When designing a curve on a road with a design speed of 70 mph, what is the minimum radius that can be used if the maximum superelevation rate is 6% and the side friction factor is 0.10?

To determine the minimum radius of a curve for a roadway designed for a speed of 70 mph, one must consider the effects of superelevation and side friction. The relationship among these factors is represented in the formula used in highway design:

R = V^2 / (g(e + f))

Where:

• R is the radius of the curve,

• V is the design speed expressed in feet per second (fps),

• g is the acceleration due to gravity (approximately 32.2 ft/s²),

• e is the superelevation rate (in decimal form), and

• f is the side friction factor.

First, convert the design speed from mph to fps:

70 mph * (5280 ft/mile) / (3600 seconds/hour) = 102.67 fps.

Now, we can plug in the values into the formula. The maximum superelevation rate is given as 6%, which can be expressed as 0.06 in decimals. The side friction factor is also provided, which is 0.10.

Insert these values into the formula for minimum radius:

R = (102.67^2) / (32.2 * (0.06 + 0.10))

This simplifies to