ds, THETA
= the angle of superelevated surface _c-d_, with the horizontal _c-a_.
_R_ represents the radius of the curve upon which the vehicle is
moving. _w_ is the component of the weight parallel to the surface
_c-d_, _v_ = velocity of the vehicle in feet per second. _m_ = mass
of vehicle = _W/g THETA_

_w_ = _W_ tan _THETA_

_mv^2_ _wv^2_
_F_ = ------- = ------
_R_ _gR_

If _F_ = _w_ there will be no tendency to skid; hence the rate of
superelevation necessary in any case is as follows:

_Wv^2_
_W_ tan _THETA_ = -------
_gR_

_v^2_
tan _THETA_ = -------
_gR_

The amount of superelevation required, therefore, varies as the square
of the velocity and inversely as the radius of the curve.

Theoretically, the amount of the superelevation should increase with a
decrease in the radius of the curve and should also increase as the
square of the speed of the vehicle. On account of the variation in
speeds of the vehicles, the superelevation for curves on a highway can
only be designed to suit the average speed. At turns approaching
ninety degrees, the curve is likely to be of such short radius that it
is impossible to maintain the ordinary road speed around the curve,
even with the maximum superelevation permissible. It is good practice
to provide the theoretical superelevation on all curves having radii
greater than 300 feet for vehicle speeds of the maximum allowed by
law, which is generally about 25 miles per hour. Where the radii are
less than 300 feet, the theoretical superelevation for the maximum
vehicle speeds gives a superelevation too great for motor trucks and
horse drawn vehicles and generally no charge is made in superelevation
for radii less than 300 feet, but all such curves are constructed with
the same superelevation as the curve with 300 foot radius.

The diagram in Fig. 7 shows the theoretical superelevation for various
curve radii.

[Illustration: Fig. 7. Curves showing Theoretical Superelevation for
Various Degrees of Curve for Various Speeds of Vehicle]

At the intersection of important highways, the problem is complicated
by the necessity for providing for through traffic in both directions
and for traffic which may turn in either direction and the engineer
must provide safe roadways for each