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The formula for tangent length can be given as __________
T=R×tan2∆
T=2R×sin2∆
T=R(sec2∆−1)
T=R(1−cos2∆)
T=R×tan2∆
In simple circular curve surveying, the tangent length (T) represents the distance from either point of curvature (PC or PT) to the point of intersection (PI). It is determined by the radius of the curve (R) and the deflection angle (or intersection angle, Δ).
In simple circular curve surveying, the tangent length (T) represents the distance from either point of curvature (PC or PT) to the point of intersection (PI). It is determined by the radius of the curve (R) and the deflection angle (or intersection angle, Δ).
T=Rtan(2Δ) — Tangent length (T)
L = \frac{\pi R \Delta}{180° — Length of the curve (L)
C=2Rsin(2Δ) — Length of long chord (C)
E=R(sec(2Δ)−1) — External distance (E)
M=R(1−cos(2Δ)) — Mid-ordinate (M)
From the geometric properties of a simple circular curve, the intersection lines form a right-angled triangle with the radius drawn to the tangent points. The tangent length is opposite to half the deflection angle (Δ/2) relative to the center, leading to the trigonometric relationship T=Rtan(Δ/2).
The tangent points are designated as T1 (Point of Curve) and T2 (Point of Tangency).
The tangent distance is measured along the straight line from the Point of Intersection (PI) to either tangent point.
Setting out simple circular curves in railway and highway alignment designs.
Determining the chainage of starting and ending curve points during field surveying.
Option B (2Rsin(Δ/2)) is the formula for the Length of the Long Chord (C).
Option C (R(sec(Δ/2)−1)) is the formula for Apex Distance or External Distance (E).
Option D (R(1−cos(Δ/2))) is the formula for Mid-Ordinate distance (M).
A is correct — The tangent length of a simple circular curve is directly calculated as T=Rtan(Δ/2).
Memorize the core trigonometrical multipliers for curve elements relative to Δ/2: tan(Δ/2) for Tangent Length, sin(Δ/2) for Chord/2, sec(Δ/2)−1 for Apex Distance, and 1−cos(Δ/2) for Mid-Ordinate.
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