Introduction To Surveying
Surveying:
It is the art of determining the relative positions of different object on the surface of the earth by measuring the horizontal distance between them and by preparing a map to any suitable scale. Thus, in this process, the measurements are taken only in the horizontal plane.
Levelling:
Levelling is the art of determining the relative vertical distance of different points on the surface of earth. Hence, in levelling, the measurements are taken only in the vertical plane.
Types of Surveying [Classification]:
A. Primary Classification or Primary Division :
1. Plane surveying and
2. Geodetic surveying
1. Plane Surveying :
The shape of the earth is spherical. Thus the surface is obviously curved. But in plane surveying the curvature of earth is not taken into account. This is because plane surveying is carried out over a small area, so the surface of the earth is considered as a plane. The degree of accuracy required in this type of surveying is completely low. Plane surveying is done on an area of less than 250km^2.
2. Geodetic surveying :
In geodetic surveying the curvature of the earth is taken into consideration. It is extended over a large area greater than 250km2. The line joining any two points considered as a curved line. Very refined methods and instruments are used in this type of surveying. IN this method very high precision or accuracy is required.
B. Secondary classification:
Survey can be classified on different bases.
1. Based on instrument:
A. Chain Survey
B. Compass survey
C. Plane Table survey
D. Theodolite survey
E. Tacheometric Survey
F. Photographic survey
2. Based on methods:
A. Triangulation Survey
B. Traverse Survey
3. Based on Objects:
A. Geological survey
B. Mine survey
C. Archeological Survey
D. Military survey
4. Based on nature of field
A. Land Survey
B. Marine survey
C. Astronomical survey
Again Land Survey is classified into following Classes:
1. Topographical Survey
To determine natural features of a country such as valleys, rivers and artificial features such as road, railways, etc.
2. Cadastral Survey:
To determine boundaries of field, estate
3. City survey:
To locate premises, streets, water supply and drainage systems
4. Engineering survey:
To collect detailed data for the design for of projects involving roads, railways, etc Engineering surveys are sub divided into:
1. Reconnaissance Survey
2. Preliminary Survey
3. Location Survey
Object, Use & Principles of Surveying
Objects of surveying:
The primary object of survey is the preparation of plan estate or buildings roads, railways, pipelines, canals, etc. Or to measure area of field, state, nation.
Object of geodetic surveying is to determine precise positions on the surface of the earth of widely distant points.
Uses of Surveying:
To prepare a topographical map this shows the hills, valley, rivers, villages, town, etc, of a country.
To prepare a cadastral map showing the boundaries of fields houses, and other properties.
To prepare an engineering map to show details like roads, railways, canals, etc.
To prepare military map showing roads and railways, communication with different parts of country.
To prepare contour map and to determine capacity of a reservoirs and ton find the best possible route for roads, railways etc.
To prepare archeological map including places where ancient relics exist.
To prepare a geological map showing areas including underground resources.
Principles of surveying:
There are two fundamental principles.
To work from the whole to the 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.
To fix the position of new stations by at least two independent process. The stations are fixed from points already fixed by
Linear measurement or
Angular measurements or B
Both the linear and angular measurements.
E.g. Chain surveying- main lines & stations points are checked by means of check or tie lines.
Difference between Plane and Geodetic Surveying
Plane Surveying
Geodetic Surveying
Curvature of the earth is not taken in to consideration
In this curvature of earth is considered.
In plane Surveying, line joining any two points of triangle formed by any three points is considered as straight line and plane triangle are assumed to be plane angles.
In geodetic surveying line joining two points of triangle formed by three points is considered as curved line of spherical triangle and angles of triangle are considered as spherical angles.
This survey is done on smaller area less than 250km2
This survey is done on large area greater than 250 km2
Required accuracy is competitively low.
High accuracy is required
Simple methods and instruments can be used as the required accuracy is low.
Very refined methods and instruments are used.
Instruments used in Surveying
Instruments Used for Measuring Distance:
1. Chain
a. Metric chain
b. Steel band chain
c. Günter’s Chain
d. Revenue Chain
e. Engineers chain
2. Arrows (chain pins)
3. Tapes
a. Cloth or linen Tape
b. Metric Woven Metallic Tape
c. Metric steel Tape
d. Invar tape.
e. Synthetic Tape.
f. Wooden pegs.
5. Ranging Road.
6. Ranging Poles.
7. Offset Rod.
8. Laths
9. Whites
10. Plumb Bob
1. Chain
The chain is composed of 100 or 150 pieces of galvanized mild steel wire 4mm in diameter called links. The end pf each link are bent into a loop and connected together by means of three oval rings. The ends of the chain are provided with brass handles for dragging the chain on the ground. The length of link is the distance between the centers of the two consecutive middle rings. The end links includes the handles. Metallic tags or indicators are fixed at various distinctive of the chain to facilitate quick reading.
a. Metric surveying chains:
The chains are made in lengths of 20 and 30 meters. To enable the reading of factious of a chain, tallies (tags) are fixed at every five meter length and small brass rings are provided at every meter length. To facilitate holding of the arrows in position with the handle, a groove is cut on the out side surface of the handle. The handle joints are flexible. the tallies used for marking the distances in a metric chain are marked with letters ‘Me’ and ‘m’.
b. Steel Band Chain:
It consists of a ribbon of steel with bras handle at each end. It is 20 or 30long and 16 mm wide. It is wound on an open steel cross or on the metal reel in a closed case. The graduations are etched as meters decimeters, centimeters on one side and 0.2 m links on the other. Brass tallies are fixed at every 5 m length of the band.
c. Günter’s Chain:
It is 66 fit long and is divided into 100 links. Each link is 0.66 ft long. It is very convenient for measuring distance in miles and furlongs. Also for measuring area and when the units of area is an acre
d. Revenue Chain:
It is commonly used for measuring fields in cadastral survey. It is 33 ft long and divided into 16 links. Each link is 2.0625 ft long.
e. Engineer’s chain:
It is 100 ft long and it is divided into 100 links. Each link is 1 ft in a length. Used in all Engineering surveys.
2. Arrows (chain pins):
They are also called as marking or chaining pins and are used to mark the end of chain during the process of chaining. They are made up of good quality hardened and tempered steel wire of 4mm in diameter. The arrows are made 400 mm in length. They are pointed at one end of inserting in to the ground. The other end is in to a ring.
3. Tapes:
a. Cloth or Linen Tape:
Used for taking subsidiary measurements, such as offset. It is very light and handy. It is easily affected by damp. If wet it shrinks. It stretches easily and likely to twist.
b. Metric Woven Metallic Tape:
They are available in 2, 10, 30, and 50 meters. The tape is made of yarn and metal wire. A metal ring is attached to the outer end of tapes. The length of the tape includes the metal ring. At every centimeter a black line 8 to 10 mm in height is drown. Every 5 centimeters is marked with an arrow in black. Every decimeter and meter is marked with a back line extending over the full width of the tape/ the graduation marks at every decimeter and meter are numbered with black and red figures, respectively.
c. Metric Steel Tape:
Tape is available in 1, 2, 10, 30, and 50 meters. The tape is of steel or stainless steel. The outer end is provided with a ring. The length of the tape includes the metal ring. The tape is marked with a line at every five millimeters, centimeters, decimeters, and meter. Every decimeter and meter shall be marked with Hindu Arabic numerals in bold. When the button release devised is pressed, the tape automatically rewind in to the case.
d. Invar Tape:
For highest precision work the invar tape in used. It is made of an alloy of steel and nickel (36%).
It is 6 mm wide and may be obtained in length of 30m and 100m. It is not calibrated through its length but has terminal lines. Each terminal division has ten 1 mm division. It is very expensive.
e. Synthetic Tape:
The tapes are manufactured of glass glass fiber having PVC coating. They are graduated every 10 mm and figured every 100 mm. Meter, figures are shown in red. They are convenient for measuring shorts lengths.
Instruments for marking stations:
1. Wooden Pegs:
These are used to mark the positions. They are made of hard timber and tapered at one end. They are usually, 2.5 cm square and 15 cm long. But in soft ground 40 to 60 cm long and 4 to 5 cm square is suitable. They should be driven in the ground with about 4 cm lengths, projecting above the ground.
2. Ranging rods:
Used for making the positions of stations and for ranging. They are made of seasoned timber of teak, blue pine, sisov or deodar. They are circular or octagonal in cross section of 3 cm diameter. Lower shoe is 15 cm long. They are made in two sizes as 2 meters and 3 meters and are divided in to equal parts each 0.2 m long. They are painted alternatively black and white or red and white. Now a day instead of timber, mild steel hallo pipes are used.
3. Ranging Poles:
Similar to the ranging rods but are heavier, they vary in length from 4 m to 6 m or more. Used in the case of very long lines.
4. Offset Rod:
Similar to the ranging rod, they are usually 3 m long and is divided into parts each 0.2 m length. Top is an provided with an open ring for puling or pushing the chain through a hedge. It has two short narrow vertical slots. It is used for aligning short offsets.
5. 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. Unusually 1.0m long
6. 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.
7. Plumb Bob:
The plumb bob is required when measuring the distance along slopes in order to transfer points to the ground. It is also used for testing the verticality of ranging poles.
Instruments for Setting out Right Angles
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
There are three forms of cross staff
Open cross staff
The French and
The Adjustable
Optional Square
Prism square, the first one is commonly use.
1. Open Cross Staff:
It is a simple. It consists of two parts: - 1) the head; 2) the leg. The common type of cross staff consists of 4 metal arms with vertical slits for sighting through.
The head is fixed to the top of an iron stand about 1 .2 to 1.5 m long this is driven in to the ground.
For setting perpendiculars lines, one pair of opposite arms is aligned with the chain line. It is specially used for setting off and marking contour lines.
To find the foot of perpendicular from a given point to a given lines:
To take offset, the cross staff is held vertically on chain where the offset is likely to occur, and turn until one pair of opposite slits directed to arranging rod at the forward end of the chain line, the offset is taken is bisected. If not the cross staff is moved forward or back word the chain line until the line of sight through the pair of slits at right angle the chain lines, does bisect the point.
In setting out a right angle at point on the chain line:
The cross staff is held vertically over the given point on the chain and turn until the ranging road at either end of the chain line is bisected the line of slight through 1 pair of the opposite slits. Then the line through the other pair of slits which is at right angles to the chain line through the other pair of slits which is at right angles to the chain line. Line may be marked by a ranging rod at inconvenient point on the sighted.
2. French Cross Staff:
The octagonal form cross staff is the French cross staff. It consists of an octagonal brass tube with slits on all eight sides. If has an alternate vertical slit and an opposite vertical window with a vertical horse hair or affine wire on each of the four sides. These are used for setting our right angles. On the other side are vertical slits, which are at 45 degree to those previously mentioned, for setting out angles of 45 degree.
The base carries a socket so that it may be fitted on the pointed staff when the instrument is to be used. The sight being too close (only 8 cm apart) it is inferior to the open type.
3. Adjustable Cross Staff:
It consists of a brass cylindrical tube about 8 cm in diameter and 1 cm in deep, and is divided in the centre. The upper cylinder can be rotated relatively to the lower one by a circular rack and pinion arrangement actuated by screw. Both are provided with sighting slits. The lower part is graduated to degrees and sub divisions, while the upper one carries a vernier. Thus it may be use for setting out angles of any magnitude. It has a magnetic compass at the top, which may serve to take the bearing of the line.
4. Optional Square:
An optional square is an compact hand instrument used in setting out right angles with greater accuracy than a cross staff. It consists of a circular box about 5 cm in diameter and 1.25 cm deep in which two mirrors are fitted at right angles to the plane of instruments . The mirror ‘h’ called the horizontal glass which is half silvered and half uncovered. The mirror ‘I’ is known as index glass is known as wholly silvered. There are three openings on the side of box at e, b and ,c. the opening e is pin whole for eye , b is small rectangular slot placed opposite to pin hole and c is large rectangular slot placed at right angle to line joining e & b
The surveyor simply turns the optical square upside down which throws the aperture for the object on that side.
5. Prism Square:
It is a modern instrument and is a very use full for setting out right angles. It is based on the same principles as the optical square and is used in same manner. It requires no adjustment, since the angle between reflecting surface of the prism (45 degree) is fixed. It is unaffected by dust & can be used in poor light. For taking offset to an object the observer holds the instrument in his hand & slights directly over the prism at ringing of station.
Method of Measuring Distance
Direct Method of Measuring Distance.
Competitive Method
Direct Method of Measuring Distance
1. Pacing:
Where approximate result is required, distance may be determined pacing. This method is used for reconnaissance survey, for preparation of military plans. Also used for approximate checking distance. The method consists of walking over a line and counting the number of paces (80cm) the required distance may be obtained by multiplying the number of paces by the average length of pace. The length of pace varies with the:
Individual, age, height and physical condition
The nature of the ground (uphill and down hill)
The slope of the country and
The speed of pacing
2. Passometer:
It is a pocket instrument. It automatically records the number of paces. It should be carried vertically, in waistcoat pocket or suspended from a button. The mechanism being operated by motion and strain of the body
3. Pedometer:
It is similar to passometer. But it registers the distance walked by the persons carrying it. The distance is read by means of an indicator. It is fitted with a stud or
Knob, which when pressed release indicator to zero, it may be carried in the same way as the passometer.
4. Odometer:
It measures the distance approximately. It can be attached to the wheel of any vehicle, such as carriage, cart bicycle, etc. It registers the number of revaluation of the wheel. Knowing the circumference of the wheel, the distance traversed may be obtained by multiplying the number of revolutions. By the circumference of the wheel
5. Speedometer:
The Speedometer of an automobile may be used to measure distances approximately. It gives better results than pacing, provided the route is smooth.
6. Perambulator:
It can measure distance rapidly. It consist a single wheel provide with forks and a handle. It is wheeled along the line, the length of which is desire. The distance traversed is automatically registered on the dial. The reading approximates an rough ground.
7. Judging distance:
This is very rough method of determining distance. It is used reconnaissance survey.
8. Time Measurement:
Distance is roughly determined by time intervals of travel. Knowing the average time per km for a person at walk or a horse, the distance traversed may be easily obtained.
9. Chaining:
Measuring distance with chain or rope is the most accurate and common method, called as chaining. For work of ordinary precision a chain is used. Where great accuracy is required, a steel tape is used.
Ranging out Survey Line
In measuring the length of a survey line called chain line, it is necessary that the chain should be laid out on the ground in a straight line between the end stations.
Ranging:
“The process of establishing intermediate point on a straight line between two end points is known as ranging”
Ranging must be done before a survey line is chained. It may be necessary to establish a number of intermediate points prior to chaining when chain line is much longer. Ranging may be done by direct observation by the naked eye or by line ranger or by Theodolite. Generally, ranging is done by naked eye with the help of three ranging rods.
Ranging is of two kinds:
1. Direct Ranging
2. Indirect or reciprocal ranging
1. Direct Ranging:
When intermediate ranging rods are fixed on a straight line by direct observation from end stations, the process is known as direct ranging. Direct ranging is possible when the end stations are intervisible.
Assume that A and B two end stations of chain line, where two ranging rods are already fixed. Suppose it is required to fix a ranging rod at the intermediate point P on the chain line in such a way that the points A, P & B are in same straight line. The surveyor stands about two meters behind the ranging rod at A by looking towards line AB. The assistant holds ranging rod at P vertically at arms length the rod should be held tightly by the thumb and forefinger. Now the surveyor direct the assistant to move the ranging rod to the left or right until the three ranging rods come exactly the same straight line. The ranging will be perfect, when the three ranging rods coincide and appear as a single rod. When the surveyor is satisfied that the ranging is prefect, he signals the assistant to fix the ranging rod on the ground. By following the same procedure, the other ranging rods may be fixed on the line.
2. Indirect or Reciprocal Ranging:
Indirect ranging is used when the end stations are not intervisible due to high ground or a hill or if the ends are too long. In such cases, intermediate points can be fixed on the survey line by a process known as reciprocal ranging.
Let A & B be the two stations with rising ground or a hill. Let two chainmen with ranging rods take up positions at M and P, such that, chainmen at M1 can see both rods at P1 and B and the chainmen at P1 can see the ranging rods at M1 and A. The chainmen at P1 directs the chainmen at M1 to shift the ranging rod at M2 in line with A and then chainman at M2 directs the chainmen at P1 to shift the ranging rod to P2 in line with B, by successively directing each other to be in line with the end points. Their positions will be changed until finally they are both in line with A & B exactly on line AB. Now the four ranging rods at A M P & B are on same straight line. This method may also be used in ranging a line across a valley or river.
Measurements of Areas:
There are two methods of measuring areas.
Triangulation, and
Traversing.
1. in Triangulation:
The lines of survey form a network of triangles. (It is the systems of surveying in which the area is divided into simple geometrical figures and the work is carried out by taking its measurements.)
2. A Traversing:
It is one in which the frame work consists of a series of connected lines, the length and directions of which are measured by chain or tape and angular instruments respectively.
Chain Survey
Chain survey is the simplest method of surveying. In this survey only measurements are taken in the field, and the rest work, such as plotting calculation etc. are done in the office. This is most suitable adapted to small plane areas with very few details. If carefully done, it gives quite accurate results. The necessary requirements for field work are chain, tape, ranging rod, arrows and some time cross staff.
Survey Station:
Survey stations are of two kinds
Main Stations
Subsidiary or tie
Main Stations:
Main stations are the end of the lines, which command the boundaries of the survey, and the lines joining the main stations re called the main survey line or the chain lines.
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.
Tie or subsidiary lines:
A tie line joints two fixed points on the main survey lines. It helps to checking the accuracy of surveying and to locate the interior details. The position of each tie line should be close to some features, such as paths, building etc.
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.
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.
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. There are two kinds of offsets:
1) Perpendicular offsets, and
2) Oblique offsets.
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.
Procedure in chain survey:
1. Reconnaissance:
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.
2. Marking Station:
Surveyor fixes up the required no stations at places from where maximum possible stations are possible.
3. 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.
4. Then ranging roads are fixed on the stations.
5. After fixing the stations, chaining could be started.
6. Make ranging wherever necessary.
7. Measure the change and offset.
8. Enter in the field the book.
Cross Staff Survey
This type of survey is undertaken to locate boundaries of a field or a field or plat and determinations of its area.
Principle:
The principle of the survey is to divide the given area in to no of right angled triangles and trapezoids and to calculate and plot the areas of triangles and trapezoids.
Instruments/Material Required:
Two Chains, arrows taps, ranging rods, cross-staff and drawing material
Procedure:
Two chains are usually provided one for measuring distance along the chain line and other for measuring the offsets. The cross staff is used to set out the perpendicular directions for offsets. In this survey, the base line runs through the center of the area, so that the offsets are left or right side of base line are fairly equal. To check accuracy length of the boundary lines may also be measured. After the field work is over, the survey is plotted to a suitable scale.
Calculations of Field Area:
By this method of survey, the field as divided in to right angled triangles and trapezoids are calculated as under:
Area of right -angled triangle = ½ base x Height.
Area of trapezoid= sum of parallel sides/2 x Height.
Add the areas of all the triangles & trapezoids and sum is equal to the total of a field.
The computations for area should be written in a tabular from as given below.
TABLE
Serial no.
Figure
Chain age in m
base in m
Offset in m
Mean offset in m
Areas in m2 A=col. 4.xcol.6
1
2
3
4
5
6
7
Total
m2
Plane Table Surveying
Plane table is a graphical method of surveying in which the field works and the plotting is done simultaneously. It is particularly adopting in small mapping. Plane table surveying is used for locating the field computation of area of field.
Merits:
It is most suitable for preparing small scale map or surveying small area.
It is most rapid method.
Field book is not necessary.
No great skill is required for satisfactory map.
It is particularly suitable for magnetic area where prismatic compass is not reliable.
Contour and irregular object may be represented accurately.
It is less costly.
Demerits:
Plane Table Essentially a tropical instruments.
It is not suitable to work in wet climate.
There are several accessories to be carried out and therefore they are likely to be lost.
It is not suitable for accurate work.
Parts of plane Table:
Plane table essentially consist of
1. Drawing board mounted on tripod.
2. Alidade.
1. Drawing board mounted on tripod
A sheet of drawing paper, called plane table sheet is fastened to the board. Board is made up of well seasoned wood such as teak of size 40x30 to 75x60cm. it had plane and smooth top. It is mounted on a tripod in manner that it can be leveled. Leveling up of the table is done by shifting the legs of tripod. Some tripod provided with leveling screw or by ball and socket head for accurate leveling.
2. Alidade:
Alidade consists of two vertical sight vane fitted at end the end of straightedge. The straight edge ruler usually made of brass or teak wood graduated beloved edge. One of the sight veins is provided with narrow slit and the other with a central vertical wire or hair. Beveled working edge alidade is called fiducial edge.
Accessories:
A through campus for marking the direction magnetic meridian on paper.
Sprit level for leveling the table.
Forked plumb for centering the table.
Water proof cover to protect the sheet from rain.
Centering:
It is the process of keeping the table over the station that the point on the paper representing the station being occupied is vertically over the point on the ground. It is done by forked plumb bob.
Orientation:
When the table has to be set up at more than one station it is necessary that it is be oriented so that the lines on the paper remain parallel to the lie which they represent on the ground. So orientation is “the process of keeping the table to the position which is occupied at the first station”.
Orientation is done by two methods:
By use of the magnetic needle.
Orientation by back sighting.
Orientation by the magnetic needle:
To orient the table at any subsequent station, the through compass(or circular box compass) is placed along the line representing the magnetic meridian which has been drawn on the paper at the first station, and the board is then turned until the ends of the needle o\are opposite the zeros of the scale. The board is then clamped in position. It is suitable for rough small scale mapping.
Orientation by back sighting:
This is the most accurate method of orientation and is always be preferred. Suppose a table is set up over station Q on the line PQ which ahs been previously drowned as PQ from station p. The alidade is placed along the line QP and board then turned until the line of sight bisects the ranging rod at P. Board is then properly clamped.
Methods of Plane Tabling
1. Radiation:
In this position the point is located on plane by drawing a ray from the plane table station to the point, and plotting scale along the ray the distance is measured from the station to the point. The method is suitable for the survey of the small areas which can be commanded from a single station.
2. Intersection:
In this method the point is fixed on plane by the intersection of the rays drawn from the two instrument stations. The line joining at these stations is called the base line.
3. Traversing:
This method is similar to that of compass or transit traversing. It is used for running survey lines between stations which have been previously fixed by other methods of surveying to locate the topographical details. It is also suitable for the survey of roads, rivers etc.
4. Resection:
This method is used for establishing the instrument stations only. After fixing the station, details are located either by radiation or intersection. The characteristic feature of resection is that the point plotted on plan is the station occupied by the plane table.
Radiation:
Select appoint p so that all point to be located are visible from it.
Set up the table at p and leveled.
Marked the direction of magnetic meridian with through compass in top corner of sheet.
Select the point p on the sheet so that it is exactly over station p on the ground.
Centering the Alidades on p, sight the various points A, B, C etc. and draw the rays along edge of Alidades.
Measure the distance PA, PB, PC etc. from p to various point with chain or tape and plot them to scale along the co responding rays. Join the points a, b, c, etc. to give outline of survey.
Intersection:
Select two point P and Q in a commanding position so that all points to be plotted are visible from P and Q. Line joining these points are called base line. Set the table over P and mark direction of magnetic direction of magnetic meridian by means of through compass. Alidade pivoted on point P, sight the station Q and other object a, b. c, d, e, and draw rays along the edge of alidade towards Q, A, B, D, and E. measured distance from P and Q accurately and along the rays drawn towards Q. Now shift the table and set it up at point Q and adopt same procedure.
Computation of Area
One of the primary objects of land surveying is to determine the area of the land surveyed. Areas may be determined by: 1. computation from field notes: It can be done by two ways.
a. Calculation of the area of the skeleton of the survey and
b. Calculation of the area enclosed between survey lines of skeleton and boundaries.
a. Areas of skeleton:
BY geometry
Co-ordinates
By Geometry:
Area of triangle forming skeleton
Area = under route s(s-a) (s-b) (s-c)Where a, b, c, are the side of triangle and semi perimeter, s=a+b+c/2
Area = ½ x base x height
Area of rectangle = length x width
Area of square = side2
Area of Trapezium = ½ (sum of parallel sides) x distance between them
= ½ (a + b) x h
Computation of Area from Previously Plotted Plan:
The area may be calculated in the following two ways:
Case 1 – Graphical method
Case 2 - Instrumental Method
Case 1- Graphical Method:
The graphical methods are those in which the required data obtained from measurements of plan.In this case the area of figure is found as a whole, or the areas of the skeleton and the irregular strips are found separately.
A. Considering Entire Areas:
By division into triangles:
The most convenient method is to divide the figure in to a number of triangles. The base and altitude of each triangle are scaled and its area is found.
By division into square:
In this method a peace of tracing paper ruled out into squares, each responding a definite number of square meter or square centimeter is placed over the drawing. The number of whole square is measure and area is found. The portions of broken square are estimated in terms of Whole Square and broken squares.
By division into trapezoids or By drawing parallel lines and converting them to rectangle:
By placing the tracing paper over the plan the length the rectangles is obtained.
And area is calculated as:Required area = {length of rectangles} x {constant distance common breadth}
b. Considering the area along Boundaries:
The mid ordinate rule:
In this method the coordinates are measured at the mid- point of each division and the area is calculated by
Following Formula:
h1+h2+h3+……….. +hn
Area = ----------------------------------- X 1
N
Or = (h1+h2+h3+ ………+hn) d Where,h1, h2, h3… = Ordinates at the mid points
1 = length of the base line.
n = number of equal parts in to which the base line is divided
d = common distance between the ordinates 1/n
2. The average ordinate rule:
(Oo +O1+O2 +…………+0n)
Area of strip = ----------------------------------------- X L
n + 1
3. Trapezoidal rule:
Area of strangle = d/2 (0o+201+202+…………20n-1+0n)
If we consider the boundary on both side of survey line ab, thenArea of triangle = d [(0o+0n)/2 + 01+02+…………. + 0n-1)
4. Simpson’s rule:
In this rule, the boundaries between the ends of coordinates are assumed an area of a parabolaSimpson’s rule is sometimes called parabolic rule.
Area= d/3(01+402+203+404+……………….0n)
= d/3 {01+0n+4(02+04+………..)+2(03+05+…………….)}Common distance = {1st ordinate + last ordinate)
+4(sum of even ordinates)
+2(sum of remaining odd ordinates)}
Case 2: Instrumental method:
This method consists of determining the area of a given map [figure] the uses of a planimeter.It is the best and most expeditious method and gives accurate results than other methods.
Calculation from the field notes:
There are two types of planimeter:
The Amsler polar planimeter and
The rolling planimeter.
Introduction to Levelling
Leveling may be the art of determining the relative heights or elevations of points are objects on the earth’s surface. It deals with measurements in a vertical plane.
Definitions of terms used in Leveling:
A level surface:
It is any surface parallel to the mean spheroidal surface of the earth e.g. surface of a still lake. Since the earth is a oblate spheroid, a level surface may be regarded as a curved surface, every point on which is equidistant from the center of the earth. It is normal to the plumb line at all points.
A level line:
It is line lying in a level surface. It is therefore, normal to the plumb line at all points.
A horizontal plane:
It is a plane tangential to the level surface at that point. It is perpendicular to direction of gravity (plumb line).
A horizontal line:
It is any line lying in the horizontal plane. It is a straight line tangential to a level line.
A vertical line:
It is a line normal to the level surface through that point e. g. a plumb line.
A vertical plane:
It is a plane containing a vertical line.
A vertical angle:
Angle between two intersecting lines in a vertical plane, one of the two lines is commonly taken as horizontal in surveying.
A datum surface or line:
It is any arbitrarily assumed level surface or line from which vertical distances are measured in India the datum adopted for G.T.S. bench marks is the mean sea level at Karachi now in Pakistan.
The elevation:
It is vertical distance of a point above or below the datum. It is also known as the reduced level (R.L.) The elevation of a point is plus or minus according as the point is above or below the datum.
The difference in elevation (H):
It is the vertical distance between the level surfaces passing through the two different points.
A bench mark (B.M.):
It is fixed reference point of known elevation.
The line of collimation:
It is the line joining the intersection of cross hairs of the optical center of the object glass. It is also called the line of sight.
An axis of the telescope:
It is a line joining the optical center of the object glass to the center of the eye piece.
Foresight:
(Also called a foresight reading) It is a staff (or rod) reading on a point whose elevation is to be determined or on a change point. It is also termed as minus sight. It is the last staff reading denoting the shifting of the instrument.
An Intermediate sight (I. S.):
It is any other staff reading taken on appoint of unknown elevation from the same set up of the level. All sights taken between the back sight and the fore sight and the foresight are intermediate sights.
A change point (C. P):
It is appoint denoting the shifting of the level. It is a point on which is the fore and back sights are taken. Any stable and well defined object such as a boundary stone, curb stone rail, rock etc. is used as a change point. A bench mark may also be taken as a changer point. It is also called a turning point (T. P).
A Station:
It is a point whose elevation is to be determined. It may be noted that it is a point where the staff is held not the point where they leveled is set up.
The height of instrument (H. L):
It is the elevation (or the R.L.) of the plane of collimation (or plane of sight) when the instrument is correctly leveled. It is also called the height of plane of the collimation.
To determine elevation of points two instruments are required, viz.
A level
A leveling staff or rod.
The level:
Level consists of essentially
Leveling head
The limb
Telescope
bubble tube
Types of level:
Dumpy level
y level
Coke’s reversible level
Automatic level
Dumpy Level
The dummy level is simple compact and stable. Dummy level is the most commonly used level. It is cheaper, and easier to maintain in adjustment.
Part of the dummy level
1. Leveling head
2. Telescope
3. Eyepiece
4. Diaphragm
5. Focusing screw
6. Ray shade
7. Level tubes
8. Level tube rule
9. Cross bubble tube
Setting the Level:
1. The tripod legs are spread 1 or 1.2 m and pushed firmly on the ground. The legs are so adjusted that tripod head is fully level in both directions.
2. The telescopic is turned unit. It comes parallel to two opposite leveling screw and the bubble is brought to the center of tube by turning these screws.
Both screws are turned either inward or outward depending on the direction in which the bubble is required to move. The telescope is then turned around until it stands over the third screw. By manipulating that screw, the bubble is brought to the center. The telescope is rotted and brought over the third screw and the bubble is brought to center by adjusting other screws.
1. The telescope is turned to bring the level rod into the field of vision
2. Eye piece is adjusted to focus on the cross hair.
3. The rod is read at the intersection of then middle horizontal cross hair with the rod.
Leveling Rod:
Leveling rod is used with the level to obtain the vertical distance between the plane of sight and the surface or point on which the level rod is held.
Types of Leveling Rod:
1. Self reading rod.
2. Target rod.
Generally self reading rod is commonly used. They are usually of 4 and 5m length. The self reading rod is designed to read directly by the man from his level. The rod is graduated in meter, decimeters and centimeter. Reading are normally taken to two decimal points as 6.05, 9.86, etc.
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