HW4

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School

Arizona State University *

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Course

303

Subject

Mechanical Engineering

Date

Apr 3, 2024

Type

pdf

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1

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Arizona State University at the Polytechnic campus Engineering Program EGR 303 - Mechanical Systems Project I Spring 2024 Homework #4 1. A particle is shot from the ground (y = 0) with an initial speed of 80 m/sec at an elevation angle of 72 ° from the horizontal (x-z) plane. Assuming no air resistance, flat ground and constant gravitational acceleration g = 9.8 m/s 2 , formulate its 3-D flight trajectory in x (horizontal displacement pointing in the direction of target point A), y (vertical displacement) and z (horizontal displacement that is perpendicular to x and y) vs. time. With its initial speed in the x-y plane and without any change to the values of initial speed and elevation angle given above, this particle will land at target point A. What is the radius of a circle, with its center at point A, that encloses all the eight alternatives points of landing caused by combinations of the following uncertainties: ± 15 % change in in initial speed, ± 5 ° error in initial velocity’s elevation angle (i.e. the angle between its initial velocity and the x-z plane) and ± 3 ° angle between its initial velocity’s direction and the x-y plane? Your answer must be analytical and NOT rely on any computer simulation. 2. Using the information provided for problem #1 of homework #3, develop a 3- D simulation program in Excel which describes the flight trajectory of that rocket, i.e. x (horizontal displacement pointing in the target direction), y (vertical displacement) and z (horizontal displacement that is perpendicular to x) vs. time history. Find the radius of a circle, with its center at the “nominal” landing point found in problem #1 of homework #3, that encloses all the eight alternatives points of landing caused by combinations of the following uncertainties: ± 10 % change in thrust force, ± 5 ° error in launch rail’s elevation angle (i.e. the angle between its projection in the x-y plane and x- direction) and ± 3 ° angle between launch rail’s orientation and the x-y plane. Notes: This is an individual, not a team, assignment. Each student should submit his/her own solution. The submittal deadline is the beginning of class on Thursday, April 11 . You just need to summarize the results of your computer simulations in the hard (paper) copy of your homework and there is no need to include any printout of simulation software. Staple your submittal in the upper LH corner. You must submit the Excel files you created for this homework through email ( egr303asupoly@gmail.com ) before the deadline. It is important that these files are well organized and ready for review purpose .
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