Student s Guide Get Out! Designing a Highway Exit Nathaniel Lasry John Abbott College
Get Out! Designing a Highway Exit Context You have just obtained a well-paid summer internship in the renowned civil engineering firm Highways R Us. This firm recently received a substantial amount of money from the government to design and build an extra exit on Highway 15 North. With a little excitement, you enter the headquarters of the firm awaiting your project. The boss clarifies your initial assignment in the following letter: Dear New Intern, There are numerous tasks to carry out in the construction of a highway exit like Exit 43B. We must evaluate the type, quality and structural patterns of the soil before we lay down any concrete. Furthermore, effects of thermal expansion on the concrete must also be evaluated. There are also many choices to make when it comes to design. The partners in our firm have opted for a flat, circular, clockwise exit, mostly for purposes of costeffectiveness. As an intern, you will have to determine what portion of a circle we will need, as well as the optimal dimension of the circle. Security being of utmost importance, you will have to calculate the maximum speed limit on the exit. Note that the maximum speed on the highway is 100 km/h, although speeds of up to 120 km/h are common. As a designer, it is almost a rule of thumb that excesses of 20% over the speed limit are to be expected. Your calculations should be thorough enough to include different scenarios, such as exiting in rain and snow. Minimizing the number of accidents on our exit is a critical part of obtaining future contracts. Trusting the quality and thoroughness of your work, Y. Bada B. Ing CEO, Highways R Us You have little experience with blueprints, so you decide to travel to the location of the future exit. You find that the government has bought out a square plot of land measuring 5,000 m 2 adjacent to the exit. The exit must gradually lead (no stops or right-angled turns) onto a perpendicular road (Route 174 West) that crosses above the highway on a bridge. You also find out that the average stretch before entering an exit is 300 m and that vehicles taking this exit may range in masses from 100 kg (e.g., motorcycles) to 100,000 kg (e.g., fully loaded trucks). PBL/Student s Guide - Get Out! Designing a Highway Exit 2
Three-Step Cycle List all the revelant information you have gathered from the problem. Based on this information, state what you need to know to solve the problem. As new information comes in, you will want to summarize and update the relevant information you have gathered and ask new questions. List the following: What we know What we need to know Summary PBL/Student s Guide - Get Out! Designing a Highway Exit 3
Questions 1) List the two tasks that you have to work on, based on the CEO s request. 2) Sketch the gradual, circular merge between Highway 15 N and Route 174 W. PBL/Student s Guide - Get Out! Designing a Highway Exit 4
3) Give the dimensions of the circle that you have chosen and explain your choice with both qualitative (i.e., words) and quantitative (i.e., equations) arguments. 4) What is the role of friction in determining the speed limit? Does friction help or prevent cars from moving along the circle? PBL/Student s Guide - Get Out! Designing a Highway Exit 5
5) Draw a 2-D force diagram of the vehicle on the circle showing all forces in that plane (i.e., as if you are a bird looking down upon the car, showing neither gravitational force nor normal force). 6) Are there any measurements you could make or collateral information you could get that would help you determine the speed limit on the exit? If so, state explicitly what you are trying to measure and give a detailed description (i.e., an experimental protocol) of any measurements you would carry out. Hint: There are tire treads and concrete blocks available. PBL/Student s Guide - Get Out! Designing a Highway Exit 6