Summit curves are vertical curves with gradient upwards.

**Summit
curve**

Summit curves are vertical curves with gradient upwards. They
are formed when two gradients meet as illus-trated in any of the
following four ways:

= when a
positive gradient meets another positive gradient

**1 Types
of Summit Curve**

Many curve forms can be used with satisfactory
results, the common practice has been to use parabolic curves in summit curves.
This is primarily because of the ease with it can be laid out as well as
allowing a comfortable transition from one gradient to another. Although a
circular curve offers equal sight distance at every point on the curve, for
very small deviation angles a circular curve and parabolic curves are almost
congruent. Furthermore, the use of parabolic curves were found to give
excellent riding comfort

In determining the type and length of the vertical curve, the
design considerations are comfort and security of the driver, and the
appearance of the pro le alignment. Among these, sight distance requirements
for the safety is most important on summit curves. The stopping sight distance
or absolute minimum sight distance should be provided on these curves and where
overtaking is not prohibited, overtaking sight distance or intermediate sight
distance should be provided as far as possible. When a fast moving vehicle
travels along a summit curve, there is less discomfort to the passengers. This
is because the centrifugal force will be acting upwards while the vehicle
negotiates a summit curve which is against the gravity and hence a part of the
tyre pressure is relieved. Also if the curve is provided with adequate sight
distance, the length would be sufficient to ease the shock due to change in
gradient. Circular summit curves are identical since the radius remains same
throughout and hence the sight distance. From this point of view, transition
curves are not desirable since it has varying radius and so the sight distance
will also vary. The deviation angle provided on summit curves for highways are
very large, and so

the a simple parabola is almost congruent to a circular arc,
between the same tangent points. Parabolic curves is easy for computation and
also it had been found out that it provides good riding comfort to the drivers.
It is also easy for field implementation. Due to all these reasons, a simple
parabolic curve is preferred as summit curve.

Length of
the summit curve

The important design aspect of the summit curve is
the determination of the length of the curve which is parabolic. As noted earlie__r,
th__e length of the c__urve__ is guided by the sight distance
consideration. That is, a driver should be able to stop his vehicle safely if
there is an obstruction on

the other side of the road. Equation of the parabola is given
by y = ax^{2}, where N is the deviation angle and L is the length of
the In deriving the length of the curve, two situations can arise depending on
the uphill and downhill gradients when the length of the curve is great~~e~~r
than the sight distance and the length of the curve is greater than the sight
distance.

**2 Design
considerations for valley curve**

There is no restriction to sight distance at
valley curves during day time. But visibility is reduced during night. In the
absence or inadequacy of street light, the only source for visibility is with
the help of headlights. Hence valley curves are designed taking into account of
headlight distance. In valley curves, the centrifugal force will be acting
downwards along with the weight of the vehicle, and hence impact to the vehicle
will be more. This will result in jerking of the vehicle and cause discomfort
to the passengers. Thus the most important design factors considered in valley
curves are:

(1) impact-free movement of vehicles at design speed and (2)
availability of stopping sight distance under headlight of vehicles for night
driving.

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 in
vertical valley curves.

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.

**3 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} . The length of the valley transition curve
is designed based on two criteria: comfort
criteria; that is allowable rate
of change of
centrifugal acceleration is limited to a comfortable level of about
0:6m=sec3.

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
is

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.

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Civil : Highway Engineering : Geometric Design Of Highways : Summit curve |

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