2.6 Sources of Error in Making Measurements

There are basically three main sources of error in measurements namely natural, instrumental and personal.

• Natural sources of error are caused by variations in wind, temperature, humidity, atmospheric pressure, atmospheric refraction, gravity, and magnetic declination. An example is a steel tape whose length varies with changes in temperature.
• Instrumental Errors are caused by any imperfection in the construction or adjustment of survey instruments. For example, the graduations on a scale may not be perfectly spaced, or the scale may be warped. The effect of many instrumental errors can be reduced, or even eliminated, by adopting proper surveying procedures or applying computed corrections.
• Personal errors arisefrom the inability of the individual (observer) to make exact observations due to limitations of the human senses of sight and touch. As an example, a small error occurs in the measured value of a horizontal angle if the vertical cross-hair is not aligned perfectly on the target.

2.2.7 Classification of Errors

Errors in measurements are of two classes: Systematic and Random.

2.2.7 (i) Systematic Errors

A systematic error is any biasing effect in the environment, methods of observation or in the measuring instrument which introduces an error into a measurement such that the measured value is either too high or too low.

• Systematic errors are attributable to known circumstances. They could be due to instrumental imperfections or effects of the environment on the measurement.

• They are usually constant (having the same magnitude and sign) throughout an operation.
• Systematic errors which change during a measurement process are termed drifts. Drift is evident if a measurement of a constant quantity is repeated several times and the measurements drift one way during the process, for example if each measurement is higher than the previous measurement which could occur if the instrument becomes warmer during the measuring process.
• They conform to mathematical and physical laws; thus their magnitudes or values could be computed and appropriate corrections (i.e. “negative the error”) can be applied to mitigate them.
• Cumulative observations will increase or propagate the effect of systematic errors.
• Systematic errors can be detected by measuring already known quantities through a process called calibration or by comparing the measurements with ones made using a different instrument known to be more accurate.

The principal systematic errors in linear measurements made with a tape are:

(i)incorrect length of tape;

(ii)tape not horizontal;

(iii)fluctuations in the temperature of the tape;

(iv)incorrect tension or pull;

(v)sag in the tape;

(vi)incorrect alignment; and

(vii)tape not straight

2.2.7 (ii) Random Errors

A random error is the irreproducibility in making repeated/replicate measurements, and it affects the precision of the measured quantity.