w = W tan θ
| F = | mv2 | = | wv2 |
| R | gR |
If F = w there will be no tendency to skid; hence the rate of superelevation necessary in any case is as follows:
| W tan θ = | Wv2 |
| gR |
| tan θ = | v2 |
| 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.
Fig. 7. Curves showing Theoretical Superelevation for Various Degrees of Curve for Various Speeds of Vehicle