Test: Fundamental Concepts, Accuracy & Errors - 2 - Civil Engineering (CE) MCQ

Area of circle 
A = πr²
∴ dA/dr = 2πr
Let standard error in radius be e_r,
∴ Standard error in area, 

• Curvature of Earth: In geodetic surveying, the curvature of the Earth must be taken into account when measuring large distances, whereas in plane surveying, the Earth's surface is considered flat for smaller areas.


• Difference of Elevations: Geodetic surveying involves measuring large differences in elevations between various points, while plane surveying is more suitable for flat terrains with minimal elevation changes.


• Coverage of Large Areas: Geodetic surveying is used for covering very large areas such as continents or countries, requiring specialized techniques and equipment, compared to plane surveying which is suitable for smaller areas.


• Undulations of Large Areas: Geodetic surveying deals with the undulations and irregularities of very large areas, ensuring accurate measurements over vast stretches of land, unlike plane surveying which focuses on smaller, flatter regions.

Therefore, the main difference between geodetic surveying and plane surveying lies in their scope, techniques, and objectives, with geodetic surveying being more complex and specialized due to the factors like the curvature of the Earth, large elevation differences, coverage of vast areas, and undulations of expansive terrains.

True Error = Actual Value-Observed Value 
Weighted Observations = Observations taken with proportion to any quantity like an area
Conditional Error = Error occurring due to certain conditions prevailing. Like temperature error.
Residual Error = Most Probable Value- Observed Value

Cumulative Errors occurring in same direction and thus, they aggregate to make a considerable amount of error. 
Positive cumulative errors Non Horizontality, sag, bad ranging.
Positive/ Negative cumulative errors Erroneous length of chain, temperature variation.

For a well-conditioned triangle all the angles must lie in the range of 300-1200.

• Invar Tape: An invar tape is made of an alloy called Invar, which is composed of nickel and steel.


• Composition: The alloy composition typically consists of approximately 36% nickel and 64% iron.


• Properties: Invar is known for its low coefficient of thermal expansion, making it ideal for applications where dimensional stability is crucial.


• Usage: Invar tapes are commonly used in precision measurement devices, such as tape measures and surveying tools, due to their stability over a wide temperature range.

In surveying, offsets are lateral measurements taken from the main survey line (baseline) to plot the position of different points or objects. These measurements are generally taken at a right angle to the main survey lines, helping to create an accurate representation of the area being surveyed.

For example, if a surveyor is measuring a piece of land with a building on it, they would first establish the main survey line (baseline) and then measure the distance from the line to the corners of the building. These lateral measurements are called offsets.

Offsets allow surveyors to accurately map the location of various features on a piece of land, such as buildings, fences, or natural features like streams or trees. This information is then used to create maps, plan construction projects, or establish property boundaries.

• Ranging: Ranging is the process of aligning the chain in a straight line between two extremities.


• Steps involved in ranging:




• First, fix ranging rods on the extremities of the area to mark the endpoints.


• Align the chain in a straight line between these two ranging rods.


• Ensure that the chain is taut and straight to get accurate measurements.


• This process helps in determining the length of the area accurately.




• Purpose of ranging: Ranging is essential in surveying to establish straight lines for taking measurements and mapping the area.

Laws of accidental errors follow the probability law, which is having a definite law for accidental error occurrence. It defines the errors and helps in expressing them in the form of equations.

• Definition: Systematic errors are errors that consistently skew measurements in a particular direction.


• Cumulative Effects: These errors accumulate over time, leading to a significant deviation from the true value.


• Determinable: Unlike random errors, systematic errors can be identified and corrected for by understanding their nature.


• Recognizable Patterns: Systematic errors often exhibit recognizable patterns in data, making them easier to detect.


• Examples: Common sources of systematic errors include instrumental biases, environmental factors, and human errors in measurement techniques.