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.

Try these first

1. 1.

   Define the term 'radius' in the context of a circular curve.

   Hint

   Think about the distance from the center to the edge.

2. 2.

   What does the degree of curvature measure?

   Hint

   Recall how angles are used to indicate the sharpness of turns.

3. 3.

   What is the radius of a circular curve?

   • A. Distance of curve
   • B. Distance from center to curve
   • C. Angle subtended at center

   Hint

   Think about the circular nature of the definition.

4. 4.

   The degree of curve indicates what?

   • True
   • False

   Hint

   Reflect on how sharpness can be measured quantitatively.

5. 5.

   A circular curve needs to be designed for safer navigation with a minimum radius of 300 m for a speed of 70 km/h. Calculate its degree of curvature.

   Hint

   Utilize the degree calculation formula carefully.

6. 6.

   Given two points on a curve, A(5,10) and C(10,15), calculate the curve radius step-by-step using the Euclidean distance formula.

   Hint

   Focus on the relationship between the coordinates and apply the distance formula correctly.