While aligning a highway it is necessary to follow local topography or profile of land throughout the length. Topography of land is not necessarily straight all the time it can have slopes with varying magnitude.

Constructing road on such profile will result in very bad driving experience and even can result in accidents so to provide smooth vehicle movement the changes in elevation can be smoothened by vertical curves. By road curves I mean road gradient and vertical curves.

Road gradient is the rate of rise or fall along the length of the road with respect to the horizontal. It is expressed as a ratio of 1 in x(1 vertical unit to x horizontal) also gradient can be expressed in percentage.

The ruling gradient or design gradient is the maximum gradient within which the engineer attempts to design the vertical profile of the road.

Ruling gradient depends on terrain, length of the grade, speed, pulling power of the vehicle and horizontal curve.

The ruling gradient is fixed in such a way that the maximum power developed by the engine is equal to the power required to overcome the resistance to the motion on the grade at design speeds.

A gradient steeper than the ruling gradient which may be used in restricted length were restricting the gradient within the ruling gradient is not possible.

It is provided when restricting the gradient in ruling gradient resulting in enormous increase in cost of construction.

On rolling and hilly terrain, limiting gradient may be frequently adopted but the length of limiting gradient should be restricted.

The exceptional gradient should be limited for short stretches not exceeding about 100m at a stretch.

It is provided along the length of the road for drainage point of view. Camber takes care of the lateral drainage but for longitudinal drainage, it is necessary to provide some slope for smooth flow of water.

A gradient of 1 in 500 is sufficient for concrete drains and gradient of 1 in 200 for open soil drains.

Road gradient can influence the vertical speed, acceleration, deceleration, stopping distance, sight distance and also vehicular movement in the way explained below

• Long steep gradient affects vehicular speed very hard and it is worst in the case of heavy vehicles.
• In uphill gradients speed of whole traffic in mostly governed by big vehicles and due to slope and restrictive sight distance speed of heavy vehicles is already very slow.
• As a result of this operating cost of vehicle increases and capacity of road reduces.
• Due to speed difference in heavy and light vehicles, restrictive sight distance and uphill downhill slopes accidents can happen.

Road gradient can be expressed in ratio as 1 in x i.e. 1 vertical unit to x horizontal unit, and in percentage as N i.e. N in 100.

### Deviation Angle

Deviation angle is the angle which measures change in direction when two different grades meets.

Deviation angle is given by algebraic difference between two grades that is given below

[n_1 - n_2] = n_1+ (- n_2) = α_1 + α_2

When there is horizontal curve in addition to the gradient, there will be increased resistance to traction due to both gradient and curve. It is necessary that in such cases the total resistance due to grade and curve should not normally exceed the resistance due to maximum value of the gradient specified.

Then a sharp horizontal curve is to be introduced on a road which has already the maximum permissible gradient, then the gradient should be decreased to compensate for the loss of tractive effort due to the curve.

This reduction in gradient at the horizontal curve is called grade compensation.

As per IRC limitations grade compensation is not necessary for gradients flatter than 4% and thus when applying grade compensation correction, gradients needs not to be reduced beyond 4%

Grade compensation is calculated from following formula= (30+R)/R

Grade Compensation= { { 30 + R } \over R }

where, R is the radius of curve in m

Road gradient is the rate of rise or fall along the length of the road with respect to the horizontal. It is expressed as a ratio of 1 in x(1 vertical unit to x horizontal) also gradient can be expressed in percentage.