What is a Summit Curve?
A summit curve is a vertical curve with convexity upward (or concavity downward when viewed from below). It forms at any location where two road gradients meet in a way that creates a “hump” or “crest” in the road profile. As a driver travels along the road, a summit curve is the section where the road appears to rise to a peak and then descend on the other side.
The critical design concern for summit curves is sight distance — at the peak of the curve, the road ahead is hidden from view, creating a potential collision hazard if a vehicle or obstacle is on the other side. The curve must be long enough and flat enough to ensure drivers can see far enough ahead to stop safely.
Four Conditions That Create a Summit Curve
| Case | Meeting Gradients | Deviation Angle N |
|---|---|---|
| (a) | +n₁ meets +n₂ (where n₁ > n₂) | N = n₁ − n₂ |
| (b) | +n₁ meets flat (n₂ = 0) | N = n₁ |
| (c) | +n₁ meets −n₂ | N = n₁ + n₂ |
| (d) | −n₁ meets −n₂ (where |n₁| < |n₂|) | N = |n₁ − n₂| |
The deviation angle N is the algebraic difference between the two meeting gradients and directly governs the required length of the summit curve.
Key Points of a Summit Curve
- VPC (Vertical Point of Curve): The beginning of the vertical curve where the first gradient ends
- VPI (Vertical Point of Intersection): The theoretical intersection point of the two gradients (above the actual curve)
- VPT (Vertical Point of Tangent): The end of the vertical curve where the second gradient begins
Why IRC Uses a Square Parabola for Summit Curves
While a circular curve would theoretically provide equal sight distance from all points, IRC recommends the square parabola (y = ax²) for three practical reasons:
- Easy Layout: The parabola can be easily set out in the field and provides a smooth, comfortable transition between gradients
- Constant Rate of Grade Change: The second derivative d²y/dx² = 2a = constant, meaning the change in gradient is uniform — giving a constant centrifugal force change, which is comfortable for passengers
- Greater Sight Distance: The flat top of the parabolic profile provides a longer visible length than a circular curve of the same length
Length of Summit Curve
The length is governed by the sight distance requirement. Centrifugal force is not a concern for summit curves because it acts upward (opposing gravity), actually reducing the effective vehicle weight and improving comfort. Two cases are considered:
Case 1: When L > S (Curve Longer than Sight Distance)
General: L = NS² / (√h₁ + √h₂)²
IRC simplified (SSD: h₁=1.2m, h₂=0.15m): L = NS²/4.4
IRC simplified (OSD/ISD: h₁=h₂=1.2m): L = NS²/9.6
Case 2: When L < S (Sight Distance Longer than Curve)
General: L = 2S − (√h₁ + √h₂)²/N
IRC simplified (SSD): L = 2S − 4.4/N
IRC simplified (OSD): L = 2S − 9.6/N
Location of Highest Point on Summit Curve
The highest point is not always at the midpoint of the curve — it shifts toward the flatter gradient side when the two gradients are unequal. Its distance from VPC is:
x₀ = n₁ × L / N
Design Note on Vertical Curves
In case of vertical curves, the effect of gradient is generally neglected in SSD and OSD calculations — the sight distance is calculated as if the road were flat, and the vertical curve length ensures the geometry provides that sight distance. This is an IRC recommendation that simplifies design without significantly compromising safety.