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External distance is also known as __________
Apex distance
Versed sine
Both A and B
In A or B
Apex distance
In simple circular curves, the external distance (also called the apex distance) is the distance from the point of intersection (PI) to the midpoint of the circular curve along the apex line. It represents the outer clearance or offset of the intersection point from the curve.
In simple circular curves, the external distance (also called the apex distance) is the distance from the point of intersection (PI) to the midpoint of the circular curve along the apex line. It represents the outer clearance or offset of the intersection point from the curve.
E=R(sec2Δ−1) — External distance (Apex distance)
M=R(1−cos2Δ) — Mid-ordinate (Versed sine of half the deflection angle)
When two straights (tangents) intersect at an angle, a circular curve is introduced to provide a gradual change in direction. The apex line bisects the angle between the tangents, and the distance along this line from the vertex (PI) to the curve apex defines the external distance E. It is calculated using trigonometry based on the radius R and the deflection angle R(sec(Δ/2)−1).
External distance is also known as the Apex distance (E).
It is the distance between the Point of Intersection (V) and the apex point of the curve (C).
Versed sine (or mid-ordinate, M) is the distance from the midpoint of the long chord to the apex of the curve.
Determining sight clearance and spatial constraints near the intersection point of roads or railways.
Designing horizontal circular curves in highway and railway engineering alignment.
Option B (Versed sine) refers to the mid-ordinate (M), which is the offset from the long chord to the curve apex, whereas the external distance is measured outside the curve towards the vertex.
Options C and D are incorrect as Versed sine and Apex distance refer to two distinct geometric parameters of a simple curve.
A is correct — External distance is defined as the distance from the vertex (point of intersection) to the apex of the curve, which is also called the apex distance.
Always distinguish between External Distance (E=R(sec(Δ/2)−1)) measured outside the curve towards the vertex, and Mid-ordinate (M=R(1−cos(Δ/2))) measured inside the curve from the long chord.