8.1. Two straights BA and AC

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

In this section, we start by establishing some foundational terms used in surveying and curve design. The 'chainage' refers to the distance along a survey line from a reference point, often measured in meters or chains. The 'deflection angle' is the angle between two lines or tangents at a point. The radius mentioned, which is 300 m in this case, defines the distance from the center of the circular curve to any point on the curve itself. The peg interval of 30 m indicates how frequently pegs will be placed along the survey line to assist in measurement.

Imagine planning a new road. You measure out how far you start from a known point (chainage), decide how sharply the road should curve (deflection angle), ensure it's safe for vehicles to navigate (radius), and mark spots along the road with pegs every 30 m to help workers position themselves correctly.

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

To calculate the length of the tangent, we utilize the formula based on the radius and deflection angle. The tangent is the straight line that connects the ending of the curve to the beginning of the next straight segment. By applying the tangent function to half of the deflection angle and multiplying it by the radius, we obtain the tangent length, which is crucial for ensuring accurate curve layout.

Consider standing at the edge of a curved path on a playground. If you were to look straight towards the next path (the tangent), this calculation helps you determine how far that line goes before the path starts to curve again.

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

After calculating the tangent length, we use it to find the chainage at the tangent point. The chainage at point T is simply the initial chainage position minus the length of the tangent. By converting the final chainage into chains and meters, we can understand how the surveyors will layout their measurements in a standardized manner.

Think of it like following a recipe that tells you to take a few steps back after reaching a certain point in a garden path. The chainage calculation helps you pinpoint exactly where you need to go next, just like knowing the right steps to continue following the recipe.

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

To determine the length of the curve, we multiply the radius by the deflection angle converted into radians (since π is used in the calculation, we need to adjust degrees accordingly). This length is vital for budgeting the materials and understanding the curvature needed ahead of the actual construction.

If you've ever wrapped a string around a circular object, understanding the distance that the string wraps around (the length of the curve) can help you know how much string you'll need. Here, the radius helps set how large that curve will be.

Chainage of T2 = 1092.52 + 188.50 = 1281.02 m.

Once we have the length of the curve, we can calculate the chainage at the next tangent point (T2) by adding the length of the curve to the previously calculated chainage at point T. This step is crucial for laying out the complete path of the road or survey line accurately.

Think of building a path in a park where you want to create a scenic route. You first measure and mark where your initial point is, then as you add curves, you keep updating your records of where each segment leads – from T to T2, it’s like a paper trail of where the path lies.

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

Ordinates help in determining the vertical distance from the curve to the tangent at certain interval points. This calculation assists in plotting the right height of the curve at various intervals along it, allowing for correct elevation marking.

Picture setting up a rollercoaster: at various points along the track, you need to ensure that the height of the track corresponds correctly so that the ride is safe. The

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