Horizontal Measurement angle by repetition method

Aim:

This experiment aims to measure the horizontal angle by the repetition method using a theodolite and to determine the accuracy of the instrument.

Theory:

A theodolite is an instrument used to measure horizontal and vertical angles in surveying and engineering applications. It consists of a telescope mounted on a horizontal and vertical axis. The horizontal axis is used to measure the angle between two points

on a horizontal plane. The vertical axis is used to measure the angle between the horizontal plane and an object above or below it.

The repetition method is used to increase the accuracy of the horizontal angle measurement. In this method, the angle is measured several times, and the mean of the readings is calculated.

The difference between the individual readings and the mean is calculated, and the accuracy of the instrument is determined from this difference.

Apparatus and materials required:

1. Theodolite
2. Tripod Stand
3. Target or prism
4. Measuring tape

Procedure:

1. Set up the tripod stand and theodolite at the first point.
2. Adjust the theodolite using the levelling screws so that the vertical axis is perpendicular to the ground.
3. Look through the telescope and point it at the target or prism placed at the second point.
4. Note the horizontal angle reading in the horizontal circle of the theodolite.
5. Repeat steps 3 and 4 several times to get multiple readings of the horizontal angle.
6. Calculate the mean of the readings.
7. Calculate the difference between each reading and the mean.
8. Calculate the standard deviation of the readings.
9. Calculate the probable error of the instrument.
10. Repeat steps 1 to 9 for the third point and fourth point.
11. Measure the distance between the first and second points, the second and third points, and the third and fourth points using the measuring tape.

Result:

Precautions:

1. The theodolite should be placed on a stable surface to avoid any vibrations.
2. The prism or target should be placed at the exact point to get accurate readings.
3. The instrument should be handled with care to avoid any damage.
4. The telescope should be cleaned properly to avoid any distortion in the readings.

Conclusion:

The repetition method is an effective technique for increasing the accuracy of horizontal angle measurements using a theodolite. By taking multiple readings and calculating the mean and probable error, the instrument’s accuracy can be determined.

In this experiment, the probable error of the instrument was calculated to be ±21″, which indicates that the instrument has a relatively high level of accuracy. However, it is important to note,

that the accuracy of the instrument can be affected by external factors such as vibrations or poor visibility, and therefore, caution should be exercised when using the theodolite in the field.