1.3.2. By offsets perpendicular to the tangents

Try these first

1. 1.

   What does the term 'offset' refer to in the context of curves?

   Hint

   Think about how far you need to go from a straight line to reach the curve.

2. 2.

   What is the formula for the exact offset?

   Hint

   This formula involves the radius and the distance from the tangent.

3. 3.

   What is the formula for calculating the exact offset?

   • O = R + sqrt(R^2 + x^2)
   • O = R - sqrt(R^2 - x^2)
   • O = sqrt(R^2 + x^2)

   Hint

   Recall the relationship between radius and offsets.

4. 4.

   True or False: An approximate calculation for large circles is always used.

   • True
   • False

   Hint

   Consider when exact calculations might be more necessary.

5. 5.

   In a construction project, the radius of curvature is 120 meters, and the measurement is taken 30 meters from the tangent. Calculate the exact offset.

   Hint

   Make sure to square the radius and the distance properly!

6. 6.

   Discuss the implications of choosing an approximate calculation over an exact one when setting out tight curves.

   Hint

   Think about the accuracy needed in tight curves when vehicles travel at high speeds.