Ideal Banking Angle Calculation Example

What is the ideal banking angle for a gentle turn with a radius of 1.10 km and a speed limit of 115 km/h?

Using the formula for calculating the ideal banking angle, how can we determine the correct banking angle for this scenario?

Ideal Banking Angle Calculation:

The ideal banking angle for a gentle turn with a radius of 1.10 km and a speed limit of 115 km/h is approximately 5.44 degrees. The formula to calculate the banking angle is arctan((v²) / (g * r)), where v is the speed of the vehicle in m/s, g is the acceleration due to gravity, and r is the radius of the turn in meters.

To solve this problem, we need to convert the speed limit from km/h to m/s and the radius from kilometers to meters. Given the speed limit of 115 km/h and a radius of 1.10 km, the first step is to convert the speed limit to m/s.

Step 1: Convert the speed limit to m/s:

115 km/h * (1000 m/km) / (3600 s/h) = 31.944 m/s (approximately)

Step 2: Convert the radius to meters:

1.10 km * 1000 m/km = 1100 m

Step 3: Substitute the values into the formula:

banking angle (in degrees) = arctan((31.944²) / (9.8 * 1100))

Step 4: Calculate the banking angle:

banking angle (in degrees) ≈ arctan(1020.57 / 10780)

Using a scientific calculator, we find that the arctan of 1020.57 divided by 10780 is approximately 5.44 degrees.

Therefore, the ideal banking angle for a gentle turn with a radius of 1.10 km and a speed limit of 115 km/h is approximately 5.44 degrees.