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Interactive Audio Lesson
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Understanding Valley Curves
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Today we are going to dive into valley curves. Can anyone remind me what a valley curve is?
A valley curve is a vertical curve with convexity downwards, right?
Exactly! Valley curves are significant where two gradients meet. Can someone tell me how we identify the type of gradient?
If it’s a descending gradient meeting another, it’s that type, and we check the configurations.
Correct! Remember the four types we discussed: descending meeting descending, flat, ascending, or another ascending. Let's think about how these curves affect vehicle dynamics.
They help prevent discomfort from jerking, especially at higher speeds!
Right! The design must ensure an impact-free movement at design speed. Let's summarize that: We're focusing on comfort and stopping sight distance.
Calculating the Length of Valley Curves
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Let's move to the problem at hand. Can anyone summarize the problem stated about the valley curve?
It’s about a descending gradient of n = 1 in 25, with an ascending gradient of n = 1 in 30, and a design speed of 80 km/h.
That's right! We have to calculate the length of the valley curve based on provided conditions. What other information do we need?
We need to consider the stopping sight distance, which is given as 127.3 m.
Perfect! Let's apply the formulas we’ve learned to come up with maximum and minimum lengths. Who wants to start by applying the comfort criteria?
Using the formula, we get the rates and calculations necessary to find the length!
Excellent progress! Make sure to compare that with the safety calculations. In the end, which lengths did we achieve?
The results were 73.1 m and 199.5 m; the higher value has to be considered for safety.
That's the key takeaway! It’s essential to ensure all calculations meet our design criteria.
Introduction & Overview
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Quick Overview
Standard
The Problems section presents a practical problem involving the design length of a valley curve formed by specified gradients, which applies theoretical concepts covered earlier in the chapter.
Detailed
In Section 18.4, the focus is on applying the concepts of valley curves to solve a practical problem. Specifically, the problem states that a valley curve is formed by a descending gradient (n = 1 in 25) and an ascending gradient (n = 1 in 30), with a design speed of 80 km/h, and requires calculating the length of the valley curve. The hints provided guide the solving of this problem, including relevant variables such as centrifugal acceleration and stopping sight distance (SSD). The answer indicates two possible lengths derived from the formulas in the chapter: a minimum of 73.1 m and a maximum of 199.5 m. Thus, understanding and applying these design principles is essential for transportation engineering.
Audio Book
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Problem 1: Valley Curve Design
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- A valley curve is formed by descending gradient n = 1 in 25 and ascending gradient n = 1 in 30. Design the length of the valley curve for V = 80 km/h. (Hint: c = 0.6 m/cm³, SSD = 127.3 m)[Ans: L = max(73.1, 199.5)]
Detailed Explanation
In this problem, we need to design the length of a valley curve formed by a descending gradient with a slope of 1 in 25 (which means it descends 1 unit vertically for every 25 units horizontally) and an ascending gradient with a slope of 1 in 30. The vehicle speed is given as 80 km/h. To design this curve, we will apply the necessary design criteria. The hint suggests considering the rate of change of centrifugal acceleration (c) as 0.6 m/s³ and the stopping sight distance (SSD) as 127.3 m. We can calculate different lengths for the valley curve based on safety and comfort criteria and then take the maximum of these lengths as the final design length. This means ensuring that the valley curve is comfortable for the vehicle speed and safe at nighttime visibility conditions.
Examples & Analogies
Think of driving down a hill while riding a roller coaster. The way the roller coaster is designed for a smooth transition from a downhill to uphill is similar to designing a valley curve in road engineering. If the transitions are too abrupt, it can create discomfort for riders, just like it can for drivers on the road. Engineers ensure the curves are gentle enough to allow safe and comfortable speeds.