What is the Ideal Banking Angle for a Gentle Turn on a Highway?

Calculation of Ideal Banking Angle

In order to determine the ideal banking angle for a gentle turn of 1.50 km radius on a highway with a speed limit of 115 km/h, we can use the following formula:

Banking Angle = tan^-1(v² / (g * r))

Where:

• Banking Angle is the angle at which the road is banked in degrees
• v is the velocity of the car (in m/s)
• g is the acceleration due to gravity (9.8 m/s²)
• r is the radius of the turn (in meters)

Given Data:

Radius of the turn, r = 1.50 km = 1500 m

Speed limit, v = 115 km/h = 31.9 m/s

Calculation:

Substitute the given values into the formula:

Banking Angle = tan^-1((31.9 m/s)² / (9.8 m/s² * 1500 m))

Simplify the equation:

Banking Angle = tan^-1(3251.61 / 14700)

Using a calculator, we find:

Banking Angle ≈ 12.63°

Therefore, the ideal banking angle for a gentle turn of 1.50 km radius on a highway with a speed limit of 115 km/h is approximately 12.63 degrees.