Which formula is used to determine the external distance in a circular curve?

Answer: B — = R((1 / cos(I / 2)) - 1)

The formula used to determine the external distance in a circular curve is E = R((1 / cos(I / 2)) - 1). This formula derives from the geometric properties of circular curves and involves the radius (R) and the central angle (I). In this context, the external distance represents the distance from the tangent line at the beginning of the curve to the external point of the curve, effectively measuring the offset from the circular path to the straight tangent at the curve's entry point. The central angle needs to be divided by two to reflect the symmetrical nature of the curve, which is why cos(I / 2) is used in the formula. This relationship highlights how the radius and the angle combine to determine the external distance, providing insight into the geometry of circular curves. Understanding this is vital for highway and civil engineers when designing curves, ensuring safe and effective transitions for vehicles.