Question

As a civil engineer, you are given contract to construct a curved road in a ghat. In order to obtain the banking angle θ, you need to decide the speed limit. How will you decide the values of speed v and radius r?

Answer 1

The Indian Road Congress (IRC) [IRC-73-1980, Table 2, p.4] sets design speeds for Indian roads based on their classification (national and state highways, district and village roads) and topography. The basic design characteristic influences other geometric elements. IRC [ibid., Table 16, p.24] defines the minimum radius of curvature at a curve based on the design speed. For new roads, curves should be created with a larger radius than the minimum specified to ensure ‘sight distance’ and ‘driving comfort’. When designing horizontal curves, measure the radius to the inside edge of the innermost travel lane, especially on wide roads with steep curvature.

A civil engineer refers to banking as superelevation e; e = tan θ. IRC fixes e_max = 0.07 for a non-urban road and the coefficient of lateral static friction, μ = 0.15, since friction between vehicle tyres and the road is highly variable.

e + μ = `v^2/(g r)`    ...(Where both v and rare in SI units)

= `V^2/(127 r)`    ...(Where V is in km/h and r is in metre)    ...(i)

The sequence of design usually goes like this:

1. Knowing the design speed V and radius r, calculate the superelevation for 75% of the design speed, ignoring friction:
   e = `((0.75 V)^2)/(127 r) = V^2/(225 r)`
2. If e < 0.07, consider this calculated value of e in subsequent calculations. If e > 0.07, then take e = e_max = 0.07.
3. Use equation (i) above to check the value of µ for e_max = 0.07 at the full value of the design speed V:
   µ = `V^2/(127 r) - 0.07`
   If µ < 0.15, then e = 0.07 is safe. Otherwise, calculate the allowable speed V_a as in step 4.
4. `V_s^2/(127 r)` = e + µ = 0.07 + 0.15
   If V_a > V, then the design speed V is adequate.
   If V_a < V, then limit the speed to V_a with an appropriate warning sign.