For gradually introducing and increasing the centrifugal force acting downwards, the best shape
that could be given for a valley curve is a transition curve. Cubic parabola is generally preferred

HIGHWAY GEOMETRIC DESIGN
10CV755
Dept. Of Civil Engg, SJBIT
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in vertical valley curves. See figure above during night, under headlight driving condition, sight
distance reduces and availability of stopping sight distance under head light is very important.
The head light sight distance should be at least equal to the stopping sight distance. There is no
problem of overtaking sight distance at night since the other vehicles with headlights could be
seen from a considerable distance.
Length of the valley curve
The valley curve is made fully transitional by providing two similar transition curves of equal
length The transitional curve is set out by a cubic parabola y = bx
3
where b = 2N/3L
2
The length
of the valley transition curve is designed based on two criteria:
1. Comfort criteria; that are allowable rate of change of centrifugal acceleration is limited to a
comfortable level of about 0:6m\sec3.
2. Safety criteria; that is the driver should have adequate headlight sight distance at any part of
the country.
Comfort criteria
The length of the valley curve based on the rate of change of centrifugal acceleration that will
ensure comfort: Let c is the rate of change of acceleration, R the minimum radius of the curve, v
is the design speed and t isthe time, then c is given as

HIGHWAY GEOMETRIC DESIGN
10CV755
Dept. Of Civil Engg, SJBIT
Page
57
For a cubic parabola, the value of R for length L
s
is given by:
Therefore,
Where L is the total length of valley curve, N is the deviation angle in radians or tangent of the
deviation angle or the algebraic difference in grades, and c is the allowable rate of change of
centrifugal acceleration which may be taken as 0.6m\sec
3
.
Safety criteria
Length of the valley curve for headlight distance may be determined for two conditions: (1)
length of the valley curve greater than stopping sight distance and (2) length of the valley curve
less than the stopping sight distance.
Case 1 Length of valley curve greater than stopping sight distance (L > S)
The total length of valley curve L is greater than the stopping sight distance SSD. The sight
distance available will be minimum when the vehicle is in the lowest point in the valley. This is
because the beginning of the curve will have in infinite radius and the bottom of the curve will
have minimum radius which is a property of the transition curve. The case is shown in figure
below. From the geometry of the figure, we have

HIGHWAY GEOMETRIC DESIGN
10CV755
Dept. Of Civil Engg, SJBIT
Page
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Where N is the deviation angle in radians, h1 is the height of headlight beam, is the head beam
inclination in degrees and S is the sight distance. The
inclination α is almost equal to 1
0
Case 2 Length of valley curve less than stopping sight distance (L < S)
The length of the curve L is less than SSD. In this case the minimum sight distance is from the
beginning of the curve. The important points are the beginning of the curve and the bottom most