2.4.2. Setting out the compound curve

The compound curve may be set out by the method of deflection angles from two points T and N; the first curve from point T and the second one from point N.

This step involves defining how to establish a compound curve using geometric methods. When we refer to the method of deflection angles, we're essentially looking at how angles will dictate how we set out the curves. Starting with two points labeled T and N, each corresponding to the start of a curve, we will use these points to set out both curves sequentially.

Imagine you're at a junction preparing to turn left (T) and then right (N) while driving. The angles you turn at each of those points represent the deflection angles. Just as you'd need to judge how sharply you need to turn to navigate safely, the method of deflection angles helps surveyors determine how to create smooth transitions between curves in the road.

Locate B, T and T, and find out the chainage of T from the known chainage of B and length BT.

In this step, we need to establish a reference point (chainage) for properly measuring the curves of the road. Chainage is a way of measuring distance along a linear path. We need to identify point B and then measure the segment BT to find the specific location of point T along the path. This is akin to knowing where you are on a map and plotting a course to your next stop.

Think of chainage like the numbered mile markers you see while driving on highways. If you know that you are at mile marker 100 (point B) and you need to travel 5 miles to get to mile marker 105 (point T), you can easily determine where to turn or position yourself for the next direction you need to take.

Find out the chainage of F by adding the length of the first curve to the chainage of T, and find the chainage of T by adding the length of the second curve to the chainage of F.

Once we know where point T is, the next step is to navigate to points F and T using the lengths of the curves. By adding up the lengths of these curves to the chainages we previously calculated, we can accurately locate each point on the compound curve. This helps in managing distances and ensuring smooth transitions in the curvature.

Imagine you're following a recipe that tells you to add a certain number of cups of flour after measuring out some sugar. Just as adding the flour to the already measured sugar provides you with a total amount of ingredients needed, adding the lengths of the curves gives you the total distance from the starting point to where you need to be.

Set up the theodolite at T, and set out the first curve.

Setting up the theodolite involves positioning a precision instrument used for measuring angles in the horizontal and vertical planes. By establishing this instrument at point T, surveyors can accurately set out the first curve in the compound path to ensure that the angles dictated by our previous calculations are adhered to. This precision is crucial for ensuring the correct road alignment.

Think of the theodolite as a professional camera tripod. Just as photographers ensure their camera is perfectly positioned to capture the right angle and focus, surveyors need the theodolite to be set up precisely to measure angles accurately for road construction.

Shift the instrument and set it at point F. With the horizontal angle set to 3600 − α, take a back sight on T and transit the telescope and swing through α, the line of sight will be directed along the common tangent FE and the reading will read 3600.

This procedure involves moving the theodolite to a new point F and adjusting its settings to measure the correct angles. By directing the telescope back at point T and swinging through a specific angle α, we establish a reference line tangent to the curve at point F. This allows us to maintain consistency in alignment as we transition from one curve to another.

Imagine adjusting the aim of a laser pointer after moving to a new spot. When you point back to your original position while adjusting the angle, you're ensuring that the beam continues in the right direction. This is similar to how surveyors ensure their angles are set properly while moving to different points on a curve.

Set the vernier to the first deflection angle as calculated for the second curve, thus directing the line of sight to the first point on the second curve. Process is repeated until the end of the second curve is reached.

This is the final step in accurately laying out the second part of the compound curve. Using the previously calculated deflection angles ensures consistency between both curves. The process of repeatedly measuring and checking ensures that each curve aligns correctly to facilitate smooth transitions.

Think of this step as conducting a choir rehearsal. Each time a new singer joins in, they must follow the conductor's movements (the deflection angles) carefully to maintain harmony. Each repetition ensures that all the voices blend together seamlessly, just like how each curve must flow into the next for safe navigation.

Check: Measure the angle T FT, which must equal 180° − φ.

This step involves verifying that the angles created by the curves are correct. By measuring angle T FT, we ensure that the angles align according to our calculations of the deflection angles. If the measurement does not meet the expected angle, adjustments will be necessary to maintain accuracy in the entire curve layout.

Consider this step as a final quality check at a bakery to ensure that the batch of cookies is baked evenly. Just as bakers double-check the temperature and time for a perfect bake, surveyors verify their angles to ensure the road will be safe and functional.

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