Trigonometric Levelling: Base Accessible Practical Report

TITLE 

Determination of RL of the Object Whose Base is Accessible

THEORY

Trigonometric leveling is a surveying technique used to determine the reduced level (RL) of an object based on angular measurements. In this practical, we use a theodolite to measure vertical angles and a tape to measure horizontal distances. By applying trigonometric relationships, the RL of the top of an object can be determined when its base is accessible. The mathematical formula used in this experiment is:

$RL_{top} = RL_{benchmark} + s + D \tan(\alpha)$

where:

• $RL_{top}$ = Reduced Level of the top of the object
• $RL_{benchmark}$ = Reduced Level of the benchmark (provided)
• $s$ = Staff reading at the benchmark
• $D$ = Horizontal distance between the theodolite and the base of the object
• $\alpha$ = Vertical angle measured from the theodolite to the top of the object

INSTRUMENTS REQUIRED

1. Theodolite
2. Leveling staff
3. Measuring tape
4. Tripod stand
5. Plumb bob

PROCEDURE

1. Set up the theodolite at a convenient location near the object whose RL is to be determined.
2. Perform temporary adjustments of the theodolite (leveling and focusing).
3. Rotate the telescope vertically to bring the vertical angle to zero, ensuring the line of sight is horizontal.
4. Sight the leveling staff placed at the benchmark and take the staff reading, denoted as 's'.
5. Rotate the theodolite towards the top of the object and adjust it until the crosshairs align with the top.
6. Record the vertical angle $\alpha$.
7. Measure the horizontal distance $D$ between the theodolite and the base of the object using a measuring tape.
8. Compute the RL of the top of the object using the given formula.

OBSERVATION

CALCULATION

Using the formula: $RL_{top} = RL_{benchmark} + s + D \tan(\alpha)$

RESULTS AND CONCLUSIONS

The RL of the top of the object was found to be _______. The practical demonstrates the effective use of theodolite and trigonometric principles in determining elevation differences. The accuracy of the results depends on proper instrument handling and precise angle and distance measurements.

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