Leveling

Leveling :

• Find the elevation of given points with reference to a given or assumed datum, and
• Establish points to a given elevation or assumed datum
• Establish points at a given elevation or at different elevations with reference to a given or assumed datum.
• Deals with angular and linear measurements in a vertical plane

Fundamental Definition:

Level surface : A curved surface which at each point is perpendicular to the direction of gravity at the point. The surface of a still water is a truly level surface. Any surface  parallel to the mean spheroid surface of the earth is, therefore, a level surface.

Level line: Normal to the plumb line at all points.

Horizontal plane: Tangential  the level surface at the point.

Horizontal line: Straight line tangential to the level at a point. 

Vertical line: Line normal to the level line at a point

Datum: Any surface to which elevations are referred.

Elevation: Vertical distance above or, below an arbitrarily assumed level surface or datum.

Bench Mark: Relatively permanent point of reference whose elevations with reference to

some assume datum known. Used either as a starting point for leveling or as a point upon which to close as a check.

Methods of leveling : Three methods:

Barometric leveling : Makes use of the phenomenon that difference in elevations

between two points is proportional to the difference in atmospheric pressures at these points.

Trigonometric leveling : (Indirect leveling) : In a modified form called Stadia leveling. This method is commonly used in mapping .

Spirit leveling (direct leveling): In this a spirit level and sighting device (telescope)

are combined and vertical distances are measured by observing an graduated rods placed on the points. It is the most precise method.

Commonly used leveling instruments:

• Level
• A leveling staff

Level: is to provide a horizontal line of sight. 

It consists of Four parts.

• A telescope to provide line of sight.
• A level tube to make the line of sight horizontal.
• A leveling head to bring the bubble in its centre of run
•  A tripod to support the Instrument. .

 Chief types of levels are: 

•  Dumpy 
• Wye or Y
• Reversible and  
• Tilting.  

Dumpy Level: The name originated from the fact that formerly this level was equipped with an inverting eyepiece and hence was  shorter then way level of the same magnifying power.

Advantages:

• Simpler construction with fewer movable parts
• Fewer adjustment to be made
• Longer life of the adjustments.

Eye Level: The essential difference between the dumpy level and the way level is that in the former case the telescope is fixed to the spindle while in the way level ,the telescope is carried in two vertical "wye "supports.

The wye level has an advantages over the dumpy level in the fact that the adjustments can be tested with greater rapidity and case.

Reversible Level: Combines  the features  of both the dumpy level and the wye level.

Tilting level: In this the line of sight and the vertical axis need not be exactly perpendicular to each other. It helps in quick leveling.

A Tilting Level is mainly designed for precise leveling work.

Plane Table Survey

• Plane tabling is a graphical method of survey in which the field observations and plotting proceed simultaneously.

Instruments used:

 Plane table: Three types of the plane tables are commonly used in practice:

1. The traverse tables: Leveled by adjusting tripod less, usually by eye estimation.
2. Johnson table: Consists of drawing bound usually 45 X 60cm or 45 X 75cm. head consists of ball and socket joint.
3. Coast survey table: Leveling done very accurately with the help of three foot screws.

 Alidade: A straight edge with same form of fighting device. Two types: .

1. Plain alidade:  Consists of metal of wooden rule with two vanes at the ends. The working edge against which lines are drawn is also known as “bevelled edge or edge”.         Not very much suitable on hilly area since inclination of the line of sight is limited.
2. Telescopic alidade:

Significance: We can take inclined sights.

• Accuracy and range of sights are increased by its uses.
• Horizontal distance between the instrument and the point sighted can be computed by taking stadia readings on the staff kept at the point.
•  Elevation of points can also be computed by using usual technometric relations.
• All the above things can be done very quickly

Plumbing fork: used in large scale work. Meant for centering the table are the point of station occupied by the plane table when the plotted position of point is already known as the sheet.

Spirit level : For proper leveling

Compass : For orientation - generally tough compass is used.

Drawing paper : of superior quality.

        

• Working operations:

Fixing

Setting 

Consist of :

1. Leveling the table
2. Centering 
3. Orientation: The process of putting the plane table into some fixed direction so that line representing a certain direction on the plane is parallel to that direction on the ground.

• If orientation is not done, the false will not be parallel to itself at different positions resulting in an overall distortion of map.
• Significance: This is an essential condition to be fulfilled when more than one instrument station is to be fixed.
• Methods of orientation: 

 Orientation by through compass : used when

• speed is more important than accuracy
•  there is no second point available for orientation. .

 Orientation by back sighting : Two methods

1. when it is possible to set the plane table on the point already plotted on the sheet by way of observation from previous table. When it is not possible to set the plane table on the point already plotted. The method is also known as “Resection".

• Methods of plane tabling:

1. Radiation 
2. Intersection
3. Traversing 
4. Resection .

The First two methods arc generally employed for locating the details while the other two methods are used for locating the plane table stations

 Radiation: Suitable when the distances are small (with in a tape length) and are single instrument can control  the points to be  detailed. 

Intersection: 

• Also known as graphic triangulation.
• Suitable for hilly areas

Traversing: used to plot areas.

Resection: The process of determining the plotted position of the station occupied by the plane table, by means of sights taken towards known points, location of which have been plotted. Resection can be done by the following methods. 

•  By compass
• By back sighting
• Three point problem
• Two point problem 

Three point problem: The location of plane table station can be located by three well defined points on ground.

1. Mechanical (Tracing paper) method
2. Graphical (Bessel’s) method
3. Trial and error (Lehmann’s) method

Two point problem: Plane table station can be located by two well defined points on the ground.

Compass Survey

Definition: A branch of surveying in which directions of survey lines are determined with a  compass and lengths of lines arc measured with a tape or chain. Generally used to run a traverse.

Types of Meridians:

Meridian : Fixed line of reference about which directions or angles arc measured.

• True Meridian: line joining,true  north and true south. Established by Astronomical observations .
• Magnetic meridian: Direction shown by a  freely floating and balanced magnetic needle free from all other attractive forces (Line passing through magnetic north and south). Established by magnetic compass.
• Grid meridian: For survey of a state, the true meridian of central place is taken as a reference meridian for. whole state and is called Grid meridian.
• Arbitrary meridian : Meridian taken in any convenient direction towards a permanent and prominent mark or signal.

Used to determine relative  direction of various lines in a small traverse or small area. 

Types of Bearings: Bearing of a line is the angle between a meridian and a survey line

• True Bearing : True bearing of a line is horizontal angle between true meridian and the line. Also known as Azimuth. Does not change with time, it is a constant.
• Magnetic beating: Magnetic beating of a line is the horizontal angle which the line makes with magnetic north. Changes with time. Used for small areas. Measured with a magnetic compass.
• Grid bearing: Grid bearing of a line is the horizontal angle with Grid meridian.
• Arbitrary bearing : Arbitrary bearing of line is the horizontal angle with “Arbitrary meridian”.

Systems of Bearings:

Whole circle Bearing system (WCB):

• Bearing of line OA = θ1 ;OB = θ2 ; OC = θ3 ;OD = θ4
• Bearing of a line is measured always in clockwise from North end of reference.
• Bearing varies from 0° to 360°
• Prismatic compass is graduated in this system.
• Also called "Azimuthal system"

 Quadral Bearing(QB) system:

• Bearing   OA = NθE, OB = SαE, OC = SγW, OD = Nν W
• Bearing of a line is measured eastward or westward from North or South, which ever is nearer.
• Varies from 0° to 90°.
• Observed by surveyors compass
• Also called “Reduced bearings”.

Conversion of bearings from one system to other: very easy with the aid of a diagratm

•  Conversion of  W.C.B. Into R.B

Line	WCB	Rule for R.B or Q.B	Quadrant
OA	0° & 90°	Nϴ E	I
OB	90° & 180°	S ( 180°-ϴ ) E	II
OC	180° & 270°	S (ϴ - 180°) W	III
OD	270° & 360°	N( 360°-ϴ)	IV

•  Conversion of R.B into W.C.B

Line	WCB Between ()	Rule for R.B or Q.B	Quadrant
OA	N ϴ E	ϴ	I
OB	SϴE	(180°-ϴ)	II
OC	SϴW	(180°+ϴ)	III
OD	NϴW	(360°-ϴ)	IV

Note: When a line points towards North, East, South or West, it Is written as “Due North”, “Due

east”,"Due South” or “Due West” respectively.

Thus, N0° = Due North; N 90°E = S90°E=Due east

S0° = Due South; N90° W = S90°W =Due West

Fore bearing and backing hearing:

• The bearing of a line ¡n the direction of progress of survey indicated by an arrow is called fore. bearing (F.B).
• The bearing in an opposite direction to F.B or in the direction opposite to the survey is Back bearing (B.B) 
  

Determination of B.B for F.B:

1. F.B and B.B differ by 180°

• If F.B is given as W.C.B:    B.B = F.B + 180° if F.B < 180° and B.B = F.B- 180° if F.B > 180°
•  If F.B of a line is given as quadrantal bearing: B.B is numerically equal to F.B change ‘N’ for ‘S’ and vice versa. Change ‘E’ for ‘W’ and vice versa.

Important Note: Always better to draw rough sketch either for conversion of one system to

another or for working out B.B from F.B or vice versa.

Included ‘angle between bearings:

Can be calculated ‘very easily using a diagram

Whole circle bearings are given:

• Bearings of two lines measured from a common point. Included angle θ = θ2 - θ1 two lines from
  
• Bearing of two lines not measured from a common point.

             = B.B of previous line - F.B of next line

             =(180+ θ1)-θ2

Quadrantal bearings of two lines are given:

• Measured from a common point:

Calculation of bearings from Angles:

• Bearing of any one line (generally, the first line) is also required along with included angles.
• In a closed traverse, clock wise angles will be the interior angles if the traverse is run in the anti-clockwise direction.
• Bearing of any line = Bearing of preceding line + Included angle.
• If the sum is more than 180° deduct 180°. if the sum is less than 180° add 180°

Magnetic compass: 

It gives directly the magnetic bearings

Dip: is the inclination of the magnetic needle with the horizontal.

• Northern end is ,deflected down in the ‘Northern hemisphere” while the southern end is deflected down in the “Southern; hemisphere” 
• The dip is zero at equator and needle will remain horizontal.
• At a place near 70° North latitude and 96° West longitude, dip will he 90° This area is called north magnetic pole.
• Similarly near south magnetic pole, dip is 90°

Magnetic declination:---  (True bearing — magnetic bearing)

• Isogonic line is the line drawn through points  of same declination.
• Agonic line  is the line made up of points having a zero declination.
• If the magnetic meridian is to the right side (or eastern  side) of the true meridian, declination is Eastern or positive.
• If is  to the left side (or western side), it is said to  be western or negative.
• Magnetic declination at a place is not constant but varies from time to time.

Duirnal variation :-

• Variation ¡n a day
• More during day time and less during night time.
• More at magnetic  poles and less at equator.
• Considerably more in Summer  than in winter.
• Changes from year  to year.

Annual Varition: variation over a period of an year

Secular variation: variation over a period approximately 250 years.

Irregular variations : are due to magnetic storms, earthquakes and solar influences etc. 

Determination of true bearing

True bearing = magnetic bearing ± declination

+ sign for eastward declination

- Sign for westward declination. (WCB)

If Reduced bearing is given , it is advisable to draw diagram and calculate bearing.

Local Attraction

• If BB- FB ≠ 180
• The local attraction is due to influence of magnetic materials like heavy steel or nickel objects , electric poles, transmission lines etc.
• The local attraction due to key chains, steel buttons, steel pens should be ignored

Adjustments of Prismatic Compass :

Temporary adjustments : are those made at every set up of the instrument. They are

1. Centering: Process of keeping the instrument exactly over the station. Done by adjusting legs of tripod and using plumb bob. 
2. Levelling : Generally, tripod is provided with ball and socket arrangement with the help of which leveling is done.
3. Focusing the prism: Prism is moved up or down ¡n its  slice till the graduations in the ring are seen clear.

Permanent adjustments: Done when, the fundamental relations between parts  are disturbed.

Chain Survey

Chain Survey is  a methods of making linear measurements.

Direct Measurement: Distance is actually measured in the field using “Chain or tape’

Approximate Methods: Used in reconnaissance survey are pacing, passometer, pedometer, odometer, measuring wheel and speedometer (speed and distance).

Chaining is the most accurate method of making direct measurements.

Chain Survey:

• It is the simplest and oldest form of land surveying of an area using linear measurements only.
• It can be defined as the process of taking direct measurement, although not necessarily with a chain.

Types of equipment used in Chain Surveying:

Chain: This is an instrument used for measuring distance. There are four types of chains.

1. Metric chain: In metric system the chains are of 20 m and 30 m are commonly used. The chain is made with galvanized steel wire of 4mm diameter. Each meter is divided into 5 links of 20mm length. It is provided with brass handles on either ends. The tallies are fixed at every 5m length and small brass rings are provided at every meter length.   20 m Chain - 100 Links,   30 m Chain - 150 links
2. Engineer’s chain: The Engineer’s chain is 100 ft length and made of 100 links.
3.  Gunter chain: It is 66 feet long and has 100 links. It is useful for measuring the distance in miles and areas in acres.                                                                             10 square Gunter chain = 1 acre = 4840 sq. yards. 
4. Revenue chain: This chain is of 33ft length and is divided into 16 links.

Tape: The tapes are divided according to the materials used as following (i) Metallic tapes (ii) Steel tapes (iii) Invar tapes

1. Metallic tapes: This tape is made with waterproof linen with brass, copper wires to avoid stretching. The tapes available in lengths 2, 5, 10, 20 and 30m.
2. Steel tapes: This is most accurate tape for taking measurements. If carelessly handled it gets broken.
3. Invar tapes: If the measurements are to be made with the highest precision this tape is used. These are 6mm wide and available in lengths of 30, 50 and 100m.Invar tape is made of alloy of nikel 36% & steel 64%. It has low coefficent of thermal expension ( 1/ 10th of steel)  
   

Ranging rods: These are wooden or metal poles 2m or 3m long and having a diameter of 30mm. They are provided with iron shoes at the lower ends to facilitate easy driving in the ground. They are painted in bands alternatively in black and white or red and white. Ranging rods used for ranging a line.

Offset rods: This is mainly used to measure offsets of shorter lengths. It is usually 5m long.

Cross staff: Cross staff is an instrument used for setting perpendicular offsets. These are three types.

1. Open cross staff: It consists of 4 metal arms at right angles to each other having eye vane at two adjacent ends and object vane at the other ends. @90°
2. Adjustable cross staff: With this cross staff the object can be set at any angle.@ 15° interval.
3. French cross staff: This cross-staff is an octagonal brass tube with slits on its eight faces. With this cross staff we can set the object at an angle of 450 also. @ 45° & 90° 

Optical Square: This is an instrument used for setting out right angles to the chain lines and to find out the foot of the perpendicular on the chain line from an object. It works on the principle of reflection.

Arrows: These are used for marking the ends of a chain during the process of chaining. These are steel pins 400mm long and are pointed at one end.

Plumb bob: It is used to define the vertical line while measuring distance along slopes.

General Procedure in making a Chain Survey

• Reconnaissance: Walk over the area to be surveyed and note the general layout, the position of features and the shape of the area.
• Choice of Stations: Decide upon the framework to be used and drive in the station pegs to mark the stations selected.
• Station Marking: Station marks, where possible should be tied - into a permanent object so that they may be easily replaced if moved or easily found during the survey. In soft ground, wooden pegs may be used while rails may be used on roads or hard surfaces.
• Witnessing: This consists of making a sketch of the immediate area around the station showing existing permanent features, the position of the stations and its description and designation. Measurements are then made from at least three surrounding features to the station point and recorded on the sketch. The aim of witnessing is to relocate a station again at much later date even by others after a long interval.
• Offsetting: Offsets are usually taken perpendicular to chain lines in order to dodge obstacles on the chain line.
• Sketching the layout on the last page of the chain book, together with the date and the name of the surveyor, the longest line of the survey is usually taken as the baseline and is measured first.

Linear Measurements

Tape Corrections

• Correction due to standardization or (correction due to absolute length)

                                             

where, Ca = Correction for absolute length

L = Measured length of the line

l = Designated length of the tape

C = Correction per tape length

• Correction due to temperature

CT = Lα(Tm – T0)

where, Tm = Temp. at the time of measurement

T0 = Temp. at the time of standardization of the tape

α = Coeff. of thermal expansion

L = Measured length

• Correction for pull or tension

where, Cp = correction for pull

Pm = pull applied at the time of measurement

P0 = Pull applied at the time of standardization

L = Measured length

A = Cross-sectional area

E = Young’s modulus of tape

• Sag Correction

where, Pm = Pull applied, W = Total weight of tap = wl

w = Weight per meter length, l = length of tape

Case: Normal Tension

At a particular value of pull (where Pm > P0) pull correction and sag correction neutralize each other. This value is called normal tension.

• Correction due to slope

where,

h = difference in elevation between the ends

L = Inclined length measured

l = Horizontal length

Cs = Correction due to sag

•  Correction due to the wrong alignment

where, L = length measured along wrong alignment

l = Correct length

h = Error in alignment

Limiting Length of Offset

• Effect of error in laying out direction only

where, l = Limiting length of offset

S = Scale (1 cm = S meter)

Combined error in length and direction

where,

X = error in length measurement.

S = Scale (1 cm = S meter)

Basic definition:

• Main survey stations : Are prominent points, at the beginning and ends of survey lines.
• Survey lines: Lines joining main survey stations
• Check lines : Lines run to check the accuracy of main frame work of triangles. Also called proof lines.
• Offsets : Are the lateral distances measured from the survey lines. Perpendicular offset (or simply offsets) and oblique offset (or tie) are the two types.
• Tie lines:  Are the Lines run to locate details to avoid long offsets. It is also called a subsidiary lines run or secondary line. it is also used as a check line.
• Subsidiary stations : Stations located on the survey lines between which is tie lines or subsidiary lines run.
• Base line : Is a long survey line which is run through the middle of the area to he surveyed. The frame work of triangles is built upon the base line.

Well conditioned triangles:

A triangle is said to be well conditioned if it can be plotted accurately by the intersections of arcs from the ends of base line. The best one is equilateral triangle. A triangle in which no angle is less than 30° or more than 120° can be treated as a well condition triangle.

NEXT TOPIC: COMPASS SURVEYING

Introduction Of Surveying

Surveying is the process of determining relative positions of different objects on the surface of the earth by measuring horizontal distances between them and preparing a map to any suitable scale. Measurements are taken in a horizontal plane.

OBJECTS OF SURVEYING:

(a) Determining relative positions of various points, above or below the surface of earth

(b) To mark the positions of proposed structure on ground.

(c) To determine areas, volumes and other related quantities.

PRIMARY Divisions OF SURVEYING:

• Primary division is based whether the curvature of earth is considered or not.
• The actual shape of earth is an oblate spheroid.
• The polar axis (12713.168 km) is shorter (than the equatorial axis (12756.602 km) by about 43.434 km (0.34%)
• The average radius of earth is taken as 6370 km for all calculations point of view.

PLANE SURVEYING: The surveying in which the curvature of earth is neglected and is assumed to be a flat surface.

•  Plane survey can safely be used when the extent of area is less than 260 Sq km.
• Also when the difference between an arc distance of 18.2 km on the surface of earth and corresponding chord distance is about 10mm. 
• Also when the difference between the sum of angels  in a plane triangle and spherical triangle is only one second(1")  for a triangle at the earth’s surface having an area of 195 Sq. km.

GEODETIC SURVEYING: Shape of earth is taken into account.

• All lines lying on the surface are curved lines and triangles arc spherical triangles.
• Preferred for works of large scale with high degree of precision.
• The directions of plumb lines at various Points  are converging towards center of earth.

Functional classification of Surveying:

1. Control Surveying: Establishing the horizontal and vertical positions of widely spaced control points  using principles of Geodetic Surveying. ln India, control survey is  done by ‘Survey of India”
2. Topographical Survey : To show natural Features of the country such as rivers, hills, lake, etc.
3. Cadastral Surveys : Fixing of property lines, to show boundaries of fields, buildings etc. This is to be done by a revenue engineer.
4. Engineering Surveys : To obtain data  for designing any type of project such as roads, railways. water supply systems etc. An engineer is interested in this survey works.
5. Mine Survey: Under ground works such as mines, shafts, pits, bore holes etc.
6. Hydro graphic Survey : Surveying under water bodies e.g., determination of channel depth etc.
7. Astronomic Survey: To determine absolute location of a point on earth by taking latitude, longitude, azimuth, local time etc.

Classification based on instrument:

1. Chain surveying :This is the simple method of taking the linear measurement using a chain or tape with no angular measurements made.
2. Compass Surveying : Here horizontal angular measurements are made using the magnetic compass with the linear measurements made using the chain or tape.
3. Leveling:This is the measurement and mapping of the relative heights of points on the earth’s surface showing them in maps, plane and charts as vertical sections or with conventional symbols.
4. Plane Table Surveying: This is a quick survey carried out in the field with the measurements and drawings made at the same time using a plane table.
5. Theodolite Survey: Theodolite survey takes vertical and horizontal angles in order to establish controls.
6. Techeometric Survey
7. Photogrammetry
8. EDM Surveys

PRINCIPALS OF SURVEYING

1. Working from whole to part: First a system of control points are fixed with higher precision for a large area. It prevents accumulations of errors
2. Location of a point by measurement from two points of reference.

Scales: Scale is the fixed ratio that every distance on the plan bears with the corresponding distance on ground. A good draftsman can plot a length to accuracy with in ± 0.25 mm

Classification of scales

1. Large scale : 1cm = 10m
2. Medium scale: 1cm = 10m to 100m
3. Small  scale: 1cm > 100m

Representing scales: The proportion between the drawing and the object can be represented by two ways as follows:

• Scale: 1cm = 1m or 1cm =100cm or 1:100
• Representative Fraction: (RF) = 1/100 (less than one) i.e. the ratio between the size of the drawing and the object.

Types of Scales:

• Plain Scales: Plain scales read or measure upto two units or a unit and its sub-division, for example centimeters (cm) and millimeters (mm). When measurements are required up to first decimal, for example 2.3 m or 4.6 cm etc. 
• Diagonal Scales:Diagonal scales are used to read or measure up to three units. For example: decimetres (dm), centimetres (cm) and millimetres (mm) or miles, furlongs and yards etc. This scale is used when very small distances such as 0.1 mm are to be accurately measured or when measurements are required upto second decimal. For example: 2.35 dm or 4.68 km etc.
• Use of verniers in scales
  A vernier is a device for measuring accurately the fractional part of the smallest divisions on a graduated scale.

Direct Verniers:  It is constructed as (n-1) divisions of the main scale is equal to n division of the vernier. In direct vernier, vernier scale moves in same direction of main scale.

nv = (n-1) s

where, s = value of one smallest division of main scale

n = number of division on the vernier

v = value of one smallest division of vernier

Retrograde vernier: It is so constructed that (n + 1) division of main scale is equal to n division of vernier. In retrograde vernier, vernier scale moves in opposite direction of main scale.

Error Due to Use of the Wrong Scale

• Correct Length

• Correct Area

Shrunk scale

Shrunk scale = original scale x shrinkage factor

NEXT TOPIC: CHAIN SURVEYING