TACHOMETRIC SURVEY
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Q1. What is tachometry. What are its advantages?
Answer:
Tachometry is a branch of surveying in which horizontal and vertical distances are determined by taking angular observations with an instrument known as tachometer. Advantages:
(i) The chaining operation is completely eliminated in this type of survey.
(ii) It is commonly used in location survey for railways, roads, reservoirs etc.
(iii) It is adopted in rough and difficult terrain where direct leveling and chaining are either not possible or very tedious,
(iv) It requires much less time.
Q2. Give the list of equipment necessary to conduct the tachometric survey. Show the tabular form of recording field observations in a tachometric survey.
Answer :
The equipments required to conduct the tachometric survey
(i) Tachometer
(ii) Leveling staff
(iii) Stadia rod
(iv) Pegs
(v) Hammer
(vi) Ranging rods
(vii) Tape
Table for recording field observations in a tachometric survey
Q3. Write down the formula for finding the horizontal distance from the instrument station explaining the terms used. What is the purpose for providing an anallatic lens in a tachometer?
Answer:
The formula for finding the horizontal distance from the instrument station by fixed hair method to staff rod -
(i) When the line of sight is horizontal and staff is held vertically,
D = f/i x S +(f+d)
(ii) (a) When line of sight is inclined but staff is held vertically and considering angle of elevation, D = f/i XS cos²θ +(f+ d ) cosθ
(b) Line of sight is inclined but staff is held vertically and considering angle of depression,
D = f/i ×S cos²θ + ( f + d ) sinθ
Where, D = horizontal distance between the instrument station to leveling staff or stadia rod,
f= focal length of object glass,
i = length of real image when anallatic lens is provided
s = staff intercept
d = distance between optical centre of the object glass and vertical axis of the instrument
θ= angle of elevation or depression
The quantities f/i and (f +d) are known as tachometric constant. f/i is called multiplying constant and (f+d) is called additive constant.
Q4. Determine the constants of a tachometer from the following readings of staff held vertically.
Distance (m) staff reading
Lower upper
30 1.085 1.380
60 0.925 1.520
Answer:
We know from the theory of stadia tachometer
D = f/i × S + (f + d)
Then, 30 = f/i × ( 1.380 - 1.085 ) + (f+d) .....(1)
And, 60= f/i × (1.520 - 0.925)+(f+d) ..... (2)
By (2) - (1) , we get , 30 = 0.3 × f/i
Then , multiplying constant =f/i = 100
And, addiative constant (f+d)=60-100×f/i =0.05
Q5 , what is anallatic lens ? Why it is providing in a tachometer ? Differentiate leveling staff stadia rod .
Answer:
additional convex lens is provided between the eye piece and the object glass at a fixed distance from the object glass. This convex lens is known as an anallatic lens such a lens is provided in the external focusing telescope.
The object providing this lens is in the telescope is to make the additional constant (f+d) is exactly zero.
Difference between leveling staff and stadia rod:
Staff
1. It is used for short distance leveling.
2. In a leveling staff the graduations are marked that a minimum reading of 0.005 m.
Stadia rod
1. It is used for long distance leveling.
2. In a stadia rod the graduations are marked marked that a minimum reading of 0.001 m.
Q6. Determine the constants of a tachometer from the following readings of staff held vertically:
Answer:-
We know from the theory of stadia tachometer
D = f/i × S + ( f + d)
Then , 150 = f/i × ( 2.750 - 1.255) + ( f +d) ...... (1)
And , 250 = f/i × (3.255-0.750)+(f+d) ....... (2)
By (2) - (1) , we get , 100 = 1.010×f/i
Then, multiplying constant = f/i = 99
And , addiative constant ( f + d ) = 250- 99 × f/i = 2.005 m.
Q7. How tachometric survey differs with theodolite survey ?
Answer:
Tachometric survey differs with theodolite survey in the following:
(i) Tachometer is able to measure horizontal distance besides measuring vertical angles. For measuring distance in theodolite survey chain is used.
(ii) Tachometric survey is a rapid survey, while theodolite is a slow process.
(iii) In a tachometric an additional lens is provided.
Q8. What are the methods tachometric survey?
Answer:
Tachometric survey
(i) stadia method
(a) fixed hair method &
(b) moveable hair method,
(ii) tangential method.
Q9. What is the basic principle of Tachometer survey?
Answer:
The principle of tachometry is based on the property of isosceles triangles where the distance of the base from apex and the lengths of the base is always constant.
Q10. Write short notes on —
(a) Stadia rod,
(b) Stadia traverse,
(c) Multiplying constant and additive constant,
(d) Stadia diagram.
Answer:
(a) Stadia rod:
For long sights a specially designed graduated rod is used which is known as stadia rod. It is 4 m Ing and may be folded or telescopic. The graduations are coinparatively bold and clear and the minimum reading that can be taken is 0.001 m.
(b) Stadia traverse:
Stadia traverse is mainly used for filling in details and for contouring. To locate the various details an open or closed traverse is run as the case may be. For narrow strips an open traverse is run, but when the area is extensive, various stations are selected form a closed polygon. In very large areas stations are arranged to form triangle or a series of traverses are run. In between these main stations tachometer's stations are selected to command a clear view of the area.
(c) Multiplying constant and additive constant:
The formula for finding the horizontal distance from the instrument station by fixed hair method to staff rod -
D= f / i XS+(f+d)
The quantities f/i and (f +d) are known as tachometric constant. f/i is called multiplying constant and has a value of 100 and (f +d) is called addiative constant and has a value of 0.
(d) Stadia diaphragm:
Tachometer is nothing but a transit theodolite fitted with a stadia diaphragm and an anallatic lens. Following figure shows the different forms of stadia diaphragm.
Q11. Determine the multiplying and additive constants of an instrument having fixed stadia wires and without anallatic lens. Readings were taken on a vertical staff at a distance of 91.5 m and 183.0 m and the observed staff intercepts were 0.890 m and 1.780 m respectively. Write the distance equation for the instrument.
Answer:
D = f/i ×S+ (f+d)
Then , 91.5 = f/i x 0.890+ (f+d) .....(1)
And , 183 = f/i x 1.78 + (f+d) .......(2)
By (2) - (1), we get, 91.5 = 0.89 × f/i
Then, multiplying constant
= f/i =102.8
And, additive constant (f+d) = 91.5 - 102.8 x .89 = .008
The distance equation is , D=102.8 S + 0.008
Q12. Describe the method of tacheometry. Also explain the theory of tacheometry.
Answer:
In stadia tacheometry with fixed hair method, horizontal sights may not always be available, particularly in rough and hilly terrain where differences of elevation between the instrument and staff stations are large. The measurements involve recording of vertical angle (elevation or depression) to the central stadia hair in tacheometric surveying addition to the staff intercept. There may be two cases one in which staff is held vertical and another in which staff is held normal to the line of sight. Generally, the former is preferred.
A tacheometer is similar to an ordinary transit theodolite, generally a vernier theodolite itself, fitted with two stadia wires in addition to the central cross-hair.
The stadia diaphragm has three horizontal hairs viz., a central horizontal hair and upper and lower stadia hairs. The upper and lower stadia hairs are equidistant from the central horizontal hair. Stadia hairs are sometimes called stadia lines.
For the purpose of tacheometry, even though an ordinary transit can be employed, accuracy and speed are increased if the instrument is specially designed for the work. The magnification of the telescope in tacheometer should be at least 20 to 30 diameters, with an aperture of at least 40 mm for a sufficiently bright image.
The magnifying power of the eyepiece is also greater than for an ordinary transit to produce a clearer image of a staff held far away. Further, the altitude bubble is made more sensitive, since vertical angles form an important part of the data for calculation of elevation differences.
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