2.2. Chainage of PI

Length of tangent = R tan Δ/2 = 300 tan 36/2 = 97.48 m

To find the length of the tangent, we use the formula which involves the radius (R) and the deflection angle (Δ). In this case, we first take half of the deflection angle (36°) and calculate the tangent of that value, then multiply it by the radius of 300 m. When we plug in the numbers, we find that the length of the tangent is approximately 97.48 m.

Think of walking along a straight path and wanting to know how far you can walk straight before needing to turn to change direction. The tangent length helps us determine that distance, just like finding the shortest path before making a turn.

Chainage of T = 1190 – 97.48 = 1092.52 m = 36 chains of 30 m + 12.52 m

Once we have the tangent length, we can find the chainage of point T by subtracting the tangent length from the chainage of the point of intersection (PI), which is 1190 m. So, 1190 m - 97.48 m gives us the new chainage of 1092.52 m. This chainage can also be expressed in chains, where there are 36 full chains of 30 m and an additional 12.52 m.

Imagine you have a string of 30-meter sections (like chains) laid out on the ground. If you measure back from a known starting point, the chainage helps you visualize how many full sections fit into that distance plus any remainder for accuracy.

Length of curve = RΔ (π/180) = 300 * 36 (π/180) = 188.50 m

To find the length of the curve, we apply the radius (R) and the full deflection angle (Δ) using the formula. Specifically, we convert the angle from degrees to radians by multiplying it with π and dividing by 180. The resulting calculation shows that the length of the curve is approximately 188.50 m.

Picture a race car track. This length calculation tells us how long one section of the curved part of the track will be, which is crucial for planning how far the cars need to travel before making a turn.

Chainage of T2 = 1092.52 + 188.50 = 1281.02 m

After calculating the length of the curve, we find the chainage at the end of the curve, known as T2, by simply adding the length of the curve to the previously calculated chainage of T. So, 1092.52 m + 188.50 m results in a final chainage of 1281.02 m for T2.

Think of following a winding path: just as you would keep adding up distances as you travel around bends until you reach your destination, chainage helps you keep track of the total distance you've covered during your journey around curves.

Ordinates are O = C2 /2R = (17.48)2 /2 *300 = 0.51 m

To find the ordinates, we use a specific formula that incorporates the length of the chord (C) and the radius (R). The calculation indicates that the first ordinate O is approximately 0.51 m, which helps determine how high above the horizontal line the curve reaches.

If you imagine the path of a hanging swing, the ordinates show how high the swing rises at various intervals. Just like the swing’s height at different points provides insight into its movement, the ordinates give valuable data about the curve's elevation.

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