15.6. Problems

1. A national highway passing through a rolling terrain has two horizontal curves of radius 450 m and 150 m. Design the required superelevation for the curves as per IRC guidelines.

In this problem, we are tasked with designing the superelevation necessary for two different horizontal curves of a national highway. First, we will assume that the ruling design speed is 80 km/h, with the maximum permissible superelevation (e) set at 0.07 and the coefficient of lateral friction (f) at 0.15. We'll apply the IRC guidelines to calculate the required superelevation for both curves, which involves breaking down the process into clearly defined steps.

Imagine driving on a highway with two different curved sections. Just like your car needs to tilt toward the inside of the curve to stay on the road safely, engineers need to ensure that the road is designed with the right slope (superelevation) to help cars maneuver safely on curves.

Assumptions The ruling design speed for NH passing through a rolling terrain is 80 kmph. The coecient of lateral friction f=0.15. The maximum permissible super elevation e=0.07. Case: Radius = 450m Step 1 Find e for 75 percent of design speed, neglecting f, i.e e = (0.75v)^2 / gR. Here, v = 80 km/h = 22.22 m/sec. e1 = (0.75 * 22.22^2) / (9.81 * 450) = 0.0629. Step 2 Since e1 < 0.07, the design is sufficient.

To compute the required superelevation at a curve with a radius of 450 m, we first convert the vehicle speed to meters per second. Next, we calculate the required superelevation (e1) using the formula provided, which factors in the reduced design speed (75% of the maximum speed) and the radius of the curve. Since the computed value (e1 = 0.0629) is less than the maximum permissible superelevation (0.07), our design is considered adequate.

Think of balancing a marble on a tilted surface. If the tilt is too steep (more superelevation), the marble rolls off easily; if it’s too flat (less superelevation), it may not roll smoothly at all. The goal here is to find just the right angle to let the cars navigate the curve safely without losing traction.

Case: Radius = 150m Step 1 Find e for 75 percent of design speed, neglecting f, i.e e = (0.75v)^2 / gR. v = 80 km/h = 22.22 m/sec e1 = (0.75 * 22.22^2) / (9.81 * 150) = 0.188 Max. e to be provided = 0.07 Step 3 Find f for the design speed and max e, i.e f = v^2 / gR - e. Step 4 Find the allowable speed v for e = 0.07 and f = 0.15.

In the second case, with a radius of 150 m, we again calculate the superelevation (e1). This time, the calculated value (0.188) exceeds the maximum allowable (0.07), indicating that we need to assess the required coefficient of friction (f) for that design speed at this tighter curve. If the required f is too high (over 0.15), adjustments would need to be made to either increase superelevation or implement speed control measures.

It’s like riding a bicycle around a tight corner. If you don’t lean in enough (not enough superelevation), you risk falling over; if you lean too much (too much superelevation), you might not be able to brake in time either. The balance between how much you lean and how fast you're pedaling is crucial to making it around the corner safely.

Find the allowable speed v for the maximum e=0.07 and f=0.15. v = √(0.22 * g * R) = √(0.22 * 9.81 * 150) = 17.99 m/sec = 64 km/h.

After establishing that the allowable maximum superelevation is 0.07, we can calculate the maximum safe speed (v) that can be taken at this curve. The formula incorporates gravitational acceleration (g) and the radius of the curve to establish a safe traveling speed, which, in this case, comes out to approximately 64 km/h. This speed helps in ensuring that vehicles can negotiate the curve safely without skidding off.

Think back to riding a bike; going too fast on a sharp turn can make you slide off. When the bike’s angle matches just the right speed limit for that corner, you smoothly navigate through without losing control. This calculation helps determine that optimal speed for cars on the curve.

2. Given R=100m, V=50 kmph, f=0.15. Find: (a) e if full lateral friction is assumed to develop. (b) find f needed if no super elevation is provided. (c) Find equilibrium super-elevation if pressure on inner and outer wheel should be equal (Hint: f=0).
3. Two-lane road, V=80 kmph, R=480m, Width of the pavement at the horizontal curve=7.5m. (i) Design super elevation for mixed traffic. (ii) By how much the outer edge of the pavement is to be raised with respect to the centerline.
4. Design rate of super elevation for a horizontal highway curve of radius 500 m and speed 100 kmph.
5. Given V=80 kmph, R=200m Design for super elevation. (Hint: f=0.15).
6. Calculate the ruling minimum and absolute minimum radius of horizontal curve of a NH in plain terrain.
7. Find the extra widening for W=7m, R=250m, longest wheel base, l=7m, V=70kmph.
8. Find the width of pavement on a horizontal curve for a new NH on rolling terrain.

This set of additional practice problems allows students to apply their knowledge of superelevation design in various situations. Each problem challenges students to utilize the formulas and principles previously covered, reinforcing their understanding and offering hands-on experience with real-world engineering scenarios related to road safety and design.

Imagine you're getting ready for a road trip with friends. You know the roads might curve in certain areas, and you've got to ensure your car's set to handle those turns—much like handling problems that help you understand the safest ways to navigate those curves successfully.

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