2.49. A right hand simple circular curve connects two straights AI and IB where A and B are the tangent points. The azimuth of each straight is 50° 43' 12" and 88° 22' 14", respectively. The curve passes through point C of coordinates (321.25, 178.1) m. If the coordinates of A are (240.40, 125.90) m, compute the radius of curve and degree of curve.

This section discusses a right-hand simple circular curve connecting two straight lines (AI and IB) with specific tangent points (A and B).

A circular curve is used in road design to provide a smooth transition between two straight sections of a road. The tangent points A and B are where the curve meets the straight lines AI and IB, respectively. The right-hand curve indicates that as a vehicle travels along the road, it will turn to the right when moving from point A to point B.

Imagine driving through a roundabout. As you approach the roundabout from a straight road, you smoothly curve following the arc of the roundabout, which is similar to the way a circular curve transitions from one straight segment to another.

The azimuth of the straight lines is provided: AI at 50° 43' 12" and IB at 88° 22' 14". Coordinates of points are also given: C (321.25, 178.1) m and A (240.40, 125.90) m.

Azimuths represent the direction of a line in degrees measured from North. In this case, the lines AI and IB are at specific angles relative to the North direction. The coordinates specify the exact points A and C on a two-dimensional plane, allowing us to compute the dimensions of the curve accurately.

Think of using a map application on your phone where you can enter coordinates to find specific locations or navigate between them. The azimuths help indicate the direction you should travel to reach your destination.

The calculation process involves computing the radius and degree of curvature based on given azimuths and coordinates. The assumptions include neglecting point C and assuming a radius of 450 m.

To calculate the radius of a curve, we typically use geometric relationships between the points involved. The degree of curve is related to the angle subtended by a chord at the center of the curve and is calculated based on the internal angle between the two straight segments. In this specific case, calculations would involve determining the angle between azimuths and using the distances between coordinates to find the radius.

Think about measuring how tightly a car can turn on a road. The tighter the turn (smaller radius), the sharper the angle. In contrast, a wider turn (larger radius) allows a smoother and more comfortable driving experience.

If the radius of the curve is considered as 450 m, we further compute the chainages of tangent points A and B, the external distance E, mid-ordinate M, and lengths of various chords.

Chainage refers to the distance along the curve or the road from a reference point, allowing us to locate where tangent points A and B lie along the design. The external distance E is a measure of the space from the midpoint of the curve to the intersection of the tangents. The mid-ordinate M helps determine the height at which the curve deviates from the straight line path. Various chords are straight lines connecting points along the curve, important in measuring the physical layout of the curve.

Picture bowing a string between two points: the string represents the curve, and the distance from the midpoint to the string's lowest point represents the mid-ordinate. This idea helps visualize how curves get measured and constructed in real life.

Finally, we need to find the deflection angles associated with the values calculated.

Deflection angles are the angles through which a line or a curve deviates from a reference line. These angles are crucial in determining how much and in what direction the road bends, affecting how drivers navigate through curves. In planning, these angles must be precise to ensure safe transition at high speeds.

Think of a racetrack: the sharper the corner (higher deflection angle), the more significant adjustments a driver must make to navigate without losing speed or control. Understanding these angles in road design helps create safer roadways.

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