4 ways to measure the height of a building | How to measure the height of a building indirectly

How to measure the height of a building

We can measure the height of a building in various ways when it is not possible to measure the height directly. Thus to measure the height of a building or a tree various instruments are also used depending on different conditions. The methods for finding out the height of a building or a tree are as follows:

1. Using only ranging rods and tape.
2. Using the Shadow of the building or the tree.
3. Using a clinometer.
4. Using a transit theodolite.

Using only Ranging rods and Tape-

Conditions: This method is suitable when the ground is level. 

Instruments required: Two ranging rods and Measuring tape.

Procedure: Let us assume the height of the building is PT, which is to be determined. T is the base and P is the peak of the building. Two ranging rods are fixed at A and B on level ground at some distance apart. On these ranging rods, C and D are marked in such a way that AC = BD.

Now point E is marked on the building by looking through the line CD. Next, point P is sighted from point C, while keeping points C, F, and P at a straight line. Then AT, AB, and DF are measured.

From  ΔPEC and ΔFDC we can say, 

PE/CE =DF/CD

or, PE= (FD/CD) x CE

i.e., PE = (FD/AB) x AT.

we can easily measure the ET with tape.

Height of the building = PE +ET. 

Using the Shadow of the building or the tree

Conditions: This method is suitable when the ground is level. 

Instruments required: One ranging rods and Measuring tape.

Procedure: Let us assume the height of the building is EF and the length of its shadow is DE. Now we put a ranging pole at some distance. The height of the ranging rod is BC and the length of its shadow is BC.

length AB, BC, and DE can be easily measured by tape.

So from Δ ABC and Δ DEF, we can say,

( BC/AB )=( EF / DE)

or, EF = ( BC / AB ) x DE = height of the building.

Using the Shadow of the building or the tree

Conditions: This method is suitable when the ground is at a slope. 

Instruments required: One ranging rods and Clinometer.

Clinometer

A clinometer is an instrument used for measuring the angle of inclination. A clinometer is basically similar to a graduated semi-circular protector. There are two pins near the straight edge for sighting objects. A plumb bob is suspended from the center of the clinometer.  The plumb line coincides with 0° when there is no slope( i.e., horizontal).

For measuring any slope, the clinometer is tilted, but the plumb line remains vertical. In this tilted condition, the plumb line coincides with a graduation on the clinometer. This graduation indicates the inclination of the object.

Procedure

A clinometer may be used to measure the height of a building or a tree. At first, a ranging rod is fixed at the point from where the angle is going to be measured. Now the surveyor measures the inclination of the top of the building. Let’s say the angle is Θ°. In the next step, the distance between the ranging rod is measured, say the distance is L.

So we can say, height = base x tanΘ° = LtanΘ°. 

So the height of the building is TP = (LtanΘ°+ the height of the clinometer).

Using a transit theodolite.

Instruments required: One ranging rods and a transit theodolite

Theodolite.

A theodolite is a universal instrument in surveying. This instrument can measure various types of measurements. We can measure different types of horizontal and vertical angles with it. We can also measure distance with a theodolite when it is impossible to chaining. Basically, a theodolite can measure-

1.  horizontal angle
2. vertical angle 
3. deflection angle
4. magnetic bearing 
5. ranging and extending a line 
6. horizontal distance
7. vertical height.

A theodolite is classified into two types:-

1. transit theodolite
2. non-transit theodolite

What is transiting and swinging?

The rotating of the telescope of a theodolite around a horizontal axis in a vertical plane is called transiting. The other terms of transitioning are reversing or plunging. 

If a theodolite can transit then it is called transit theodolite. 

The rotation of the telescope in a horizontal plane around a vertical axis is called swinging.

Procedure

To measure the height of a building with the help of a theodolite is as follows.

1. Finding the vertical angle of the top of the building.
2. Measuring the horizontal distance between theodolite and the building. 
3. calculating the vertical height of the building.

Finding the vertical angle of the top of the building.

1. At first, the theodolite is set up by centering at the position from where the angle is to be measured.
2. Then we have to level the theodolite with the foot screw and check the bubble tubes.
3. Sight the object approximately. Then restrained the horizontal rotation of theodolite by locking lower and upper clamp screws.
4. After that, adjust the zero of the vertical circle with the zero of the vertical vernier scale.
5. Now bisect the top of the building by adjusting vertical clamp screw and tangent screws.

Measuring the horizontal distance between theodolite and the building

If the ground surface is a level surface, we can easily measure the distance with a chain or tape. But if the ground surface is steep with undulation, then we cannot measure with a chain or tape. In that case, we have to measure the distance with the help of a tacheometer.

A tacheometer is a transit theodolite fitted with an additional lens and a stadia diaphragm.

Calculating the vertical height of the building.

Let us assume that the angle measured by the surveyor with the theodolite is Θ°. The distance is L. So the height of the building above the line of sight is H= L x tanΘ°.

The total height of the building is the height of the instrument + LtanΘ°.

Conclusion

Among these four methods to measure the height of a building indirectly, the method with the theodolite gives the most accurate results. In a case where theodolite is not available, a clinometer may be used.