Basics of SURVEYING
PLANE SURVEYING
- Curvature of earth is not taken into consideration.
- Extend over small area.
- Degree of accuracy is low.
- Area less than 250 km2.
- When survey extend over limited area, Difference between arc & chord is 0.1 m for distance of 18.2 km, 0.3 m for distance of 54.3 km & 0.5 m for distance of 91 km.
- Difference between the sum of angles of spherical triangle and the plane triangle is only 1 (one) second for 195.5 km2.
GEODETIC SURVEYING
- Curvature of earth is taken into consideration.
- Also called Trigonometrical surveying.
- Extend over large area.
- Area more than 250 km2.
- Degree of accuracy is great.
CLASSIFICATION OF LAND SURVEY
- Topographical Survey
- Determining natural feature of the country like hill, valleys, rivers, lakes etc.
- Also used for artificial objects such as canals, railways, roads, towns, villages etc.
- Cadastral Survey
To determine additional details as boundaries of fields, houses & other property.
- City Survey
Work with town planning schemes such as drainage, water supply etc.
- Engineering Survey
Determining for roads, railways, reservoirs.
- Levelling staff held inclined at staff station, R.L. calculated is less than true R.L.
- Parallex bar is used to measure parallex difference.
- Instrument attached to the wheel of vehicle to measure distance travelled = odometer.
PRINCIPLE OF SURVEYING
“ To work from Whole to the Part”.
SCALE
R.F. (Representative Fraction) = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑛 𝑚𝑎𝑝𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑛 𝑔𝑟𝑜𝑢𝑛𝑑
- Plain scale
Read only two dimension.(m & deci m)
- Diagonal scale
Read in three dimension.(m, cm & deci m)
- Comparative scale
Read in different direction.
- Vernier scale
Used for measuring fractional part of the smallest division of the scale.
Also known as Graduated scale.
Read in one direction.
Two types of vernier :-
1. Direct Vernier
2. Retrogate Vernier
Direct Vernier
Smallest division of a vernier is shorter than the smallest division of primary sacle.
Retrogate Vernier
Smallest division of a vernier is longer than the smallest division of primary sacle.
Least count of vernier = 𝑆𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛 𝑜𝑛 𝑚𝑎𝑖𝑛 𝑠𝑎𝑐𝑙𝑒𝑁𝑢𝑚.𝑜𝑓 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛 𝑜𝑛 𝑣𝑒𝑟𝑛𝑖𝑒𝑟
- True Length = 𝑊𝑟𝑜𝑛𝑔 𝑠𝑐𝑎𝑙𝑒𝐶𝑜𝑟𝑟𝑒𝑐𝑡 𝑠𝑐𝑎𝑙𝑒 x Measured Length
- True Area = 𝑊𝑟𝑜𝑛𝑔 𝑠𝑐𝑎𝑙𝑒𝐶𝑜𝑟𝑟𝑒𝑐𝑡 𝑠𝑐𝑎𝑙𝑒 x Calculated Area
ERROR IN LENGTH
- Correct distance = 𝐿′(𝐼𝑛𝑐𝑜𝑜𝑟𝑒𝑐𝑡 𝑙𝑒𝑛𝑔𝑡)𝐿(𝐶𝑜𝑟𝑟𝑒𝑐𝑡 𝑙𝑒𝑛𝑔𝑡) x Measured distance
- When chain is too long then error is negative & correction is positive.
- When chain is too short then error is positive & correction is negative.
CHAINING ON SLOPING GROUND
Slope are measured by clinometer (Abney level = Measure Vertical angle).
Clinometer is Indirect method.
- First method
D = l cos𝜃 where, l = sloping distance & 𝜃 = Angle of slope.
- Second method
Difference in elevation between end of slope is known than
D = √(l^{2}−h^{2})
- Third method
BC = 100 (secθ – 1) link
Where, secθ – 1 = Hypotenusal Allowance.
CORRECTION FOR SLOPE
Correction for slope if vertical distance between first & last point is known,
Ch = h^{2}/2l
Correction if angle of slope is known,
Ch = l (1-cosθ) = 2l sin^{2}(θ/2)
ERROR IN CHAINING
Positive if the measured length more than the actual length.
Negative if the measured length less than the actual length.
Compensating error are proportional to L .
Cumulative error are proportional to L.
CORRECTION FOR TAPE
- Correction for Length
May be positive or negative.
- Correction for Temperature
Correction is plus (+) if Tm > To.
Correction is minus (-) if Tm < To.
- Correction for Pull(Tension)
Positive if P > Po.
Negative if P < Po.
- Correction for Sag
Always Subtractive (negative) = w2l224p2
- Correction for slope
Always Negative = h22l
- Diurnal variation is more in summer than winter for magnetic needle.
- Principal of chain survey is Triangulation.
- In well conditioned triangle no angle should be less than 30° and greater than 120°.
CROSS STAFF
Three types of cross staff
1. Open cross staff
2. French cross staff
3. Adjustable cross staff
- Open cross staff
Used for setting out an offset at right angle.
Used for long offset.
- French cross offset
Used for setting out an offset at angle of 45°.
- Adjustable cross offset
Used for setting out an offset at any angle.
OPTICAL SQUARE
- More accurate than staff.
- Setting out long offset.
- Based on principle of reflection.
- Angle between Incident ray & Reflected ray is 90°.
- Horizon glass and Index glass placed at angle of 45°.
- Horizon glass is half silvered & half un-silvered.
- Index glass is wholly silvered.
- In Prism Square, Angle between reflecting surfaces is 45°.
TRAVERSE SURVEYING
- In this surveying, Length is measured with the Chain or tape & angle is measured with the Box sextant, Compass & Theodolite.
True Meridian :- Where north and south pole is intersect.
True Bearing :- Angle between the true meridian & a line.
Magnetic Meridian :- Direction indicated by magnetic needle un-affecting the local attraction.
Magnetic Bearing :- Angle between the magnetic meridian & a line.
In Prismatic Compass, zero is located at south end.
WHOLE CIRCLE BEARING (W.C.B)
Always measured clockwise from the north point.
Any value between 0° to 360°.
Bearing observed with a prismatic compass or theodolite.
QUADRANTAL BEARING (Q.B)
It is measured clockwise or anticlockwise from the north point or the south point whichever is nearer to the line, towards the east or west side.
Bearing observed with a Surveyor’s compass.
W.C.B | R.B | Quadrant |
0° to 90° | W.C.B | N – E |
90° to 180° | 180° – W.C.B | S – E |
180° to 270° | W.C.B – 270° | S – W |
270° to 360° | 360° – W.C.B | N – W |
Fore Bearing (F.B) :- The bearing of line in direction of survey is called F.B.
BACK BEARING (B.B)
The bearing of line in opposite direction is called Reverse bearing.
Back bearing = Fore bearing ± 180°
If F.B < 180°, then ‘+’ sign.
If F.B > 180°, then ‘−‘ sign.
Local Attraction :- It is used to denote the amount of deviation of the needle from its normal position.
DIP
Inclination of the needle with the horizontal.
Angle of slope of bed with horizontal.
Dip is 0° at the equator & 90° at the magnetic pole.
Magnetic Declination :- Horizontal angle between the magnetic & true meridian.
Azimuth :- Angle between the true meridian & survey line.
Aerial photograph are perspective view.
Perspective view is in the vertical plane.
THEODOLITE
Theodolite is used for measuring the Horizontal & Vertical angle.
Can measure in Diff. in level, Bearing of line & Zenith angle.
- Two types of theodolites
1. Transit –When telescope can be transited.
2. Non-transit – When telescope cannot be transited.
Centring
Setting the theodolite over station mark.
Transiting
Also known as the Plunging or Reversing.
Turning the telescope over the horizontal axis in vertical plane.
Line of Collimation
Also known as Line of Sight.
The line joining point of intersection of cross hair of diaphragm and optical centre of the object glass.
Line of collimation is perpendicular to the horizontal axis.
Axis of Telescope
Line joining the optical centre of object glass and centre of eye piece.
It is parallel to the line of collimation.
Axis of Bubble Tube or Level Tube
Line tangential to the longitudinal curve of level tube at the centre of the tube.
Axis of level tube is perpendicular to the vertical axis.
SURVEYING TELESCOPE
In surveying telescope, cross-hair fitted in front of the eye piece & diaphragm is held nearer to the eye piece.
Real image of object formed by the objective must lie in the plane of cross-hairs.
If does not lie in plane of cross-hairs, then the parallex should be removed. It is done
by focussing the eye piece and by focussing the object piece.
Two types of Surveying telescope
1. External Focussing telescope
2. Internal Focussing telescope (Concave lens is used)
Magnification = Focal length of objective Eye piece of telescope
To measure a horizontal angle more accurately, the method of repetition is used.
DIRECT ANGLE
An angle which is measured clockwise from the proceeding survey line to the following survey line is called direct angle.
Value of direct angle is between 0° to 360°.
DEFLECTION ANGLE
An angle between the survey line with proceeding line is called the deflection angle.
Deflection angle is = Included angle – 180°
Value of the deflection angle is between 0° to 180°.
Vertical Angle :- An angle between the inclined line of sight and horizontal line is called vertical angle.
Latitude :- Distance measured which is parallel to the meridian (north & south).
Departure :- Distance which is measured perpendicular to the meridian (east & west).
Level Surface :- It is normal to the plumb line.
Horizontal Surface :- It is perpendicular to the plumb line.
Datum Surface :- The surface from which elevation of point measured.
ELEVATION OF POINT
Vertical distance above or below datum.
Known as Reduced level.
Elevation of point is positive or negative.
Bench Mark :- Fixed reference point of known elevation is bench mark.
BACK SIGHT (B.S)
The staff reading are taken on point of the known elevation.
The first staff reading after the level is set up and levelled.
Plus sight.
FORE SIGHT (F.S)
Staff reading is taken on point whose elevation is to be determined.
Last staff reading is taken before shifting of the level to another position.
HEIGHT OF THE INSTRUMENT
Elevation of the plane of collimation when the instrument is correctly levelled.
H.I = R.L. of B.M + B.S.
The Collimation Method is used in the profile levelling and setting out levels for constructional works purpose.
Rise and Fall Method is used for check and differential levelling and precise levelling operations.
Fly levelling is used to carry out the reconnaissance of survey area.
Operation of levelling when across any river is Reciprocal levelling.
In case levelling, correction for curvature = 0.0785 D2.
In case levelling, correction for curvature & refraction = 0.0673 D2.
In case levelling, Effect of refraction is 17 of that due to curvature.
If the diameter of chord is 30 m, then R = 1720D.
If the diameter of chord is 20 m, then R = 1146D.
CONTOUR
Line of joining the points having the same elevation above the datum surface is called contour.
Vertical distance between the two contour = Contour Interval.
Horizontal distance between two contour are= Horizontal Equivalent.
Contour interval depends upon the nature of the ground, the scale of map & purpose of the survey.
Horizontal equivalent depends upon the slope of ground.
Contour line are widely separated, it indicate flat ground.
Contour line are when closely together, it indicate steep ground.
Contour line when cross the ridge or valley line at right angle (90°).
If the higher value inside the bend then its ridge.
If the higher value outside the bend then its valley.
When the contour cross one another on map, its overhanging cliff.
When the contour coincides and the horizontal equivalent become zero then its vertical cliff.
Method of contouring
Two types of methods:
1. Direct method
2. Indirect method (Trigonometric method)
Three types of indirect methods are as follows :
a) By squares
b) By cross section :- It is suitable for survey of long narrow strip, lie railway, canals etc.
c) By tacheometer :-It is suitable for contouring of hill.
PLANE TABLE SURVEYING
Principle of this survey is the Parallelism.
Size of plane table = 75 x 60 cm.
Size of field book = 200 x 120 cm.
Field work and plotting are done by simultaneously.
Telescopic alidade is used to measure the horizontal and vertical distance.
To making the North direction Trough compass is used.
Levelling
Operation of the setting up the plane table over the station point.
Levelling done by the levelling screws.
Centring
The setting up table exactly over the station.
It is done by plumbing fork & U-frame.
Orientation
The operation in which line on the paper are parallel to the corresponding line on the ground.
METHODS OF PLANE TABLING
Radiation
It is suitable for plotting of small area.
Intersection
For locating all the inaccessible points.
Traversing
This process suitable for roads, river etc.
It is used for running survey line between stations.
Resection
It is used for establishing the instrument station only.
Two point & Three-point problems are the methods of resection & orientation.
CURVES
Simple Curve
Single arc of circle with connecting two straights.
Compound Curve
Two or more simple curve which having diff. Radius bending in the same direction.
Centre lie on the same side of the curve.
Reverse or Serpentine Curve
Two arcs having equal or different radius bending in the opposite direction.
In this case centres lie on the opposite side of the curve.
Deviation Curve
It is combination of the two reverse curves.
Transition Curve
Ideal shape of this curve is generally Clothoid.
Cubic parabola & Cubical spiral is used on railways and highways.
Lemniscates is used on the highways only.
TACHEOMETRIC SURVEYING
Tacheometer is transit type theodolite.
Multiplying constant is = fi = 100.
Additive constant is = f + d = 30 cm to 45 cm.
If the convex lens (Analltic lens) is used, then f + d = 0.
Agonic Lines :- A line of joining the points of zero declination is called agonic lines.
Isogonic Lines :- A line of joining the points of same declination is called isogonic lines.
Heliograph is the type of sun signal used in triangulation work.
SIMPSON RULE
Number of ordinates is Odd.
Shape of the line joining ordinates is Parabolic.
TREPEZOIDAL RULE
Number of ordinates is Even or Odd.
Shape of the line joining ordinates is Elliptical.
The line joining top coordinates is Straight.
Invar Tape = It is used in measurement of base line.
Revenue Chain =It is used in cadastral survey.
Steel arrow are made from 4 mm dia. wire.
Size of the wooden peg = 2.5 cm x 2.5 cm x 15 cm.
1 nautical miles = 1.853 km.
Geodimeter | It is used to Measure length of visible wave |
Telurometer | It is used to Measure length of Microwave |
Distomate | It is used to Measure length of Infrared wave |
Type of chain | Length | Link | Length of Link |
Gunter Chain | 66 ft. | 100 | 0.66 ft. |
Engineer Chain | 100 ft. | 100 | 1 ft. |
Revenue Chain | 33 ft. | 16 | 2116 ft. |