(Case : 1 When the line of sight is horizontal and staff is held Vertical) Example 3

Example 3

A staff held vertically at a distance of 50 m and 100m from the centre of the theodolite with a stadia hair, the staff intercept with the telescope is 0.500 and 1.000 respectively. The instrument was then setup over a station P of RL 1850.95 m and the total height of the instrument was 1.475m. The hair reading on a staff held vertically at station Q were 1.050, 1.900 and 2.750 with the line of sight horizontal. Calculate the horizontal distance of PQ and RL of Q point.

Ans.=>

            D = KS + C 

D= (f/i) S + (f + d) ........... (1)

D₁= 50M S₁= 0.500M  

D₂= 100M S₂= 1.000M

Calculate the

1) horizontal distance of PQ = D=? 

(Haire reading Bottom = 1.050m, Middle =1.900M,Top = 2.750M )

2) RL of Q point.=? ( RL .of P =1850.950M) (Height of instrument = 1.475M)

D = KS + C 

50 = K(0.005) + C ................(1) 

100 = K(1.000) + C ...............(2) 

C = 50 – 0.005 K ..................(3) 

Put the value of C in Eq 2

100 = K(1.000) + C ...............(2) 

100 = 1.000 K + 50 – 0.005 K 

K = 100 (Now put the value of K in eq 3 )

C = 50 – 0.005 K ..................(3) 

C = 50 – 0.005 (100) C = 0 

Note: if K = 100 and C = 0 means your instrument is perfect

Calculation horizontal distance between  PQ

 D = KS + C ...........................(1)

  Now S = 2.750 – 1.050 = 1.700m

 K = 100 & C = 0 

Put all the value in equation no 1 

D = 100 (1.700) + 0  

D= 170m

Calculation of RL of Q point 

• RL of Q = 1850.95 + 1.475 – 1.900 

RL of Q = 1850.525m

(Case : 1 When the line of sight is horizontal and staff is held Vertical) Example 2

Example 2

The stadia reading with horizontal sight at a vertical staff held 50 m away from the tacheometer were 1.385 and 2.380. the focal length of the object-glass was 25cm. The distance between the object-glass and trunnion axis of a tacheometer was 15 cm. Calculate the stadia interval.

Ans.=>

            D = KS + C 

D = (f/i) S + (f + d) ........... (1)

    Here D = 50m 

    S = 2.380 – 1.385 = 0.995 

    f = 25cm = 0.25m 

    d = 15cm = 0.15m Put the all value in equation no 1

            50 = ((0.25 x 0.995) / i) + (0.25 + 0.15) 

            i = 0.005 m

         i = 5 mm

Principal of Tacheometry

 

Principle of Tacheometry

The principle of techeometry is based on the property of the isosceles triangle.

Statement :-

• In isosceles triangle the ratio of the perpendiculars from the vertex on their bases.

In the figure, let two rays OA and OB be equally inclined to central ray OC. Let A₂B₂, A₁B₁ and AB be the staff intercepts. Evidently,

 

= constant k = (1/2) cot (β/2)

This constant k entirely depends upon the magnitude of the angle β

 

Errors and Precautions in Tacheometric Surveying

 

Errors and Precautions in Tacheometric Surveying:

The errors may be instrumental errors, due to manipulation and sighting or due to natural causes.

The instrumental errors may be due to imperfect permanent adjustments in the instrument and due to incorrect graduations on the stadia rod.

When the instrument is in perfect permanent adjustment before starting the work, the constants of the instrument given by the manufacturer should be verified in the field by actual observation. This is very necessary for important surveys where accuracy (and not the time) is the main criterion.

The graduations on the rod should be carefully examined, and if any discrepancy is observed, suitable corrections should be applied to the observed readings.

The errors due to manipulation and sighting depend on the efficiency and skill of the surveyor. These are due to inaccurate centring and levelling of the instrument and taking incorrect Stadia readings.

To view the stadia rod clearly, there should be no Parallax. While taking stadia hair readings, care should be taken to see that the axial hair is not mistaken for stadia hair.

The accuracy of the stadia hair readings may be checked by seeing whether the mean of the stadia hair readings is equal to axial hair reading.

The errors due to natural causes may be due to wind, unequal expansion of the instrument parts, and visibility and unequal refraction. Out of these, the last one is the most important.

This happens due to unequal refraction of rays of light when they pass through layers of air of different densities. Therefore, to avoid this error, taking readings in the mid-day should be avoided as far as possible.

Also, the lines of sight should not be within a meter from the ground.

The average permissible error in the distance is 1 in 500 to 1 in 900 and in elevations 0.08 to 0.10 m.

The closing error in a tacheometry traverse should not be more than 0. l√P, where p is the perimeter of the traverse in meters.

Procedure for Tacheometric Surveying

 

Procedure for Tacheometric Surveying:

(1) Set up the instrument over the station selected by the chief of the party and accurately level the instrument with reference to the altitude level.

(2) Set the vernier of the vertical circle to zero. With the altitude level at the centre of its run, measure the height of the instrument (the vertical distance from the top of the peg to the centre of the objective) with a measuring tape accurately.

Alternatively, the height may be found out by keeping the stadia rod first in front of the telescope and reading through the object-glass.

(3) Now, orient the instrument. This is done as follows.

The reference meridian may be the magnetic meridian or the true meridian.

When the reference meridian is a magnetic meridian, set one of the vernier to zero and revolve the telescope about the vertical axis loosening the lower clamp till the compass needle points towards the north.

For orienting the instrument with reference to the true meridian, the true bearing of a reference point or some other station of the traverse with reference to the first station should be known.

Then, set up the vernier to read this bearing and revolve the telescope about the outer axis until the station or the reference object is bisected.

(4) Hold the staff on the benchmark and take the bearing, read the vertical angle and the top, bottom, and axial hair readings, (the line of sight may be horizontal or inclined).

If any benchmark is not nearby the area of traversing, the fly level may be carried out from the available Bench Mark (BM), and a temporary BM may be established near the area.

(5) All the representative points under the command of the instrument station are located by taking the bearings, the vertical angles and the staff reading (to the top, bottom and the axial hairs). These observations are termed as “side shots.”

(6) After all the representative points are located from the first station, take a foresight at the second station and note down the bearings. Vertical angle and the staff readings corresponding to the top, bottom and axial hairs.

(7) Shift the instrument to the second station. Set up, centre and level the instrument and measure the height of the instrument as before.

(8) Take a back a sight to the first station. Also observe the bearings, vertical angle, and the staff reading to the top, bottom and axial hairs.

(9) As each station is sighted twice two Values for the distances and elevations of the stations are obtained which should be within the permissible limits; otherwise, the work should be repeated.

Methods of Tachometric Survey

 Methods of Tachometric Survey:

Various methods of tacheometry survey are based on the principle that the horizontal distance between an instrument Station “A” and a staff station “B” depending on the angle subtended at point “A” by a known distance at point “B” and the vertical angle from point “B” to point “A” respectively.

This principle is used in different methods in different ways. Mainly there are two methods of tachometry survey.

(1)Stadia system, and

(2) Tangential system.

1. Stadia System of Tacheometry;

In the stadia system, the horizontal distance to the staff Station from the instrument station and the elevation of the staff station concerning the line of sight of the instrument is obtained with only one observation from the instrument Station.

In the stadia method, there are mainly two systems of surveying.

(1) Fixed hair method and,

(2) Movable hair method.

i. Fixed Hair Method:

In the fixed hair method of tacheometric surveying, the instrument employed for taking observations consist of a telescope fitted with two additional horizontal cross hairs one above and the other below the central hair.

These are placed equidistant from the central hair and are called stadia hairs.

When a staff is viewed through the telescope, the stadia hairs are seen to intercept a certain length of the staff and this varies directly with the distance between the instrument and the stations.

As the distance between the stadia hair is fixed, this method is called the “fixed hair method.”

ii. Movable Hair Method:

In the movable Hair method of tacheometric surveying, the instrument used for taking observations consist of a telescope fitted with stadia hairs which can be moved and fixed at any distance from the central hair (within the limits of the diaphragm).

The staff used with this instrument consists of two targets (marks) at a fixed distance apart (say 3.4 mm).

The Stadia interval which is variable for the different positions of the staff is measured, and the horizontal distance from the instrument station to the staff the station is computed.

Note: Out of the two methods mentioned above of tacheometric surveying, the “fixed hair method “is widely employed.

2. Tangential System of Tacheometric Surveying:

In this system of tacheometric surveying, two observations will be necessary from the instrument station to the staff station to determine the horizontal distance and the difference in the elevation between the line of collimation and the staff station.

The only advantage of this method is that this survey can be conducted with ordinary transit theodolite.

As the ordinary transit theodolite is cheaper than the intricate and more refined tacheometer, so, the survey will be more economical.

So, as far the reduction of field notes, distances and elevations are concerned there is not much difference between these two systems.

But this system is considered inferior to the stadia system due to the following reasons and is very seldom used nowadays.

This involves the measurement of two vertical angles, and the instrument may get disturbed between the two observations.

The speed is reduced due to more number of observations and the changes in the atmospheric conditions will affect the readings considerably.

The staff used in this method is similar to the one employed in the movable hair method or stadia surveying. The distance between the targets or vanes maybe 3-4 m.

Introduction to tacheometric surveying

 

Tacheometric surveying is a method of angular surveying in which the horizontal distance from the instrument to the staff stations are determined from instrumental observations only.

Thus the chaining operations are eliminated.

Field Work can be completed very rapidly Tacheometry is mainly used for preparing the contour plans of areas.

As chaining is avoided, as far as possible, this method of surveying is best suited in broken and hilly areas, areas covered with stretches of water, Swamps, etc. where chaining will become very slow, tedious and inaccurate.

Even though this method is not very accurate owing to the above-mentioned advantages, it is employed in location surveys of lines of communications such as roads, railways, etc.

What is Tacheometer?

A tacheometer is similar to an ordinary transit theodolite fitted with stadia wires in addition to the central cross-hairs.

As accuracy and speed are necessary, the telescope fitted with a tacheometer must fulfill additional requirements. Also, the vertical circle should be more refined.

The telescope of the tacheometer is usually longer than that of the Ordinary theodolite and has a higher power of magnification.

The object glass is of greater diameter, and the lens system is of better quality. The magnification power should not be less than 20-25.

The effective aperture should not be less than 3.5-4.5 cm in diameter facilitating the obtaining of a bright image.

The multiplying constant of the instrument (f/I) is generally kept as 100. Sometimes an additional pair of cross-hairs is provided such that the multiplying constant (f/I) is 50.

This is used for close sights. As the top and bottom hairs are read, arrangements may be provided by rack-and-pinion for the movement of the eyepiece in the vertical plane.

It should be possible to take direct readings up to an angle of 5 degrees on the vertical circle.

A Sensitive spirit level should be fixed on the “underarm.” An instrument fulfilling the above requirements is used in fixed hair method of stadia surveying.

For use in the movable hair method of stadia surveying, the above tacheometer will have a different type of diaphragm.

Generally, the fixed central cross-hair and the vertical hair are stretched in the diaphragm frame.

The movable top and bottom cross-hairs are mounted on different slides which can be moved by a micrometre screw.

The diaphragm and the slides carrying the stadia wires are located in different vertical planes to prevent wear and tear.

Micrometre screws that operate the stadia hairs are provided with milled heads and drum scales. The drums are divided into 100 parts.

Readings may be taken up to 0.001 of the pitch of the screws. This instrument is also called as a subtense theodolite.

Surveying principal and method of Civil Engineering

 Surveying is the process of determining the 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 the horizontal plane only. Surveying is the art of determining the relative positions of points on, above or beneath the surface of the earth by means of direct or indirect measurements of distance, direction and elevation.

Levelling is a branch of surveying the object of which is to find the elevations of points with respect to a given or assumed datum and to establish points at a given elevation or at different elevations with respect to a given or assumed datum.

The survey is performed to prepare a map of relative positions on the surface of the earth. It shows the natural feature of a country such as towns, villages, roads, railways, etc. They may also include details of different engineering works such as bridge, canal, dam etc.

Before commencement of any major engineering project, the survey is carried out to determine the location of the site and its surrounding. To understand the topography of the site and natural resource availability. A survey is carried out to prepare the cadastral map showing property boundaries.

Principles of Surveying

The fundamental principle upon which the various methods of plane surveying are based can be stated under the following two aspects.

Location of a point by measurement from two points of reference

According to this principle, the relative position of a point to be surveyed should be located by measurement from at least two points of reference, the positions of which have already been fixed.

If P and Q are the two reference points on the ground, any other point, such as R, can be located by any of the direct methods shown in the above figures. But, although a single method is sufficient to locate the relative position of ‘R’ with respect to reference points P and Q, it is necessary to adopt at least any two methods to fix the position of point ‘R’.

While the measurements made in either of the first method or second method will be helpful in locating the point ‘R’, the measurements made in the other method will act as a check.

Working from whole to part

According to this principle, it is always desirable to carry out survey work from whole to part. This means, when an area is to be surveyed, first a system of control points is to be established covering the whole area with very high precision. Then minor details are located by less precise methods.

The idea of working this way is to prevent the accumulation of errors and to control and localize minor errors which, otherwise, would expand to greater magnitudes if the reverse process is followed, thus making the work uncontrolled at the end.

Method of Surveying in Civil Engineering

Primary types of Surveying are:

• Plane surveying
• Geodetic surveying

1. Plane surveying

Plane surveying is conducted by state agencies as well as private agencies. As we know earth is spherical in shape but its diameter is big enough to consider a plane in small dimensions. It is that type of surveying in which the mean surface of the earth is considered as a plane and the spheroidal shape is neglected. All triangles formed by survey lines are considered plane triangles. The level line is considered straight and the plumb lines are considered parallel. Plane surveying is done of the area of survey is less than 250 km2.

2. Geodetic surveying

The geodetic survey is conducted by the survey department of the country. It is that type of surveying in which the curved shape of the earth is taken into account. The object of geodetic survey is to determine the precise position on the surface of the earth, of a system of widely distant points which form control stations in which surveys of less precision may be referred. . Line joining two points is considered as curved line and angles are assumed as spherical angles. It is carried out if the area exceeds over 250 km2.

Secondary classification of Surveying

Surveys may be classified based on the nature of the field of survey, the object of survey and instruments used.

1) Surveying based on Nature of Survey

a) Topographical Surveys

They are carried out to determine the position of natural features of a region such as rivers, streams, hills etc. and artificial features such as roads and canals. The purpose of such surveys is to prepare maps and such maps are called topo-sheets.

b) Hydrographic Survey

The hydrographic survey is carried out to determine M.S.L. (Mean Sea Level), water spread area, depth of water bodies, the velocity of flow in streams, the cross-section area of flow etc.

c) Astronomical Survey

The Astronomical Survey is carried out to determine the absolute location of any point on the surface of the earth. The survey consists of making observations of heavenly bodies such as stars.

d) Engineering Survey

This type of survey is undertaken whenever sufficient data is to be collected for the purpose of planning and designing engineering works such as roads, bridges and reservoirs.

e) Archeological Survey

This type of survey is carried out to gather information about sites that are important from archaeological considerations and for unearthing relics of antiquity.

f) Photographic Survey

In this type of survey, information is collected by taking photographs from selected points using a camera.

g) Aerial Survey

In this type of survey data about large tracks of land is collected by taking photographs from an aero-plane.

h) Reconnaissance Survey

In this type of survey, data is collected by marking physical observation and some measurements using simple survey instruments.

2) Surveying based on Type of Instruments

a) Chain Surveying

Chain surveying is the basic and oldest type of surveying. The principle involved in chain survey is triangulation. The area to be surveyed is divided into a number of small triangles. Angles of triangles must not be less than 30 degrees and greater than 120 degrees. Equilateral triangles are considered to be ideal triangles. No angular measurements are taken, tie line and check lines control accuracy of the work.

This method is suitable on level ground with little undulations and the area to be survey is small.

b) Compass Surveying

Compass survey uses the principle of traversing. This method does not require the need to create triangles. It uses a prismatic compass for measuring the magnetic bearing of the line and the distance is measured by the chain. A series of connecting lines is prepared using a compass and measuring distances using a chain. Interior details are located using offset from main survey lines.

They suitable for large area surveying crowded with many details. It can be used to survey a river course.

c) Plane Table Surveying

The principle of the plane table survey is parallelism. They are plotted directly on paper with their relative position. The rays are drawn from the station to the object on the ground. The table is placed at each of the successive station parallels to the position of the last station.

They are basically suitable for filling interior detailing and is recommended when great accuracy is not required.

d) Theodolite Surveying

The theodolite is an instrument used mainly for accurate measurement of the horizontal and vertical angles. They are accurate to measure up to 10″ or 20″ angles.

Theodolite can be used to measure:

• Horizontal angles
• Vertical angles
• Deflection angle
• Magnetic bearing
• The horizontal distance between two points
• Vertical height between two points
• Difference in elevation

Nowadays theodolite is shadowed and replaced by the use of Total Station which can perform the same task with greater ease and accurate results

e) Tacheometric Surveying

Tachometer is a branch of surveying in which horizontal and vertical distances are determined by taking angular observations with an instrument known as a tacheometer. Tacheometer is nothing but a transit theodolite fitted with a stadia diaphragm and an anallatic lens. There is no need for chaining in such a survey. The principle of the Tacheometer is based on the property of the isosceles triangle, where the ratio of the distance of the base from the apex and the length of the base is always constant.

A different form of stadia diaphragm commonly used:

f) Photographic Surveying

The photographic survey is based on the technique of taking photographs from a different angle to prepare topographic details with relatively high speed.

There are two types of photographic surveying

i). Terrestrial or ground photogrammetry

In terrestrial photogrammetry, maps are prepared from ground photographs from different points on the earth surface for measurement purpose.

ii). Aerial photogrammetry

In aerial photogrammetry, maps are produced from the air from an aeroplane or helicopter.

Photogrammetry encompasses two major areas of specialization.

• Metrical photogrammetry
• Interpretive photogrammetry

Metrical photogrammetry is of principal interest to surveyors since it is applied to determine distances, elevations, areas, volume, etc. to compile topographic maps made from measurements on photographs.

Intuitive photogrammetry involves objects from their photographic image and their significance. Critical factors considered in identifying an object of shape, sizes, patterns, shadow.