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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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The distance between the point of curve to intersection point is called
Tangent distance
Length of long chord
Mid ordinate distance
External distance
Tangent distance
The tangent distance (or tangent length) in a simple circular curve is the distance along the tangents from the point of curve (PC or T₁) to the point of intersection (PI or V), or from the point of intersection to the point of tangency (PT or T₂) · It represents the straight distance along the back or forward tangent before the circular arc begins or after it ends.
The tangent distance (or tangent length) in a simple circular curve is the distance along the tangents from the point of curve (PC or T₁) to the point of intersection (PI or V), or from the point of intersection to the point of tangency (PT or T₂) · It represents the straight distance along the back or forward tangent before the circular arc begins or after it ends.
T=Rtan(2Δ) — Tangent distance (T) formula where R is radius and Δ is deflection angle
L=2Rsin(2Δ) — Length of long chord (L)
E=R(sec(2Δ)−1) — External distance (E)
M=R(1−cos(2Δ)) — Mid-ordinate distance (M)
In highway and railway surveying, straight lines (tangents) are connected by circular arcs to ensure smooth transitions · The two straight tangents intersect at the Point of Intersection (PI) at an deflection angle Δ. The curve starts at the Point of Curve (PC) and ends at the Point of Tangency (PT) · By geometry of the right triangle formed by the center of the curve, PC, and PI, the tangent distance is derived using simple trigonometry.
The Point of Curve (PC) is the beginning point where the straight alignment touches the circular curve.
The Point of Intersection (PI) is the point where the back tangent and forward tangent intersect.
The tangent distances from PC to PI (T1V) and from PT to PI (T2V) are equal in a simple circular curve.
Setting out circular curves on roads, railways, and pipelines during surveying.
Calculating chainages of important curve points like PC and PT.
Option B (Length of long chord) is the straight distance joining the Point of Curve (PC) to the Point of Tangency (PT).
Option C (Mid ordinate distance) is the distance from the midpoint of the long chord to the apex of the curve.
Option D (External distance) is the distance from the point of intersection (PI) to the apex of the curve.
A is correct — Tangent distance is defined as the distance between the point of curve (PC) and the point of intersection (PI).
Remember the order of curve components for fast calculations: T=Rtan(Δ/2) for tangent, while E=R[sec(Δ/2)−1] gives the external distance measured from PI to the mid-point of the arc.