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Microsoft Word - ENME 406 hw3_s23.docx 406 CT ENME 406: Roller Coaster Engineering Homework Assignment 3 Learning Outcomes. 1. Developing algorithms for planning roller-coaster layouts for theme parks, given the constraints, evaluating values for key rider and coaster parameters along the track and 2. Generating the corresponding ?????? code to generate history plots of key parameters. Assignment. Consider the roller coaster layout, shown in figures 1 to 5 on the next page. Consider three segments of the descending side of the lift-hill region, shown in fig. 6. The scope of this assignment is the track in these three segments. Part 1. ?????????. Consider 1) a representative point i in the middle of segment 1, 2) a representative point i in the middle of segment 2, and 3) a representative point i in the middle of segment 3. For these locations: draw the FBDs and KDs for the coaster, and derive the expression for N, normal force on the coaster, in terms of the velocity at the point of interest and other variables/parameters symbolically, using equations of motion and kinematic relationships. Part 2. ?????????. For each of these three segments, Create an algorithm that can be directly used to implement calculate the following parameters throughout the path (Note: the algorithm must be complete in all aspects (such as definition of constants and initialization of variables initially, and then definitions for position (? , ? ), ? , ? , etc. for each segment). o At nodes: velocities (? or ? ) Normal reactions ? o At the midpoints of segments enclosed between every pair of neighboring nodes: Accelerations ? , ? , and ? , Positions ? , Time ? , and normal reaction forces ? (imagine forces normal to the tangent to the track at the bottom surface of the carts only for now). Part 3. ??????. Based on the algorithm you wrote, write a matlab code to generate the values for above parameters, choosing coarse grid sizes initially and refining until values for the normal reaction force at the bottom-most point of the track do not change by 0.1%. 406 CT Part 4. ???? ??????????. Demonstrate grid independence using the normal reaction force at the bottom-most point of the track (by increasing the total number of nodes for each run, as noted above). For this part, you will be plotting the values of N against the total number of nodes used in different runs. Did this exercise matter for this assignment (with no losses)? Part 5. ???????. Create graphs of: 1) N vs. imax3 for different runs (at least five) 2) Grid-independent parameter values for: V vs. t at vs. t a vs. t N on the coaster vs. t For all plots, provide: figure numbers, captions, and axis labels (but not titles) per professional practice. ???????????. For this assignment, 1) neglect the size of the rider and cart; 2) ignore friction and aerodynamic drag; 3) assume one rider per cart and only one cart on the track at any time; 4) assume the cart to be starting from rest; 5) assume the units to be in English system of units with mass in slugs; and 6) assume the weight of the rider to be 200 lb and that of the cart to be 600 lb, if necessary. Deliverables 1. Hand-written work for the FBDs and KDs, expression for Ns, and all information required for the algorithm. 2. A functional ?????? code that is ready to be tested by the TA 3. Results showing a. Grid-independence b. History (time history) graphs for parameters Submission All three parts indicated above must be submitted separately. Optional, for your own practice for the exam: Consider the third segment. Assume that this segment will be broken into 10 segments, each segment spanning an arc length of ?? . Consider the sixth segment. If the velocity at the beginning of this segment is determined to be 50 ft/s, find the ?, ? , ? , ?, and ? at the middle of this segment, using the formulae you have developed for your algorithm. 406 CT Figure 1. 3-D line sketch of the coaster layout under consideration. Figure 2. Orthographic projections of the coaster layout under consideration. Figure 3. Top view of the coaster layout with appropriate dimensions. Figure 4. Front view of the coaster layout with dimensions shown for features in the front plane. 406 CT Figure 5. Front view of the coaster layout with dimensions shown for features in the rear plane. Dimensions with a ∗ are repeated dimensions. See next page (fig. 7) for a zoomed version. Figure 6. Segments and geometry of the coaster layout considered for this assignment. 406 CT F ig u re 7 . F ro n t vi ew o f th e co as te r la yo u t w it h di m en si on s sh ow n f or f ea tu re s in t h e re ar p la ne ( zo om ed v er si on o f fi g. 5 ). 406 CT Segment 1 Segment 2 Segment 3