Compass Surveying and Theodolite MCQ Quiz - Objective Question with Answer for Compass Surveying and Theodolite - Download Free PDF

Concept: 

Least count = \(\frac{S}{n}\)

n → no. of divisions on vernier scale

s → smallest division of main scale

Calculation: 

s = 10’ = 10 minutes

L.C = 10” = \(\frac{{10'}}{{60}} = \frac{1}{{6}}\) minutes

\(\frac{1}{{6}} = \frac{{10}}{n}\)

n = 10 × 6

n = 60

Concept:

Prismatic compass:

• The graduated ring is attached to the needle and does not rotate with the line of sight.
• The graduations have 0 at S, 90° at W, 180° at N, and 270° at E.
• Graduations are engraved inverted since the graduated ring is read through the prism.
• The readings are taken with the help of a prism provided at the eye vane.
• Sighting and reading can be done simultaneously.
• The instrument can be held in hand also while making the observations.
• The eye vane consists of a metal vane with large silt.

Additional Information

• The graduations have 0 at N and S, 90° at  East and West in the surveyor compass.

Explanation:

Magnetic Declination and Magnetic Bearing of the Sun

Definition: Magnetic declination is the angle between the geographic north (true north) and the magnetic north at a specific location. It is an essential parameter in navigation and surveying as it helps correct compass readings. Magnetic declination can be either east or west depending on whether the magnetic north is to the east or west of true north. The magnetic bearing of the sun is the direction to the sun, measured clockwise from the magnetic north.

Given Scenario: In the problem, the magnetic bearing of the sun at noon is 185°20'. At noon, the sun is due south in the sky when viewed from the northern hemisphere. The magnetic declination is calculated by comparing the magnetic bearing of the sun with its true bearing (geographic direction).

Calculation:

At noon, the sun’s true bearing is 180° (due south). However, the magnetic bearing of the sun is given as 185°20'. This means the compass is reading a direction that is west of the true bearing.

To find the magnetic declination:

• Magnetic Declination = Magnetic Bearing - True Bearing
• Magnetic Declination = 185°20' - 180°
• Magnetic Declination = 5°20' West

The declination is west because the magnetic bearing is greater than the true bearing, indicating that the magnetic north is west of true north.

Explanation:

1. The whole circle bearing (WCB) and the reduced bearing (RB) of a line will be the same when the line lies in the north-east quadrant.
2. This is because, in the north-east quadrant, both the WCB and RB are measured in a similar manner (0° to 90° from the north direction), so they will have the same value.

 Additional InformationWhole Circle Bearing (WCB):

1. The Whole Circle Bearing is the angle measured in a clockwise direction from the north direction, ranging from 0° to 360°.

2. It is called "whole circle" because it considers a full 360° rotation to describe the direction of a line.

3. WCB is used in situations where you need a full circular measurement from the north, with values from 0° to 360°, irrespective of whether the line is heading towards the north, south, east, or west.

Reduced Circle Bearing (RCB):

1. The Reduced Circle Bearing (also known as Quadrantal Bearing) is used to express the bearing relative to the nearest cardinal direction (north or south), and it uses a range of 0° to 90° for each quadrant (north-east, north-west, south-east, south-west).

2. The direction is measured as an angle from either north or south, depending on which quadrant the line is in, and then it is written as a combination of cardinal direction and angle.

Explanation:

Statement I: Magnetic declination is more at magnetic poles and less at equator.

• True.

• Magnetic declination is the angle between true north and magnetic north.

• Near the magnetic poles, this angle becomes large and erratic.

• Near the magnetic equator, the deviation is generally smaller and more stable.

Statement II: Magnetic declination is more in the summer than in the winter.

• True

• In summer, the Earth's ionosphere experiences more solar radiation, which increases magnetic activity.

• As a result, there is more fluctuation in the magnetic field, leading to a slightly higher magnetic declination.

Statement III: Magnetic declination is more at night and less in the day.

• False.

• Daily (diurnal) variation is minor, and during daytime, solar radiation affects ionospheric currents, causing slightly more variation than at night—not the other way around.

Additional InformationMagnetic Declination

• It's the angle between true north (geographic north) and magnetic north.

• Measured east or west from true north.

• Essential in navigation, surveying, and compass correction.

• The Earth's magnetic field is not uniform.

• It changes over time due to movement in the Earth's molten outer core (known as secular variation).

• Declination maps (isogonic charts) are used to track local values.

• Long-term (secular): Slowly changes over years/decades.

• Short-term (diurnal): Slight daily shifts due to solar radiation, but typically <0.1°.

• Sudden changes: Can happen during geomagnetic storms or strong solar activity.

Concept:

Dip:

• It is the inclination of the magnetic needle with the horizontal. The dip is zero at the equator and the needle will remain horizontal.
• At a place near 70° north latitude and 96° west longitude, the dip will be 90°. This area is called the magnetic north pole. Similarly, near the south magnetic pole, the dip is 90°.

​
Declination: 

• It is the angle between the magnetic and geographic meridians or the angle in the horizontal plane between magnetic north and true north.

Explanation:

Explanation:

The difference (degree) in the magnitude of the fore bearing and back bearing of any line is 180° or if the difference is exactly 180°, the two stations may be considered as not affected by local attraction.

For regular hexagon, Sum of interior angles = (n - 2)180° 

Sum of interior angles = (6 - 2)180° = 720° 

Each interior angle = \(\frac{720}{6}\) = 120° 

Back bearing = 180° + Fore bearing = 180° + 36°45' = 216°45'

∴ Fore bearing of BC = 216°45' - 120° = 96°45'

The least count of a vernier is equal to the difference in length of one division of main scale and one division of vernier scale.

In a direct vernier (n-1) divisions of the main scale is equal to the ‘n’ divisions on the vernier scale.

Thus,

n 'v' = (n – 1) 's'

\(\Rightarrow {\rm{v}} = \frac{{\left( {{\rm{n}} - 1} \right){\rm{s}}}}{{\rm{n}}}\)

Thus the least count is given by,

L.C = s – v

\(\Rightarrow {\rm{L}}.{\rm{C}} = {\rm{s}} - \frac{{\left( {{\rm{n}} - 1} \right){\rm{s}}}}{{\rm{n}}}\)

⇒ L C = s/n

Given:

Total division on main scale = 1440

Thus,

Length of one division (s) = 360°/1440

n = 60

\(\Rightarrow {\rm{L}}.{\rm{C}} = \frac{{360^\circ /1440}}{{60}} \times {3600^{{\rm{''}}}} = {15^{{\rm{''}}}}\)

Important Points

A theodolite is an important instrument used to measure horizontal and vertical angles.

There are two types of theodolites based on the method of obtaining reading:

a) Vernier Theodolite:-

• These theodolites use verniers to take readings and are most commonly used. The upper plate of a transit theodolite has two verniers which are diametrically opposite to each other. If this plate is unclamped the upper plate rotates and the reading of the vernier changes.

b) Precise optical theodolites:-

• Mostly used for astronomical works.

Concept:

We know the relationship between FB and BB 

Back bearing (BB) = Fore bearing (FB) ± 180°. 

+ve sign is used if FB is less than 180° and –ve sign is used if FB is more than 180°.

Included angle = Fore Bearing of next line - Back Bearing of the previous line

Calculation:

Fore Bearing of AB = 150°15'

Included Angle ABC = 110°30'

Back Bearing of AB = 150°15' + 180° = 330°15' 

Included angle ABC = F.BBC - B.BAB 

110°30' = F.B._BC - 330° 15'

F.B._BC = 440°45' 

F.B.BC = 440°45' - 360° = 80° 45'

Note: 

If the included angle is negative, then add 360°.

If the included angle is greater than 360° then deduct 360°.

Explanation:

Accuracy

The accuracy of a set of repeated observations is defined as the amount of closeness of their mean to the population or distribution mean, i.e., the closeness of the mean of observations to the true value.

Degree of accuracy

• The degree of accuracy indicates the accuracy attained in the measurements.
• It is usually expressed as the ratio of the error and the associated measured value.
• For example, a degree of accuracy of 1 in 10,000 indicates that there is an error of 1 unit in 10,000 units of measured/observed value.

Note:

For linear measurement:

The degree of accuracy of linear measurement is usually expressed as the ratio of the probable error and the measured distance.

For example, if there is a probable error of ± 0.05 m in a measured distance of 584.65 m, the degree of accuracy is 1 in 11700 as explained below.

For angular measurement:

For angular measurements, the degree of accuracy is usually expressed as k × √N, where N = Number of angles measured

Explanation:

• Fore-bearing (FB) is the direction of a line measured in the forward direction from a known point. The angle between the survey line and the north direction is measured clockwise.
• Back-bearing (BB) is the direction of the same line but measured in the reverse or backward direction from the endpoint back to the starting point. It is in the opposite direction to the fore-bearing and is measured in the opposite direction (180 degrees different).
• Relation between FB and BB:

BB = FB + 180°, if FB < 180°

BB = FB – 180°, if FB > 180°.​

Here there is no local attraction given, so we have to solve by the include-angle method.

Include angle: The horizontal angle measured between two consecutive survey lines or directions.

Include angle = Fore-bearing of next line - Backbearing of previous

The sum of Include angle in clockwise direction (i.e, excluded angle) = (2n+4)90 = (2x5+4)x90° = 1260°

So, the error = 1260°25' - 1260° = 25' 

So, Corrected include angle D = 239°20' - (25'/5') = 239°15' 

Thus, Include angle D = FB_DE - BB_CD 

FBDE = Include angle D +BBCD = 239°15' - 350°50' = 590°05' (- 360°) = 230°5'

Concept:

TB (True Bearing) = MB (Magnetic bearing) ± Declination

(Use + ve for eastern and – ve for western declination)

Calculation:

• At Noon, the sun is exactly on the geographical meridian.
• Hence, the true bearing of the sun at noon is zero or 180° depending upon whether it is to the North of the place or to the South of the place.
• Since the magnetic bearing of the sun is 178°, the true bearing will be 180 °.

True Bearing at Noon = 180°

Magnetic Bearing = 178°

Declination = True Bearing - Magnetic Bearing = 180° - 178° = + 2°

∴ Magnetic Declination = 2° East (+ve sign indicates East)

• Sometimes the direction of declination may not be mentioned in the question and in such cases, standard sign conventions used for declination must be considered.
• Since declination was given a positive value in the above case we would assume is to be eastern declination for computing the value of true bearing.

Agonic lines:

A line having zero degree declination is known as Agonic line

True bearing and magnetic bearing both are equal for agonic lines.

Isogonic lines:

Isogonic lines are lines of same declination.

Agonic lines are always isogonic lines.

Additional Information

Isoclinic Line: Line connecting points of equal dip.

Aclinic Line: Line connecting points of zero dip.

Important terms:

Arbitrary bearing: The horizontal angle made by the survey line with reference to arbitrary meridian passing through one of the extremities.

True Bearing: It is horizontal angle between the true meridian and the survey line measured in a clockwise direction.

Azimuth: it is the horizontal angle or direction of a compass bearing.

Arbitrary Meridian: Any convenient direction from a survey station to some well defined permanent object is known as arbitrary meridian. This is used for small area survey or to determine the relative directions of small traverse.

Concept:

Compass surveying:

Compass surveying is a type of surveying in which the directions of surveying lines are determined with a magnetic compass, and the length of the surveying lines are measured with a tape or chain or laser range finder. The compass is generally used to run a traverse line. There are mainly two types of compass are used:

• Prismatic compass
• Surveyor's compass

Explanation:

Surveyor's compass:

• It can only be used on a tripod.
• In the graduated card, The East and West are interchanged.
• Gives bearing in the quadrantal bearing system
• Range of angle measured 0-90⁰.
• The needle is of edge bar type. 
• The diameter of the compass is 150mm. 
• The least count is 15 minutes.