Unit - 6

Tacheometric Survey

6.1 Tacheometric Survey

• Tacheometry is a branch of surveying in which horizontal & vertical distances are determined by taking angular observation with an instrument known as Tacheometer.
• The chaining operation is completely eliminated in such a survey.
• Tacheometric survey is adopted in rough & difficult terrain where direct levelling & chaining are either not possible or very tedious. It is also used in location survey for railways, roads, reservoir's etc.
• It is very rapid & reasonable contour map can be prepared for investigation works within a short time on the basis of such a survey.

Applications and Limitations:

• When obstacles such as steep and broken ground, stretches of water or swamps are met with, tachometry is best adapted from the speed and accuracy point.
• In rough country both horizontal and vertical measurements are tedious and chaining is inaccurate, difficult and slow.
• In locating contours and filling in detail in a topographic survey, this method is usually the quickest and best.

Key Takeaways:

This method is usually the quickest and best.

6.2 Instruments used

The contraptions hired in tachometry are the engineer's transit and the leveling rod or stadia rod, the theodolite and the sub tense bar, the self-decreasing theodolite and the leveling rod, the gap wedge and the horizontal distance rod, and the discount tacheometer and the horizontal distance rod.

The foremost contraptions utilized in tacheometry are: (i) A tacheometer, and (ii) A levelling or stadia rod.

(i) Tacheometry:

A tacheometer in preferred experience is a transit theodolite having a telescope equipped with a stadia diagram, i.e. a telescope ready with horizontal hairs referred to as stadia hairs further to the same old valuable hair. The extra hairs are ready from the valuable one and also are referred to as stadia lines. The forms of stadia diagram generally used

The sorts of telescopes utilized in stadia surveying are:

(a) The outside focusing,

(b) The inner focusing,

(c) The outside focusing outfitted with an analytic lens.

The time period tacheometer is constrained to a transit theodolite furnished with an analytic telescope.

The critical traits of a tacheometer are:

(a) The price of the multiplying regular f/i have to be 100

(b) The telescope have to be effective having magnification20 to 30 diameters.

(c) The aperture of the goal have to be big approximately four cm in diagram with a view to have a sufficiently vibrant image.

(d) The eye — piece have to be of extra magnifying strength to render clean personnel studying even from a protracted distance.

(ii) Stadia Rod:

A normal levelling group of workers may be used if the points of interest are quick however in tacheometry for the reason that points of interest are normally of lots extra length, therefore, an normal levelling group of workers cannot serve the purpose. But a mainly designed graduated rod called stadia rod is used.

The stadia rod is transport, it is able to be folding or telescopic. It is three to 4m lengthy and 5cm to fifteen cm wide. The graduations are formidable and clean with a least be counted number normally much less than the least be counted number of an normal levelling group of workers, the stadia rods must be as mild as possible

Key takeaways:

The stadia rod is transport, it is able to be folding or telescopic. It is three to 4m lengthy and 5cm to fifteen cm wide

6.3 Principle

• The principle of tacheometry is to enable horizontal and vertical distances to be computed from readings upon a stadia rod, and thus eliminate chaining operation.
• The observations that are required for complete location of a point say P with referenceto the instrument station O are,

1. The bearing of the line OP.
2. The angle of elevation or depression recorded on vertical circle of the instrument.
3. The readings of three diaphragm hairs upon a stadia rod at P sighted through thetelescope; top, middle and bottom.

• The middle hair reading is known as axial hair reading or central hair reading.

Key takeaways:

The principle of tacheometry is to enable horizontal and vertical distances to be computed from readings upon a stadia rod, and thus eliminate chaining operation.

6.4 Determination of tachometric constant

• The values of the constants and (f+ c) for a given instrument may be determinedexperimentally as follows:
• In this method the value of (f + c) is obtained by measurements.
• The value of is computed as i being too small to be measured accurately.

Procedure:

1. Sight any distant object and focus it carefully.
2. With the help of scale measure the distance between the object glasses and plane of cross hairs along the top of telescope.
3. Let (f) be the focal length of objective.
4. Measure the distance (c) from the object glass to the vertical axis of the instrument.
5. Measure distance x1, x2, x3, etc from the instrument.
6. Let the corresponding staff intercepts be S1, S2, S3 etc.
7. In the formula X = (S) + (f + c) knowing (f + c) as directly measured in above steps and measured distance X1, X2, X3 etc.
8. Several values of is computed.
9. And the mean of the above values give constant.

Key takeaways:

• The values of the constants and (f+ c) for a given instrument may be determined experimentally as follows:
• In this method the value of (f + c) is obtained by measurements.

Tacheometric Contouring:

• Tacheometric technique is followed for contouring of very steep hills.
• The steps are as follows:

1. Set up the tacheometer on the pinnacle of the steep hill. Tacheometer is a theodolite equipped with stadia diaphragm. The stadia diaphragm has 3 horizontal parallel hairs in preference to one as observed in a traditional move hair diaphragm.
2. With the assist of a tacheometer, it's far viable to decide the horizontal distance of the factor from the telescope as nicely its vertical degree.
3. The steep hill is surveyed at 3 levels – the bottom of the hill, the mid-degree of the hill and the pinnacle degree of the hill.
4. Using the tacheometer studying are taken all over the hill at identical angular durations on some of these 3 levels.
5. The radial plot therefore acquired is labored within side the workplace to interpolate factors of identical elevation for contour mapping.

Key Takeaways:

Tacheometric technique is followed for contouring of very steep hills.

Examples:

A tacheometer having constant 100 and 0.4 m readings were taken on vertical staff at station P and Q as follows:

Calculate the horizontal distance between A and Q and reduced level of Q. Assume line if sight horizontal.

Step 1: The line of sight horizontal and staff is held vertical.

X= (S) + (f + c)

Step 2: The horizontal distance between O and A by observation at A

X =100 × (3.900-0.300) +0.4

X=360.4 m

Step 3: RL of instrument axis = RL of BM+ central hair reading

=100+2.3

=102.3 m

RL of Q = RL of instrument axis –central hair reading

= 102.3-2.1

=100.2 m

6.5 Methods of Tacheometry: Stadia Method and Tangential Method

The underlying precept not unusual place to exceptional strategies of tacheometry is that the horizontal distance among an device station and a factor in addition to the elevation of the factor notably to the device may be decided from the attitude subtended on the device station with the aid of using a acknowledged distance at factor and the vertical attitude from device to the factor. The numerous tachometric strategies rent the precept in exceptional approaches and fluctuate each other in strategies of remark and reduction, however can be categorized below heads:

(i)                The stadia method

(ii)             The tangential method

The stadia method

In the stadia device, the remark are fascinated by the stadia wires of the tacheometer and within side the tangential device the angles of elevation are measured from device station to the factors with a theodolite and their tangents are used to decide the horizontal of the telescope for vital however the stadia device wishes best one and is greater typically used.

The Stadia System of Tacheometry:

The Stadia System of Tacheometry: In the stadia machine of tacheometry there are strategies of surveying viz: (i) Fixed hair approach, and (ii) Moveable hair approach.

(i)                Fixed Hair Method: In this approach, the gap among the stadia hairs is constant. When personnel is sighted via the telescope, its sure period is intercepted via way of the stadia hair and from tins cost of personnel intercept, the gap from the tool to the personnel may be determined. The personnel intercept varies with its distance from the tool. This approach is maximum usually utilized in tacheometry.

(ii)             Moveable Hair Method: In this strategies, the stadia hair aren't constant however may be moved by way of micrometer screws. The stall is supplied with vanes or goals constant at a regarded distance apart. The variable stadia distance is measured, and from this cost the specified horizontal distance can be determined out. The approach is now not often used. General Principle of Stadia Tacheometry:

The consistent f/i is referred to as the a couple of consistent and its cost is commonly 100, even as the consistent (f+d) is referred to as the additive consistent and its cost varies from 30 cm to 60 cm in case of outside focusing telescope, it's miles very small various from 10 cm to twenty cm and is consequently oftenly ignored. To make the cost of additive consistent zero, a further convex lens, called analytic lens, is furnished within side the telescope among the object – glass and eye piece at a hard and fast distance from former. By this arrangement, calculation paintings is decreased considerably. The equation 10.1 is relevant most effective while the road of sight is horizontal and the body of workers is held vertical.

The tangential method

Determination of Stadia Constants of a Tacheometer: There are techniques to be had for locating the values of the stadia steady f/i and f + d of a given tool. First method: In this method, the values of the constants are acquired through the computations shape the sphere measurements. Procedure: (i) Measure as it should be a line OA approximately three hundred m long, on a reasonably stage floor and attach pegs alongside it at periods of say, 30m. (ii) Set up the tool at O and acquired the group of workers intercepts through taking stadis analyzing at the group of workers held vertically at every of the pegs. On substituting the values of D and S withinside the Equations 10.1, we get some of equations which whilst solved in pairs, provide the numerous values of the constants: their imply price being followed to the values of the constants. Thus, if D1,D2, D3, etc.=the distances measured from the tool, and S1, S2, S3 etc.= the corresponding group of workers intercepts.

Second Method: In this method, the cost of the multiplying steady f/i is located through computations from the sphere measurements and that of the additive steady (f+) is acquired through the direct measurements on the telescope. Procedure: (i) Sight any some distance distant – item and cognizance it. (ii) Measure correctly the gap alongside the pinnacle of the telescope among the item -Glass and the aircraft of the cross -hairs (diagram screw) with a rule, the measured distance being identical to the focal length (f) of the objective. (iii) Measure the gap (d) from the item— glass to the vertical axis of the tool. (iv) Measure numerous lengths D1, D2, D3 etc. alongside OA from the tool – role O and acquired the team of workers intercepts S1, S2, S3 ate. At every of those lengths. (v) Add f and d locate the values of the additive steady (f+d). (vi) Knowing (f+d), decided the numerous values of f/i from the equation 10. 1. (vii) The suggest of the numerous values offers the desired cost of the more than one steady f/i. Calculation paintings is an awful lot simplified, of the tool is located at a distance of (f+d) past the start O of the line. Note: The cost of the additive steady in case of an inner focusing telescope can not be decided on this way. One has to depend on the cost furnished through the maker

Key takeaways:

In the stadia device, the remark are fascinated by the stadia wires of the tacheometer and within side the tangential device the angles of elevation are measured from device station to the factors with a theodolite and their tangents are used to decide the horizontal of the telescope for vital however the stadia device wishes best one and is greater typically used.

References:

1. Duggal, S.K. Surveying Vol. I and II, Tata McGraw Hill, 2004.

2. Punmia, B.C. Surveying Vol. I and II, Standard Publishers, 1994.

3. Arora, K. R. Surveying Vol. I and II, Standard Book House, 1996

4 N.N Basak. Surveying and levelling