ADVANCED SURVEYING (S-II)

(LAB)

KISHANGANJ COLLEGE OF ENGINEERING AND TECHNOLOGY, KISHANGANJ DEPARTMENT OF CIVIL ENGINEERING.

ADVANCED SURVEYING (S-II) LAB DEPARTMENT OF CIVIL ENGINEERING

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Experiment No- 1

Aim: Determination of the Multiplying and additive constant of given Tacheometer. Apparatus: A tacheometer with tripod, tape, levelling staff, wooden pegs, ranging rods etc. Figure:

Formulae:

When the line of sight is horizontal, then D = KS + c

Where, D = Horizontal distance between instrument station and staff station. K = Multiplying constant of a tacheometer S = Staff intersect i.e. difference between top and bottom stadia hair

reading. When line of sight is inclined and staff vertical then:

D = KS cos2 q + c cosq Where,

D = Horizontal distance between instrument station and staff station. K = Multiplying constant of a tacheometer S = Staff intersect i.e. difference between top and bottom stadia hair

reading. q = The inclination of the line of collimation to the horizontal. c = The additive constant of the tacheometer.

Theory: PRINCIPLE OF STADIA METHOD

The stadia method is based on the principle that the ratio of perpendicular to the base is Constant in similar isosceles triangles. In fig let two rays OA and OB be equally inclined to the central ray OC. Let A2B2, A1B1 and AB be staff intercepts. Evidently

ADVANCED SURVEYING (S-II) LAB DEPARTMENT OF CIVIL ENGINEERING

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Determination of Constant k and C:

Procedure:

1) Select an instrument station A on a fairly levelled ground and fix a peg.

2) Do the temporary adjustment over A. 3) With vertical circle to the left of the observer and reading 00000’00” bisect staff held at 10m, 20m, and 30m from A along straight line.

4) Note down the staff reading against top and bottom stadia hair on staff held at 10m, 20, 30m from A.

5) In case of inclined line of sight the same procedure as stated above is followed step by step with a vertical angle of 05000’00” in the vertical circle of the theodolite. In this case, the vertical circle is held to the left of the observer and with the reading 05000’00” in the circle the staff is bisected at 10m, 20m, and 30m from A along straight but inclination line of collimation.

ADVANCED SURVEYING (S-II) LAB DEPARTMENT OF CIVIL ENGINEERING

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Calculation: D = Ks + c

For three staff stations, D1 = Ks1+c ------- (1) D2 = Ks2+c ------- (2) D3 = Ks3+c ------- (3)

As ; s1, s2, s3 can be known solving (1) &(2), (2) & (3) , (1) & (3) to get 3 values of m & c ,then average of three values is required answer.

D = Ks cos2 q + c cosq

For, three station the equations are; D1 = Ks1 cos2 q1 + C cosq1 ------- (1) D2 = Ks2 cos2 q2 + C cosq2------- (2) D3 = Ks3 cos2 q3 + C cosq3------- (3) As ; s1, s2, s3 can be known solving (1) &(2), (2) & (3) , (1) & (3) to get 3 values of K & C ,then average of three values is required answer. Result: a) For horizontal line of collimation; 1) The additive constant ‘c’ for a given tacheometer is found out to be --------- 2) The multiplying constant ‘m’ for a given tacheometer is found to be --------- b) For inclination line of collimation; 1) The additive constant ‘c’ for a given tacheometer is found out to be ---------- 2) The multiplying constant ‘k’ for a given tacheometer is found to be ---------

ADVANCED SURVEYING (S-II) LAB DEPARTMENT OF CIVIL ENGINEERING

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Experiment No-2

Aim: Determination of Elevation of points by Tacheomentric surveying.

Apparatus: A tacheometer with tripod, tape, leveling staff, wooden pegs, ranging rods etc. Figure:

Formulae:

When line of sight is inclined and staff vertical then:

D = KSCos 2 ϴ+ CSin ϴ

Where, K= Multiplying constant =100 C= Additive constant S= Staff intercept. V =Vertical distance measured from horizontal line of straight

Central stadia hair reading on staff. H = Central stadia hair reading on staff.

ϴ = vertical angle

Theory:- The Tacheometer is an instrument which is generally used to determine the horizontal as well as vertical distance . It can also be used to determine the elevation of various points which cannot be determined by ordinary levelling. When one of the sight is horizontal and staff held vertical then the RLs of staff station can be determined as we determine in ordinary levelling .But if the staff station is below or above the line of collimation then the elevation or depression of such point can be determined by calculating vertical distances from instrument axis to the central hair reading and taking the angle of elevation or depression made by line of sight to the instrument made by line of sight to the instrument axis.

ADVANCED SURVEYING (S-II) LAB DEPARTMENT OF CIVIL ENGINEERING

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Procedure: 1) Set up the instrument in such a way that all the point should be

visible from the instrument station. 2) Carryout the temporary adjustment and set vernier zero reading

making line of sight horizontal. 3) Take the first staff reading on Benchmark and determine height of

instrument. 4) Then sight the telescope towards the staff station whose R.Ls are to

be calculated. Measure the angle on vernier if line of sight is inclined upward or downward and also note the three crosshair readings. 5) Determine the R.Ls of various points by calculating the vertical

distance.

Calculation:

D = KSCos 2 ϴ+ CSin ϴ

1) For ground floor:- V1 = (K

1S

1sin2ϴ)/2 + C sin ϴ

R.L of ground floor = RL of BM + h + V1-h1 Result: The RLs of Various points are found as follows.

ADVANCED SURVEYING (S-II) LAB DEPARTMENT OF CIVIL ENGINEERING

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Experiment No- 3 Aim: - Setting out of simple circular curve by offsets from chord produced method.

Problem Two straight intersect at chainage (30+10), the deflection angle being 44º. Calculate the necessary data for laying out a curve by the method of offsets from the chord produced. The degree of the curve being 7º. The peg interval being equal to 20meters.

Procedure for setting out of curve 1) Locate the tangent points T1 and T2 on the straights AB and CB. 2) Cut T1D1 equal to the length of the first sub chord (C1) already

calculated along the tangent T1B. 3) With T1 as centre and T1D1 radius, swing the chain or tape such

that the arc D1D= calculated offset O1, thus fixing the first point D on the curve.

4) Keep the chain along T1D and pull it straight in the forward direction of T1D until the length DE1 becomes equal to second C2 (i.e the length of normal chord).

5) With D as centre and DE1 as radius, swing the chain such that the arc E1E=calculated offset O2, thus fixing the second point E on the curve.

6) continue the process repeating the point (d) and (e) until that end the curve is reached. The last point so fixed must coincide with the previously located points T2 (the last curve tangent point) if not, find out the

ADVANCED SURVEYING (S-II) LAB DEPARTMENT OF CIVIL ENGINEERING

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closing error. If it is small (say within 2m) it should be distributed to all the points by moving them sideways by an amount proportional to the square of their distances from the point T1, otherwise the whole curve should be set out again. Solution: - Given degree of curve ,D=7º Deflection angle, Ø=42º

Radius of curve R

245.55m

Tangent length = R Tan Ø/2 =245.55 0.4040=99.20m

Length of Curve =

Chainage at the point of intersection = (30+10) chains = 30 20+10=610m Chainage at 1st tangent point=610.00-99.20=510.80m (25+10.80) chains

Chainage at end of curve or second tangent point = 510.80+188.57 = 699.37m (34+19.37) chains Note:-20m chain used. Length of 1st Sub- chord =(26 +00)-(25+10.80) =9.20m Number of full chord =34-26=8 Length of last sub-chord = (34+19.37)-(34+00)=19.37m Check: Length of Curve = 1ST sub chord +Full chord + last sub chord = 9.20+8 20+19.37 =188.57m

Now from equation length of first offset,

Length of second offset,

Offsets from O3 to O8 are given by equation

Last offset,

Results:- By offsets from chord produced method the simple circular curve was plotted on the ground.