5. Example 2.13:

Two straights intersect at a chainage of 1764 m with a deflection angle of 320, which are to be joined by a 50 curve. Work out the data required to set out a curve by the deflection angle method. Take length of chain as 30 m, peg interval at 30 m, and least count of theodolite as 20".

This problem presents a scenario where two straight lines (straights) intersect, creating a need for a curve to connect them smoothly. The key elements provided are the intersection point, the deflection angle, and the radius of the curve to be constructed. The lengths of the chain, interval distances for pegs, and the least count of theodolite are also mentioned as necessary instruments for measuring the curve's arc.

Imagine you are constructing a road that meets another road at an angle. Just like how you would need a smooth curve to connect both roads properly, in engineering, we also require calculations and tools to ensure this curve is designed and set out correctly for vehicles to transition smoothly.

For a 30 m chain length, R = 1719 / Degree of curve of Degree = 343.8 m.

The radius (R) of the curve is determined based on the degree of curvature and the length of the chain used for measurement. The formula given indicates a relationship where the total length considered impacts the resulting radius. This shows the importance of understanding how measurements translate to physical dimensions in roadwork.

Think of measuring a large pie. The degree of curvature is like how curved the pie slice is, and the chain length is how long your measuring tape is. Both of these influence the size of the slice you can get, just as they affect how sharp or gentle the curve in a road will be.

Tangent Length T= R tan Δ /2 = 343.8 tan 32 / 2 = 98.58 m.

The tangent length (T) is calculated using the radius (R) and the deflection angle (Δ). By using the trigonometric function tangent, this formula allows engineers to determine how far along the road needs to be flat before beginning the curve. This is important to establish proper transitions for drivers.

Consider riding a bike - you need to have a straight part before turning the corner so you don’t tip over. This tangent length is similar; it's the straight part before the curve where vehicles can stabilize before making the turn.

Length of the curve (l) = π R Δ/ 180 = 343.8 * 32 π/ 180 = 192.01 m.

The length of the curve (l) is calculated using the formula which relates the radius of the curve, the deflection angle, and the mathematical constant pi (π). This equation provides the total distance of the curve along the path that vehicles will travel.

If you think of the curve as a circular track, the length calculation helps you figure out how long the track is around the circle. It’s similar to determining how far you have to run if you were racing around that curved track instead of on a straight path.

Chainage at point of curve (T ) = Chainage at the point of intersection – tangent length = 1764 – 98.58 = 1665.42 m.

To find the chainage (the distance along the road) at the point where the curve starts, you subtract the tangent length from the point of intersection. This helps in placing markers or signs correctly and ensures that construction happens at the right distances along the road.

Imagine marking a start line for a race. You calculate how far away that mark is from a known point (like the starting gun) and adjust for any space in between. Here, you’re effectively doing the same with road markers — calculating precisely where to place them based on previous measurements.

Length of initial sub chord (C ) = 1680 – 1665.42= 14.58 m.

The length of the initial sub-chord represents the small straight segment between the initial point of the curve and the beginning of the curve itself. Understanding this length is crucial for establishing grading, drainage, or any additional construction elements that need to be placed along the curve.

If you think about building a path with a slight curve, the initial portion straight before the curve can be likened to the first few steps on a path. It allows you to gather your balance before the path takes a turn.

Chainage at point of tangency (T ) = Chainage at point of PCC + Length of second curve = 1475.43 + 87.16 = 1562.59 m.

Finally, calculating the chainage at the point of tangency involves incorporating the length of the curve into the previous calculations. This final number helps define the end of the curve and locate where roads will start transitioning back to the original straight line.

Think of marking the end point of a curved path in a garden. You would measure from your starting point to determine exactly where the curve ends and the straight path begins again. This final calculation does just that for the road layout.

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