a7_cee3804_2011_sol

a7_cee3804_2011_sol - CEE 3804: Computer Applications in...

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Unformatted text preview: CEE 3804: Computer Applications in Civil Engineering Spring 2011 Assignment 7: Simulink and Modeling Systems Solution Instructor: Trani Problem 1 Your task is design an emergency exit ramp for a runaway truck. Figure 1 illustrates the situation. Figure 1. Emergency Exit Ramp. The truck has a mass of 40,000 kg. and enters the ramp at a speed of 42 m/s (~80 mph) while on a -5% grade. The ramp is constructed in two segments: a) curved section with a radius of 1000 meters and b) straight section with a grade of 15%. neglecting the aerodynamic drag acting on the truck, a free-body diagram showing the forces acting on the truck are shown in Figure 2. Figure 2. Free Body Diagram of Truck. CEE 3804 Trani Page 1 of 9 Define a common set notation to solve the problem. When the truck is going downhill, the gravity force helps accelerate the truck. When is going uphill the gravity force helps slow down the motion. The fundamental equation of motion to describe the deceleration of the truck on the exit ramp is: m dV = − mg cos(δ )µ + mg sin(δ ) dt Here we adopt the nomenclature that when angle δ is positive (i,e., downhill) the term mg sin(δ ) will be positive and thus opposite to the friction term. In this case, the gravity helps accelerate the truck. When going uphill δ is negative and the term mg sin(δ ) is negative helping decelerate the truck. Task 1 Model the curved section of the road as either a series of line segments or by deriving an equation that relates the local grade of the curve as a function of the path length along the curve. The curved section is made of two segments: a) a downhill segment ( l1 ) and an uphill segment ( l2 ). The length of these segments is easily calculated below: l1 = G1 ⎡ 2π R ⎤ −5 = (1000 m ) = 50 meters 100 ⎢ (2π ) ⎥ 100 ⎣ ⎦ l2 = G2 ⎡ 2π R ⎤ 15 = (1000 m ) = 150 meters 100 ⎢ (2π ) ⎥ 100 ⎣ ⎦ The total length of the curved segment is then 150 meters. For the curved road of radius 1,000 meters the grade decreases at a rate of 1/1000 radians per meter (i.e., 0.05 radians in 50 meters for the first segment of the road). An equation that relates the local grade of the road with path length (s) is then, ⎛ dG ⎞ G ( s ) = G1 − ⎜ s ⎝ ds ⎟ ⎠ G ( s ) = 0.05 − ( 0.001) s ⎛ dG ⎞ is the rate of change of the grade (in radians/meter) vs.path distance traveled (s), G1 is the initial grade of the ⎜ ⎝ ds ⎟ ⎠ road (in radians) and s is the path length along the curved section of the road in meters. verify this equation by examining the value of G ( s ) when s = 200 meters ( G (200 ) = −0.15 radians). This equation can be discretized as a table function by selecting values of grade vs. path distance. For example, if 10 segments are selected along the path, the values of G ( s ) are where: shown in Table 1 in table lookup function. Path Length (m) Grade (Rad.) 0 0.0500000000000000 20 0.0300000000000000 40 0.0100000000000000 60 -0.0100000000000000 CEE 3804 Trani Page 2 of 9 Path Length (m) Grade (Rad.) 80 -0.0300000000000000 100 -0.0500000000000000 120 -0.0700000000000000 140 -0.0900000000000000 160 -0.110000000000000 180 -0.130000000000000 200 -0.150000000000000 Figure 3. Simulink Model to Model Runaway Truck. Equation Used to Relate Grade and Path Length (s). According to this model, 334.4 meters are needed to bring truck to a full stop at the end of the hill. CEE 3804 Trani Page 3 of 9 Figure 4. Acceleration, Speed and Distance Profiles for Truck. Equation Used to Relate Grade and Path Length (s). CEE 3804 Trani Page 4 of 9 Figure 5. Simulink Model to Model Runaway Truck. Table Lookup Function Used to Relate Grade and Path Length (s). Figure 6. Lookup Table Values to Relate Grade and Path Length. Vector of Input Values are Path Length. Table Data is the Grade in Radians. CEE 3804 Trani Page 5 of 9 Figure 7. Acceleration, Speed and Distance Profiles for Truck. Table Lookup Function Used to Relate Grade and Path Length (s). According to this model, 334.5 meters are needed to bring truck to a full stop at the end of the hill. CEE 3804 Trani Page 6 of 9 Problem 2 An Excel file contains data for thousands of public airports in the U.S. A sample of the file is shown below. The file is called airports_2011.xls. Task 1 Create a Matlab script and use the Matlab function xlsread to read the data file into a Matalb Cell Array. Rename the variables with names that represent the data. The airport name is a 3-letter code used by the FAA to name airports (column 1). ___________ Matlab Script ___________ % Script file for Task1 of Problem 2 (Assignment 7) % Read the file using the xlsread command in Matlab % reads numeric and text sections seperately [num txt]=xlsread('airports_2011.xls'); % Define variables in the problem header=txt(1,:); % header is the first row of the file read txt(1,:)=; airportID=txt(:,1); name=txt(:,2); state=txt(:,3); % erase the first row of txt array % airport id is the first column of the txt variable % airport name is the second column of the txt variable % airport state is the third column of the txt variable % Extract other variables )passengers, latitude and longitude form the % numeric array (num) passengerPerYear=num(:,1); latitude=num(:,2); longitude=num(:,3); % passengers per year % % longitude (deg) ___________________________________ Task 2 Add to the script created in Task 1 code to estimate the number of airports in the state of Colorado. Use the string comparison function in Matlab (strcmp). Repeat for the number of airport in the state of Virginia. CEE 3804 Trani Page 7 of 9 ___________ Matlab Script ___________ % Count airports in Colorado and Virginia count=strcmp(state,'CO'); % count airports in Colorado numAirportsInCO=sum(count); % number of airports in Colorado count=strcmp(state,'VA'); numAirportsInVA=sum(count); disp(['Airports in the State of Colorado ', num2str(numAirportsInCO) ]) disp(['Airports in the State of Virginia ', num2str(numAirportsInVA) ]) ___________________________________ Airports in the State of Colorado 44. Airports in the State of Virginia 37. Task 3 Add to the script in Task 2 to plot the location of airports in the State of Colorado. Use the usamap.mat file provided. Label your map as needed. ___________ Matlab Script ___________ % Script file for Task3 of Problem 2 (Assignment 7) matchAirportsCO=strcmp(state,'CO'); % finds indices of airports in Colorado index=find(matchAirportsCO==1); (optional step) latCO=latitude(index); longCO=longitude(index); % Extracts indices of airports in Colorado % Saves latitudes of airports in CO % Saves longitudes of airports in CO load usamap h=plot(uslon, uslat,'k-', longCO, latCO,'r *'); xlabel('Longitude (deg)') ylabel('Latitude (deg)') grid ___________________________________ CEE 3804 Trani Page 8 of 9 Figure 2. U.S. Map with Airports in the State of Colorado. Task 4 Find the total number of passengers boarding planes at airports in the state of Virginia. ___________ Matlab Script ___________ % Script file for Task 4 of Problem 2 (Assignment 7) matchAirportsVA=strcmp(state,'VA'); indexVA=find(matchAirportsVA==1); % Finds indices of airports in VA % Extracts indices of airports in VA totalNumPssngr=sum(passengerPerYear(indexVA)); disp(['Total Passengers at Airports in the State of Virginia ', num2str(totalNumPssngr) ]) ___________________________________ Total Passengers at Airports in the State of Virginia 4,448,500. Note that IAD and DCA airports are considered to be in the District of Columbia for some strange reason in the database. CEE 3804 Trani Page 9 of 9 ...
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This note was uploaded on 01/01/2012 for the course CEE 3804 taught by Professor Aatrani during the Spring '07 term at Virginia Tech.

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