15.1. A compound curve AB and BC

Chainage of apex V = 1190 m, Deflection angle D = 36°, Radius R = 300 m, Peg interval = 30 m.

In this section, we start by defining some essential parameters for the compound curve. The chainage of apex V is the position along the alignment where the curve starts, measured in meters. The deflection angle D is the angle between the two tangents at the apex of the curve, which in this case is 36 degrees. The radius R is the distance from the center of the circular arc to any point on the curve, set at 300 meters. Lastly, the peg interval corresponds to the distance between measurement points along the curve, which is specified as 30 meters.

Think of a racetrack where sharp turns (curves) are essential for racing. Just as drivers need to know the angle of the turn to navigate effectively, civil engineers use angles and radii to ensure the road curves are safe for vehicles.

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

To determine the length of the tangent, we use the formula Length of tangent = R tan(Δ/2). Here, Δ represents the deflection angle, which is halved since we are only interested in one side of the apex. For R set at 300 meters and Δ at 36 degrees, we calculate the tangent length to be approximately 97.48 meters. This tangent acts as a reference for measuring distances to the actual curve.

Consider a car driving toward a turn. Before making the turn, the driver can see the distance to the point where the road begins to curve — this is similar to the tangent length that helps drivers understand how much distance they have until they need to start turning.

Chainage of T = 1190 – 97.48 = 1092.52 m = 36 chains of 30 m + 12.52 m. C = 30 – 12.52 = 17.48 m, and C = 30.

The chainage of point T, which is where the tangent line intersects the curve, is calculated by subtracting the length of the tangent we just found (97.48 m) from the chainage of the apex V (1190 m). Thus, 1190 m - 97.48 m gives us 1092.52 m. To convert this measurement into chains, we recognize that 1 chain is equal to 30 meters, so we find that it corresponds to 36 chains and an additional 12.52 meters. C represents the remaining distance from the end of the tangent to the next peg, found by subtracting 12.52 m from 30 m, giving us 17.48 m.

Imagine laying out a running track where markers are placed at regular intervals. Understanding how far you have run (chainage) is similar to calculating how much distance there is left before you hit the next corner (C).

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

To calculate the length of the curve itself, we use the formula Length of curve = R * Δ * (π/180). This formula converts the angle in degrees to radians (since most calculations in trigonometry are based on radians). With R at 300 meters and Δ at 36 degrees, we find that the length of the curve is about 188.50 meters. This gives us the actual distance along the curve between the two tangents.

Imagine laying a rope along a circular path; the length of the rope corresponds to the length of the curve. Just as knowing the correct amount of rope is essential for covering the curve, calculating the length of the curve accurately is crucial in road design.

Chainage of T2 = 1092.52 + 188.50 = 1281.02 m Ordinates are O = C2 /2R = (17.48)2 /2 *300 = 0.51 m.

After calculating the length of the curve, we find the chainage of the tangent T2 by adding this length (188.50 m) to the previous tangent point T (1092.52 m). This results in a total of 1281.02 m for the chainage of T2. Furthermore, we compute the ordinates O, which represent the vertical offsets from the tangents to points on the curve, using the formula O = C2 / 2R. Here, we square the chord length C and divide by twice the radius, which yields approximately 0.51 m. This is essential for ensuring the curve is correctly shaped.

When drawing a road, think of the ordinates as adjustments that ensure the curve's height doesn’t abruptly change. It's like making sure your road smoothly elevates or descends without sudden bumps.

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