15.2.1. Design of super-elevation

For fast moving vehicles, providing higher superelevation without considering coefficient of friction is safe, i.e. centrifugal force is fully counteracted by the weight of the vehicle or superelevation.

When vehicles move quickly around curves, the design focuses on increasing superelevation to help counteract the centrifugal forces acting on the vehicle. This means tilting the road surface to encourage vehicles to stay on track. In this scenario, the friction of the tires doesn't need to be heavily considered because the design assumes that the road's incline effectively prevents vehicles from skidding off.

Imagine a race car going around a racetrack. The track is banked on the curves, allowing the car to hug the turn tightly without sliding off, even at high speeds. The car's weight and speed work in harmony with the incline of the track.

For slow moving vehicles, providing lower superelevation considering coefficient of friction is safe, i.e. centrifugal force is counteracted by superelevation and coefficient of friction.

For vehicles that travel at lower speeds, the design of superelevation needs to change. Here, the road may not be banked as steeply, and the coefficient of friction plays a significant role in preventing the vehicle from sliding off. This means that a careful balance must be struck between the road incline and the friction between the tires and the road to ensure safety.

Think about a delivery truck making turns in a city. This vehicle moves more slowly around corners, and if the road is too steeply banked, it might slide down the slope. A gentler incline, combined with the friction between the tires and the road, helps it stay safe.

Step 1: Find e for 75 percent of design speed, neglecting f, i.e e = (0.75v)² / (gR).

This step involves calculating the required superelevation (e) by first taking 75% of the vehicle's design speed (v) and applying a formula that incorporates gravitational force (g) and the radius of the curve (R). This helps establish a baseline for how much banking the road needs to provide for safe navigation.

Imagine trying to estimate how much to tilt a ramp for a toy car to ensure it rolls down smoothly. By calculating how fast the car should go on a straight path, you can figure out the right angle of the ramp. Similarly, here, the speed must be calculated first before determining the proper superelevation.

Step 2: If e ≤ 0.07, then use e = e calculated. If e > 0.07, go to step 3.

Step 3: Find f for the design speed and max e, i.e. f = v² / (gR) - (e / gR). If f < 0.15, then the maximum e = 0.07 is safe for the design speed, else go to step 4.

In Step 2, you check if the calculated superelevation is within a specified maximum of 7%. If it exceeds this, you need to proceed to Step 3. Here, you calculate the coefficient of friction (f) based on the vehicle's speed and the maximum allowable superelevation. If the friction is low enough, the maximum superelevation is considered safe. If not, further adjustments must be made.

Imagine you're riding a bike on a curve. If the angle of the road is too steep, and you find it hard to maintain balance, you might realize you need a smoother, gently sloped curve - that's similar to checking if the banking is too high in this procedure to ensure safety.

Step 4: Find the allowable speed v for the maximum e = 0.07 and f = 0.15, i.e. from equation v = √(0.22gR). If v ≥ v, then the design is adequate; otherwise use speed control measures or look for speed control measures.

In the final step, you calculate the maximum safe speed (v) for the calculated superelevation and the friction limit. If this speed is greater than or equal to the design speed, then the designed curvature is sufficient. If it's not, speed control measures need to be implemented, which may involve adjusting the road or placing signs to encourage slower driving.

Think of a speed limit sign on a curved road. If the curves and banking allow cars to go as fast as the limit safely, everything is fine. If not, the sign needs to persuade drivers to slow down to prevent accidents, much like how designers adjust the curve based on these calculations.

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