# Length of Valley Curve Design Method

19th November 2018## Length of Valley Curve

The length of the valley curve is designed on the basis of two criteria:

**i)** The allowable rate of change of centrifugal acceleration of 0.06 m/sec. **ii)** The headlight sight distance.

The higher of the two values is adopted.

### Criteria (i)

The length of valley transition curve (Ls) according to the first criteria is given by the following equation:

**Ls = [ Nv^{3} /C]^{1/2}**

Where N is the deviation angle,v is speed in m/sec and C is the allowable rate of change of centrifugal acceleration. The length of the valley curve (L) is taken to 2Ls.

### Criteria (ii)

The length of valley curve (L) according to the second criteria may be determined for two condition

**1.** When the total length of valley curve (L) is greater the stopping sight distance.

**2. **When the total length of valley curve (L) is less than the stopping sight distance.

When the total length of valley curve (L) is greater than the stopping sight distance, the value of L is calculated from the following equation.

**L = NS^{2} /(2h1 + 2Stanα)**

Where h1 is the height of headlight, is the angle of inclination of the beam of light, S is the stopping sight distance and N is the deviation angle.

When the total length of valley curve(L) is less than the stopping sight distance, the value of L is calculated from the following equation:

**L = 2S – (2h1 + 2Stanα )/N**

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