1.1. Chainage of Apex V

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

In this chunk, we are provided key parameters for calculating the chainage at the apex V of a curve. The chainage is defined as the distance along a path that is measured from a fixed point. Here, it is given that the chainage of apex V is 1190 meters. Additionally, a deflection angle, which is the angle by which a path deviates from a straight line, is provided as 36 degrees, and the radius of the curve is 300 meters. The peg interval, or distance between measurement points (pegs), is 30 meters.

Imagine you are measuring a winding road. The apex V is the peak point of a turn, which in a way acts as a reference point similar to how a hilltop marks a high point in a landscape. When you navigate this turn, the deflection angle helps you understand how sharply you must turn, while the radius gives you an idea of how gentle or tight the turn is—just like a roundabout.

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

The length of tangent is calculated using the formula Length of tangent = R * tan(Δ/2), where R is the radius and Δ is the deflection angle. Here, we calculate Δ/2, which is half of the deflection angle, to find the tangent’s length. By substituting the values into the formula, we find the length of the tangent to be approximately 97.48 meters.

Think of a car approaching a bend. Before it can smoothly transition into the curve, it travels on a straight path (the tangent) for a short distance. The length of this tangent helps ensure that the car doesn’t lose control as it transitions into the curve, similar to how a runner might take a few swift strides before smoothly transitioning into their next direction.

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

In this step, we calculate the chainage 'T' by subtracting the tangent length from the apex V’s chainage. When we do the math, we find that chainage T is 1092.52 meters. This means that if we lay out this path with pegs every 30 meters, we would have 36 full chains (30 meters each) and an additional 12.52 meters to reach the point T.

Consider it like laying out a path in a park with markers every certain distance. After placing down 36 markers at 30 meters apart, you realize you need just a little more—12.52 meters—to get to your desired point along the path, much like marking distances on a sports track.

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

The length of the curve is calculated based on the radius of the curve and the deflection angle. The formula used is Length of curve = R * Δ * (π/180), converting the angle from degrees to radians. Substituting the given values yields a length of approximately 188.50 meters for the curve.

Imagine measuring out a circular track in a playground. The length of the track around the curve can be determined by the size of the circle (the radius) and how much of the circle you are measuring (the deflection angle). The longer the curve, the greater the running distance for children, similar to calculating an athlete's sprint on a curved track.

C = 188.5–17.48– 30*5 = 21.02 m.

In the last calculation, we find 'C' by subtracting the initial calculations from the length of the curve. This involves recognizing that we have lengths that need to be accounted for from previous points and pegs placed along the curve. The final value of C is calculated to be 21.02 meters.

Analogous to creating a detailed route for a running race, where the organizers assess how much distance has been covered through various checkpoints. The residual distance indicates how much remains to reach the next critical point, which in this case is represented by C.

--