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In which are the following vertical curve.
A) Summit
B) Valley
C) Both A and B
D) None of these
Both A and B
Vertical curves are gradient-changing curves provided in highway and railway engineering to ensure smooth transitions between intersecting gradients. Both Summit curves (convex upwards) and Valley curves (concave upwards) are types of vertical curves used to provide adequate sight distance and driver comfort.
Vertical curves are gradient-changing curves provided in highway and railway engineering to ensure smooth transitions between intersecting gradients. Both Summit curves (convex upwards) and Valley curves (concave upwards) are types of vertical curves used to provide adequate sight distance and driver comfort.
N=g1−g2 — Deviation angle or algebraic difference in gradients
L=4.4NS2 — Length of summit curve for S<L (based on Stopping Sight Distance)
L=2S−N4.4 — Length of summit curve for S>L
Vertical curves operate by gradually altering the slope of a alignment, preventing sudden changes in direction when shifting from an upgrade to a downgrade or vice versa. Summit curves are designed primarily based on sight distance considerations (SSD, OSD), while Valley or Sag curves are designed based on headlamp sight distance and comfort criteria under centrifugal force acceleration.
Vertical curves are provided in the vertical plane, whereas horizontal curves are provided in the horizontal plane.
Parabolic curves are universally preferred for vertical curves because of the constant rate of change of grade.
Summit curves are convex upwards (crest curves), formed when an upgrade meets a downgrade or flatter upgrade.
Valley or Sag curves are concave upwards, formed when a downgrade meets an upgrade or flatter downgrade.
Ensures smooth transition between different gradient slopes.
Provides required sight distances (SSD and OSD) to ensure driver safety.
Improper design of valley curves can cause severe impact/comfort issues at high speeds.
Inadequate summit curve lengths can restrict driver visibility, increasing head-on collision risks.
Design of highway road alignments.
Design of railway gradient transitions.
| Feature | Summit Curve | Valley Curve |
|---|---|---|
Shape/Shape Orientation | Convex Upward | Concave Upward |
Primary Design Criteria | Sight Distance (SSD/OSD) | Comfort & Headlamp Sight Distance |
Centrifugal Force Direction | Acts Upwards (reduces effective weight) | Acts Downwards (increases impact on suspension) |
Square parabola (y=ax2) is standard for summit curves due to constant vertical acceleration.
Option A (Summit) and Option B (Valley) are both valid classifications of vertical curves based on curvature profile.
C is correct — Both Summit and Valley curves are standard classifications of vertical curves used to transition between different gradients.
Remember that parabolic curves are used for vertical curves (constant rate of change of grade), while spiral or transition curves (like the cubic parabola or clothoid) are used for horizontal curves.