Superelevation with Side Friction

\[e+f=\frac{v^2}{gR}\]

Variables

esuperelevation rate (m/m)

fside friction factor

vvehicle speed (m/s)

ggravitational acceleration (m/s²)

Rhorizontal curve radius (m)

Description

What is this formula?

The Superelevation with Side Friction equation calculates the relationship between roadway banking and tire-pavement friction required to safely negotiate a horizontal curve.

Unlike the ideal equilibrium superelevation equation, this formulation recognizes that both roadway cross slope and tire friction contribute to resisting lateral acceleration.

When to use it

Use this formula when designing:

- Highways

- Expressways

- Rural roads

- Urban arterials

- Horizontal curves

Example

A roadway curve has:

v = 25 m/s

R = 300 m

f = 0.12

Formula:

e = (v²/(gR)) - f

Substitution:

e = (25²/(9.81×300)) - 0.12

e = 0.212 - 0.12

e = 0.092

Result:

e = 9.2%

Applications

- Highway geometric design

- Road safety

- Horizontal curve design

- Transportation engineering

Note

This equation is widely used in highway design standards. The side friction factor is not constant and depends on speed, pavement condition, vehicle characteristics, climate, and design criteria. Most highway agencies specify maximum allowable values for both superelevation and side friction.