2.2. Two theodolites method

This method is very useful in the absence of distance measurement by tape, and also when the ground is not favorable for accurate distance measurement. It is a simple and accurate method but essentially requires two theodolites to set the curve, so it is not as popular method as the method of deflection angles.

The Two Theodolites Method is primarily used when measuring distances on the ground is challenging. Rather than relying on a tape measure, which may be impractical on uneven or obstructed terrain, this technique utilizes two theodolites positioned at different points. Each theodolite helps measure angles from its position, allowing for the precise location of different points on a curve without the need for direct distance measurements.

Imagine trying to measure the distance across a rocky hillside with a long tape. It would be very difficult and the tape could easily snag or get misaligned. Instead, using two theodolites positioned at each end of the hillside allows surveyors to accurately plot the curve of the hillside without needing to measure the distance directly between points.

1. Set up two theodolites, one at T and the other at T.
2. Set horizontal angle reading of the theodolite at T to zero along T B, and similarly the theodolite at T to zero along T T.

To begin the process, two theodolites are established at two tangent points on the curve, referred to as T1 and T2. The first important step is calibrating these instruments by setting the horizontal angle reading to zero along the tangents formed by each theodolite. This calibration ensures that the measurements taken from both devices are consistent and can be accurately related to the points on the curve.

Think of it like calibrating two compasses before going on a treasure hunt. If one compass points north and the other points southeast, you won't find the treasure easily! By making sure both theodolites point correctly along their respective tangents, you ensure that all subsequent measurements will be accurate.

3. Set both the theodolites at T1 and T2 to read the first deflection angle Δ1. Now the line of sight of theodolite at T will be along T D and that of the theodolite at T along T D.
4. Establish point D on the ground with the help of ranging rods.

Once both theodolites are set up and calibrated, the next step involves measuring the first deflection angle, denoted as Δ1. This deflection angle is crucial as it defines the angle between the tangent at T1 and the line leading to the next point on the curve (point D). After setting this angle, the sightline from each theodolite will guide a surveyor to point D on the actual ground. Ranging rods or markers are then used to precisely mark point D according to the calculated deflection.

Imagine you're playing darts. You first aim at the board, which represents your tangent. The angle you adjust your throw by to hit the bullseye is akin to the deflection angle. Once you take that shot and see where the dart lands (point D), you use a friend to help mark where it landed!

5. Now set both the theodolites to second deflection angle Δ2, towards T1E and T2E respectively, and proceed as before to establish the second point E on the curve.
6. Repeat the process until the other points on the curve are set out.

After locating and marking point D, the process is repeated for the next point on the curve, labeled E. This involves adjusting the theodolites to measure the second deflection angle, indicated as Δ2. The surveyor continues to mark the next point on the curve with the same steps, ensuring each point corresponds to the accurate deflection angles until the curve is fully established. This iterative process allows for a highly accurate mapping of the curve's trajectory.

Picture a game of connect-the-dots. Once you find and mark one dot, you must figure out the angle and distance to the next dot. Each dot is like the points on your curve, and you simply repeat the process of finding the next angle and marking the next dot until you've outlined the entire picture.

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