University of Virginia Library

SUPERELEVATION:

Railroad engineers learned that rolling stock and track were
subjected to greater lateral stresses at the beginnings and ends
of curves in the rails (changes in direction). In order to prevent
overturning, they adopted the practice of raising the outside rail
and lowering the inside rail (superelevation). They learned, too,
that the ride could be made smoother and the stress on rolling
stock could be reduced if horizontal curves followed gradual
changes (transitions) rather than abrupt changes (circular curves).
The engineers formulated tables combining the physical principles
of superelevation and spirals.

With the introduction of the automobile, the engineers used the
tables they had developed for railroads to lay out auto roads. Many
inserted superelevation into the tangent but omitted the spiral in
the belief that automobiles could make transitions within the travel
lane. Accidents on the highways increased where the transition
curves were omitted. Joseph Barnett, an outstanding engineer in
Public Roads Administration, argued for transition curves with superelevation
in order to improve safety and to provide a smoother ride
along a graceful curve. (He had gained experience earlier in the

design of parkways in Westchester County with Clarke and Downer.)

Barnett studied the behavior of drivers as they were affected
by superelevation and friction. He learned that drivers did not
adjust their speed to the importance of the road, but to the physical
limitations of curvature, grade, sight distance, and smoothness of
surface. He found that longer transitions were necessary at higher
speeds to encourage drivers to stay in their occupied lane rather
than encroaching on the adjoining lane.

Barnett learned, too, that vehicles traveling around a curve at
low speed tended to slide down the superelevated incline when centrifugal
force was reduced. An analysis of 900 driving tests showed
that resistance to transverse sliding was developed around a curve
at friction coefficients of 0.16 for speeds of 30 to 60 MPH, or
0.14 for speeds of 70 MPH. and that the limiting factor for ice was
10%, or about 1¼ inches per foot.

From these findings, Barnett applied the coefficients of superelevation
and friction to the equation for Equilibrium: the centrifugal
force of a vehicle traveling around a curve of constant radius
at a constant velocity is equal to the superelevation S plus side
friction F, i.e. the vehicle is not skidding.

Let us examine the equation for centrifugal force which is
represented by Wv2/gR, where W is the weight of the vehicle, v is the
velocity in feet per second, g is the acceleration of gravity in
feet per second, and R is the radius of the curve in feet:

Eliminate W, change v in feet per second to V in miles per hour, and
substitute 32.16 for g.

Barnett proposed that the maximum superelevation practical for
all but the sharpest curves should be 39% according to the following:

This would result in all but the flattest curves being superelevated
to 10%; therefore, Barnett argued, superelevation should
account for 75% of the design speed. For example, curves on a highway
with an assumed design speed of 60 MPH would be superelevated
to compensate for the centrifugal force developed at 45 MPH. Barnett
developed his tables for superelevation accordingly.