10.1. Two parallel railway lines

Chainage of apex V = 1190 m, Deflection angle D = 36°, Radius R = 300 m, Peg interval = 30 m. Length of tangent = R tan Δ/2 = 300 tan 36/2 = 97.48 m Chainage of T = 1190 – 97.48 = 1092.52 m = 36 chains of 30 m + 12.52 m C = 30 – 12.52 = 17.48 m.

In this section, we initially set out the foundation for calculating the positional aspects of the railway lines. The chainage refers to the distance measured before a specific point along the railway line. The initial chainage of 1190 m is given, establishing a reference for any further measurements. A deflection angle of 36 degrees signifies how much the direction of the line changes at a particular point. The radius of 300 m is the curvature's radius for the curve connecting the two parallel lines. To find the tangent length (the straight distance from the end of the curve to the point of intersection), we calculate it using the formula Length of tangent = R tan(Δ/2), where Δ is divided by 2 because it is the angle relevant to the tangent. After determining the tangent length of 97.48 m, we compute the new chainage (T), indicating the position after the tangent length is subtracted from the apex. Lastly, we calculate the length of a smaller straight segment along the curve, C, reinforcing the understanding of distances involved in railway construction.

Think of a curved racetrack. The point where the curve begins is like 'apex V,' and the length of straight distance before a curve (the tangent) is the lead-in track, allowing racelines to smoothly navigate the curve. Just like how racers need to know the angle of turn and how sharp the curve is (radius), engineers working on railway lines need this information to ensure trains can operate safely.

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

Next, we determine the length of the curve that connects the straight sections of two railway lines. We use the formula Length of curve = RΔ(π/180) to calculate this arc length, where R is the radius and Δ is the deflection angle in degrees. Here, the radius is 300 m, and the deflection angle is 36 degrees. By inserting these values into the formula, we find that the length of this specific curve is 188.50 m, which illustrates just how long the curve will be. This dimension is crucial, as it helps in assessing the space needed on-site and ensures trains can navigate the curve without derailing.

Imagine you're measuring a piece of spaghetti that you want to bend into a curve for a dish. The longer the spaghetti (length of curve), the more room you need to create the bend (the radius). Just like in cooking, where you need to ensure that you don't snap the spaghetti, engineers must ensure the railway curve is gentle enough for trains to pass safely and smoothly.

Chainage of T2 = 1092.52 + 188.50 = 1281.02 m.

After establishing the length of the curve, we calculate the chainage of the end point, referred to as T2, which is the point where the curve finishes and the next straight begins. This is achieved by adding the previously calculated chainage of T (1092.52 m) and the length of the curve (188.50 m). Hence, Chainage T2 calculates to 1281.02 m, indicating the total distance from the starting point to where the curve ends, ready for engineers to plan the next stage of construction.

Think of a race that starts at a checkpoint (the beginning) and heads into a series of curves. If the first straightaway leads into a curve of a specific length, the finish point of that curve tells you where the next straight starts. It’s like giving directions; if you say, "drive straight for 1 km, then turn left into the next road" – you need to know both how far to go straight and where the turn is, just like how the railway line is designed.

Ordinates are O1 = C2 /2R = (17.48)2 /2 *300 = 0.51 m.

In this part of the section, we need to calculate the ordinates, which are the vertical distances from the point of the curve to the baseline of the rail. These measurements provide essential data on how high or low adjustments need to be made along the curve for stationery measures. Using the formula O = (C²)/(2R), we substitute the calculated values (C = 17.48 m and R = 300 m) to find O1, which results in 0.51 m. This calculation ensures that the curvature does not cause bumps or dips along the railway line, keeping it level for trains.

It’s similar to making a road from the ground up. If your curve needs to be smooth and level, knowing how high (ordinate) to raise the surface at different points shows you how to shape the road for a comfortable ride, preventing potential mishaps during travel, much like flattening a path as you pave a new way.

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