Surveying And Levelling

The height of the beam above the floor is calculated as:
Height of the beam = Staff reading (inverted) + Staff reading (floor).
Given:
• Staff reading on the floor = 1.40 m,
• Staff reading when inverted = 3.67 m.
Substitute the values:
Height of the beam =

The least-squares method is used for traverse adjustment when angular measurements are more precise than linear measurements. It minimizes the sum of the squares of the residuals, ensuring the best possible adjustment for both linear and angular observations.

The spire test is conducted to adjust the horizontal axis of a theodolite. This ensures that the horizontal axis is truly perpendicular to the vertical axis, which is essential for accurate angular measurements in surveying

At noon, the true bearing of the sun is . The difference between the magnetic bearing and the true bearing gives the magnetic declination: A positive declination indicates an easterly direction, so the magnetic declination is .

Oblique offsets are used to measure distances at an angle to a survey line, and they are particularly useful in locating the center of structures like buildings. This method ensures accurate placement of features that are not directly aligned with the main survey lines

A geodimeter measures distances based on the propagation of modulated light waves. These waves are sent to a target and reflected back, allowing the instrument to calculate distance by measuring the phase difference or travel time of the light.

The sag correction for a tape is calculated using the formula:

Where:
sag correction,
weight of the tape per unit length,
length of the tape,
applied pull.
Given:
Total weight of the tape = 12 N,
Length of the tape, ,
Applied pull, .
The weight per unit length is:

Substitute these values into the formula:

Simplify:


Calculate:

Topographical surveys are conducted to map the natural and man-made features of a land area, including mountains, water bodies, and vegetation. These surveys are essential for planning large-scale projects and understanding terrain conditions.

The relationship between the measured length and the true length is based on the scale ratio. If the wrong scale was used, the true length can be recalculated using:

Given:
Measured Length = 500 m,
True Scale = 1 cm = 50 m,
Wrong Scale = 1 cm = 40 m.
Substitute these values into the formula:

Simplify:

Calculate: