1.18.5. Measurement of vertical angles

A vertical angle is an angle between the inclined line of sight and the horizontal. It may be an angle of elevation or depression, according as the object is above or below the horizontal plane.

Vertical angles are angles measured in relation to the horizontal plane. If you're looking up at an object above you, you measure an angle of elevation. Conversely, if you're looking down at an object below your horizontal line of sight, that is a vertical angle of depression. These angles help us understand how high or low something is compared to a flat baseline.

Imagine you're standing on a flat surface and looking at the top of a tree. The angle you look up at the top of the tree from where you are standing is the angle of elevation. If you then look down at a hole in the ground, the angle you make with the horizontal is the angle of depression.

In both the methods of measuring horizontal angles, if the object is bisected at the intersection of cross hairs (centre), vertical angles can also be read at the same time on verniers C and D. The average of both the verniers readings are taken. It is important that the altitude bubble is in the centre for each reading of vertical angle.

When measuring vertical angles using a theodolite, the object you're observing is centered in the crosshairs of the instrument. The readings for vertical angles are taken from the two verniers labeled C and D. The average of these two readings gives you the vertical angle. For accuracy, the altitude bubble, a small level on the theodolite, must be perfectly centered before you take your readings.

Think of the altitude bubble like a level you would use when hanging a picture frame. Just as you need the frame to be level for it to look right on the wall, the altitude bubble needs to be centered so that your angle measurements are accurate.

To measure the vertical angle of an object A at a station O (Figure 1.41a), the following steps are followed: (i) Set up the theodolite at ground point O and centre it and level it accurately. The instrument should be on face left. (ii) Set the zero reading at verniers of vertical circle by using the vertical clamp and tangent screw. The line of sight is thus made horizontal. (iii) Loosen the vertical circle clamp screw and bisect object A exactly by using the vertical circle tangent screw. Bring the bubble in the altitude level in centre position by using the screw. (iv) Read both the verniers C and D on the vertical circle. The mean of the two vernier readings gives the value of the required vertical angle AOA’ directly. (v) Change the face of the instrument from left to right and repeat the process at (iii) and (iv) above. Thus, one more value of vertical angle AOA’ on face right. (vi) The average of the two values of the angle is taken which is the required value of vertical angle. The vertical angle could be angle of elevation (+ive) of angle of depression (-ive).

To measure a vertical angle using a theodolite, follow these steps: First, set up the theodolite on a stable platform and ensure that it is level, with the instrument oriented to the left. Next, adjust the vernier scale on the vertical circle to zero; this makes your initial line of sight horizontal. Using the tangent screw, focus on the object you want to measure, making sure the altitude bubble is centered for accuracy. After taking readings from both verniers (C and D), you calculate the mean of these readings to find your vertical angle. It is also crucial to repeat this process after changing the instrument's face from left to right and averaging the two results to confirm accuracy.

Imagine you are using a specialized camera that measures angles to capture the precise height of a skyscraper. You start by aligning the camera horizontally. As you tilt it up towards the top of the building, you're exactly following the steps of the vertical angle measuring process. Each time you confirm the angle you’re measuring, you make sure the bubble on the camera lens is centered, just like you would with a theodolite.

--