Highway Engineering

Table 6.9 details the minimum radii permitted for a given design speed and

value of superelevation which should not exceed 7%.

6.5.2 Deriving the minimum radius equation

Figure 6.11 illustrates the forces acting on a vehicle of weight Was it is driven

round a highway bend of radius R. The angle of incline of the road (superele-

vation) is termed a.Pdenotes the side frictional force between the vehicle and

the highway, and Nthe reaction to the weight of the vehicle normal to the

surface of the highway.Cis the centrifugal force acting horizontally on the

vehicle and equals M ¥v^2 /Rwhere Mis the mass of the vehicle.

As all the forces in Figure 6.11 are in equilibrium, they can be resolved along

the angle of inclination of the road:

(Weight of vehicle resolved parallel to highway) +(Side friction factor)

=(Centrifugal force resolved parallel to highway)

168 Highway Engineering

Design speed (km/hr)

Horizontal curvature (R) 120 100 85 70 60 50

Minimum Rwith e=2.5% (not recommended 2040 1440 1020 720 510 360

for single carriageways)

Minimum Rwith e=3.5% (not recommended 1440 1020 720 510 360 255

for single carriageways)

Desirable minimum Rwith e=5% (m) 1020 720 510 360 255 180

Absolute minimum Rwith e=7% (m) 720 510 360 255 180 127

One step below absolute minimum with e=7% 510 360 255 180 127 90

Table 6.9Horizontal radii for different design speeds and superelevation,e

(source: TD 9/93 (DOT, 1993))

W = Mg

C = M ¥ v^2 /R

P

N

a

Figure 6.11Forces on a vehicle negotiating a horizontal curve.