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TOPICS TO BE COVERED : Principles of Surveying, Technical terms. Calculation of reduced level by Height of instrument. Rise & Fall method, Simple problems in levelling. SURVEYING & LEVELLING :

SURVEYING Surveying is the art of and science of determining the relative positions of various points or stations on the surface of the earth by measuring the horizontal and vertical distances , angles , and taking the details of these points and by preparing a map or plan to any suitable scale .” Surveying has been an essential element in the development of the human environment since the beginning of recorded history (5000 years ago). it is a requirement in the planning and execution of nearly every form of construction . Its most familiar modern uses are in the fields of transport , building and construction, communications , mapping, and the definition of legal boundaries for land ownership.

TYPES OF SURVEYING Divisions of Surveying - The approximate shape of the Earth can best be defined as an oblate tri-axial ovaloid. But, most of the civil engineering works, concern only with a small portion of the earth which seems to be a plane surface. Thus, based upon the consideration of the shape of the earth, surveying is broadly divided into two types : Surveying Plane Surveying Geodetic Surveying

Plane surveying : Earth surface is considered a plane of x-y dimensions. Z-dimension (height) referenced to the mass spherical surface of the earth (Mean Sea Level). Most engineering and property survey are plane survey correction to curvature is made for long strips (e.g. Highway). For small projects covering Area less than 200 sq.km. Earth curvature is not counted in calculating the distances. Earth surface is considered as plane. (Angular error of 1” in 200 sq. km. area by assuming plane).

Geodetic surveying : Earth surface is considered spherical in revolution (actually ellipsoid) Z is referenced to MSL (surface of earth) Very precise surveys (boundaries and coastal networks). When survey extends over a large areas more than 200 sq. km. and degree of accuracy is also great. The curvature of earth is also taken into account. Geodetic survey is used to provide control points to which small surveys can be connected.

All distances and directions are horizontal; The direction of the plumb line is same at all points within the limits of the survey; All angles (both horizontal and vertical) are plane angles; Elevations are with reference to a datum.

PRINCIPLES OF SURVEYING The fundamental principles upon which the surveying is being carried out are Working from whole to part . Control points: - triangulation of traversing. Triangulation divided into large triangle. Triangles- subdivided in to small triangles To control and localize minor errors. On the other hand –It we work from the part of the whole; small errors are magnified & uncontrollable at the end.

Deciding the position of any point, with reference to at least two permanent objects or stations whose position have already been well defined. Linear measurement Angular measurements Both the linear and angular measurements. E.g. Chain surveying- main lines & stations points are checked by means of check or tie lines.

WORKING FROM WHOLE TO PART The purpose of working from whole to part is to localize the errors and to control the accumulation of errors. This is being achieved by establishing a hierarchy of networks of control points. The less precise networks are established within the higher precise network and thus restrict the errors. To minimize the error limit, highest precise network (primary network) of control points are established using the most accurate / precise instruments for collection of data and rigorous methods of analysis are employed to find network parameters

Introduction The horizontal distance between points, projected onto a horizontal plane, is required to be measured in order to prepare plan or map of the area surveyed. This is done through chain surveying In surveying there are several methods for measurement of distance. These are Direct methods Optical methods Electronic method. In any work, the choice of a method depends on many factors like field condition, accuracy required, availability of resources (instruments, time, skill, fund etc). Table 8.1 summarizes the principal methods, instrument required, precision, use, errors of measurement of distance METHODS OF MEASUREMENT

Direct Measurement When the distance between points / stations are measured directly, usually by using tape or chain is known as direct method. Chain (or) Tape Arrows Pegs Ranging Rods Offset Rods Plasterer’s laths and whites Plumb bob Instruments Used in Chain Survey:

Chains: They are formed of straight links of Galvanized mild steel wires . Metric Chain Gunter’s Chain (or) Surveyor’s Chain Engineer’s Chain Revenue Chain Steel band (or) band chain One tally = 2m Two tally = 2 X 2m = 4m Three tally = 3 X 2 m = 6 m

TECHNICAL TERMS USED IN SURVEYING Technical Terms : Survey Stations Chain Line or survey lines Main Survey Line Base line Tie Lines Check Lines Offsets Perpendicular offsets Oblique offsets long offsets short offsets

Survey Stations : Main Stations Subsidiary or tie Main Stations: Main stations are the end of the lines, which command the boundaries of the survey Subsidiary or the tie stations: Subsidiary or the tie stations are the point selected on the main survey lines, where it is necessary to locate the interior detail such as fences, hedges , building etc.

Chain / Survey Lines Main Survey Line: The lines joining the main stations are called the main survey line or the chain lines. Base Lines: It is main and longest line, which passes approximately through the Centre of the field. All the other measurements to show the details of the work are taken with respect of this line. Tie or subsidiary lines : A tie line joins two fixed points on the main survey lines. It helps to check the accuracy of survey and to locate the interior details. The position of each tie line should be close to some features, such as paths, building etc.

Check Line: A check line also termed as a proof line is a line joining the apex of a triangle to some fixed points on any two sides of a triangle. A check line is measured to check the accuracy of the framework. The length of a check line, as measured on the ground should agree with its length on the plan. A B C D Road Check Line Check Line Tie Line Base Line Main Survey Line Main Survey Line Main Survey Line Main Survey Line

Offsets These are the lateral measurements from the base line to fix the positions of the different objects of the work with respect to base line. These are generally set at right angle offsets. It can also be drawn with the help of a tape. Perpendicular offsets - The measurements are taken at right angle to the survey line called perpendicular or right angled offsets Oblique offset - The measurements which are not made at right angles to the survey line are called oblique offsets or tie line offsets. Long offset - Length of offset ≥ 15 m Short offset - Length of offset < 15 m A1 A2 A3 A4 A5 ө 1 ө 2 90 o

Metric Chains: Available in lengths of 5, 10, 20 and 30 m Tallies are fixed at every 2 m intervals Circular tally is placed at the center of the chain Grooves are provided at the ends to facilitate the placement of arrows Length of the Chain is engraved on the brass handle of the chain Chains Contd…

Gunter’s Chain / Surveyor’s Chain: Before Independence, India used to follow FPS system …in which length is measured in foot Length of the Chain is 66’ , consisting of 100 links, each link being 0.66’. 10 Gunter’s square chains = 1 acre. 10 Gunter’s Chains = 1 furlong = 660’ 80 Gunter’s Chains = 1 mile =80X66 = 5280’ 10 X 66’ 10 X 66’ Engineer's Chain: Length is 100’ with 100 links, each link being 1’ Brass tag is provided at every 10 links [number of 10 link segments are indicated on the tags.] Here, number on the tag represents the segments of links Ex. If n=3, length from beginning to that point = 3 X 10 X 1’ = 30’ 1 2 3

Revenue Chain: Length of the Chain is 33’ and consists of 16 links. Each link length is Used in Cadastral Survey Steel band or band Chain: It consists of a long narrow strip of steel of uniform width (12 – 16 mm width and 0.3 to 0.6 mm thickness) They are available in 20 or 30 m lengths Brass studs are provided at every 20 cm and it is numbered ate very meter. First and last links are subdivided into cm and mm. For convenience, steel bands are wound on special steel crosses / metal reels from which they are unrealed. Chains Contd…

Testing and Adjusting Chain : As we use the chain continuously, the length of it may be shortened [bending of the links, wearing out of the links ] or elongated [stretching of the links, opening of the rings etc. ] . So, it becomes essential to check the chain length often before using it. It should be done by constructing a permanent test gauge , with which the chain is compared. + + + + 10 m 10 m 10 m 10 m 20 m 30 m 0 m Permanent Test Gauge 20 cm X 20 cm Dressed Stones Temporary gauge station is established by driving two pegs at requisite distance apart, and inserting nails into their tops to mark exact points. Overall length of a chain, when measured at 8 kg pull and checked against a steel tape @20 o C shall be within the following limits 20 m Chain = ± 5 mm 30 m Chain = ± 8 mm.

Adjusting the Chain : If the Chain is found to be long : Closing the joints of the rings Reshaping the elongated rings Removing one or more small circular rings Replacing worn out rings Adjusting the links at the ends. If the Chain is found to be short : Straightening the links Flattening the circular rings Replacing one or more small circular rings by bigger ones Inserting additional circular rings Adjusting the links at the end.

Adjustment of error due to length of chain Where l= Design length of the chain l’ = Actual length of the chain D’ = actual length of the chain line D = measured length of the chain line

Similarly For area = For volume =

TAPES Cloth or linen tape Metallic tape Steel tape Invar tape Cloth or Linen Tape: Closely woven linen, 12 to 15 mm wide varnished to resist moisture. Commonly available in 10, 20, 25 and 30 m; 33’, 50’, 66’ and 100’. End of tape is provided with small brass ring whose length is included in the total length of the tape. They are not used for accurate measurements. WHY? It is easily affected by moisture Its length gets altered by streaching It is likely to sag Further, its life is short.

TAPES Cloth or linen tape Metallic tape Steel tape Invar tape Metallic Tape: Metallic tape is nothing but a cloth tape that is reinforced with brass or copper wires. Commonly available in 10, 15, 20, 30 and 50m. End of tape is provided with small brass ring whose length is included in the total length of the tape and they are supplied in a leather case.

TAPES Cloth or linen tape Metallic tape Steel tape Invar tape Metallic Tape: Metallic tape is nothing but a cloth tape that is reinforced with brass or copper wires. Commonly available in 10, 15, 20, 30 and 50m. End of tape is provided with small brass ring whose length is included in the total length of the tape and they are supplied in a leather case. Steel Tape: They are made of steel strips having width of 6 – 10 mm. Available in lengths of 1, 2, 5, 10, 20, 30 and 50 m. These tapes are more durable and accurate than the metallic tape. End of tape is provided with small brass ring whose length is included in the total length of the tape. They are supplied in a leather case or a corrosion resistant metal case. They are used for accurate measurement of distance.

TAPES Cloth or linen tape Metallic tape Steel tape Invar tape Invar Tape: Invar tapes are made of alloy Steel - 64% Nickel - 36% Its coefficient of thermal expansion is very less ≈ 0.000000122 / 1 o C It is 6 mm in width and available in lengths of 10, 20, 30, 50 and 100m. Invar is soft in nature and so, should be carefully handled to avoid damage. They are used for accurate survey. They can also be used in places where the temperature varies drastically.

Arrows: They are used to mark the position of the ends of the chain on the ground. They are made of steel wires of diameter 4 mm. The length of the arrow ranges from 25 to 50 cm. One end of the arrow is bent in the form of a loop / circle and the other end pointed. Ranging Rods: Ranging rods are used to fix up intermediate points on an or establish the position of a station. They are made with well seasoned timber with an iron shoe at the bottom or of light steel tubes. They are circular in C/S with 3 cm Dia. Their lengths vary from 2 to 3 m. They are painted alternately with white-red (or) white-black bands. Each band being 20 cm in length.

Plumb bob: It consists of a string attached at the top of the metal bob. As the bob always points towards the gravity, it represents the vertical line. They are used to transfer the points on the ground while chaining along a sloping ground. It is further used in the primary adjustments of all the surveying instruments. Pegs: They are used to mark the positions of the survey stations or the end points of a survey line They are made of stout timber. They are generally square in section and tapered at the end They are 22 mm X 25 mm in C/S and 150 mm long. These pegs are driven by hammer.

Laths: Useful for ranging long lines, also used over uneven ground where the ranging rod is not visible due to obstructions, They are light, cheap, being white; they are easily visible at a great distance. Usually 1.0m long Whites: When the ranging rod is not available or insufficient, whites are used. These are thin strip of bamboo and 40 cm to 1 m in length. One end is sharp and the other end is split for inserting pieces of white papers. They are also useful for temporary marking of counter points. Cross staff: The cross staff is used for a) Finding out foot of the perpendicular from a given point to a line b) Setting right angle at a given point on a line .

Technical Terms used in chain Survey ing : Survey Stations Chain Line or survey lines Main Survey Line Base line Tie Lines Check Lines Offsets Perpendicular offsets Oblique offsets long offsets short offsets

Survey Stations: Main Stations Subsidiary or tie Main Stations: Main stations are the end of the lines, which command the boundaries of the survey Subsidiary or the tie stations: Subsidiary or the tie stations are the point selected on the main survey lines, where it is necessary to locate the interior detail such as fences, hedges, building etc. Main Survey Line: The lines joining the main stations are called the main survey line or the chain lines. Base Lines: It is main and longest line, which passes approximately through the centre of the field. All the other measurements to show the details of the work are taken with respect of this line. Tie or subsidiary lines : A tie line joins two fixed points on the main survey lines. It helps to check the accuracy of survey and to locate the interior details. The position of each tie line should be close to some features, such as paths, building etc. Chain / Survey Lines

Check Line : A check line also termed as a proof line is a line joining the apex of a triangle to some fixed points on any two sides of a triangle. A check line is measured to check the accuracy of the framework. The length of a check line, as measured on the ground should agree with its length on the plan. A B C D Road Check Line Check Line Tie Line Base Line Main Survey Line Main Survey Line Main Survey Line Main Survey Line

Offsets These are the lateral measurements from the base line to fix the positions of the different objects of the work with respect to base line. These are generally set at right angle offsets. It can also be drawn with the help of a tape. Perpendicular offsets Oblique offset Long offset Short offset The measurements are taken at right angle to the survey line called perpendicular or right angled offsets The measurements which are not made at right angles to the survey line are called oblique offsets or tie line offsets. A1 A2 A3 A4 A5 ө 1 ө 2 90 o Length of offset ≥ 15 m Length of offset < 15 m

Procedure for carrying Chain Survey : There are four steps in chain survey: Reconnaissance Survey Marking stations Running Survey Lines Taking offsets Reconnaissance Survey : The preliminary inspection of the area to be surveyed is called reconnaissance. The surveyor inspects the area to be surveyed, survey or prepares index sketch or key plan . Marking Stations : Surveyor fixes up the required no stations at places from where maximum possible stations are possible. Running Survey Lines : Then he selects the way for passing the main line, which should be horizontal and clean as possible and should pass approximately through the centre of work. Then ranging roads are fixed on the stations. After fixing the stations, chaining could be started. Make ranging wherever necessary. Measure the change and offset. Enter in the field the book.

Selection of Survey Stations : Survey stations must be mutually visible Survey lines must be few as practically possible so that the frame work can be plotted conveniently The frame work must have one or two base lines. If one base line is used, it must run along the length and through the middle of the field. If two base lines are there, it should cross in the form of letter ‘X’ The lines should run on a level ground as far as possible The main lines should form well conditioned triangles Each triangle or portion of frame work must be provided with sufficient check lines

All the lines from which the offsets are taken should be placed close to the corresponding surface features so as to get short offset As far as possible, the main survey lines should not pass through any obstacle. To avoid any trespassing, the main survey lines should fall with in the boubdaries of the property to be surveyed.

Ranging When the distance to be measured is more than a tape length, a straight line is required to be laid between the points/ stations along which measurements are to be carried out. The process of laying out a straight line between points is known as ranging. Direct Ranging When the end stations are inter visible, ranging is being carried out directly. The intermediate points are placed at distances having interval less than one tape/chain length. The intermediate points are found by moving a ranging pole in transverse direction and thus, points are selected in such a way that the end points and the intermediate points lie in a straight line. In this method, two flags, one ranging pole and a bunch of pegs are required in a team of at least one surveyor and one assistant. Indirect Ranging When the end stations between which a straight line is to be laid, are not inter visible, indirect method of ranging is being adopted. It is being carried out either by reciprocal method or by random line method. Reciprocal Ranging Random Line Method

Ranging :: Direct Ranging e B A Distance ≤ Chain Length

In-Direct Ranging:

27 March 2020 GDRCET Basic Civil Engineering In-Direct Ranging:

Field Book : Book in which chainage , offsets and sketches of features are entered is called a field book It is a rectangular book of about 20 cm X 12 cm in size. It is of two types: Single line Double line 15 mm Rules: Field notes are entered from bottom to top No. of chain lines and No. of stations should be marked

Instructions for booking field notes: All the measurements should be recorded as soon as they are taken Each chain line, tie line, name of the survey line should be clearly written The chainage of the starting station is zero and increases as we proceed forward. The notes should be complete, accurate and neat Suitable scale is chosen Writing should always be from the bottom The figure should not be crowded together In case of a long survey lines, there should be an entry at the end of every 10 chains. General requirements/entries A layout of the lines The details of the lines The date of the survey A page index of the lines Name of the surveyor and its assistants.

Mistakes in Chaining Adding or dropping a full length of chain Adding or dropping a part of the length of chain Other points incorrectly taken as 0 or 30 meter marks on chain Reading numbers incorrectly Calling numbers incorrectly or not clearly

LEVELLING It a branch of survey in which The elevations of given points on/above or below the ground with respect to an assumed datum are determined Points at a given elevation or at different elevations with respect to a given datum are established.

Basic Definitions in Levelling : Level Surface Level Line Horizontal Plane Horizontal line Vertical Line Datum Elevation Vertical angle Mean Sea Level Bench Mark or

Basic Definitions in Levelling : Level Surface Level Line Horizontal Plane Horizontal line Vertical Line Datum Elevation Vertical angle Mean Sea Level Bench Mark Level line is defined as a line that lie in a level surface. It is perpendicular to the direction of gravity at that point.

Basic Definitions in Levelling : Level Surface Level Line Horizontal Plane Horizontal line Vertical Line Datum Elevation Vertical angle Mean Sea Level Bench Mark Horizontal plane through a point is a plane tangential to the level surface at that point. It is perpendicular to the direction of gravity at that point.

Basic Definitions in Levelling : Level Surface Level Line Horizontal Plane Horizontal line Vertical Line Datum Elevation Vertical angle Mean Sea Level Bench Mark Vertical line is a line normal to the level line. It is normally considered to be plumb line. Datum: Datum is a surface with reference to which elevations are referred. Usually MSL is taken as Datum

Basic Definitions in Levelling : Level Surface Level Line Horizontal Plane Horizontal line Vertical Line Datum Elevation Vertical angle Mean Sea Level Bench Mark Bench Mark : It is a fixed point of reference whose elevation with respect to a datum is known. It is by using this BM, we determine the elevations of all other points. Bench Mark GTS Bench Mark Permanent Bench Mark Arbitrary Bench Mark Temporary Bench Mark

Bearings and Angles: Direction of a survey line can be represented by: θ A B C θ A B C N Φ (a) Between the two lines (b) With reference to a given direction Bearing: It is defined as the angle of a line with reference to a particular direction . This particular direction with reference to which angel is measured is known as meridian All bearings are angles where as all angles are not Bearings

Meridian : Fixed direction on the surface of the earth with reference to which the directions of the survey lines are expressed is known as Meridian Meridian True Meridian Magnetic Meridian Arbitrary Meridian Direction indicated by a freely suspended and properly balanced magnetic needle unaffected by local attractive force is called magnetic meridian. True meridian at a place is a direction indicated by an imaginary circle passing around the earth through that place and the two geographical poles. For small surveys, any temporary direction shall be taken as fixed direction and the angles of the lines are measured with respect to this. This temporary direction i.e. assumed is termed as arbitrary meredian.

27 March 2020 Basic Civil Engineering Bearing : The Horizontal angle between the reference meridian and the survey line in clock-wise direction is known as bearing. Bearing True Bearing Magnetic Bearing Arbitrary Bearing The Horizontal angle between the Magnetic meridian and the survey line in clock-wise direction is known as Magnetic bearing. The Horizontal angle between the true meridian and the survey line in clock-wise direction is known as true bearing. The Horizontal angle between the arbitrary meridian and the survey line in clock-wise direction is known as arbitrary bearing . The above classification is based on the reference direction

Observing Bearing : The compass centered over station A of the line AB and is leveled. Having turned vertically the prism and sighting vane, raise or lower the prism until the graduations on the rings are clear and look through the prism. Turn the compass box until the ranging rod at the station B is bisected by hair when looked through the prism. Turn the compass box above the prism and note the reading at which the hair line produced appears to cut the images of the graduated ring which gives the bearing of line AB.

Relationships between bearings True bearing = Magnetic bearing ± Declination Dip and Declination: θ Φ True meridian (TM) Magnetic meridian (MM) Φ E TM MM Φ W TM MM If MM is towards east it is +ve and If MM is towards west , it is -ve

Magnetic bearing of a line AB is S 28 30 ’ E. Calculate the true bearing if the declination is 7 30 ’ west We know that TB = MB± Declination As the declination is towards west, it is –ve. TB = [180- 28 30 ’ ]- 7 30 ’

Fore Bearing & Back Bearing : Every line has two bearings one observed at each end of the line. The bearing of the line in the direction of progress of the survey is called Fore Bearing (FB), while the bearing in the opposite direction is called Back Bearing (BB). Therefore BB of a line differs from FB by exactly 180 o .

Fore and Back bearing : N N N N N N ө 1 ө 3 ө 2 ө 4 ө 5 ө 6 ө 7 ө 9 ө 8 ө 10 A B C D E F Line Fore Bearing Back Bearing AB Ө 1 Ө 2 BC Ө 3 Ө 4 CD Ө 5 Ө 6 DE Ө 7 Ө 8 EF Ө 9 Ө 10

Relationship between Fore bearing and back bearing : N N ө 1 ө 1 ө 2 180 o A B o to 180 o [OR] 1 st and 2 nd Quadrant

27 March 2020 GDRCET Basic Civil Engineering Relationship between Fore bearing and back bearing : N N ө 1 ө 1 ө 2 180 o So, Back Bearing = Fore Bearing ± 180 o N N ө 1 ө 2 ө 1 180 o A B B A o to 180 o [OR] 1 st and 2 nd Quadrant 180 o to 360 o [OR] 3 rd and 4 th Quadrant

There are two systems commonly used to express the bearing. WHOLE CIRCLE BEARING : In this system the bearing of a line measured with the magnetic north in clockwise direction. The value of bearing thus varies from 0 o to 360 o . QUADRANTAL SYSTEM : In this system the bearing of a line is measured eastward or westward from north or south whichever is near. The directions can be either clock wise or anti clockwise depending upon the position of the line.

Whole Circle Bearing and Quadrantal / Reduced Bearing E N W S ө 1 ө 2 ө 3 ө 4 C B A D E Line WCB AB θ 1 AC θ 1 AD θ 1 AE θ 1 The horizontal angle which a line makes with the magnetic meridian in the clock wise direction is known as Whole Circle Bearing [WCB]

27 March 2020 GDRCET Basic Civil Engineering Whole Circle Bearing and Quadrantal / Reduced Bearing E N W S Φ1 Φ 2 Φ3 Φ4 C B A D E Line QB AB N Φ1 E AC S Φ2 E AD S Φ3 W AE N Φ4 W The horizontal angle which a line makes with the magnetic meridian in the clock wise or anti0clock wise direction from Magnetic North or Magnetic south is known as Quadrantal Bearing [QB]

W E N S ө 1 ө 2 ө 3 ө 4 C B A D E Line WCB AB θ 1 AC Θ 2 AD Θ 3 AE θ 4 QB N θ 1 E S [180- θ 2 ] E S [ θ 3 – 180] W N [ 360- θ 4 ] W Conversion of WCB to QB / Reduced Bearing

Convert the following WCB to QB 65 o 35’ 140 o 20’ 255 o 10’ 336 o 40’ Convert the following QB to WCB N 56 o 30’ E S 32 o 15 ’ E S 85 o 45’ W N 15 o 10’ W Find the back bearings of the following observed fore bearing of lines AB 63 30 ’ BC 112 45 ’ CD 203 45 ’ DE 320 30 ’ A B C D E

The bearings of the sides of a closed traverse A, B, C, D, E, A are as follows Side F.B. B.B. AB 107 15’ 287 15’ BC 22 202 CD 281 30’ 101 30’ DE 189 15’ 9 15’ EA 124 45’ 304 45’ N N N N N A B E C D 107 15’ 22 281 30’ 189 15’ 124 45’ 287 15’ 202 101 30 ’ 9 15’ 304 45’ θ A θ B θ C θ D θ E A 107 15’ 304 45’ θ A N = θ A =360- [ BB of EA – FB of AB ] = 360-[304 45’ - 107 15’ ] =360-197 30’ =162 O 30’

The bearings of the sides of a closed traverse A, B, C, D, E, A are as follows Side F.B. B.B. AB 107 15’ 287 15’ BC 22 202 CD 281 30’ 101 30’ DE 189 15’ 9 15’ EA 124 45’ 304 45’ N N N N N A B E C D 107 15’ 22 281 30’ 189 15’ 124 45’ 287 15’ 202 101 30 ’ 9 15’ 304 45’ θ A θ B θ C θ D θ E θ B = 360- [BB of AB – FB of BC ] = 360- [287 15’ - 22 ] = 94 45’ N 22 287 15’ θ B B

The bearings of the sides of a closed traverse A, B, C, D, E, A are as follows Side F.B. B.B. AB 107 15’ 287 15’ BC 22 202 CD 281 30’ 101 30’ DE 189 15’ 9 15’ EA 124 45’ 304 45’ N N N N N A B E C D 107 15’ 22 281 30’ 189 15’ 124 45’ 287 15’ 202 101 30 ’ 9 15’ 304 45’ θ A θ B θ C θ D θ E θ C = [FB of CD – BB of BC ] = [281 30’ – 202 ] = 79 30’ N C 281 30’ 202 θ C

The bearings of the sides of a closed traverse A, B, C, D, E, A are as follows Side F.B. B.B. AB 107 15’ 287 15’ BC 22 202 CD 281 30’ 101 30’ DE 189 15’ 9 15’ EA 124 45’ 304 45’ N N N N N A B E C D 107 15’ 22 281 30’ 189 15’ 124 45’ 287 15’ 202 101 30 ’ 9 15’ 304 45’ θ A θ B θ C θ D θ E θ D = [FB of DE – BB of CD ] = [189 15’ – 101 30’ ] = 87 45’ N D 189 15’ 101 30 ’ θ D

The bearings of the sides of a closed traverse A, B, C, D, E, A are as follows Side F.B. B.B. AB 107 15’ 287 15’ BC 22 202 CD 281 30’ 101 30’ DE 189 15’ 9 15’ EA 124 45’ 304 45’ N N N N N A B E C D 107 15’ 22 281 30’ 189 15’ 124 45’ 287 15’ 202 101 30 ’ 9 15’ 304 45’ θ A θ B θ C θ D θ E θ E = [FB of EA – BB of DE ] = [124 45’ – 9 15’ ] = 115 30’ N E 124 45’ 9 15’ θ E

The bearings of the sides of a closed traverse A, B, C, D, E, A are as follows Side F.B. B.B. AB 107 15’ 287 15’ BC 22 202 CD 281 30’ 101 30’ DE 189 15’ 9 15’ EA 124 45’ 304 45’ N N N N N A B E C D 107 15’ 22 281 30’ 189 15’ 124 45’ 287 15’ 202 101 30 ’ 9 15’ 304 45’ θ A θ B θ C θ D θ E θ A = 162 30’ θ B = 94 45’ θ C = 79 30’ θ D = 87 45’ θ E = 115 30’ Sum of Internal angles = 540 Sum of the internal angles of a closed traverse with n sides = [ (2 X n ) -4] *90 In the present case, no. of sides = 5. i.e. n = 5. So, [ (2 X 5 ) -4] *90 = 540 Check

The bearings of the sides of a closed traverse A, B, C, D, E, A are as follows Side F.B. AB 70 30’ BC 132 CD 56 00’ DE 215 30’ EA 310 00’ N N N D N C N A B E 70 30’ 132 56 00’ 215 30’ 310 00’

Bench Marks GTS Bench Mark Grand Trigonometrical Survey [GTS] Bench Mark 100 100 100 km 2 They are established by “Survey of India” with very high degree of precision with respect to MSL. MSL

Bench Marks Permanent Bench Mark GTS Bench Mark These bench marks are established between GTS bench marks. They are marked/ located on tops of culverts, piers of bridges, kilometer stones, Railway Platforms. They are established by Survey of India (or) PWD of that area. Permanent Bench Mark

Bench Marks Arbitrary Bench Mark These bench marks are selected on some permanent objects and their elevations are arbitrarily assumed. These bench marks are used in small scale leveling operations. Arbitrary bench marks are not related to GTS or Permanent Bench marks. Temporary Bench Mark These bench marks are left at the end of a day’s leveling operation. The leveling operation for the next day may be continued with respect to the bench mark left previous day. Such bench marks do not have any use later.

PBM TBM Day -2 TBM Day 3 TBM Day -1 TBM Day 4

Instruments used for Levelling Level Level Staff Plumb Bob

Focusing Screws Foot Screws Upper parallel plate (Tri-branch) Telescope Object piece / Object end Eye Piece Longitudinal Bubble Traverse Bubble Tube Lower parallel plate (Trivet) Bubble tube adjusting screw Level Head

Digital level There are fundamentally two types of automatic levels. First, the optical one whose distinguishing feature is self-leveling i.e., the instruments gets approximately leveled by means of a circular spirit level and then it maintains a horizontal line of sight of its own. Second, the digital levels whose distinguishing features are automatic leveling, reading and recording Digital Level

Automatic Level Base Plate Horizontal Circle Eyepiece Circular Bubble Sighting Pointer Objective Lens Focusing Knob Fine Motion Drive Footscrew Bubble Mirror

Leveling Staffs The staff is simply a large ruler, available in lengths of 3, 4 or 5 metres and usually made of wood or aluminium.

Level Staff Self reading Target Staff Solid Staff Folding Staff Telescopic Staff Solid staff is available as a single unit with no joints or hinges. Smallest division on the staff is 5 mm. These are made of well seasoned wood. They are available in both Foot and Meter. Their length are upto 3 m.

Level Staff Self reading Solid Staff Folding Staff Telescopic Staff Folding staff is available in two pieces each of 2 m in length hinged together so that it can be folded to a single piece. Width of such staff is 75 mm and 18 mm thick. Staff has two handles, one on each section, for folding the staff. They are more convenient to handle and also to transport.

Level Staff Self reading Solid Staff Folding Staff Telescopic Staff Telescopic staff consists of three pieces which can be extended to the full length of 4 m. The upper piece is a solid piece while the lower two pieces are hollow from inside. The over all length of the staff thus becomes 1.5 m when the staff is not in use.

Level Staff Self reading Target Staff Solid Staff Folding Staff Telescopic Staff Target staff is a solid staff having a sliding target equipped with vernier. The rod is graduated in feet, tenths and hundredths, and the vernier of the target enables the reading to be taken up to a thousandth part of the feet. It is used for long distance sighting.

Setting up the level Leveling the instrument Removal of parallax Temporary Adjustment of Dumpy Level At each setting of a level instrument, temporary adjustment is required to be carried out prior to any staff observation. It involves some well defined operations which are required to be carried out in proper sequence. It consists of Setting Leveling Focusing

During Setting , the tripod stand is set up at a convenient height having its head horizontal (through eye estimation). The instrument is then fixed on the head by rotating the lower part of the instrument with right hand and holding firmly the upper part with left hand. Before fixing, the leveling screws are required to be brought in between the tribrach and trivet. The bull's eye bubble (circular bubble), if present, is then brought to the centre by adjusting the tripod legs. Leveling of the instrument is done to make the vertical axis of the instrument truly vertical. It is achieved by carrying out the following steps: Step 1: The level tube is brought parallel to any two of the foot screws, by rotating the upper part of the instrument. Step 2: The bubble is brought to the centre of the level tube by rotating both the foot screws either inward or outward. (The bubble moves in the same direction as the left thumb.) Step 3: The level tube is then brought over the third foot screw again by rotating the upper part of the instrument. Step 4: The bubble is then again brought to the centre of the level tube by rotating the third foot screw either inward or outward. Step 5: Repeat Step 1 by rotating the upper part of the instrument in the same quadrant of the circle and then Step 2. Step 6: Repeat Step 3 by rotating the upper part of the instrument in the same quadrant of the circle and then Step 4. Step 7: Repeat Steps 5 and 6, till the bubble remains central in both the positions. Step 8: By rotating the upper part of the instrument through 180 ° , the level tube is brought parallel to first two foot screws in reverse order. The bubble will remain in the centre if the instrument is in permanent adjustment.

Levelling

Focusing is required to be done in order to form image through objective lens at the plane of the diaphragm and to view the clear image of the object through eye-piece. This is being carried out by removing parallax by proper focusing of objective and eye-piece. For focusing the eye-piece, the telescope is first pointed towards the sky. Then the ring of eye-piece is turned either in or out until the cross-hairs are seen sharp and distinct. Focusing of eye-piece depends on the vision of observer and thus required whenever there is a change in observer. For focusing the objective, the telescope is first pointed towards the object. Then, the focusing screw is turned until the image of the object appears clear and sharp and there is no relative movement between the image and the cross-hairs. This is required to be done before taking any observation.

Removal of Parallax Eye piece is focused on to the cross hairs. The image of the level staff should fall in the plane of the cross hair. If the above condition is not satisfied there shall be errors in readings So, it is essential to establish the afarsaid condition before taking readings. Focusing the eye piece. Focusing the objective To eliminate the parallax error, white paper is place in front of the eye piece and then it is focused by the screw for distinct vision of the cross hair. To bring the image of the staff in the plane of the cross hair. Telescope is directed towards the staff and the focusing screw is turned till the image appears clear and sharp.

Fundamental Lines Bubble tube axis Vertical axis Optical axis Line of collimation Line tangential to the curved surface of the bubble tube is called bubble tube axis.

Fundamental Lines Bubble tube axis Vertical axis Optical axis Line of collimation Axis about which the telescope rotates is called vertical axis.

Fundamental Lines Bubble tube axis Vertical axis Optical axis Line of collimation The straight line passing through the optic center of eye piece and optic center of the object lens is called Optical axis.

Fundamental Lines Bubble tube axis Vertical axis Optical axis Line of collimation The straight line passing through the intersection of the cross wires and the optic center of the object lens is called Line of collimation.

Relationship between Fundamental Axis Line of collimation should be parallel to the bubble tube axis Line of collimation should coincide with the optical axis of the telescope Bubble tube axis should be perpendicular to the vertical axis of the instrument.

Permanent Adjustments of the level There exist a relationship between the fundamental lines. Instruments when used for a period of time gets disturbed and fail to satisfy the conditions/relations. In such case we need to perform permanent adjustments. They are done by the manufacturer and it is a part of advanced surveying.

Technical Terms used in Leveling Height of Instrument Back Sight Fore Sight Intermediate Sight Change Point Back Sight : It is the sight / reading taken on the level staff held on the point of known elevation i.e. Bench Mark. Fore Sight : It is the last reading taken on the level staff kept at a station from the instrument station before shifting the instrument. Intermediate Station : Readings taken after back sight and before fore sight for a particular set up of the instrument is know as IS. Change Point : This is also known as Turning point. This is the point on which both FS and BS are taken. After taking FS, the instrument is shifted at other convenient point and BS is taken on the staff held at the same point. Height of instrument (HI) – It is the elevation of the line of sight of the telescope.

F A [BM] B C E D IP - 1 BS-1 FS-1 IP - 2 BS-2 IS-1 IS-2 FS -2 IP - 3 BS -3 FS - 3 A,B,C,D,E,F – Survey stations IP-1,2,3 : Instrument positions FS- Fore sight BS- Back Sight IS- Intermediate Sight Station BS IS FS Remarks A (BM) BS-1 IP-1 B BS-2 FS-1 IP-1 TO IP-2 C IS-1 IP-2 D IS-2 IP-2 E BS-3 FS-2 IP-2 TO IP-3 F FS-3 IP-3

Methods of Levelling Simple (or) Direct leveling Differential leveling Fly leveling Profile leveling Cross sectioning Reciprocal leveling A + 200.00 B 2.7 m 0.3 m RL of A : +200.00 m Height of Instrument (station) : +200.00 + 2.7 m Fore Sight of B = 0.3 m Back sight of A = 2.7 m RL of B : +202.7 – 0.3 = 202.4 m Simple or Direct Levelling is used for finding the level difference between two stations that are nearer.

Methods of Levelling Differential leveling A + 200.00 B Differential Levelling: If the distance between point whose difference in elevations is to be determined is large, then it is not possible to take the readings on A and B from a single setup. In this case, instrument is set at more than one position, each shifting facilitated by a change point. CP-3 CP-2 CP-1

Methods of Levelling Fly leveling Fly Levelling: If the work site is away from the permanent bench mark, surveyor starts the work with the BS on the bench mark. He proceeds towards the site by taking fore sights and back sights on a number of change points till he establishes a temporary bench mark in the site. This type of levelling in which only BS and FS are taken, is called fly levelling, whose purpose is to connect a permanent bench mark with temporary bench mark or vice versa. Thus Differential levelling and fly levelling differ only in the purpose.

PBM Fly leveling (Contd…)

Methods of Levelling Profile leveling Profile Levelling: This is known as longitudinal sectioning. In projects like highways, railways, sewer lines, irrigation canals etc…, profile of the ground along them are required. In such cases, at regular intervals, readings are taken along their length and they are then plotted to get the profile. In this case, instrument is set at more than one position, each shifting facilitated by a change point. Longitudinal Profile of the road

Methods of Levelling Cross sectioning Cross Sectioning: In projects like highways, railways, sewer lines, irrigation canals etc…, in addition to longitudinal profile of the ground, cross section profile is also essential. These profiles help in calculating the earth works involved in the projects. In such cases, at regular intervals, readings are taken along their chain line for longitudinal profile and in addition to this, at each station on chain line, readings are taken at close intervals on either side for cross sectioning. 20 40 60 140 80 120 100 Station Distance in m Readings RL Remarks L C R BS IS FS

Methods of Levelling Reciprocal Levelling Reciprocal Levelling: This is a type of levelling in which the difference between two stations separated by an obstruction is determined.

Level Field Book Station Distance in m Readings RL Remarks L C R BS IS FS

Methods of Booking and Reducing the Levels Height of Instrument Method Rise and Fall Method

Height of Instrument Method In this method, Height of instrument for first setting of the instrument is calculated as HI = RL of Bench Mark + Back sight From HI, subtract intermediate sight and Fore sight to compute the RL of intermediate stations and change points. Add back sight to RL of change point to get new height of instrument. Similarly, compute RL of other Intermediate stations and change points. Finally find the sum of BS, FS. Check:

Rise and Fall Method In this method, Height of instrument is not calculated. Difference of level between consecutive points is found by comparing the staff readings on the two points for the same instrument setting. Difference between their staff readings indicate a rise or fall according as the staff reading at the point is smaller or greater than at the preceding point. RL of the stations are calculated by either adding or subtracting the rise or fall between the two stations to the RL of previous station. Arithmetic Check / Check

General

A B

IP-1 S-1 A Station BS IS FS A X

IP-1 A A-1 Station BS IS FS A X A1 X

IP-2 A A-1 Station BS IS FS A X A1 X x

Station BS IS FS A X A1 X X A2 x IP-2 A A-2

Station BS IS FS A X A1 X X A2 X X IP-3 A-2

Station BS IS FS A X A1 X X A2 X X A3 X IP-3 A-3

Station BS IS FS A X A1 X X A2 X X A3 X X IP-4 A-3

IP-4 A-4 Station BS IS FS A X A1 X X A2 X X A3 X A4 X

IP-5 A-4 Station BS IS FS A X A1 X X A2 X X A3 X A4 X X

IP-5 B Station BS IS FS A X A1 X X A2 X X A3 X A4 X X B X

Height of Instrument The following staff readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 , 2.090, 2.864, 1.262 , 0.602, 1.982, 1.044, 2.684 m. [CSVTU, 2009]

Height of Instrument Station BS IS FS HI RL A 2.228 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 B 1.606 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 B 1.606 C 0.988 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 B 1.606 C 2.090 0.988 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 B 1.606 C 2.090 0.988 D 2.864 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 B 1.606 C 2.090 0.988 D 2.864 E 1.262 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 B 1.606 C 2.090 0.988 D 2.864 E 0.602 1.262 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 B 1.606 C 2.090 0.988 D 2.864 E 0.602 1.262 F 1.982 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 B 1.606 C 2.090 0.988 D 2.864 E 0.602 1.262 F 1.044 1.982 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 B 1.606 C 2.090 0.988 D 2.864 E 0.602 1.262 F 1.044 1.982 G 2.684 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 200.0+2.228 = 202.228 200.00 B 1.606 C 2.090 0.988 D 2.864 E 0.602 1.262 F 1.044 1.982 G 2.684 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 2000+2.228 = 202.228 200.00 B 1.606 202.228 – 1.606 = 200.622 C 2.090 0.988 D 2.864 E 0.602 1.262 F 1.044 1.982 G 2.684 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 2000+2.228 = 202.228 200.00 B 1.606 202.228 – 1.606 = 200.622 C 2.090 0.988 202.228 – 0.988 = 201.24 D 2.864 E 0.602 1.262 F 1.044 1.982 G 2.684 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 2000+2.228 = 202.228 200.00 B 1.606 202.228 – 1.606 = 200.622 C 2.090 0.988 201.24+2.09=203.33 202.228 – 0.988 = 201.24 D 2.864 E 0.602 1.262 F 1.044 1.982 G 2.684 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 2000+2.228 = 202.228 200.00 B 1.606 202.228 – 1.606 = 200.622 C 2.090 0.988 201.24+2.09=203.33 202.228 – 0.988 = 201.24 D 2.864 203.33-2.864=200.466 E 0.602 1.262 F 1.044 1.982 G 2.684 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 2000+2.228 = 202.228 200.00 B 1.606 202.228 – 1.606 = 200.622 C 2.090 0.988 201.24+2.09=203.33 202.228 – 0.988 = 201.24 D 2.864 203.33-2.864=200.466 E 0.602 1.262 203.33-1.262=202.068 F 1.044 1.982 G 2.684 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 2000+2.228 = 202.228 200.00 B 1.606 202.228 – 1.606 = 200.622 C 2.090 0.988 201.24+2.09=203.33 202.228 – 0.988 = 201.24 D 2.864 203.33-2.864=200.466 E 0.602 1.262 202.068+0.602=202.67 203.33-1.262=202.068 F 1.044 1.982 G 2.684 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 2000+2.228 = 202.228 200.00 B 1.606 202.228 – 1.606 = 200.622 C 2.090 0.988 201.24+2.09=203.33 202.228 – 0.988 = 201.24 D 2.864 203.33-2.864=200.466 E 0.602 1.262 202.068+0.602=202.67 203.33-1.262=202.068 F 1.044 1.982 202.67-1.982=200.688 G 2.684 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 2000+2.228 = 202.228 200.00 B 1.606 202.228 – 1.606 = 200.622 C 2.090 0.988 201.24+2.09=203.33 202.228 – 0.988 = 201.24 D 2.864 203.33-2.864=200.466 E 0.602 1.262 202.068+0.602=202.67 203.33-1.262=202.068 F 1.044 1.982 200.688+1.044=201.732 202.67-1.982=200.688 G 2.684 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F

Height of Instrument Station BS IS FS HI RL A 2.228 2000+2.228 = 202.228 200.00 B 1.606 202.228 – 1.606 = 200.622 C 2.090 0.988 201.24+2.09=203.33 202.228 – 0.988 = 201.24 D 2.864 203.33-2.864=200.466 E 0.602 1.262 202.068+0.602=202.67 203.33-1.262=202.068 F 1.044 1.982 200.688+1.044=201.732 202.67-1.982=200.688 G 2.684 201.732-2.684 =199.048 SUM 5.964 6.916 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F Abs(5.964-6.916) = abs(199.048-200)

Solve the above problem by Rise and Fall method

Height of Instrument Station BS IS FS Rise Fall RL A 2.228 200.00 B 1.606 C 2.090 0.988 D 2.864 E 0.602 1.262 F 1.044 1.982 G 2.684 The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. A B C E D G F

Rise and Fall The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F Station BS IS FS Rise Fall RL A 2.228 200.00 B 1.606 0.622 200.622 C 2.090 0.988 D 2.864 E 0.602 1.262 F 1.044 1.982 G 2.684

Rise and Fall The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F Station BS IS FS Rise Fall RL A 2.228 200.00 B 1.606 0.622 200.622 C 2.090 0.988 0.618 201.24 D 2.864 E 0.602 1.262 F 1.044 1.982 G 2.684

Rise and Fall The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F Station BS IS FS Rise Fall RL A 2.228 200.00 B 1.606 0.622 200.622 C 2.090 0.988 0.618 201.24 D 2.864 0.774 200.466 E 0.602 1.262 F 1.044 1.982 G 2.684

Rise and Fall The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F Station BS IS FS Rise Fall RL A 2.228 200.00 B 1.606 0.622 200.622 C 2.090 0.988 0.618 201.24 D 2.864 0.774 200.466 E 0.602 1.262 1.602 202.068 F 1.044 1.982 G 2.684

Rise and Fall The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F Station BS IS FS Rise Fall RL A 2.228 200.00 B 1.606 0.622 200.622 C 2.090 0.988 0.618 201.24 D 2.864 0.774 200.466 E 0.602 1.262 1.602 202.068 F 1.044 1.982 1.38 200.688 G 2.684

Rise and Fall The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F Station BS IS FS Rise Fall RL A 2.228 200.00 B 1.606 0.622 200.622 C 2.090 0.988 0.618 201.24 D 2.864 0.774 200.466 E 0.602 1.262 1.602 202.068 F 1.044 1.982 1.38 200.688 G 2.684 1.64 199.048

Rise and Fall The following staf readings were observed successively with a level, the instrument having been moved after 3 rd , 6 th and the 8 th readings. 2.228, 1.606, 0.988 ,2.090,2.864, 1.262 ,0.602, 1.982, 1.044,2.684 m. The RL of BM is 200.00 m A B C E D G F Abs(5.964-6.916) = abs ( 2.842 – 3.794) = abs(199.048-200) Station BS IS FS Rise Fall RL A 2.228 200.00 B 1.606 0.622 200.622 C 2.090 0.988 0.618 201.24 D 2.864 0.774 200.466 E 0.602 1.262 1.602 202.068 F 1.044 1.982 1.38 200.688 G 2.684 1.64 199.048 SUM 5.964 6.916 2.842 3.794

Station BS IS FS RL A 0.865 560.5 B 1.025 2.105 C 1.58 D 2.23 1.865 E 2.355 2.835 F 1.76 Station BS IS FS RL A 1.622 B 1.874 0.354 C 2.032 1.78 D 2.362 E 0.984 1.122 F 1.906 2.824 G 2.036 83.50 The following consecutive readings were taken with a level and 5 m leveling staff on continuously sloping ground at a common interval of 20 m: 0.385, 1.030, 1.925, 2,825, 3.730, 4.685, 0.625, 2.005, 3.110, 4.485. the reduced level of the first point was 208.125 m. Rule out a page of level field book and enter the readings. Calculate the RL of the points and also find the gradient of the line joining the first and the last point. Numericals

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