Tacheometric Surveying MCQ Quiz - Objective Question with Answer for Tacheometric Surveying - Download Free PDF

Explanation:

The Stadia Method:

• The term stadia is now applied to the crosshairs and rods used in making measurements, as well as to the method itself.
• Stadia readings can be taken with most surveying instruments.
• The equipment for stadia measurements consists of a telescope with two horizontal hairs called stadia hairs and a graduated rod called a stadia rod.
• Well adapted to mapping requirements and is widely used for locating details and contour points in topographic surveying.

Stadia Interval Factor:

The ratio of the focal length (f) of the object to the stadia interval (i) is called the stadia interval factor and is designated by the letter K

∴ K = \(\frac{f}{i}\)

For any given instrument, this value remains constant and depends only on the spacing between the stadia hairs.

The most common value of K is 100.

Explanation:

Tacheometer:

(i) This is another method of surveying wherein the horizontal distance and the difference in elevations are determined indirectly by an instrument called as tacheometer.

(ii) Tacheometer is nothing but a transit theodolite fitted with a stadia diaphragm.

(iii) The stadia diaphragm generally consists of two stadia hairs, one above and one below and equidistant from central horizontal hair.

Major Characteristics of a Tacheometer:

(i) The multiplying constant (k) of the tacheometer is usually a round figure and mostly it is 100.

(ii) The additive constant (C) of the tacheometer is kept very small and mostly it is kept zero.

(iii) An additional convex lens is provided between eyepiece and object glass at a fixed distance and known as anallactic lense to make additive constant zero.

(iv) The magnifying power of the eyepiece is kept high to make the staff graduations clearly visible even at a large distance.

(v) The aperture of the objective is kept usually 35 mm to 45 mm to make the image sharp. 

Concept:

In tacheometry, when the line of sight is horizontal (vertical angle = 0), the horizontal distance \( D \) is given by:

\( D = K \cdot S + C \)

Where:

• K = multiplying constant = 100
• C = additive constant = 0.5
• S = staff intercept = upper - lower staff reading

Also, elevation of B is calculated using HI (Height of Instrument) method:

\(HI = RL_{BM} + Staff \, reading_{BM}\)

\(RL_B = HI - Staff \, reading_{B_{central}}\)

Given:

• Staff readings at B: 2.980 m, 2.660 m, 2.340 m
• Multiplying constant (K) = 100
• Additive constant (C) = 0.5
• BM Elevation = 1020.50 m
• Staff reading on BM = 2.85 m

Calculation:

1. Distance AB:

Staff intercept S = 2.980 – 2.340 = 0.640 m

Using the formula:

\(D = 100 \cdot 0.640 + 0.5 = 64.0 + 0.5 = 64.5 \, m\)

2. Elevation of Point B:

HI = 1020.50 + 2.85 = 1023.35 m

RL at B = HI – Central staff reading = 1023.35 – 2.66 = 1020.69 m

Concept:

The stadia method of tachometry is used to measure horizontal distances using the formula:

\( D = kS + i \)

• \( D \) = Horizontal distance
• \( k \) = Stadia interval factor (typically around 100)
• \( S \) = Stadia interval (difference between upper and lower stadia readings)
• \( i \) = Instrument constant (assumed 0 in modern instruments)

Since \( i = 0 \) for properly calibrated instruments, the equation simplifies to:

\( D = kS \)

The horizontal distance (D) to the rod is directly proportional to the stadia interval (S) and can be calculated using the formula \( D = kS \).

Explanation:

• Stadia diaphragm is used in Tacheometric surveying.
• The stadia diaphragm has three horizontal hairs i.e., a central horizontal hair and upper and lower stadia hairs. The upper and lower stadia hairs are equidistant from the central horizontal hair.
• Nowadays, the stadia lines are etched on the diaphragm on which the horizontal and vertical cross hairlines are also used.

Concept:

According to principal of stadia method if line of sight is horizontal and staff is held vertical then horizontal distance between vertical axis of instrument and staff station is given by tacheometric distance equation.

D = kS + c

In this equation, Additive constant (c) and Multiplying constant (k)

Calculation:

Given:

D₁ = 200 m, D₂ = 298 m

S₁ = 2 m, S₂ = 3 m

200 = k × 2 + c    ….. Eq. 1

298 = k × 3 + c    ….. Eq. 2

From equations 2 and 3, the value of k = 98 and c = 4

Explanation:

• Stadia diaphragm is used in Tacheometric surveying.
• The stadia diaphragm has three horizontal hairs i.e., a central horizontal hair and upper and lower stadia hairs. The upper and lower stadia hairs are equidistant from the central horizontal hair.
• Nowadays, the stadia lines are etched on the diaphragm on which the horizontal and vertical cross hairlines are also used.

Concept:

Slope, temperature, and tension corrections are required in chain surveying, not in Tacheometric surveying.

In Method of Tacheometry

In this figure, the Line of sight is horizontal and staff is held truly vertical.

Tacheometric distance formula

\(D=\left(\dfrac{f}{i}\right)s + (f+d) \)

D = KS + C

Where,

K is (f/i) → called a multiplying constant

C is (f + d) → called an additive constant

As

f = focal length of the lens, i = stadia hair interval

Calculations:

Given, f = 200 mm = 0.2 m

d = 180 mm = 0.18 m, s = 2.5 m

\({\rm{i}} = \frac{{3.2}}{{1000}} × 100 = 0.32\) mm

k = \(\frac{f}{i}\)

⇒ k = 200/0.32 = 625

C = f + d

C = 0.2 + 0.18 = 0.38 m

s = 2500 mm = 2.5 m

D = 625 × 2.5 + 0.28 = 1562.8 m

Tachometer: It’s a transit theodolite fitted with a stadia diaphragm which gives both horizontal and vertical control with an accuracy of 1 in 1000.

Horizontal Distance (D) ⇒

\(\rm{D = k \times s \times {\left( {\cos \theta } \right)^2} + c \times \cos \theta}\)

Vertical distance (V) ⇒

\(\rm{V = k \times s \times \sin \theta \times \cos \theta + c \times \sin \theta}\)

Where,

k = multiplying constant, c = additive constant, s = staff intercept, and θ = angle of inclination of measurement

For given condition: (θ = 0°),

Assuming analltic lens i.e. k = 100 and c = 0

∴ Tachometric formula for horizontal distance using inclined sights through θ is obtained by multiplying the multiplying constant by cos2 θ and additive constant by cos θ.

Concept:

Length of limiting offset is given by:

\({\rm{l}} = \frac{{0.025 \times {\rm{s}}}}{{{\rm{Sinθ }}}}\)

where

s = scale of the drawing

θ = Maximum allowed error in laying direction of an offset.

l  = limiting length of the offset

Calculation:

θ = 2°, s = 1 cm to 100 m i.e. s = 100,

\(l = \frac{{0.025 \times {\rm{100}}}}{{{\rm{Sin\;}}2^\circ }}=71.63\; m\)

Explanation:

Stadia Method:

In a tachometer, the various wires, in addition to the cross-wires on the diaphragm are known as stadia wires and the vertical distance between these stadia wires is termed as stadia interval. When the parallactic angle β, defined with the help of stadia wires, is kept fixed and the staff intercept is varied.

The stadia method is based on the principle that the ratio of the perpendicular to the base is constant in similar isosceles triangles.

\({OC''\over A''B''}={OC'\over A'B'}={OC\over AB}=K\)

Constant (K) = \({1\over 2}\times Cot({β \over 2}) \)

Constant (K) = \({1\over 2}\times cot({34^{'}22.64''\over 2}) \)

Constant (K) = 100

Hence both statements (i) & (ii) are correct.

Concept:

Tacheometric surveying:

• It is the branch of angular surveying in which horizontal and vertical distances of points are measured by optical means
• This method is very  rapid a convenient
• The telescope is truly analytic.

The telescope used in stadia surveying is three types.

1. Simple external-focusing telescope.
2. Focusing on the external analytic telescope (porro's telescope)
3. The internal focusing telescope.

The external focusing analytic telescope in Tacheometric surveying is also known as the porro's telescope.

Explanation:

Stadia system of Tacheometric :

(i) In the stadia system of tacheometry, the tachometer is set up at station A and staff at station B as shown in the figure.

(ii) The staff intercept between the upper and lower stadia is measured along with vertical angle θ made with the horizontal.

(iii) The horizontal distance D between the instrument station A and staff station B and the difference of elevations between stations A and B are determined from the staff intercept (s) and the vertical angle so we can say that intercepts on measuring rods are proportional to the distance

Explanation:

Electronic Tacheometers or Total station:

• Electronic Tacheometers or Total station is a combination of an electronic theodolite, an electronic distance measurement  (EDM), and an electronic data collector.
• It is an optical instrument used to measure distances & angles in digital form.
• The maximum range of a total station is typically 1 to 3 km to a single prism assuming good visibility.
• The total station is activated through its control panel, which consists of a keyboard and multiple-line liquid crystal display (LCD).
• The total station is used to determine horizontal and vertical angles together with the slope distance from the instrument to the points to be surveyed.
• The precision of a typical total station is 5mm. 

Explanation:

The sources of errors in stadia measurements are as follows:

Instrument errors

Personal errors

Errors due to Natural Causes:

• Unequal expansion of the instrument parts
• Unequal refraction and
• Bad visibility
• Due to wind

Errors due to Instruments:

• Imperfect permanent adjustments in the instrument
• Incorrect graduations on the stadia rod

Errors due to Manipulation and Sighting or personal errors:

• These errors depend on the efficiency and skill of the surveyor and  due to inaccurate leveling and centering of the instrument
• These errors may occur and by these incorrect stadia, readings are taken.

So, Parallax is not an error due to natural causes.