All questions of Geomatics Engineering (Surveying) for Civil Engineering (CE) Exam

Given information:
Consecutive readings taken with a dumpy level and a 3 m staff on a continuous sloping ground: 0.425, 1.035, 1.950, 2.360, 2.950, 0.750, 1.565, 2.455.

To determine which readings are back sights.

Backsight:
A backsight is a reading taken on a point of known level or elevation, also known as a bench mark, which is used as a reference height for other readings.

Solution:
To determine which readings are back sights, we need to identify the points for which we have a known level or elevation. From the given readings, we can identify that:

- The initial reading of 0.425 is not a backsight as it is the starting point of the survey and there is no known level or elevation for this point.
- The reading of 2.950 is not a backsight as there is no indication that this point is a known level or elevation.
- The reading of 0.750 is a backsight as it is immediately followed by the reading of 1.565, which is higher. This indicates that the point with reading 0.750 is at a lower level or elevation and is a point of known height.
- The final reading of 2.455 is not a backsight as there is no indication that this point is a known level or elevation.

Therefore, the readings that are backsights are:
Option C: 0.425, 0.750.

Hence, option C is the correct answer.

**Explanation:**

The indirect method of contouring is a technique used in surveying to determine the shape of the land surface, particularly in areas with uneven terrain. It involves the use of contour lines, which connect points of equal elevation, to create a contour map.

The indirect method of contouring has several advantages over the direct method, which involves physically measuring the elevation at each point on the ground. These advantages include:

**1. Economy:**
- The indirect method is generally more economical than the direct method because it requires fewer field measurements.
- It relies on the interpolation of elevation values between known points, reducing the need for extensive field work.

**2. Suitability:**
- The indirect method is suitable for areas with complex terrain or limited access.
- It can be used in situations where it is difficult or impractical to measure the elevation at every point on the ground.

**3. Suitability for large projects:**
- The indirect method is particularly well-suited for large projects that cover a wide area.
- It allows for the efficient collection of elevation data over a large extent of land.

However, the indirect method of contouring does have one disadvantage compared to the direct method:

**4. Accuracy:**
- The indirect method may not be as accurate as the direct method because it relies on interpolation and estimation.
- It assumes that the elevation values between known points vary smoothly and continuously, which may not always be the case.
- In areas with abrupt changes in elevation or irregular topography, the indirect method may produce less accurate results.

Therefore, the correct answer is option 'C' - Accuracy. The indirect method of contouring does not have an advantage in terms of accuracy compared to the direct method.

Given data:
- Backsight reading on benchmark = 2.685 m
- Foresight reading on the point = 1.345 m
- Reduced level of benchmark = 500.00 m

We need to find the reduced level of the point.

Steps to find reduced level:

1. Calculate the height of instrument (HI):
- HI = Benchmark RL + Backsight reading
- HI = 500.00 m + 2.685 m
- HI = 502.685 m

2. Calculate the Reduced Level (RL) of the point:
- RL = HI - Foresight reading
- RL = 502.685 m - 1.345 m
- RL = 501.340 m

Therefore, the reduced level of the point is 501.340 m.

Hence, option (c) is the correct answer.

The formula for the radius of a curve is:

R = (L^2/24C) + C/2

Where R is the radius, L is the length of the curve, and C is the degree of curve.

Given that the degree of curve is 1 and the length of the curve is 30m, we can substitute these values into the formula:

R = (30^2/24(1)) + 1/2
R = 112.5 m

Therefore, the radius of the curve for a 30m chain with a degree of curve of 1 is 112.5 meters.

Horizontal Angle and Bearings in Surveying

In surveying, horizontal angles and bearings are used to determine the location of points on the earth's surface. A horizontal angle is the angle measured in a horizontal plane between two lines or points. Bearings are used to describe the direction of a survey line or the location of a point with respect to a reference line or direction.

True Bearing

True bearing is the horizontal angle between the true meridian and the survey line measured in a clockwise direction. The true meridian is the line passing through the geographic north and south poles. True bearing is also known as geodetic bearing or astronomical bearing.

Magnetic Bearing

Magnetic bearing is the horizontal angle between the magnetic meridian and the survey line measured in a clockwise direction. The magnetic meridian is the line passing through the magnetic north and south poles. Magnetic bearing is used when magnetic declination is taken into account.

Grid Meridian

Grid meridian is the line passing through the grid north and south poles. Grid north is the direction of the y-axis of a map projection, while grid south is the opposite direction. Grid meridian is used in plane surveying or when using a coordinate system.

Arbitrary Meridian

Arbitrary meridian is any reference line or direction chosen by the surveyor for a particular survey project. It could be a line passing through a prominent landmark, such as a building or a hill, or a line aligned with a particular feature of the landscape.

Conclusion

In surveying, bearings are used to describe the direction of a survey line or the location of a point with respect to a reference line or direction. True bearing is the horizontal angle between the true meridian and the survey line measured in a clockwise direction. The other types of bearings are magnetic bearing, grid meridian, and arbitrary meridian.

Corrections for Curvature and Refraction in Staff Readings

Correction for Curvature
- The correction for curvature is done to compensate for the effect of the earth's curvature on the staff readings.
- The earth's surface is not perfectly flat, so the line of sight between the observer and the staff is curved.
- This causes the staff readings to be higher than they should be, especially over long distances.
- The correction for curvature is a subtractive correction, which means that it reduces the observed staff readings.
- The correction formula for curvature is given by: Correction = (D/2R)^2 x 100, where D is the distance between the observer and the staff, R is the radius of the earth, and 100 is a conversion factor.

Correction for Refraction
- The correction for refraction is done to compensate for the bending of light rays as they pass through the earth's atmosphere.
- The atmosphere has varying densities and temperatures, which cause the light rays to bend and follow a curved path.
- This causes the staff readings to be lower than they should be, especially over long distances.
- The correction for refraction is an additive correction, which means that it increases the observed staff readings.
- The correction formula for refraction is given by: Correction = (0.13t/D) x 100, where t is the air temperature in degrees Celsius and D is the distance between the observer and the staff.

Correct Answer: Option B
- Option B states that the corrections for curvature and refraction are respectively - and +.
- This means that the correction for curvature is subtractive and the correction for refraction is additive.
- This is the correct combination of signs for the two corrections.

The included angle between the two lines is A, then the whole circle bearing of the new line formed by extending the preceding line by the included angle A is:

W3 = W1 + A - 180°

Note: This formula assumes that the angles are measured in degrees and that the bearings are given in the whole circle notation (i.e. from 0° to 360°).

Explanation:

The least count of a Vernier is the smallest measurement that can be read or measured using the Vernier scale. It is the difference between one main scale division and one Vernier scale division.

Understanding the Vernier Scale:

A Vernier scale is a secondary scale that is used to measure more accurately than what is possible with a regular scale or ruler. It consists of a main scale, which is a regular scale with evenly spaced divisions, and a Vernier scale, which is a smaller scale with divisions that are slightly smaller or larger than the divisions on the main scale.

Concept of Least Count:

The least count is the smallest measurement that can be made using an instrument. In the case of a Vernier scale, it is determined by the difference between one main scale division and one Vernier scale division. This difference is used to measure or read values that fall between the evenly spaced divisions on the main scale.

Calculation of Least Count:

To calculate the least count of a Vernier scale, we need to determine the difference between one main scale division and one Vernier scale division. This can be done by dividing the length of one main scale division by the number of divisions on the Vernier scale.

For example, if the length of one main scale division is 1 mm and the Vernier scale has 10 divisions, the length of one Vernier scale division would be 1 mm / 10 = 0.1 mm.

Therefore, the least count of the Vernier scale in this case would be 0.1 mm, which means that the smallest measurement that can be made using this Vernier scale is 0.1 mm.

Conclusion:

The correct answer to the question is option 'D' - the least count of a Vernier is the difference between one main scale division and one Vernier scale division. This difference is used to measure or read values that fall between the evenly spaced divisions on the main scale.

Error due to Centering in Plane Table Survey

In plane table surveying, the process of centering involves setting up the plane table over a point on the ground from where the survey is to be conducted. It is essential to ensure that the table is accurately centered to minimize errors in the survey measurements. One such error is the misplacement of the station point, which can lead to inaccuracies in the plotted positions of the various survey points.

Significance of Scale in Plane Table Survey

The scale is an important aspect of a plane table survey as it determines the ratio between the distances on the map or drawing and the actual distances on the ground. It allows for the representation of large areas on a smaller piece of paper. The scale is usually expressed as a representative fraction (RF) or a graphic scale.

Error Due to Centering

The error due to centering in plane table surveying occurs when the station point is not accurately positioned on the ground. This misplacement can lead to the incorrect plotting of survey points and subsequent errors in the survey measurements. The error due to centering is dependent on various factors such as the accuracy of the centering process and the scale used in the survey.

Relation Between Error Due to Centering and Scale

The error due to centering should not exceed the scale divided by a certain factor. This factor represents the maximum allowable error due to centering, beyond which the accuracy of the survey may be compromised.

Calculation of Maximum Allowable Error

To calculate the maximum allowable error due to centering, the scale is divided by the factor specified in the question. In this case, the correct answer is option 'B,' which states that the error due to centering should not exceed the scale divided by 40.

For example, if the scale of the survey is 1:5000, the maximum allowable error due to centering would be 1/40 * 5000 = 125 units. This means that the misplacement of the station point should not exceed 125 units on the ground.

Importance of Limiting the Error Due to Centering

Limiting the error due to centering is crucial in achieving accurate survey measurements. Any misplacement of the station point can lead to cumulative errors in the plotted positions of the survey points. These errors can affect the overall reliability and precision of the survey data, leading to incorrect interpretations and decisions based on the survey results.

Conclusion

In plane table surveying, it is important to minimize the error due to centering to ensure the accuracy of the survey measurements. The maximum allowable error due to centering is determined by dividing the scale by a specified factor. Option 'B' in this question correctly states that the error due to centering should not exceed the scale divided by 40. By adhering to this criterion, surveyors can obtain reliable and precise survey data for various engineering and construction projects.

Correct Answer: D) The effect of curvature is to cause the objects sighted to appear lower than they really are.

Explanation:
In levelling, the curvature of the Earth is one of the sources of error that needs to be considered. The effect of curvature is to cause the objects sighted to appear lower than they really are. This is because when we sight an object, we are effectively looking along a tangent line to the Earth's surface, and as we move away from the object, the line of sight becomes more and more parallel to the tangent line. This means that the line of sight does not follow the curve of the Earth, causing the object to appear lower.

Effects of Curvature in Levelling:
The effect of curvature can be significant in levelling, especially when measuring over long distances. This is because the curvature of the Earth causes the line of sight to deviate from the horizontal plane. As a result, the measured elevation of a point will be lower than the true elevation.

Compensating for Curvature:
To compensate for the curvature of the Earth, corrections need to be applied to the measured elevations. One common method is to use a correction factor called the curvature correction. The curvature correction is calculated based on the distance between the instrument and the target point. By subtracting the curvature correction from the measured elevation, the true elevation can be determined.

Other Sources of Error in Levelling:
While the effect of curvature is one source of error in levelling, there are other sources of error that also need to be considered. These include:

- Atmospheric refraction: The bending of light rays as they pass through the Earth's atmosphere can cause errors in levelling measurements. In reciprocal levelling, the error due to refraction is eliminated by taking a foresight and a backsight from each instrument station.

- Instrument errors: Levelling instruments can have inherent errors that need to be taken into account. These errors can include misalignment of the telescope, imperfect leveling of the instrument, and errors in the graduated staff.

- Personal errors: Errors can also be introduced by the surveyor, such as misreading the staff or misjudging the position of the crosshair in the telescope.

In conclusion, the correct statement is that the effect of curvature is to cause the objects sighted to appear lower than they really are in levelling. This is an important source of error that needs to be considered and corrected for in levelling measurements.

The correct statement is option C: The rise and fall method for the reduction of levels provided checks on all sights.

Explanation:
The rise and fall method is a commonly used method in surveying for determining the reduced levels of points. It involves taking readings of the staff at different points and applying corrections to account for errors and variations in the measurements. This method provides checks on all sights, ensuring the accuracy of the levelling process.

Here is a detailed explanation of the rise and fall method for the reduction of levels:

1. Procedure:
- The surveyor sets up the instrument at a known benchmark or reference point.
- The staff is placed at the desired points where readings are to be taken.
- The surveyor looks through the telescope of the instrument and reads the staff at each point.
- The readings are recorded, and corrections are applied to account for various factors.

2. Backsight and Foresight:
- The first reading taken on the staff is called the backsight. It is taken on a staff held at a point of known reduced level.
- The backsight reading helps to establish a starting point for the levelling process.
- The subsequent readings taken on the staff are called foresights. They are taken on staffs held at points whose reduced levels need to be determined.

3. Rise and Fall Calculation:
- After taking the backsight and foresights, the surveyor performs a calculation known as the "rise and fall" to determine the reduced levels of the foresight points.
- The rise and fall is the algebraic sum of the differences between each foresight reading and the preceding backsight reading.
- This calculation ensures that any errors or mistakes in the readings are identified and corrected.

4. Accuracy and Checks:
- The rise and fall method provides checks on all sights, which means that the accuracy of the levelling process can be verified.
- By comparing the calculated reduced levels of the foresight points with their actual known reduced levels (if available), the surveyor can check for any discrepancies or errors.
- This helps to ensure the reliability and accuracy of the levelling results.

In summary, the rise and fall method in levelling provides checks on all sights, allowing for the verification and correction of errors in the readings. This makes it a valuable and widely used method in surveying.