20.1. Two straights AB and BC

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

This chunk introduces some key concepts: chainage, deflection angle, and radius. Chainage is a way of measuring distances along a route, starting from a point of reference (in this case, apex V). The deflection angle (D) is the angle between two straight paths, here measured as 36 degrees. The radius (R) indicates the curvature of a bend or arc, which is set at 300 meters. Peg intervals are predetermined distances (30 meters) used for measuring and marking the route.

Imagine you are marking a path in a park for a new walking trail. You start at a certain point (apex V), measure the distance from that point to various spots along your expected trail (chainage), and determine how sharply the trail will curve around features like trees (radius). The sharpness of your turns is like the deflection angle, guiding how easily someone can follow the path.

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

The length of the tangent is calculated using the formula 'Length of tangent = Radius * tan(Deflection angle / 2)'. Here, we plug in our values—radius = 300 meters and deflection angle = 36 degrees (divided by 2). The tangent length gives you a straight line distance before you start to curve, calculated as approximately 97.48 meters.

When driving, as you approach a curve in the road, you first travel a straight distance before you begin turning. This straight stretch can be compared to the tangent length. The longer the tangent length, the more time you have to prepare before entering a turn.

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

The chainage of point T is calculated by subtracting the length of the tangent from the apex (V). Here, we take the starting chainage (1190 m) and subtract the tangent length (97.48 m), leading us to a new chainage for point T at 1092.52 m. This means that if we divide this distance into chains using the peg interval of 30 m, we can see that this is equivalent to 36 chains with an additional 12.52 m.

Think of a marathon runner at the start line (apex). As they run straight ahead (along the tangent), they can calculate how far they are from a checkpoint (point T) by simply subtracting the distance they have already run from their total expected distance.

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 * Deflection angle in radians'. First, convert the deflection angle from degrees to radians by multiplying it by π and dividing by 180. With our values, we find the curve's length at approximately 188.50 meters. This indicates how long the curved section will be.

If you ever rode a roller coaster, knowing the length of the curved track helps the designers understand how steep the turns can be and how thrilling the ride will be. In our calculations, length of the curve reflects the excitement and challenges on the road ahead!

Chainage of T2 = 1092.52 + 188.50 = 1281.02 m.

To find the chainage of point T2, simply add the length of the curve to the chainage of point T. This gives a final value of 1281.02 meters. This process of addition helps to track the progression of the route from the starting point through the tangent and onto the curve.

Imagine you are building a LEGO path. First, you place straight pieces (the tangent), which you measure easily, and then you add curved pieces (the curve). The final length will total the straight (T) plus any additional lengths from the curved pieces (length of curve).

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