Mechanical Engineering and MATLAB Environment - Assignment Example

MECHANICAL ENGINEERING MATLAB ASSIGNMENT NAME INSTITUTIONAL AFFILIATION DATE Table of Contents Introduction 3 Step 1: The Physics behind the Problem 3 Step 2: Plan of Program 6 Step 3: Program Code to be Executed in MATLAB Environment 9 Conclusion 15 Reference 15 Introduction This report considers a parachute designer who is working in a European Space Agency and who is required to design and implement a software for testing of the consequences of altering the parachute’s effective cross-sectional area, Ap to be applied in the spacecraft while the aircraft is making its way back to earth from space. The program designed herein takes the input data from the user. The main inputs include the spacecraft mass, m, and the cross-sectional area of the spacecraft, As, alongside the parachute’s effective cross-sectional area, Ap and the height of the spacecraft above earth, H. The overall report can be divided into three main steps: (i) Understanding the Physics behind the problem (ii) Planning the program (iii) Designing the Code that can be executed in a MATLAB Environment Step 1: The Physics behind the Problem Some basic physics background is required before solving the problem. For example, the equations of motion shown bellow will be applied: s = vt ………………………………………………………………………………………………………….. Equation 1 for constant velocity . For constant acceleration, the following equations (2-4) will apply: v = u + at …………………………………………………………………………………………………….. Equation 2 s = ut + ½ at2 ……………………………………………………………………………………………….. Equation 3 v2 = u2 + 2as ……………………………………………………………………………………….……….. Equation 4 Where, S = The distance covered or travelled in meters t= the time taken in seconds (s) u = initial velocity in m/s1 ­­v = Final velocity in m/s1 a = acceleration in ms-2­­­ For the case of a falling parachute, the acceleration due to gravity will apply and therefore, where is acceleration due to gravity. When a = g and initial velocity is zero (u = 0 m/s), then Equation 2, 3 and 4 becomes: v = gt …………………………………………………………………………………………………….. Equation 5 s = ½ gt2 ……………………………………………………………………………………………….. Equation 6 v2 = 2gs ……………………………………………………………………………………….……….. Equation 7 Further, the physics part for this problem will consider a set of four questions with the following common information: Spacecraft whose mass is 850 kg, Effective cross-sectional area of 5 m2 The height above the earth 150 km The starting velocity of 0 m/s Considering a spacecraft accelerating towards earth under the influence of gravitational pull, and at a height of 100km above the earth, its velocity will be given by the formula shown below: FD = W – ma But W = Mg where g = (40 x 107)/(637+H)2 d = H/71+1.4 A = FD/ (0.5 * C * d * v^2 m= 850 kg a = 9.81 A = FD/ (0.5 * C * d * v^2; C = 0.7 D = density = -H/71 + 1.4 Kg/m3 t = (2s/g )1/2 for time of travel Step 2: Plan of Program Preliminary planning of this program entails breaking down the entire program into small problems as shown in the chart bellow. Explanation for the Chart above: The start stage entails identification of the program needs in terms of output and input. The program plan is developed under the design stage prior to coding. The program coded is tested. If successful, it is ready for use and if not successful, it is rolled back into the design stage as indicated in the diagram (Register, 2007). Plan for the program Question 1: Data Input: g = 9.81 m/s^2 u = 0 m/s max_height = 50,000 m s_step = 1000 m Calculations or processing of data: The following is worked out for each value of s v = u+ (g*t) s = (u*t)+(0.5*g*t^2) v2 = u2 + 2as For s>=1000m, keep calculating the value of s Output: show results for v, s and t Question 2: Data Input: g = 9.81m/s^2 u = 0 m/s max_height = 100,000 m s_step = 1000 m Calculations or processing of data: The following is worked out for each value of s v = u+ (g*t) s = (u*t)+(0.5*g*t^2) v2 = u2 + 2gs For s>=1000m, keep calculating the value of s Output: show results for v, s and t Question 3: Data Input: g = 9.81m/s2 u = 0 m/s max_height = 3000 m s_step = 100 m Calculations or processing of data: The following is worked out for each value of s v = u+ (g*t) s = (u*t)+(0.5*g*t^2) v2 = u2 + 2gs For s>=3000m, keep calculating the value of s Output: show results for v, s and t Question 4: Data Input: g = 9.81m/s2 u = 0 m/s max_height = 3000 m s_step = 100 m Calculations or processing of data: The following is worked out for each value of s v = u+ (g*t) s = (u*t)+(0.5*g*t^2) v2 = u2 + 2gs V_min = sqrt (2 * g * s; For s>=3000m, keep calculating the value of V_min Output: show results for V_min, s and t Question 5: Data Input: g = 9.81 m/s2 FD = W- ma vmax = 10 m/s C = 0.7 A = 5 m2 Calculations or processing of data: A = FD/ (0.5 * C * s * v^2; Output: Show results for A and v Step 3: Program Code to be Executed in MATLAB Environment Section 1: Graphs Graph Code for Question 1: %Program for calculation of velocity %Solution for Question 1 %Input Data u = 0; % The initial velocity in m/s a = 9.81; % acceleration due to gravity max_height = 50000; % maximum height from 150km to 100km s_step = 1000; % displacement intervals for the plot %While Loop % initialization of displacement, time and velocity i=1; V(i)=0; t(i)=0; S(i)=0; % the start of the while control loop while S(i) Read More