7.1. Two straights AC 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 the chainage of the apex point V, which is 1190 meters. The deflection angle D is given as 36 degrees, which is the angle formed between two straight lines when they meet at the apex. The radius R is given as 300 meters, which is the radius of the curve connecting the two straights. Moreover, a peg interval of 30 meters is set, which means markers (pegs) will be placed every 30 meters along the curve.

Imagine you're building a circular track in a park. You need to know where to place markers on the track. Here, the apex is like your starting point at the 1190-meter mark, and the deflection angle tells you how sharply the path will curve at that point. The radius gives you the curvature, similar to using a big round bowl edge for your track.

Length of tangent = R tan Δ/2 = 300 tan 36/2 = 97.48 m Chainage of T = 1190 – 97.48 = 1092.52 m. Length of curve = RΔ (π/180) = 300 * 36 (π/180) = 188.50 m

The length of the tangent is calculated using the radius and the deflection angle. The formula used is Length of tangent = R tan (D/2), where D is the deflection angle. The calculated length is 97.48 meters. This means the straight section before the curve is 97.48 meters long. The chainage of point T, where the curve begins, is found by subtracting this length from the chainage of the apex. Next, the length of the curve is determined using the formula Length of curve = R × Δ × (π/180). Here, the result is 188.50 meters, indicating how long the curved section will be.

If you picture the beginning of a racetrack that curves, the tangent length is how long the straight section is before the racetrack starts to turn. The length of the curve is how far along the racetrack the curve extends. Knowing these measurements helps you understand how to design the racecourse smoothly.

Chainage of T2 = 1092.52 + 188.50 = 1281.02 m.

To find the chainage of the second tangent point T2, we add the length of the curve (188.50 m) to the chainage of point T (1092.52 m). Thus, T2 is located at 1281.02 m along the surveyed path. This indicates where the curve will end and connect back to another straight section.

Think of a long winding road that leads to a mountain. The point T2 represents the end of the curve where the road becomes straight again, just as you'd want to know how far ahead that point is on your journey.

Ordinates are O = C^2 / 2R = (17.48)^2 / (2 * 300) = 0.51 m.

In surveying, ordinates are used to determine the vertical distance from the curved line to the tangent points at various intervals. For example, the first ordinate calculation gives us an offset of 0.51 meters at a specific point. This is crucial for setting out the curve accurately on the ground, ensuring that the design aligns with the intended angles and lengths.

Imagine trying to hang a picture on a slightly curved wall. The ordinates tell you how high off the floor the picture needs to be at various points along that curve, making sure it looks just right.

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