Valley Curve Length And Design Considerations

This Article Covers Definition Of Valley Curve Its Design Consideration And Length One By One.

Valley Curve

When two grades meet at the valley (sag) and the curve will have convexity downwards, the curve is simply referred as the valley (sag) curve.

As in the case of horizontal curves, the different types of curves according to geometrical configuration are:

  1. Circular
  2. Quadratic parabola
  3. Cubic parabola and other forms of transition curves

V curve or sag curves are vertical curves with convexity downwards. They formed when two gradients meet in any of the following four ways:

  1. When a descending gradient meets another descending gradient.
  2. When a descending gradient meets a flat gradient.
  3. And When a descending gradient meets an ascending gradient.
  4. When an ascending gradient meets another ascending gradient.

Design Considerations

As compared to the design of summit curve, valleyy curve requires more consideration. During day time the visibility in valley curves not hindered but during night time the only source of visibility becomes headlight in the absence of street lights. And in V curves, the centrifugal force generated by the vehicle moving along a valleyy curve acts downwards along with the weight of the vehicle and this adds to the stress induced in the spring of the vehicle which causes jerking of the vehicle and discomfort to the passengers.

Thus, the most important things to consider during design are:

  • Impact and jerking free movement of vehicles at design speed
  • Availability of stopping sight distance under headlight of vehicles during night driving

The best shape for a valley curve is transition curve. Some prefer to use the circular curve or quadratic parabola or combined circular spiral curve but mostly cubic parabola generally preferred in vertical valley curves. It made fully translational by providing two similar transition curves of equal length. It is set by cubic parabola y = bx3 where b = 2N / 3L2

Length Of The Valley Curve

The valley curves made fully transitional by providing two similar transition curves of equal length The 2N 3 The length of the valley transition curve transitional curve set out by a cubic parabola y = bx where b = 2 3L is designed based on two criteria:

  1. Comfort criteria; that allowable rate of change of centrifugal acceleration limited to a comfortable 3 level of about 0.6m/sec.
  2. Safety criteria; that is the driver should have adequate headlight sight distance at any part of the country.

For, L > S

For, S > L

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