Ethiopian Civil Service UniversityCenter for Training and Consultancy

Basic Surveying Training manual

Course title: Basics of Surveying

Course description: This Module aims to cover the knowledge, skills, attitudes and professional

code ethics required to conduct basic land/boundary surveys, make accurate computation, proper field procedures, and keep neat and readable surveying field books.

Objectives: After completing this course, the trainees will be able to

o Explain the comprehensive theories and applications of surveying

o Identify various types of surveys

o Identify type and sources or errors

o Acquire an awareness of the limitations of the basic surveying

instruments and the possible errors that could arise. o Apply geometric and trigonometric principles to basic surveying

calculations. o Keep accurate, legible and complete notes in a well-prepared field

book. o Understand field procedures in basic types of surveys, and the

responsibilities of a surveying teamo Understand the roles and responsibilities of surveying professionals

Course content: To meet the objectives stated above, the course may include, but not limited

to, the following topics:o Introduction

Purpose and importance of surveying Types of surveying Spatial referencing

Coordinate systems Horizontal and vertical datum

Planning surveying activities and resources Supervise surveying activities and team work Survey report writing and documentation

o Theory of Measurements and Errors

Units of measurements Errors: sources and elimination Accuracy and precision Direct and indirect methods of measurements Preparation of field notes and sketching in field works

o Basic Surveying computations

Angles and Directions

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Traversing and traverse computations Resection theory and computations Intersection theory computations Principle of stadia Area, ...

o Roles and responsibilities of land surveyors

The prestige of the survey profession Highest standards of honesty and integrity Surveyor - Client Relationships, ...

Methodology: The course shall be delivered as 70% practical exercise accompanied by

conceptual explanations (30%); where the practical aspect is supposed to be supported by co-operative training in an appropriate company (if applicable) in order to give exposure to the actual world of work and enable the trainees to get hands-on experience.

o A variety of training methods could be used: lectures (presentations),

exercises, a class project, laboratory practice, field practice...

Duration: 36 hrs

Mode of assessment: Practical exercises Project work Group work Individual assignment Theoretical exam/written tests, ...

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One: Basic concepts of surveying 1.1Introduction

Surveying is the science and art of determining the relative positions of various points above on or below the surface of the earth. The relative positions are determined by measuring horizontal distance, vertical distance (elevations), horizontal angles and vertical angles accurately using various surveying instruments. After taking the measurements in the field, computations are done and the plans and the maps are prepared in the office. These plans and maps are used for planning of engineering works, making boundaries, computation of areas and volumes, and various other purposes. Surveying also includes the art of setting out or locating the points on the ground from the plan or map. Surveying although simple in concept, requires great skill and practice for doing the work accurately and economically. It requires basic knowledge of various disciplines such as mathematics, physics, geodesy and astronomy. The need for accurate surveying is increasing rapidly with the development in technology. The construction of modern buildings, highways, railways, high dams, long bridges and tunnels requires accurate surveying is increasing rapidly; high accuracy is also required in making boundary and land sub division surveys.

1.2 History of surveying It is impossible to determine when exactly surveying was first used. Around 1400B.C. the Egyptians first used it to accurately divide land into plots for the purpose of taxation and about120 B.C. Greeks developed the science of geometry and were using it for precise land division. Greeks developed the first piece of surveying equipment and standardized procedures for conducting surveys.

About 1800 A.D. beginning of the industrial revolution, the importance of "exact boundaries" and the demand for public improvements (i.e. railroads, canals, and roads) brought surveying into a prominent position. More accurate instruments for the Science of Geodetic and Plane surveying were developed.

Today surveying affects most everything in our daily lives. A few of the areas where surveying is being used:

To map the earth above and below the sea. Prepare navigational maps (land, air, sea). Establish boundaries of public and private lands. Develop data bases for natural resource management. Development of engineering data for Bridge construction, Roads,

Buildings, Land development.

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1.3. Primary divisions of surveyingPrimary divisions of surveying are made on the basis whether the curvature of the earth is considered or whether the earth is assumed to be a flat plane. The shape of the earth is an oblate spheroid. It is an ellipsoid if revolution, flattened at the poles and bulging at the equator (see figure 1.1). The length of polar axis is about 12713.168km and that of the equatorial axis is about 12756.602km as computed by Clark in 1866. Thus the polar axis is shorter than the equatorial axis by about 43.43km.

Because of the curvature of the earth’s surface the measured distances on the earth are actually curved. However, when the distances are small, compared with the radius of the earth, there is no significant difference between the curved distances and the corresponding straight line distances and the curvature of the earth can be neglected. Primarily surveying is divided in to two types: Plane Surveying and Geodetic Surveying.1. Plane SurveyingIt is the type of surveying in which the curvature of the earth is neglected and it is assumed to be a flat surface. All distances and horizontal angles are assumed to be projected upon to a horizontal plane. A horizontal plane at a point is the plane which is perpendicular to the vertical line at that point and assumes that the survey area is a flat plane. Generally covers small areas (less than 300 sq. mi.)It is themost common method used.

Plane surveying can safely be used when one is concerned with small portions of the earth’s surface. It is worth nothing that the difference between an arc distance of 18.5 km on the surface of the earth and the corresponding chord distance is less than 10mm. Further the difference between the sum of the angles of a spherical triangle having an area of 200sq.km on the earth’s surface and that of the corresponding angles of the plane triangle is only 1 second. In plane surveying the angles of polygons and triangles are considered as plane angles.

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2. Geodetic SurveyingIt is the type of surveying in which the curvature of the earth is taken in to consideration, and a very high standard of accuracy is maintained. The main object of geodetic surveying is to determine the precise location of a system of widely spaced points on the surface of the earth. It takes into account the theoretical shape of the earth. Generally high in accuracy, and covers large areas greater than 300 sq. mi.In geodetic surveying, the earth’s major and minor axis is computed accurately and a spheroid of reference is visualized. The spheroid is a mathematical surface obtained by revolving an ellipse about the earth’s polar axis. The earth’s mean sea level surface, which is perpendicular to the direction of gravity at every point, is represented by a geoids. Because of variation in the earth’s mass distribution the surface of the geoids is irregular. However, if the irregularity of the surface are neglected the geoids can be very closely approximated as spheroid. The dimension of the spheroid is selected so as to give a good fit to the geoids over large area.

1.4 Functional classifications of surveying Based on the purpose for which they are conducted, surveys may be classified in the following types;

1. Control surveying : it consists of establishing the horizontal and vertical positions of widely spaced control points using principles of geodetic surveying.

2. Land surveying : land surveys are conducted to determine the boundaries and areas of tracts of land. These are the oldest types, as land surveys have been used since the early civilization. These are also known as property surveys, Boundary surveys or Cadastral surveys. These surveys are also used to provide data for making a plan of the area.

3. City surveys : These surveys are conducted within the limit of a city for urban planning. They are required for the purpose of layout of streets, buildings, pipes, sewers etc.

4. Topographical surveys : topography is defined as the shape or configuration of the earth’s surface. These surveys are required to establish horizontal locations of the various points as well as their vertical locations. Information pertaining to relief and undulations on the earth’s surface is generally shown in the form of contours of equal elevations.

5. Route surveying : These surveys are especial type of surveys conducted along a proposed route for highway, railway, sewer line etc. Route survey is done along a wide strip. In general route surveying also includes the staking out and calculation of the earth work.

6. Engineering surveys : these are conducted to collect data for the designing and planning of engineering works such as building, roads, bridges, dams, reservoirs, sewers and water supply lines. These surveys generally include the surveys mentioned above.

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7. Construction Surveys : All the above mentioned surveys are conducted to obtain information required for preparation of maps, plans, sections, etc. After the plans have been prepared and the structures designed, the construction Survey is conducted. The points and lines are established on the ground and the lay out plan of the structure is marked on the ground.

1.5. Classification of Surveying based on instruments usedBased on instruments used, the surveys can be classified as under:

1. Leveling : This a type of survey in which a leveling instrument is used for determination of relative elevations (levels) of various points in the vertical plane

2. Theodolite surveying : A theodolite is a very precise instrument for measuring horizontal and vertical angles. The theodolite survey can be broadly classified in to two types; Traverse and Triangulation.

3. Tachometric surveying ; a tachometer is a special type of theodolite that is fitted with a stadia diaphragm having horizontal cross hairs in addition to the central horizontal hair. In tachometric surveying horizontal angles, horizontal distances and elevations are measured with a tachometer.

4. Photogrammetric surveying : Photogrammetry is a science of taking measurements with the help of photographs. Photogrammetric surveys are generally used for topographic mapping of vast areas.

5. EDM surveying : is an electronic distance measurement, used to carry our surveys of large measurement which requires high precession.

1.6. Basic measurements in surveying Basically surveying consists of the following four measurements.

1. Horizontal distance: a distance measured in a horizontal plane. If a distance is measured along a slope, it is reduced to its horizontal equivalent.

2. Vertical distance: a distance measured along the direction of gravity at that point. The vertical distances are measured to determine the difference in elevations (height) of the various points.

3. Horizontal Angle: an angle measured between two lines in a plane that is horizontal at that point.

4. Vertical Angle: an angle measured between two lines in a plane that is vertical at a point.

1.7. Units of measurementsThere are two systems of measurements:

1. M.K.S(meter, kilogram, second) Metric system(SI = System International)2. F.P.S (foot ,pound, second) British System

A) The SI unit of length is the base unit meter (m)1decameter =101 = 1dam1 hectometer = 102m=1hm1kilometer = 103m=1Km1Megameter = 106m=1Mm1gigameter=109m=1Gm

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1Terameter=1012m=1Tm1Decimeter=10-1m=1dm1centimeter=10-2m=1cm1milimeter=10-3m=1mm1micrometer=10-6m=1µm1nanometer=10-9m=1nm1picometer=10-12m=1pm

B) The SI unit for aria is derived units square meter (m 2 ) 1 hectare=104m2=100m*100m=1ha 1square Kilometer=106m2=1000m*1000m=1Km2=100ha

C) The SI unit for volume is the derived unit cubic meter (m 3 ) 1000cubic millimeter =1cubic centimeter 1000cubic centimeters = 1 cubic decimeter 1000cubic decimeter = 1 cubic meter

D) The SI units of plane angles There are three systems for angular unit, namely sexagesimal graduation, centesimal graduation and radian:1. Radian: the radian (rad) is the basic unit of measurement of angles. The radian is defined as that angle where the ratio between the arc length L and the radius R of the circle equals l (see figure 1.2). We are talking about a full circle; if the arc length equals the circumference, in a unit circle with the radius 1 the full circle equals 2∏rad.

figure 1.22. Sexagesimal graduation*The circle is divided in to 360 parts.1 full circle = 3600(degrees)10 = 1/360 full circle = 2∏/360rad = ∏/180 rad10 = 60’ (minutes) 1’ = 60”(seconds)3. Centesimal graduation *The circle is divided in to 400 parts.1 full circle = 400gon1 gon = 1/400 full circle = 2∏/400rad = ∏/200 rad

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1 gon = 100cgon (centigon)1cgon = 10 mgon (milligon)1mgon = 10cc (centi centigon)1.8. ScaleScale of a map is the ratio of the distance marked on the map to the corresponding distance on the ground. Scales of a map are generally classified as large, medium and small. A large scale map shows the feature in a bigger size then a small scale map. Large denominator numbers refer to small scale, where as small denominator numbers are indicative of large scale.

Large scale 1:1,000Medium scale 1:1,000 to 1:10,000Small scale 1:10,000 or more

1.9 Representation of scaleThe following three methods are used to represent the scale of a map.1. by statement (engineer’s scale): According to this scale, a specified distance on the map represents the corresponding distance on the ground.For example: 1 cm = 50 meter that means 1 cm on the map represents 50 m on the ground2. By representative fraction (RF): It is the ratio between the distance on the map (plan) and the distance on the ground.RF = dm with

dm = map distance and da = actual distance

da * the unit in the numerator and denominator must be the same

For example: 1: 5000 or 1 / 5000, that means 1cm on the map represents 5000 cm (50 m) on the ground.3. By graphical scale: A graphical scale is a line drawn on the map so that its map distance corresponds to a convenient unit of length on the ground. For example: Scale 1: 1000

i.e. 1 cm on the map represents 10 m on the ground

Figure 1.3 1.10 Difference between a plan and a map A plan graphically represents the features on or near the earth’s surface as projected on a horizontal plan. If the scale of the graphical projection on a horizontal plane is small the plan is termed map. In addition a map generally shows some additional features, such as relief, hachure, or contour lines to indicate undulation on the ground.

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1.11 Duties of a surveyorPrimarily the surveyor should have full information about his/her duty, the project, its objective and in what scale to do.In general, any kind of surveying can be performed in the following six duties; 1. Research, analysis, and decision making i.e. selecting the survey methods, equipment performing reconnaissance survey of the site and so on. 2. Field work (Data acquisition) i.e. Making Measurements and recording data in the field. While recording data field books or field notes are very essential. Field books are required by the surveyor in order to record the surveyors’ notes by means of sketches and measurements, in general the work done in the field. They are valuable documents because the time and expense in obtaining such data. No parts of the operation of surveying is greater important than the field notes. The following points are considered in appraising a set of field notes: - 3. Computing (Data processing) i.e performing calculations based on the recorded data to determine locations areas, volumes and so on. 4. Mapping (Data representation) i.e. plotting measurements or computed values to prepare maps, plans or charts or portraying the data in a numerical or computer format. 5. Stake-out or marking (placement of monuments) i.e. to delineate boundaries or pages to guide construction operations.6. Reporting i.e. preparing a concise written report forms, logical conclusions over the entire surveying task.

1.12 Types of Errors in measurementsThe value of a measurement obtained in the field is never exactly true value with the exception of by chance. The measured value approaches the True value as the number and size of errors in the measurements become increasingly small.Every measurement contains an error, since no measurement is exact. The surveyor’s task is to keep errors in measurement with in prescribed limits. In order to do so, he/she must know source of errors, types of errors, the effects of errors and how to evaluate his/her results.There are three basic types of errors. These are; 1. Mistakes (Gross errors) 2. Systematic errors 3. Accidental errors1. Mistakes (Gross errors) These are serious mistakes and occur when the surveyor blunders through lack of experience and lack of care. The effects are unpredictable and often large. Field works

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should be free from mistakes before calculations and plotting are carried out. Common examples are:; - Incorrect booking of measurements E.g. writing 2.324m instead of 2.34 m- Incorrect reading of the measurement E.g Reading 5.655 instead of 15.655- Interchanging the figures - 3.24 instead of 2.34Miscounting the number or reputations of measurementMistakes can be eliminated only by proper and careful methods of observing & booking and constantly checking both operations.

1. Systematic (cumulative ) errorsThese are constant errors, which can be calculated and so corrected. Cumulative errors are constant errors when predictable variations in equipments performance occur, or when conditions result in the measurement mode being different from the measurement required, systematic errors are occurred.

3. Accidental (Random) ErrorsThese errors are remaining after mistakes & systematic errors have been eliminated. They are caused by factors beyond the control of the surveyor.

1.13 Source of ErrorsThe source of errors is fall into three groups:1. Natural errors Curative; refraction; strong winds; Temperatures variations loose muddy and swampy areas2. Instrumental errorsSag; Vertical and horizontal Axis; lateral and collimation error; plate level test; cross hair ring Test; collimation in azimuth test; vertical circle; Index Test.3. Personal ErrorsMistakes in reading and recording, focusing, setting up, holding staffs

1.14 Accuracy & PrecisionSince surveying is after all a measurement science, it is necessary to distinguish the two terms: Accuracy & Precision, which if not understood, cause unnecessary confusion.Accuracy: The accuracy of a measurement is an indication of how close it is to true value of the quantity that has been measured; the closer the measured value to the true value the smaller the error.Precision: the precision of a measurement has to do with the refinement used in taking the measurement, the quality (but not necessarily the accuracy) of an instrument, and the repeatability of the measurement, and the finest or least count of the measuring devices. It refers to the fines of measurements. Accuracy – Result - to be right Precision – method to - get right

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Bearing in mind the purpose for which the survey is being made, it is better to achieve a high degree of accuracy than to aim for precision (exactness).

2.0. Linear measurement2.1. IntroductionMeasurement of horizontal distance is probably the most basic operation performed in surveying. The horizontal distance between the two points is the distance between the plumb lines through the points. There are various methods of making linear measurements and their relative merit depends upon the degree of precision required.

Figure 2:1 linear measurement

2.2. Methods of making linear measurements1) Direct means of distance measurement

2) Indirect means of distance measurement

In the case of direct measurements, distances are actually measured on the ground with the help of a chain or a tape or any other instrument. In the optical methods, observations are taken through a telescope and calculations are done for the distances, such as in tachometry and triangulation. In the electro-magnetic method, distances are measured with instruments that rely on propagation, reflection and subsequent reception of radio waves, light waves or infrared waves.

Various methods of measuring the distances directly are as follows: Pacing, passometer, Pedometer, odometer, measuring wheel and tapping.

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Figure 2:2 measuring wheel.

2.3. TappingChaining or Taping: Chaining is a term which is used to denote measuring distance either with the help of chain or a tape and is the more accurate method than the above mentioned methods, for making direct measurements.

figure 2:3 different types of tapes

2.4. Accessories for tapingIn addition to the tape, accessories e.g., pegs, arrows, ranging rods, offset rods; plumb bobs are required for chaining operations.

1. Pegs: These are used to mark the definite points on the ground either temporarily or semi permanently. Wooden pegs, iron/tubular pegs and concrete pegs are generally used.

2. Arrows: These are the chaining pins which are used to mark the end of each chain during the chaining process. These are made of hardened and tempered steel wire 4mm in diameter. The length of an arrow is kept at 400mm. These are pointed at one end where as a circular ring is formed at it’s other end.

3. Ranging rods: These are also known as flag poles or lining rods. These are made of

Well seasoned straight grain timber of teak, deodar etc, or steel tubular rods. These

are figure: 2:4 ranging pole (ranging road)

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Used for marking a point in such a way that the position of the point can be clearly and exactly seen from some distance away. These are 30mm diameter and 2-3 M long. Sometimes, these rods are used as signals to indicate the locations of points or the directions of line.

4. Plumb bobs: The plumb bob plays a very important role in surveying. As a freely suspended plumb bob always points towards the gravity, it indicates the direction of the vertical line. In linear measurements plumb bobs are used for measuring distances on sloping ground. It is made of steel in a conical shape, and is used while measuring, distances in slopes, with all instruments that require centering.

Figure 2:5 Plumb bob

5. Offset rods: It is similar to ranging rods except at the top one recessed hook is provided. It is mainly used to align the offset line and measuring short offsets.

6. Clinometers: It is an instrument used for measuring the angle of slope.

7. Line ranger: It is a small instrument used to establish intermediate points between two distant points on a chain line without the necessity of sighting from one of them.

8. Cross staff: It is essentially an instrument used for setting out right angles.

9. Optical square: This is a compact hand instrument to set out right angles and superior to a cross staff.

Figure 2:6 optical squares

10. Prism square: It is based on the same principle as the optical square and is used in the same manner. It has an advantage over the optical square in that no adjustment is required, since the angle between the reflecting surfaces of prism is kept at 450

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2.5. Taping over Level GroundIf Taping is done on fairly smooth and level ground where there is little underbrush the tape can rest on the ground. The taping party consists of the head tape man and the rear tape man. The head tape man leaves one taping pin with the rear tape man for counting purposes and perhaps to mark the starting point. The head tape man takes the zero end of the tape and walks down the line toward the other end.

When the 50 - m end the tape reaches the rear tape man, the rear tape man calls “ tape” or “chain” to stop the head tape man. The rear tape man holds the 50 – m mark at the starting point and aligns the head tape man ( using hand and perhaps voice signals) on the range pole which has been set behind the ending point. Ordinarily, this “eyes ball” alignment of the tape is satisfactory, but use of the transit is safer and will result in better precision. Sometime there are places along a line where the tape man cannot see the end point and there may be positions where they cannot see the signals of the instrument man. For such cases it is necessary to set intermediate line points before the taping can be started.

It is necessary to pull the tape firmly. This can be done by wrapping the leather thong at the end of the tape around the hand or by holding a taping pin that has been slipped through the eye at the end of the tape, or by using a clamp. When the rear tape man has the 50 – m mark at the starting point and has satisfactorily aligned the head tape man, he or she calls “ all right” or some other such signal. The head tape man pulls the tape tightly and sticks a taping pin in the ground at right angles to the tape down to the pavement or the point may be marked with a colored lumber crayon, called keel.

The rear tape man picks up a taping pin and the head tape man pulls the tape down the line, and process is repeated for the next 50 m. It will be noticed that the number of hundreds of feet which have been measured at any time equals the number of taping pins that the rear tape man has in his or her possession. After 500 m has been measured, the head tape man will have used his eleventh pin and he calls “ tally “ or some equivalent word so that the rear tape man will return the taping pins and they can start on the next 500 ms.

When the end of the line is reached, the distance from the last taping pin to the end point will normally be a fractional part of the tape. For older tapes, the first meter of the tape (from 0 to 1m) is usually divided into tenths, as shown in figure 2:6 below. The head tape man holds this part of the tape over the end point while the rear tape man moves the tapes backward or forward until he has a full foot mark at the taping pin.

The rear tape man reads and calls out the foot mark, say 72 m and the head tape man reads from the tape end the number of tenths and perhaps estimates to the nearest hundredth, say 0.46, and calls this out. This value is subtracted from 72 m to give 71. 54 m and the number of hundreds of meters measured before is added. These numbers

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and the subtraction should be called out so that the math can be checked by each partner.

For the newer steel tapes with the extra divided meter, the procedure is almost identical except that the rear tape man would for example just described, hold the 71 m mark at the taping pin in the ground. He or she would call out 71 and the head tape man would read and call out plus 54 hundredths, giving the same total of 71.54 ms.

A comment seems warranted here about practical significant figures as they apply to taping. If ordinary taping is being done and the total distance obtained for this line is 2771.34 ms the 4 at the end is ridiculous and the distance should be recorded as 2771.3 or even 2771 ms because the work is just not done that precisely.

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Figure 2:6 tape reading

2.6. Taping along sloping ground or over underbrush When sloping distances are to be measured, there are three taping methods that can be used:

The tape may be horizontally The tape may be held along the slope: the slope determined and a correction

made to obtain the horizontal distance The sloping distance may be taped: A vertical angle measured for each slope,

and the horizontal distance later computed. The latter method is sometime referred to as dynamic taping. Description of each of these methods follows.

Holding the tape horizontally: Ideally, the tape should be supported for its full length on level ground or pavement. Unfortunately, such convenient conditions are often not available because the terrain being measured may be rough and covered with underbrush. For sloping, uneven ground or areas with much underbrush, taping is handled in a similar manner to tapping over level ground. The tape is held horizontally, but one or both tape man must be use a plumb bob as shown in figure below.If tapping is being done uphill, the rear tape man will have to hold his or her plumb over the last taping pin, while the head tape man may be able to hold his or her end on the ground Fig a). If they are moving downhill is preferable to taping uphill, If the measurement is over uneven ground or ground where there is considerable underbrush, both tape man may very well have to use plumb bobs as they hold their respective ends of the tape above the ground (see fig below).

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Figure 2:7 holding tapes horizontally

Considerable practice is required for a person to be able to do precise taping in rolling or hilly country. Although for many surveys the tape men may estimate the horizontal by eye, it pays to use a hand level for this purpose. Where there are steep slopes, it is difficult to estimate by eye when the tape is horizontal because the common tendency is for the downhill person to hold his or her end much too low, causing significant error. If a precision of better than approximately 1: 2 500 or 1: 3000 is desired in rolling country, holding the tape horizontally by estimation will not be sufficient.

Another problem in holding the tape above the ground is the error caused by sagging of the tape, both of these error (tape not horizontal and sag ) will cause the surveyor to get too much distance. In other words, either it takes more tape lengths to cover a certain distance or the surveyor does not move forward a full 50 ms each time he or she uses the tape.

If the slope is less than approximately 5 % (a height above the ground at which the average tape man can comfortably hold the tape), the tape men can measure a full 30 ms tape length at a time. If they are tapping downhill, the head tape man holds the plumb – bob string at the 0 end of the tape with the plumb – bob a few cm above the ground. When the rear tape man is ready at his or her end, the head tape man is lined up on the distance point, and when the tape is horizontal and pulled to the desired tension, the head tape man lets the plumb – bob fall to the ground and sets a taping pin at the point.

For slopes greater than approximately 5%, the tape man will be able to hold horizontally only parts of the tape at a time. Holding the tape more than 1,5 meters above the ground is difficult. And wind can make it more so. If the tape is held at height of 1.5 m or less above the ground both forearms can be braced against the body and the tape can easily be pulled firmly without swaying and jerking.

Assuming that are proceeding downhill, the head tape man pulls the tape along the line for its full length and then, leaving the tape on the ground, returns as far along the tape as necessary for them to hold horizontally the part of the tape from his or her point to the rear tape man.

The head tape man holds the plumb bob string over a whole foot mark, and when the tape is stretched, lined and horizontal, lets the plumb bob fall and sets a taping pin. He or she holds the intermediate foot mark on the tape until the rear tape man arrives, at which time he or she hands the tape to the rear tape man with the foot mark that he or she has been holding. This careful procedure is followed because it is so easy for the head tape man to forget which foot he or she was holding if he or she drops it and walks ahead. The tape man repeat this process for as much more o the tape as they can hold horizontally until they reach the 0 – end of the tape.

This process of measuring with sections of the tape is referred to as breaking tape or breaking chain. If the head tape man follows the customary procedure of leaving a

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taping pin at each of the positions that he or she occupies when breaking tape, counting the number of hundreds of meters taped (as represented by the number of pins in the possession of the rear tape man) would be confusing. There, at each intermediate point the head tape man sets a pin in the ground and then takes one pin from the rear tape man. Instead of breaking tape, some surveyors find it convenient to record the partial tape lengths in their notes.

It is probably wise for beginners to measure a few distances on slopes of different percentages holding the tape horizontally and then again with the tape along the slopes with no correction made. These measurements should give him or her feeling for the magnitude of slope errors.

2.7. Taping on Slopes and Making Slope correction Occasionally, it may be more convenient or more efficient to tape along sloping ground with the tape held inclined along the slope. This procedure has long been common for underground mine survey but to a much lesser extent for surface surveys. Slope taping is quicker than horizontal taping and is considerably more precise because it eliminates plumbing with its consequent accidental errors. Taping along slopes is sometime useful when the surveyor is working along fairly smooth slopes or when he wants to improve precision. Nevertheless, the method is generally not used because of the problem of correcting slope distances to horizontal values. This is particularly true in rough terrain where slopes are constantly varying and the problem of determining the magnitude of the slope is difficult.

In some cases it may be impossible to hold the entire tape (or even a small part of it) horizontally. This may occur when tapping is being done across a ravine (see figure below) or some other obstacle where one tape man is much lower than the other one and where it is not feasible to “break tape”. Here it may be practical to hold both ends of the tape on the ground.

Figure 2:8 tapping over sloping ground

Once the slope distance is determined, they are corrected by means of the formula. To be able to use the formula it is necessary to obtain the values of the slope of the tape measurement. It is usually convenient to do this by determining elevation difference at the ends of the tape.

H = √s2 + v2 H = Tan∞ x s where: H = Horizontal distance

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Tape

S= slope distance

V = vertical distance

V= elevation B – elevation A

∞ = vertical angle

The slope distance can be correction by applying the formula:

H = S – C where C = V 2

2(S) L = the tape length

The Abney hand level or clinometers (Fig below) has an arc with vertical angles can be read from 00 to 900 with a vernier angle readings can be taken to approximately the nearest 10’, in addition slope values(ratio of vertical distances to horizontal distances) from 1:1 to 1:10 can be read. These devices are just about obsolete, nowadays the surveyor uses to carry over the slope distance to horizontal distance knowing the elevation of both ending points of the line by leveling procedures and the vertical angle is reached by mean of theodolite.

Dynamic Taping

With this method, which is very similar to the slope taping method, slope distances are measured. Then a transit or theodolite is set up at taping point and the vertical angle is measured to the next taping point and the horizontal distance is computed

2.8. Taping corrections (Corrections applied to the measured length by tape)Steel tapes are calibrated under a specific temperature and tension. Change in temperature, tension and mode of support affect the result of taping. The errors caused by these sources behave according physical laws and can be expressed with mathematic expressions. They are systematic errors.

V

H

S

A

B

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1 Correction for standard: A steel tape will normally be provided with standardizing data, for example it may be designated as 30m long under a tension of 50N at a temperature of

20 C when laid on the flat. With use the tape may stretch and it is imperative that the tape is regularly checked against a reference tape kept specifically for this purpose.

2 Correction for tension (Pull correction): Since a steel tape is elastic to a small extends it length is changed by variation in the tension applied. The correction, which should be applied, is

Where: P = the tension applied in the field.

Ps = the standard/ calibration tension

A = the cross sectional area of the tape.

E = Young’s modulus for the tape material (N/ mm2)

L = the observed length.

Note: The sign of the correction takes that of quantity (P-Ps)

To apply this correction a tension handle is needed.

3. Correction for sag: A tape supported only at the ends will sag in the centre by an amount that is related to its weight and the pull (tension). In the case of a long tape intermediate supports can be used to reduce the magnitude of the correction.

The correction that is applied reduces the curved length to the chord length.

Where: w = the weight of the tape per unit length

L = the observed length

P = the tension applied in the field.

Note: If the tape in used on a plane surface, which can be considered, flat then no correction is applicable.

To apply this correction a tension handle is needed.

21

4. Correction for temperature: If a tape is used at a field temperature different from the standardization temperature then the correction is:

Where = the coefficient of thermal expansion of the tape material

Steel: 0.0000115 m/(m C)

Invar: 0.000001 m/(m C)

t = the field temperature

ts = the standardization temperature

Note: The sign of the correction takes the sign of (t- ts).

To apply this correction a thermometer is needed.

5 Correction for slope: In surveying it is essential that horizontal lengths are determined. When a distance lies along a uniform slope and when the difference in height between the two end points has been determined it may be preferable to measure the distance directly (see also figure below).

Afterwards the horizontal distance can be computed by applying the following correction:

Where: h = the difference in height between the end points

s = the measured slope distance

22

6. Correction to mean sea level: In the case of long lines the relationship between the length measured on the ground and the equivalent length at mean sea level has to be considered.

If the measured length is Lm and the height of the line above datum is H then the correction to be applied is

Example:

3. LEVELLING3.1 LevelingLeveling is an operation in surveying performed to determine the difference in levels of two points.

By this operation the height of a point from a datum, known as elevation, is determined.

The most commonly used datum is the mean sea level (M.S.L)

An instrument used for taking readings for determining elevation is called Level

23

Levelling is an important method of surveying for many engineering works and construction projects; like highways, railways, and canals e.t.c. and for locating the gradient lines.

3.2. Basic Terms used levelling1. Datum (Datum Plane): is the point or a plane with reference to which levels

of other points or planes are calculated.2. Bench Mark (B.M): is a relative permanent and fixed reference point of

known elevation, and after elevation are determined from it. 3. Instrument Station (I.S): is the place where the instrument is set up for

observation.4. Staff Station: is the place where the levelling staff is held vertically for taking

readings.5. Line of Sight (Line of collimation): is the line joining the intersection of cross

hairs.6. Height of instrument (H.I): is the elevation of the line of sight with respect to

the datum; not above the ground where the levelling instrument is set up. 7. Height of Collimation (H.C): is the vertical distance from the datum to the

line of sight of the instrument.8. Back Sight (B.S): is the staff reading taken on a staff held at a point of known

elevation or at bench marks or at a point whose elevation has already been determined.The back sight is usually the first reading taken immediately after the instrument is set up.

9. Fore Sight (F.S): is the reading taken on the staff either held at last point whose elevation is required or held at the turning point just before shifting the instrument.

10. Intermediate Sight (I.S): is the reading taken on the staff held at a point whose elevations are required; but not a turning point or last point. i.e. other than B.S and F.S.

11. Turning Point (Changing point) (T.P or C.P): is a point selected on the route where back sight and for sight reading is taken before shifting the instrument.

12. Balancing of Sight: to reduce the effect of instrumental and other errors ,the distance of the point where the back sight is taken and the distance of the point where the fore sight is taken as measured from the instrument station’ should be approximately equal. This is known as Balancing of sight.

13. Reduced level (R.L): is the level of various points as heights above the datum surface or it is a height of points stated with reference to the selected datum for the work in hand.

14. Level Surface: is a curved surface which is perpendicular to the plumb line or the direction of gravity.

15. Horizontal Surface: is any surface that is tangent to the level surface at a given point and perpendicular to the vertical line.

16. Horizontal Line: is a line in a horizontal plane or perpendicular to the vertical line.

17. Vertical Line: is a line that follows the direction of gravity.

24

3.3. Parts of a level

Figure 3.1-parts of a level

3.4. Accessories of Level A. Leveling Rods (Leveling Staff)

Leveling Rods are used to measure the vertical distance between a line of sight and a survey point and a height different between two points.

25

B. Tripod

A tripod is a three- legged stand used to support a level or other surveying instrument during field measurements. There are two models of tripods: the extension leg tripod and the fixed leg tripod.

3.5 Setting up levelling instrumentsProcedures;

I. Set up the tripod at a convenient height and spread the legs then press the tripod feet firmly into the ground. The tripod head should be approximately horizontal.

II. ii. Fix the level instrument on the tripod.III. iii. Level the instrument with the foot screws until the circular bubble is in the

centre. IV. iv. Focus the eyepiece until the cross hairs appear sharp and clear, then point

the telescope towards the object (staff) and focus until you see clearly the graduation of the staff.

3.6 Booking and Reducing the LevelsFor booking and reducing the levels of points, there are two systems, namely the height of instrument or height of collimation method and rise and fall method.

The columns for booking the readings in a level book are same for both the methods but for reducing the levels, the number of additional columns depends upon the method of reducing the levels. Note that except for the change point, each staff reading is written on a separate line so that each staff position has its unique reduced level. This remains true at the change point since the staff does not move and the back sight from a forward instrument station is taken at the same staff position where the fore sight has been taken from the backward instrument station. To explain the booking and reducing levels, the leveling operation from stations A to C shown in Fig. 3.4, has been presented in Tables 3.1 and 3.2 for both the methods. These tables may have additional columns for showing chainage, embankment, cutting, etc., if required In reducing the levels for various points by the

Height of Collimation method,

The height of collimation (H.C.) for the each section highlighted by different shades is determined by adding the elevation of the point to the back sight reading taken at that point. The H.C. remains unchanged for all the staff readings taken within that section and therefore, the levels of all the points lying in that section are reduced by

26

subtracting the corresponding staff readings, i.e., I.S. or F.S., from the H.C. of that section.

Table 3.1 Height of instrument method

Station BS IS FS HC RL Remark

A S1 H.I.A=ha+s1 Ha B.M. = hA

a S2 ha = H.I.A – S2

b S3 hb = H.I.A – S3

B S5 S4 H.I.B = hB +S4

hB = H.I.A – S4 C.P

c S6 hC=H.I.B –S6

C S7 H.I.C=hC+S7 hC= H.I.C – S7

Σ B.S. ΣF.S.

Check: Σ B.S. – Σ F.S. = Last R.L. – First R.L.

In the rise and fall method, the rises and the falls are found out for the points lying within each section. Adding or subtracting the rise or fall to or from the reduced level of the backward station obtains the level for a forward station. In Table 3.2, r and f indicate the rise and the fall, respectively, assumed between the consecutive points.

Table 3.2 Rise and fall method

Station BS IS FS Rise Fall RL Remark

A S1 Ha B.M. = hA

a S2 r1=S1-S2 ha = hA + r1

27

b S3 f1 = S2 – S3 hb = ha – f1

B S5 S4 f2 = S3 – S4 hB = hb – f2 C.P

c S6 f3 = S5 – S6 hc = hB – f3

C S7 r2= S6 -S7 HC = hc + r2

Σ B.S Σ F.S Σ Rise Σ Fall

Check: Σ B.S. − Σ F.S. = Σ Rise − Σ Fall = Last R.L. − First R.L.

The arithmetic involved in reduction of the levels is used as check on the computations. The following rules are used in the two methods of reduction of levels.

(a) For the height of instrument method

(i) Σ B.S. – Σ F.S. = Last R.L. – First R.L.

(ii) Σ [H.I. . (No. of I.S.’s + 1)] – Σ I.S. – Σ F.S. = Σ R.L. – First R.L.

(b) For the rise and fall method

Σ B.S. – Σ F.S. = Σ Rise – Σ Fall = Last R.L. – First R.L.

3.7 COMPARISON OF METHODS AND THEIR USESLess arithmetic is involved in the reduction of levels with the height of instrument method than with the rise and fall method, in particular when large numbers of intermediate sights is involved.

Moreover, the rise and fall method gives an arithmetic check on all the levels reduced, i.e., including the points where the intermediate sights have been taken, whereas in the height of instrument method, the check is on the levels reduced at the change points only. In the height of instrument method the check on all the sights is available only using the second formula that is not as simple as the first one.

The height of instrument method involves less computation in reducing the levels when there are large numbers of intermediate sights and thus it is faster than the rise and fall method. The rise and fall method, therefore, should be employed only when a very few or no intermediate sights are taken in the whole leveling operation. In such case, frequent change of instrument position requires determination of the height of instrument for the each setting of the instrument and, therefore, computations involved in the height of instrument method may be more or less equal to that required in the rise and fall method. On the other hand, it has a disadvantage of not having check on the intermediate sights, if any, unless the second check is applied.

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4. ANGLES AND DIRECTIONSIn general surveying is used to determine relative positions of existing points and to establish predefined locations on or near the surface of the earth. These purposes are achieved by distance, angle and directions. In this chapter the equipment and methods of angle and direction measurement will be discussed.

4.1 Definitions Meridian: is a fixed line of reference used for defining directions of lines. The

meridian can be assumed, magnetic, grid or true meridian.

Bearing: is horizontal angle between meridian and survey line. It is defined by the quadrant in which the surveys line lies and the acute angle between it and the meridian.

Bearings of the survey lines:

OA N 450 E

OB S 200 E

OC S 650 W

OD N 600 W

Fig. 4.1 Bearings of lines

Azimuth: the horizontal angle between the meridian (usually north branch) and a survey line measured in the clockwise direction is called azimuth. The value of azimuth varies from 00 to 3600.

Azimuths of the lines

OA 450

29

N

EW

S

45 0

20 0

65 0

60 0

O

A

B

C

D

N

EW

S

45 0

20 0

65 0

60 0

O

A

B

C

D

OB 1600

OC 2450

OD 3000

Fig. 4.2 Azimuths of lines

The azimuth of a line can be forward or back azimuth.

Forward azimuth of OA = 450

Back azimuth of OA = 2250

Fig. 4.3 Forward and back azimuths

In general the following relationships hold between forward and back azimuths.

Back azimuth = forward azimuth 1800, + if forward azimuth < 1800

- if forward azimuth > 1800

Interior angles: are angles between adjacent lines of a closed polygon measured from the inside. The sum of interior angles of a closed polygon is equal to: (n-2)(1800), where n = number of sides of the polygon.

30

45 0

225 0

N

N

O

A

95 0

110 0

127 0

115 0

93 0

A

B

C

D

E

Σ interior angles = (n-2)(1800)

= (5-2)(1800)

= 5400

A + B + C + D + E = 1100+950+930+1150+1270

= 5400

Fig 4.4 Interior angles

Deflection angle: is horizontal angle measured between a line and the prolongation of the preceding line. The direction of the deflection should also be indicated as Left (L) or Right (R) from the preceding line.

Fig. 4.5 Deflection angles

Angle to the right: is angle measured from the preceding line to the following line in the clockwise direction.

Fig. 4.6 Angle to the right

Angle to the left: is angle measured from the preceding line to the following line in the anticlockwise direction.

4.2 Angle and Direction Measuring Equipment

31

25 L0

30 R0

A

B

C

D

145 0

230 0

A

B

C

D

Directions and angles are commonly measured by magnetic compass, theodolite or total station. Magnetic compass directly gives the direction of a line with reference to the magnetic north. Due to errors caused mainly by undetected deviation of the compass needle from the actual magnetic meridian, the use of magnetic compass is limited to rough survey works.

A theodolite is commonly used to measure horizontal and vertical angles to the nearest minute of arc. Total stations are capable of measuring both angles and distances digitally. Their precision varies from 1 to 20 seconds of arc.

1.3 Measurement of horizontal angles

After having performed temporary adjustments properly, the horizontal angle between two directions from a station can be computed as the difference between the corresponding horizontal circle readings. It is of normal practice to take circle readings with the theodolite in two positions: face left (the vertical circle is on the observer’s left as the target is sighted) and face right (the vertical circle is on the observer’s right as the target is sighted). Horizontal angles could be measured in two ways: Reiteration method and Repetition method.

Error in horizontal angle from maladjustment of vertical axis

For the vertical axis to be truly vertical, the plate level bubble must remain central for all positions of the theodolite. The error in horizontal angle measurement due to this maladjustment is not serious and as such, in most cases, can be ignored. The error becomes appreciable for large vertical angles. There is no observational procedure that can be employed to eliminate this error. Error in horizontal angle due to maladjustment of the line of collimation

If the line of collimation (the line joining the optical centre of the object glass to the vertical cross-hair of the diaphragm) is not perpendicular to the horizontal axis, error will be introduced in the measured angles. The error becomes appreciable when the telescope is reversed between back sight and foresight observations. If the telescope is not reversed between back sight and foresight when taking readings, no error is introduced if these distances are equal and the inclination of the line of sight is the same for both the back sight and foresight. Error due to this maladjustment can be eliminated by taking the mean of face left and face right measurements.

Error in horizontal angle when the horizontal axis is not perpendicular to the vertical axis

32

If the points sighted are at the same angle of inclination of the line of sight, no error is introduced in horizontal angles. If the points are sighted with different line of sight inclinations, error will be introduced in the measured horizontal angles. The error can be eliminated by taking the mean of face left and face right observations.

Error in vertical angle due to maladjustment of the theodolite

In a perfectly adjusted theodolite, the index for vertical circle reading should read 00 or 900 when the telescope is in the horizontal position. If this is not the case, error will be introduced in the readings. Any error in observed vertical angles due to imperfect adjustment of the theodolite can be eliminated by taking the mean of face left and face right observations.

Human errors

Human errors that affect angle measurements are gross errors and random errors. Gross errors arise from carelessness and can be avoided with careful observation. They include sighting the wrong target, mixing clockwise and counter clockwise readings, turning the wrong screw, reading the circles wrongly, and booking incorrectly. Random errors are caused by imperfections in human sight which make it impossible to bisect the target accurately and read the circles correctly. However, they are small and of little significance. They are minimized by taking several observations and accepting the mean.

Natural errors

In general, angular errors resulting from natural causes are not large enough to affect appreciably the measurements of ordinary precision. Sources of natural errors include:

- Settlement of the tripod - Heat haze or mist affecting the sighting- Unequal expansion of the telescopes parts due to temperature

changes. - Instability of the instrument in windy weather-

Settlement of the tripod (for instance when set up on boggy ground) can be avoided by using extra-long tripods or small platforms for the tripod legs. Shielding the instrument against the sun or wind and choosing favorable times for observation can avoid the other errors.

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5. TACHEOMETRY

Tachometry represents distance-measuring methods that are faster than taping. They include stadia, sub tense bar and EDM methods.

5.1 The Stadia MethodThe instruments used for determining distances by the stadia method are level/ theodolite and staff. The method employs the staff readings, vertical angle and optical parameters of the telescope to compute the horizontal distance and elevation difference between the theodolite and staff stations. The accuracies of the method are 1 part in 300 to 400 for horizontal distance and ±0.03 m for elevation difference. The method is applicable to various survey operations that include: mapping small or medium sized areas of uneven terrain. It provides a means of measuring direction, distance and elevation, all essentials in one operation. It can be used only at scales less than 1:200 or for soft details of topographic mapping.

Two formulas for computing horizontal distance and elevation difference can be derived for two cases: line of sight horizontal and line of sight inclined.

Horizontal Line of sight

The formulas for horizontal distance and elevation difference between the instrument and staff stations can be derived by referring to Fig. 2.1.

Fig. 5.1 stadia tachometry in horizontal line of sight

UWR = Upper wire readingMWR = Middle wire readingLWR = lower wire readingh.i = height of instrumenti = fixed distance between stadia hairs

S = Stadia interval (Staff intercept)RLA = Reduced level of the instrument stationRLB = Reduced level of the staff station

c fdC

A

RL A

B

RL BD

Da tum

i

UWR

LWR

M WR S

Sta ff

o F

h.i

line o f sig ht

O = Optical center of the objective lensF = focal point

f = focal length

Horizontal distance

From similar triangles in Fig. 2.1,

Hence,

Where, D = Horizontal distance between the instrument and staff stationsk = multiplying constant which is given by the manufacturer of the instrument (usually 100)C = additive constant which is given by the manufacturer of the instrument (Zero for internally focusing telescopes)

Elevation difference

From which,

Inclined line of sight

Figure 2.2 is used to derive the formulas for horizontal distance and elevation between the instrument and staff stations. For all practical purposes, the angles at M’ and N’ may be assumed to be 900 First, the inclined distance, Di, is calculated by using the formula derived for horizontal line of sight. Then the horizontal and vertical components of this inclined distance are used for computing the horizontal distance and elevation difference.

35

Fig. 2.2 stadia tachometry in inclined line of sight

Horizontal distance

If C = 0, then

Elevation difference

+V is used for angle of elevation and zenith angle-V is used for angle of depression

SM ’

N ’

M

NZ

A

B

V

h.i

RLA

RLB

D

36

V represents the vertical component of the inclined distance is computed as,

1. The Electronic Distance Measurement (EDM) method

The method is used to carry out surveys that are large in size and require great precision. Electronic distance measuring devices include electro-optical and electromagnetic instruments. The devices can be stand-alone, attached to the standards of a theodolite or integrated into the framework of a theodolite to form a total station.

EDM method using electro-optical devices involve equipment that emits light wave at one end of the line to be measured, and a reflector that reflects the light wave back to the emitter at the other end of the line. The emitter and reflector must be intervisible. Distance is computed based on velocity of light. These devices can measure distances that vary from 0.2 m to 14 km with inherent mean square errors of ± (0.2 mm + 0.2 ppm) to ± (5 mm + 5 ppm).

The electromagnetic EDM method requires two similar units, sending unit that transmits microwave and receiving unit that receives the wave from the sender and retransmits to the sender. Intervisisbility between the sending and receiving units is not a requirement; but there must not be any obstruction between them. Distance is determined on the basis of radio waves velocity. Electromagnetic EDM units are capable of measuring distances that range from 10 m to 50 km with accuracies of ± (15 mm + 3 ppm).

The EDM equipment directly gives slope distance that should be reduced to a horizontal distance by employing additional information on the vertical angle or elevation difference between the centers of the transmitter and reflector or receiving units (see Fig. 2.4).

37

Figure 4:4 electronic distance measurements

RLA = elevation of electro-optical or electromagnetic device stationRLB = elevation of reflector or receiving unit stationh.iT = height of the theodoliteh.iO = height of targeth.iEDM = height of EDM transmitterh.iR = height of the reflector or receiving unit h = (h.iR – h.iT) – (h.iEDM – h.iT) = measured vertical angleZ = measured zenith angleDi = measured slope distance between the transmitter and reflector or receiving unitD = horizontal distance between A and BV = vertical distance between centers of the transmitter and reflector or receiving unitThe measured inclined distance can be reduced to horizontal distance as follows:

The values of αE and ZE are calculated as,

Case 1: If the vertical or zenith angle is known

where,

Case 2: If the elevations of the transmitter and reflector or receiving unit are known

D i

DA

B

Re fle c to r (Re c e iving unit)

EDM Tra nsm itte r

z

Tra g e t

The o d o lite

hh.iR

h.iEDM

hc o s

E

zE

h.iT

h.iOV

RLA

RLB

38

where,

39

5. HORIZONTAL CONTROL SURVEY

Horizontal control survey deals with the determination of horizontal positions of arbitrarily located points. It can be carried out by one of the following methods:

- Traversing- Intersection- Resection- Triangulation- Trilateration- Global Positioning System (GPS)

Horizontal control surveys are conducted for purposes of establishing property lines and setting reference points that can be used for other survey operations such as topographic surveying, route and construction surveying.

5.1 Traversing

A traverse consists of a series of straight lines connecting successive established points along the route of a survey. The end points that define each line of a traverse are called traverse stations. Traversing requires two measurements:

- Horizontal distance between successive traverse stations and- Horizontal angle between adjacent traverse lines

Traversing is a convenient, rapid method for establishing horizontal control points. It is particularly useful in densely built-up areas and in heavily forested regions where the lines of sight are short and the other control survey methods are less suitable. Traverses are made for numerous purposes, including

- Establishment of property lines. - Setting supplementary horizontal control for topographic mapping.- Location and construction layout surveys for highways, railways, and other private

and public works.- Ground control surveys for photogrammetric mapping.

In general traverses are classified into two types: open traverse and closed traverse.Open traverse: starts from a point of known position and terminates on another point of unknown position. Since it is impossible to check errors in open traverse, it cannot be used for surveys which require high precession. To minimize errors angles and distances should be measured repeatedly.Closed traverse: starts and ends on points of known position. With this type of traverse it is possible to check the presence of errors in the measured angles and distances. If the starting and end point is the same, it is called closed-loop traverse. Loop traverse permits a check only on angular errors but not on distances. For this reason a closed-loop traverse should not be used for major projects.

5.2 Principles of traversing Traversing consists of fieldwork and office work principles. The fieldwork comprises reconnaissance, measurements of the traverse length and the horizontal angle between adjacent traverse lines. The direction (Azimuth/Bearing) of one of the traverse lines from the meridian should also be determined.

The office work includes the following tasks:

- Reduction of slope distances to horizontal distances- Adjustment of measured angles and/or distances- Determination of bearing (azimuth) of each traverse line- Determination of coordinates of every traverse station- Plotting the traverse

5.2.1 Fieldwork of traversingTraverse can be run by deflection angle, interior angle, angle to the right or azimuth angle. Traverse fieldwork consists of the following activities:

Selection of suitable traverse stations: The first step in traversing is to carry out a reconnaissance survey of the site with a view of selecting suitable sites for traverse stations. The station marks should be more or less permanent (e.g. concrete block into which a bolt or wooden peg is driven, nail flash driven into a road surface with a surrounding painted circle). If the distance measuring equipment is steel tape, the terrain between adjacent successive stations should not be very undulating.Measurement of distances between the traverse stations: in the field slope distances are measured which will be reduced to horizontal distances in the office. Distance could be measured by using steel tape or EDM. All necessary data that will be used for correcting the measured slope distance should be recorded.

Measurement of angles at each station: both horizontal and vertical angles should be measured at each traverse station.

Marking the stations for further reference traverse stations should be referenced from some nearby permanent objectives such as electric poles, trees, etc so that they can be readily found at later times. A witnessing sketch (see fig. 3.1) that shows the relative position of the traverse station from the reference objectives should be prepared.

Fig. 3.1 witnessing sketch for a traverse station

Plotting the traverse

After having performed some computations on the raw data, the traverse is plotted on a paper using horizontal distance and angle information. Two methods can be employed for plotting: graphical or mathematical method.

??

This method employs a scale ruler and protractor for plotting. It is not commonly used, since angles, measured in the field with an accuracy of a few seconds of arc, are plotted using a

Na il d rive n into a te le p ho ne p o le

C ro ss c ut o n a ro a d c urb

D

To s

tat io

n E

C e nte r o f a m a nho le c o ve r

2 2 . 5 m

1 4 m

9 m

protractor with an accuracy of only half of a degree, at best. Referring to the traverse data below, the procedure for plotting using the graphical method is as follows:

1. A freehand drawing of the survey is made in order to locate the survey centrally on the drawing paper.

2. A line representing the magnetic meridian is drawn lightly through the first point A of the traverse.

3. The protractor is laid on this line with the 0 graduation facing to magnetic north and the bearing of line AB, i.e. 30015, is marked off.

4. A line is drawn through this latter plotting mark and the point A and the length 34.25 m is measured along this line from A to mark B.

5. The protractor is centered on station B with the zero degree graduation pointing back to station A and angle ABC, i.e. 216032’ is marked off.

6. A line is drawn from point B through this point and the distance 28.42 m is measured to establish station C.

7. Steps 5 and 6 are repeated to plot station D.8. Circles of 2 mm diameter are drawn in ink around each survey station and the stations

clearly designated.

This method employs rectangular coordinates of each traverse station to plot the traverse. X, Y coordinates of each station is computed from azimuth/bearing and plan length of each traverse line.

Office work of traverse involves the following activities

1. Check for angular error of closure2. Correction of observed distances for all systematic errors3. Determination of azimuths of each traverse line4. Computation of coordinates5. Calculation of errors in closure in position6. Determination of closure corrections7. Adjustment of coordinates

1. Check for angular error of closure

Horizontal length Horizontal angle

AB = 26.20 m A = 60015’ (bearing)

A check on angular error of closure can be performed only for closed traverse. The angular error of closure can be distributed equally to each observed angle if it is assumed that all angles are measured with equal precision.

Deflection angle traverseIf the deflection angles in fig. 3.3 are correct, the following relationship should hold true.

Angular error of closure = Calculated azimuth of DE = Known Azimuth of line DE

In general, for a traverse with m deflection angles to the right and n to the left, the relationship becomes:

Az1 = forward azimuth of the starting line Az2 = forward azimuth of the closing line

Angular error of closure = Calculated azimuth of the last line – Known azimuth of the last lineClosed-loop traverse

A

B

C

D

R

L

R

N

R

E

AzD E

Fig. 5.3 defelection angle traverse

A

B

C

D

E

Σ interior angles = (n-2)(1800)

Error of closure = Σ Observed interior angles – (n-2)1800

Angles to the right

Fig : 5.4 angles to the right The condition for closure is

and in general it becomes

Angular error of closure = Calculated azimuth of the last line – Known azimuth of the last line

A

B

C

D

N

E

2. Correction of observed distances for all systematic errors

Distances measured in the field cannot be free from errors. Hence observed lengths of traverse lines have to be corrected and reduced to horizontal distances for further use in traverse computations. The sources of systematic errors in distance measurement and the procedures for eliminating or reducing them are indicated in Table 3.1.

Table 5.1 Systematic errors in distance measurementMethod Source of systematic error Procedure to eliminate or reduce

Taping Tape not of standard length Standardize tape and apply computed correction

Temperature Measure temperature and apply computed correction; for precise work, tape at favorable times

Change in pull or tension Apply computed correction; in precise work use spring balance

Sag Apply computed correction; use tape fully supported

Slope At breaks in slope determine differences in elevation or slope angle; apply computed correction

Stadia Multiplying constant different from that assumed

Determine the value of the constant by field observation

Staff not of standard length Standardize the staff; apply computed corrections

Inclined line of sight Note vertical or zenith angle; apply computed correction

EDM Atmospheric conditions Record the temperature and atmospheric pressure during each distance measurement

Instrumental maladjustment

Check the instrument; apply computed correction

Inclined line of sight Record vertical or zenith angle; apply computed correction

3. Determination of azimuth of each traverse line

Starting from the line with known azimuth, the forward azimuth of each traverse line is calculated from the back azimuth of the previous line and the corrected horizontal angle.

4. Computation of coordinates

Coordinates of each traverse station are calculated starting from the station with known coordinates. Referring to fig. 3.6 the method of coordinate’s calculation is given below.AzAB = Azimuth of line AB

Fig. 5.6 Coordinate calculation using departure and latitude

AzBC = Azimuth of line BCDAB = Horizontal length of ABDBC = Horizontal length of BC∆XAB = Departure of AB∆YAB = Latitude of AB∆XBC = Departure of BC∆YBC = Latitude of BC

The procedure for calculation is as follows:1. Compute the departure and latitude of each traverse line as

A

C

B

(X , Y )A A)

X AB

YA

B

YBC

AzAB

AzBC

(X , Y )B B

(X , Y )C C

D AB

D

BC

2. Calculate coordinates of each station as

3. Check for accuracy of observations and calculations

This can be performed only for closed traverse by checking the fulfillment of the following conditions:

Closed-loop traverse

Algebraic sum of all departures = 0Algebraic sum of all latitudes = 0

Closed traverse with n stations, given the starting and end stations coordinates

4. Calculation of errors in position

The relationships given above are rarely satisfied in practice, owing to random observational errors, uncorrected systematic errors in observations, and inaccuracies in the given coordinates for a closed traverse. The amounts by which the above equations fail to be satisfied are called the errors in closure in position and are computed using the formulas given below.

Fig. 3.5 Traverse closure

Closed-loop traverse

Closed traverse with known starting and end stations

The total closure error, e, is calculated as

5. Determination of closure corrections

The total closure correction is simply the opposite of the closure errors in position.Hence,

Total correction for departures, cx = -ex

Total correction for latitudes, cx = -ey

6. Adjustment of coordinates

The final coordinates of traverse stations are obtained by applying the computed closure corrections to the previously calculated coordinates. Two methods can be employed for traverse adjustment: The Bodwitch Method or The Transit Method.

(X ,Y )P PPe x

e y

e

C a lc u la te d

c o o rd ina te s o f P , G ive n

The Bodwitch Method

This is the common traverse adjustment method. Total closure is distributed to each traverse lines in proportion to its length.

The Transit method

This method assumes that corrections for departure and latitude of a line are proportional to the calculated departure and latitude.

Example

The Following Figure shows the results of field measurements for a closed-loop traverse. The given lengths are reduced horizontal distances. Assuming that the coordinate of station A is (5000, 1000), determine the coordinates of the other stations.

Fig. 5.7 Field observations for a closed-loop traverse

N

A

B

C

D

70 05’19’’0

112 42’03’’0

128 37’19’’0

48 36’43’’0

127.938m

130.038m246.843m

97.235m

92 37’26’’0

Solutiona) Angular error of closure

b) Azimuth of each traverse line

The forward azimuth (FAz) of any traverse line is calculated from the back azimuth (BAz) of the previous line and the corrected interior angle.

Line AB

Line BC

Line CD

N

A

B

D

N A

B

C

Line DA

Check for the calculation

c) Departures and Latitudes calculation

Line AB:

Line BC:

Line CD:

B

D

C

N

C

DA

N

Line DA:

d) Closure error in position and traverse accuracy

e) Departures and latitudes adjustment

The total correction for the traverse is equal in magnitude but opposite to the total error in position. Hence,

a. Adjustment using The Bodwitch Method

Line AB

Line BC

Line CD

Line DA

b. Adjustment using the Transit Method

Line AB

Line BC

Line CD

Line DA

Check

f) Coordinates of the traverse stationsCoordinates of a traverse station are obtained from the algebraic sum of the coordinates of the previous station and the departure/latitude of the line between the successive stations. Using the departure and latitude corrections obtained by the Bodwitch Method, the coordinates of all stations are calculated below.

Station A

Station B

Station C

Station D

Check

Calculated coordinates for station A = Given coordinates of A

STATION

ObservedInteriorAngles

Anglecorrec-tion

Corrected InteriorAngles

Azimuth Horizontal distance

Departure and latitude of each line Coordinates

Calculated Corrections Corrected

X Y cx cy Xcorr Ycorr X Y

A 112042’03’’ -21’’ 112041’42’’205019’08’’ 97.235 -87.894 -41.584 0.010 0.010 -87.894 -41.584

500.000 1000.000

B 70005’19’’ -21’’ 70004’58’’ 458.426 912.116

95024’06’’ 246.843 -23.242 245.746 0.025 0.026 -23.242 245.746

C 48036’43’’ -21’’ 48036’22’’ 704.197 888.900

324000’28’’ 130.038 105.214 -76.419 0.013 0.014 105.214 -76.419

D 128037’19’’ -21’’ 128036’58’’ 627.791 994.128

272037’26’’ 127.938 5.859 -127.804 0.013 0.013 5.859 -127.804A 500.000 1000.000

Triangulation and Trilateration

Triangulation and trilateration are used to establish precise horizontal controls over a large area. In both these methods, the control stations form a network of interconnected or overlapping triangles as shown in Fig. 3.15.

Fig. 3.15 Triangulation and trilateration figures

In both cases lengths and directions of base and check lines are measured. In addition, all vertex angles, in the case of triangulation, and all side lengths of the triangles, in the case of trilateration are measured.

Triangulation and trilateration consist of the following works:

- Reconnaissance to select the locations of stations- Setting station marks- Determination of lengths and directions of the base and check lines- Observation of angles of all vertices for triangulation- Measurement of all side lengths of the triangles for trilateration - Adjustment of angles

(a) Chain of triangles

(b) Braced quadrilateral (Best for narrow surveys, e.g. route survey)

(c) Center-point polygon

(Best to cover wide areas, e.g. cities)

Base

-line C

hec k-line

Base

-lin e

Ch e

ck -lin e

Base

-line

Che

c k-line

- Computation of unmeasured quantities, i.e., side lengths for triangulation using sine law, vertex angles for trilateration by applying cosine law, and azimuths of all lines.

- Calculation of coordinates of all stations3.10 Intersection

This method involves determination of coordinate of an unknown point from two known stations by measuring horizontal angles. The theodolite is set over the known stations. The method is particularly useful when the unknown point is inaccessible.

The procedures for coordinate determination, referring to Fig. 3.16, are given below.

Known quantities:

- Coordinates of A and B- Angles and Unknown:

- Coordinate of C

Procedure for solution

- Calculate length of line AB, c, and its azimuth, AzAB

- Compute lengths of AC, b, and BC, a, using Sine Law

A

B

C

b

ac

Fig. 3.16 location of a point by intersection

- Calculate azimuths of lines AC and BC

- Determine coordinate of C

5.11 Resection

This method of locating a point requires two horizontal angles observed at an unknown point and three known stations. The method is particularly useful when the unknown point is

accessible and surrounded by known points over which a theodolite cannot be set up. Three cases could be identified as shown in Fig. 3.17.

(a) (b) (c)

Fig. 5: Location of a point by three-point resection

Check

O

B C

A

A

BC

O

A

B C

O

Known:

- Coordinates of A, B and C- Angles and

Unknown:

- Angles and - Coordinates of O

Procedure for solution

- Calculate lengths and azimuths of lines AB, BC, and AC from the known coordinates- Find angles and

- Compute distances of AO, BO and CO

- Determine azimuth of AO by first computing angle CÂO and check it by using angle BÂO

- Calculate coordinates of O

- Check coordinates of O by determining lengths and directions of BO and CO

Examples on intersection and resection

1. The coordinates of station C (see Fig. 3.18) are to be determined from two existing control stations A and B by the method of intersection. Using the given data, calculate the coordinates of C.

= 42028’34’’

= 57048’10’’

Coordinates:

A: (242.45 m, 320.20 m)

B: (457.89 m, 482.86 m)

Solution

Calculate length and azimuth of line AB

AB

C

Determine angle ACB

Calculate lengths of AC and BC using sine law

Compute azimuths of AC and BC

Calculation of coordinates of C

Check

2. The field data shown in Fig. 3.19 were obtained for a three-point resection. Calculate the coordinates of station O.

= 141049’17’’

= 164038’02’’

Coordinates:

A

BC

O

A: (225.885 m, 118.829 m)

B: (146.650 m, 234.180 m)

C: (235.642 m, 264.180 m)

Solution

Lengths of AB, BC, and AC

Azimuths of AB, BC and AC

Check

Angles and

Check:

Lengths of AO, BO and CO

Azimuths of lines AO, BO and CO

Coordinates of OFrom station A

Check these coordinates by calculating from stations B and C.

Areas

Computation of areas of a tract of land is one of the primary objects of most land surveys. In ordinary surveying the area of land is taken as its projection on a horizontal plane. There are different methods of plan area computation.

1. Areas enclosed by straight linesa. Area by trianglesAreas enclosed by traverse lines can be calculated by dividing the total area into triangles and computing the areas of the triangles. The total area is the sum of the areas of the triangles. Area of a triangle can be calculated by one of the following methods:

Fig. 3.7 Area of a triangle

b. Area by coordinatesIf the coordinates of the traverse stations from certain reference axes are known, the area of the traverse can easily be calculated. This method is also called as Double Distance Meridian (DDM) method.

Or, using coordinates

Multiplying and rearranging terms, the double area is computed as and in general for a polygon having n stations

a

b

ch

A

B

C

1

2

3

4

X1

X2

X3

X4Y1

Y2

Y3

Y4

a

b

c

d

e f g h Fig. 3.8 Area by coordinates

Computations can be made conveniently by tabulating each X coordinate below the corresponding Y coordinate as follows:

The double area is then equal to the difference between the sum of the products of the coordinates joined by full lines and the sum of the products of the coordinates joined by dashed lines.

2. Areas enclosed by irregular linesa. Give and take lines

In this method irregular boundaries are replaced by straight lines (give and take lines) such that any small areas excluded from the survey plan by the lines are balanced by other small areas outside the survey but included. The positions of these lines can be estimated by eye on the survey plan. The area bounded by the straight lines is then calculated by the method triangle or coordinate.

b. Graphical methodThis method involves the use of a transparent overlay of squared paper laid over the plan. The number of squares and parts of squares which are enclosed by the area is counted. Using scale of the plan the area represented by each square and then the total area are determined. The method gives accurate estimate if the grid size becomes smaller.

1

1

3

3

2

2

1

1

X

Y

X

Y

X

Y

X

Y

X

Y

n

n

Fig. 3.9 Area by give and take line

Inc lud e d a re a

Exc lud e d a re aG ive a nd ta ke line

A

B

C

D

Let the number of squares within the survey boundary = n

Let the side length of a square on the plan = a

Total area within the survey boundary

= n x a2 x 5002

Fig. 3.10 Area by graphical method

c. Mathematical methodConsider the survey plan shown in figure 3.10.

Area within the survey boundary

= A1 + A2 + A3

A1 can be determined by the triangle or coordinate method.

A2 and A3 can be approximated by the Trapezoidal rule or Simpson’s rule which are explained below.

Fig. 3.11 Area by mathematical method

Referring to Fig. 3.11, the method of area calculation by trapezoidal or Simpson’s rule is as follows:

h1, h2, h3,…are offset distances

A1, A2, A3, … are areas of parts

Sc a le 1:500

Tra nsp a re nt o ve rla y

Surv

ey

bo

und

ary

A1

A2 A3Surve y b o und a ry

Trapezoidal RuleThis rule assumes that if the interval between the offsets is small, the boundary between the offsets can be approximated to a straight line. Hence, areas of parts can be computed as:

The Trapezoidal rule applies to any number of offsets.

Simpson’s RuleSimpson’s rule assumes that the survey boundary between offsets can be approximated by parabolic arc. The area is calculated as

To apply this rule, the number of offsets, n, must be odd. For even number of offsets, the final offset must be omitted and the rest of the area can be calculated by the Simpson’s rule. The area between the last two offsets can be calculated by the Trapezoidal rule.

L L L L L L L

h 1

h 2

h 3

h 4

h 6

h 7

h 8A1 A2 A3 A4 A5 A6A7

M N

Example 1. The following offsets, 8m apart, were measured at right angles from a traverse

line to an irregular boundary.

0 m 2.3 m 5.5 m 7.9 m 8.6 m 6.9m 7.3 m 6.2 m 3.1 m 0 m

Calculate the area between the traverse line and the irregular boundary using (a) the Trapezoidal rule (b) the Simpson’s rule.

Solution:

(a) Area by Trapezoidal rule

(b) Area by Simpson’s ruleAs the number of offsets is 10 (even), calculate the area between offsets 1 and 9 by the Simpson’s rule and the area between 9 and 10 by the Trapezoidal rule.

Exercise

The following perpendicular offsets measured at regular intervals of 5m and last interval of 2.7 m from a traverse line to an irregular boundary:

0 m 3.5 m 7.2 m 9.7 m 12.4 m 16.7 m 13.5 m 7.9 m 3.2 m 0 m

Compute the area between the traverse line and the irregular boundary.

D. Area by planimeterPlan meter is a mechanical device used for determining the area of any closed figure. The area is obtained from the measuring unit consisting of an integrating disc which revolves and alters as the tracing point is moved around the perimeter of the figure.