Coefficient of friction
The alternative approach to find R is based on Transport Research Laboratory (TRL) values for the coefficient of friction between the car tyres and the road surface.
Figure illustrates a vehicle passing around a correctly super-elevated curve. The resultant of the two forces is N. The force F acting towards the centre of the curve is the friction applied by the car tyres to the road surface. These forces are shown in greater detail in Figure from which it can be seen that
For Highways Agency requirements, the maximum value for tan θ = 0.07 = 7%, and as V2/Rg cannot exceed 0.25 the term in the denominator can be ignored and
Forces on a super-elevated road
To prevent vehicles slipping sideways, F/N must be greater than the coefficient of friction μ between tyre and road. The TRL quote value for μ of 0.15, whilst 0.18 may be used up to 50 km/h, thus:
For example, if the design speed is to be 100 km/h, super-elevation limited to 7% and μ = 0.15, then:
In the UK, the geometric parameters used in design are normally related to design speed. typical desirable and absolute minimum values for horizontal and vertical curvature; there is also an additional lower level designated ‘limiting radius’, specific of horizontal curvature.
Designs for new roads should aim to achieve the desirable values for each design parameter. However, absolute minimum values can be used wherever substantial saving in construction or environmental costs can be achieved. The Highways Agency Technical Standard TD9/93 advises that in the design of new roads, the use of radii tighter than the limiting value is undesirable and not recommended.