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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 angle by which the forward tangent deflects from the back tangent of a curve is called
Intersection angle
Deflection angle
Centre angle
None of these
Deflection angle
The deflection angle (Δ or I) is defined as the angle by which the forward tangent deflects or turns away from the extension of the back tangent at the point of intersection (PI) of a horizontal curve · It represents the total change in direction of the survey line as it transitions through the curve · In horizontal geometry, this angle is also numerically equal to the central angle subtended by the arc at the curve's center.
The deflection angle (Δ or I) is defined as the angle by which the forward tangent deflects or turns away from the extension of the back tangent at the point of intersection (PI) of a horizontal curve · It represents the total change in direction of the survey line as it transitions through the curve · In horizontal geometry, this angle is also numerically equal to the central angle subtended by the arc at the curve's center.
T=Rtan(2Δ) — Tangent length (T) in terms of Radius (R) and Deflection Angle (Δ)
L = \frac{\pi R \Delta}{180° — Length of the circular curve (L)
C=2Rsin(2Δ) — Long chord length (C)
When two straight survey lines (back tangent and forward tangent) intersect, the forward tangent is inclined relative to the direction of the back tangent extended forward · The total deviation angle measured from the forward prolongation of the back tangent to the forward tangent is the deflection angle · It determines the degree of curvature and length required for smooth vehicle transition.
Deflection angle can be directed to the right (positive/clockwise) or to the left (negative/counter-clockwise).
The intersection angle and central angle subtended at the center of curvature are both equal to the total deflection angle (Δ).
In Rankine's method of deflection angles, individual tangential angles for setting out chords are related to the total deflection angle.
Enables simple field computation and setting out of horizontal curves using a transit theodolite.
Provides a direct geometric relationship between tangent lengths, chord lengths, and curve radii.
Cumulative angular errors can occur during field layout if individual station deflection angles are not checked precisely.
Requires clear line of sight between the Point of Curvature (PC) and intermediate curve points.
Geometric design and layout of highway and railway horizontal curves.
Route surveying and alignment design for pipelines and canals.
Option A (Intersection angle) is the interior/exterior angle between back tangent and forward tangent at PI, which is supplementary to the deflection angle (180°−Δ).
Option C (Centre angle) is the angle subtended by the arc at the center of the circle, which is numerically equal to the deflection angle but defined at the center rather than between the tangents.
B is correct — Deflection angle is the angle measured from the extension of the back tangent to the forward tangent.
Always remember that Deflection Angle (Δ) = Central Angle subtended at the curve center, while the Tangential Angle for Rankine's method for a chord is δ=1718.9×RC minutes.