Highway curves and effects without superelevation

Types of highway curves

Horizontal curves

• Simple circular curve - a single arc of constant radius joining two tangents.
• Compound curve - two or more arcs of different radii in the same direction with a common tangent at the junction.
• Reverse curve - two arcs bending in opposite directions.
• Transition (spiral) curve - varying radius between a tangent and a circular curve.

Vertical curves

• Summit (crest) curve - formed when an upgrade meets a downgrade or a lesser upgrade.
• Valley (sag) curve - when a downgrade meets an upgrade or lesser downgrade.

Effects on a vehicle on a horizontal curve without superelevation

When the pavement is flat (no superelevation), the whole centrifugal force $P = Wv^2/(gR)$ must be resisted by lateral friction alone.

1. Lateral skidding: if $v^2/(gR) > f$ the tyres slip sideways and the vehicle leaves the curve; a high speed or low $f$ (wet road) makes it likely.
2. Overturning: if $v^2/(gR) > b/(2h)$ the vehicle overturns about the outer wheels, a risk for high vehicles such as buses and trucks.
3. Load transfer: the outer wheels carry more load than the inner wheels, so the outer tyres wear more and the load shifts.
4. Passenger discomfort: passengers are thrown outward.
5. Driver difficulty: to prevent skidding the driver must slow down, so the speed and capacity decrease; or, if he does not, he runs on the outer lane and may meet opposing vehicles.
6. Higher fuel use and tyre wear.

Reason: the centrifugal force has no counterbalance except friction, and the friction available ($f = 0.15$ at design) is usually not enough for the design speed. A superelevation $e$ (and an adequate radius) provides a component of weight against $P$ so that $e + f = V^2/(127R)$ is satisfied.