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 A section of an existing two-lane rural highway will be modified, requiring the connection of two intersecting one-percent grades with a vertical curve. (See Figure 1). You have been asked to determine the length of the vertical curve necessary so that sufficient sight distance is provided along this vertical curve for one vehicle to safely pass another.
This assignment is divided into several parts:
Tasks To Be Completed As you complete the following tasks, you will determine the required sight distance for passing and the required length of the vertical curve connecting the two grades. Task 1. Consider the following situation. Vehicles are traveling along a two-lane rural highway. The speed limit on the highway is 55 miles per hour. A passenger car is following a slower vehicle traveling at 45 miles per hour. The passenger car would like to travel at the speed limit of 55 miles per hour. Describe the tasks that must be performed by the driver of the passenger car in order to safely pass the slower vehicle. These tasks should be defined in terms of both the decisions and the maneuvers to be made by the driver, from the decision to pass to the maneuver back into the travel lane. Task 2. Identify the key events relating to this passing maneuver on a time-distance diagram. Plot distance on the y-axis and time on the x-axis. Sketch the key events (without regard for computations yet) relating both the lead (slower) vehicle and the following (faster) vehicle. Task 3. Calculate the kinematic characteristics (position, velocity, and acceleration) of both the passing and the passed vehicles for each stage of the passing maneuver that you identified in Task 1. What distance is traveled by each vehicle during these stages? What is the resultant position of the vehicles at each stage? How much time does each stage consume? Task 4. Now consider the effects of an oncoming vehicle. What distance is traveled by the oncoming vehicle during the relevant stages of the passing maneuver? In determining this distance, you should identify the point of the passing maneuver that can be described as the point of no return for the passing driver. Task 5. Using a spreadsheet program, prepare a time-distance plot of the three vehicles involved in this passing maneuver. This should provide a visual check for you to make sure that your assumptions and calculations are correct. Task 6. Integrate the results of Tasks 1 through 5 above to calculate the required passing sight distance for the passing vehicle. How do your results compare with the AASHTO model and design information? Why do you suppose that these differences exist? (Note: the standards used by AASHTO are based on certain kinematic assumptions and simplifications, as well as field measurements performed a number of years ago; your standard should reflect both your own reasoning regarding the passing maneuver as well as a clear documentation of this logic). Task 7. The grades of the section for which you need to design the vertical curve are both one percent. Using the relationships between sight distance and the length of the vertical curve, compute the minimum length of the vertical curve required to accommodate this passing maneuver. If the required length of the curve is more than 2000 feet, then a no-passing zone should be established for the curve. If the length of the curve is less than 2000 feet, then a passing zone can be established. Task 8. Prepare a brief report summarizing the results of your work. Assumptions The following data will be useful to you in this problem.
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