Curve Resistance and Grade Compensation

Curve Resistance for Turning Vehicle: 

Vehicles are steered by the turning of front wheel on horizontal curve, the direction of rotation of rear and front wheels are different, so direction of rotation of rear and front wheels are different, there is some loss in the tractive force. (Traction, or tractive force, is the force used to generate motion between a body and a tangential surface, through the use of dry friction, though the use of shear force of the surface is also commonly used.) 

The tractive force given by the rear wheels is T and tractive force available in the direction of movement is T cos α. 

Loss = T - T cos α

Therefore curve resistance means loss of traction force due to turning of vehicle on  horizontal curve is,   T - T cos α 

More curve resistance is on the sharpe curve. 

Grade Compensation:

When there is a horizontal curve in addition to gradient then there will be increased resistance to traction due to both curve and gradient, therefore it is necessary to compensate the gradient at horizontal curve. 

IRC suggested to  compensate the grade so that pulling power of vehicle cannot be compromise, therefore grade compensation taken is minimum of, 

where,

R = radius of curve

Compensated Grade = Gradient - Grade Compensation 

According to IRC grade compensation is not necessary for the gradient flatter than 4 % 

Camber or Cross Slope

Camber is provided to the road to drain off the surface water from pavement. It is provided by riding middle portion of the road surface. Camber is provided to allow flow of water from the road surface to drainage system in lateral direction, where as minimum gradient is provided to allow gravity flow of water inside the drainage system in longitudinal direction.

It is measured in in 1 in n or n %. Main advantage of providing camber are quick drying of pavement which in turn increases safety and sub-grade protection protection by drainage. 

Types of Camber or Cross-slope :

• Straight Line Camber  
• Parabolic or Elliptic Camber
• Combination of Straight and Parabolic Camber

Straight Line Camber : 

Made up of strong material mainly used for concrete or rigid pavement design.

Equation of camber,

 

Parabolic or Elliptic Camber :

For fast moving vehicle, most of time constructed by using bituminous material.

Equation of camber,

Where,

W = Width of pavement 

N  = Camber slope ( taken from IRC )

Combination of Straight and Parabolic Camber :

Camber Slope as per IRC:

Type of Road	High Rainfall Area	Low Rainfall Area
High type Bituminous or Cement Concrete Surface	2 % (1 in 50)	1.7 % (1 in 60)
Thin Bituminous Surface	2.5 % (1 in 40)	2 % (1 in 50)
Water Bound Macadam or Gravel Surface	3 % (1 in 33)	2.5 % (1 in 40)
Earthen Surface	4 % ( 1 in 25)	3 % (1 in 33)

The camber of shoulder should be at least 0.5 % steeper than the cross slope of adjoining pavement, subjected to a minimum of 3.0 % and a maximum of 5.0 %.

Gradient provided for pavement is consider as a twice of camber, superior the road flatter the camber.