9.1. Two straights AC and CB

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

This section begins by introducing the key parameters needed for setting out a curve based on two straight paths or tangents, AC and CB. The apex, or point of intersection of the tangents, is positioned at a chainage of 1190 meters. The deflection angle, which is the angle change at this point, is specified as 36 degrees. Additionally, the radius of the intended curve to connect the two straights is established as 300 meters. Understanding these parameters is crucial for accurately establishing the curve for successful road alignment.

Imagine two roads meeting at a junction: one road is for drivers going straight, and the other is for those turning. The point where they meet (the apex) is like a traffic light changing direction. The deflection angle represents how much you need to turn your steering wheel to remain on the new path (the curvature of the road). The radius of the curve is like the size of the turn; a larger radius means a gentler turn.

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

To calculate the length of the tangent, we use the formula: Length of tangent = Radius (R) multiplied by the tangent of half the deflection angle (D). Here, we first compute the tangent of half of 36 degrees, which is half of the total angle of deflection. By plugging in the values, the computation yields a tangent length of approximately 97.48 meters. This length represents how far out the reference line (tangent) extends from the apex before the curve begins.

Consider setting up a slide on a playground. The length of the slide from the top (the apex) to where it meets the ground (the tangent) is important to understand how steep it will be. The longer the slide, the gentler the slope, making it safer and more fun to use!

Chainage of T = 1190 – 97.48 = 1092.52 m.

After determining the length of the tangent, we can find the chainage for the tangent point (T) where the curve starts. This is calculated by subtracting the tangent length (97.48 m) from the chainage at the apex (1190 m). This results in a new chainage of 1092.52 m for the tangent point. Knowing the chainage of (T) is essential for setting out the curve accurately along the road.

Imagine you are measuring a distance while walking on a trail. If you start at a specific point (the apex), step back a certain distance (the tangent length), you can determine your new location on the trail. This helps you know where to continue your hike, just like knowing where the road begins to curve.

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

The length of the curve is calculated using the formula: Length of curve = Radius (R) multiplied by the deflection angle (Δ) in radians, scaled by π/180 to convert degrees to radians. Substituting the known values gives us a curve length of approximately 188.50 meters. This length allows planners to know how much road space will be curved versus straight.

Think of drawing a circle. The radius helps determine how wide the circle will be. Just like when you measure a piece of string to build a circular garden bed, knowing the right radius keeps everything neat and proportional. The curve length is essentially how long that string would need to be!

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