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Aero Flight Dynamics Task

This document contains an assignment submission for a course in flight dynamics and stability. The submission includes: 1) Solutions and relevant code for several problems involving aircraft stability derivatives and eigenvalues. 2) Notes indicating some answers may differ from the instructor's due to using different assumptions for steady level flight speed. 3) Requests to deduct marks for any questions where the author's assumptions led to different answers than expected. The submission provides the student's work, codes, and graphs to solve problems involving aircraft stability, dynamics, and eigenvalues using data and parameters from examples in the textbook. It also acknowledges places where the student's approach may have differed from the instructor's expectations.

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62 views34 pages

Aero Flight Dynamics Task

This document contains an assignment submission for a course in flight dynamics and stability. The submission includes: 1) Solutions and relevant code for several problems involving aircraft stability derivatives and eigenvalues. 2) Notes indicating some answers may differ from the instructor's due to using different assumptions for steady level flight speed. 3) Requests to deduct marks for any questions where the author's assumptions led to different answers than expected. The submission provides the student's work, codes, and graphs to solve problems involving aircraft stability, dynamics, and eigenvalues using data and parameters from examples in the textbook. It also acknowledges places where the student's approach may have differed from the instructor's expectations.

Uploaded by

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Copyright
© © All Rights Reserved
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INSTITUTE OF SPACE TECHNOLOGY

Flight Dynamics and Stability

Assignment No. 5

Assignment: Problems 4.3 to 4.6, 4.9 to 4.16, 4.18 to 4.21

Submitted to: Dr Jamshed Riaz

Dated: 17/12/20
Batch/Section: Aero 17A

Submitted by:
Name of student Registration No. Marks offered
Muhammad Salman Sajid 180101042

Department of Aeronautics and Astronautics


INSTITUTE OF SPACE TECHNOLOGY

1 ASSIGNMENT QUESTIONS

1.1 Note:
• All relevant MATLAB codes and Graphs are given in the APPENDIX at the end of this
assignment.
• In questions 4.12, 4.18 and 4.21 you might find that my answers deviate from those by
which you are comparing. This is because I took u0 = 283.47 ft/s using L = W and
assuming it was steady-level flight, whereas it was 220 ft/s found by the formula M = V/a
where a = 1100 ft/s and M was given in Appendix B as M = 0.2 which I didn’t notice
originally when I started solving question 4.12 and until I was done with question 4.20.
So, you’re welcome to deduct any marks from these questions :)

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2 APPENDEX

2.1 Q)4.5

2.1.1 Code:

%4.15
B = [2 -3 1;3 1 2;-5 2 -4]
eig(B)
[V,D] = eig(B)

2.2 Q)4.11

2.2.1 Code:

A = [ -2 1 ; -10 0 ];
B = [ 0 -5 ]';
C = [ 1 0 ; 0 1 ];
D = 0;
eigenvalues = eig(A)
sys = ss(A,B,C,D);
step(sys)

2.2.2 Unit Step Response Graph

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INSTITUTE OF SPACE TECHNOLOGY

2.3 Q)4.18

2.3.1 Code:

%4.18 Eigenvalues Function


%Taking values of flight conditions and aircraft data
rho = input('Enter value of density(rho):');
uo = input('Enter value of velocity(uo):');
c = input('Enter value of chord(c):');
S = input('Enter wing area (S):');
W = input('Enter weight of the aircraft(W):');
g = input('Enter value of acceleration due to gravity(g):');
m = W/g;
Q = 0.5*rho*(uo^2);

%Taking values of stability derivative coefficents


Cdu = input('Enter value of Cdu:');
Cdo = input('Enter value of Cdo:');
Clu = input('Enter value of Clu:');
Clo = input('Enter value of Clo:');
Cda = input('Enter value of Cda:');
Cmu = input('Enter value of Cmu:');
Cma = input('Enter value of Cma:');
Iy = input('Enter value of moment of inertia about y(Iy):');

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Cmadot = input('Enter value of Cmadot:');
Cmq = input('Enter value of Cmq:');
Cla = input('Enter value of Cla:');

%Defining stability derivatives


Xu = (-(Cdu+(2*Cdo))*Q*S)/(m*uo);
Xw = ((-(Cda-Clo))*Q*S)/(m*uo);
Zu = (-(Clu+(2*Clo))*Q*S)/(m*uo);
Zw = ((-(Cla-Cdo))*Q*S)/(m*uo);
Mu = (Cmu*(Q*S*c))/(uo*Iy);
Mw = (Cma*(Q*S*c))/(uo*Iy);
Mwdot = Cmadot*(c/(2*uo))*((Q*S*c)/(uo*Iy));
Mq = Cmq*(c/(2*uo))*((Q*S*c)/Iy);

A = [ Xu Xw 0 -g ; Zu Zw uo 0 ; Mu+(Mwdot*Zu) Mw+(Mwdot*Zw) Mq+(Mwdot*uo) 0 ;


0 0 1 0 ];
eigenvalues = eig(A)

2.3.2 Relevant inputs and output

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2.4 Q)4.19

2.4.1 Code:

%4.19 Eigenvalues Function


%Taking values of flight conditions and aircraft data
rho = input('Enter value of density(rho):');
uo = input('Enter value of velocity(uo):');
c = input('Enter value of chord(c):');
S = input('Enter wing area (S):');
W = input('Enter weight of the aircraft(W):');
g = input('Enter value of acceleration due to gravity(g):');
m = W/g;
Q = 0.5*rho*(uo^2);

%Taking values of stability derivative coefficents


Cdu = input('Enter value of Cdu:');
Cdo = input('Enter value of Cdo:');
Clu = input('Enter value of Clu:');
Clo = input('Enter value of Clo:');
Cda = input('Enter value of Cda:');
Cmu = input('Enter value of Cmu:');
Cma = input('Enter value of Cma:');
Iy = input('Enter value of moment of inertia about y(Iy):');
Cmadot = input('Enter value of Cmadot:');
Cmq = input('Enter value of Cmq:');
Cla = input('Enter value of Cla:');

%Defining stability derivatives


Xu = (-(Cdu+(2*Cdo))*Q*S)/(m*uo);
Xw = ((-(Cda-Clo))*Q*S)/(m*uo);
Zu = (-(Clu+(2*Clo))*Q*S)/(m*uo);
Zw = ((-(Cla-Cdo))*Q*S)/(m*uo);
Mu = (Cmu*(Q*S*c))/(uo*Iy);
Mw = (Cma*(Q*S*c))/(uo*Iy);
Mwdot = Cmadot*(c/(2*uo))*((Q*S*c)/(uo*Iy));
Mq = Cmq*(c/(2*uo))*((Q*S*c)/Iy);

A = [ Xu Xw 0 -g ; Zu Zw uo 0 ; Mu+(Mwdot*Zu) Mw+(Mwdot*Zw) Mq+(Mwdot*uo) 0 ;


0 0 1 0 ];
eigenvalues = eig(A)

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2.4.2 Relevant Inputs and output

2.5 Q)4.20

2.5.1 Code:

%4.20 For STOL Aircraft in Appendix B


%Taking values of flight conditions and aircraft data
rho = 0.002378;
uo = 154.0556159;
c = 10.1;
S = 945;
W = 40000;
g = 32.174;
m = W/g;
Q = 0.5*rho*(uo^2);

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%Taking values of stability derivative coefficents
Cdu = 0;
Cdo = 0.127;
Clu = 0;
Clo = 1.5;
Cda = 0.67;
Cmu = 0;
Cma = -0.78;
Iy = 215000;
Cmadot = -6.05;
Cmq = -35.6;
Cmdele = -2.12;
Czdele = -0.465; %As Czdele = -Cldele
Cla = 5.24;

%Defining stability derivatives


Xu = (-(Cdu+(2*Cdo))*Q*S)/(m*uo);
Xw = ((-(Cda-Clo))*Q*S)/(m*uo);
Xdele = 0;
Zu = (-(Clu+(2*Clo))*Q*S)/(m*uo);
Zw = ((-(Cla-Cdo))*Q*S)/(m*uo);
Zdele = (Q*S*Czdele)/m;
Mu = (Cmu*(Q*S*c))/(uo*Iy);
Mw = (Cma*(Q*S*c))/(uo*Iy);
Mwdot = Cmadot*(c/(2*uo))*((Q*S*c)/(uo*Iy));
Mq = Cmq*(c/(2*uo))*((Q*S*c)/Iy);
Mdele = (Q*S*c*Cmdele)/Iy;

A = [ Xu Xw 0 -g ; Zu Zw uo 0 ; Mu+(Mwdot*Zu) Mw+(Mwdot*Zw) Mq+(Mwdot*uo) 0 ;


0 0 1 0 ]
B = [ Xdele ; Zdele ; Mdele+(Mwdot*Zdele) ; 0 ]
C = [ 1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1 ];
D = 0;
sys = ss(A,B,C,D);
eigenvalues = eig(A)
step(-0.1*sys);

2.5.2 Output

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2.5.3 -0.1 Step Input Graph

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2.6 Q)4.21

2.6.1 Code:

%4.21 Pzmaps for Executive business jet


%Taking values of flight conditions and aircraft data
rho = 0.002378;
uo = 283.47;
c = 10.93;
S = 542.5;
W = 38200;
g = 32.174;
m = W/g;
Q = 0.5*rho*(uo^2);

%Taking values of stability derivative coefficents


Cdu = 0; %Changing value to 1 %Variable 4 to change Cxu
Cdo = 0.095;
Clu = 0;
Clo = 0.737;
Cda = 0.75;
Cmu = 0;
Cma = -0.8; %Changing value to -1 %Variable 1
Iy = 135869;
Cmadot = -3;
Cmq = -8; %Changing value to -30 %Variable 2
Cmdele = -0.81;
Czdele = -0.4; %As Czdele = -Cldele
Cla = 5; %Changing value to 6 %Variable 3 to change Cza

%Defining stability derivatives


Xu = (-(Cdu+(2*Cdo))*Q*S)/(m*uo);
Xw = ((-(Cda-Clo))*Q*S)/(m*uo);
Xdele = 0;
Zu = (-(Clu+(2*Clo))*Q*S)/(m*uo);
Zw = ((-(Cla-Cdo))*Q*S)/(m*uo);
Zdele = (Q*S*Czdele)/m;
Mu = (Cmu*(Q*S*c))/(uo*Iy);
Mw = (Cma*(Q*S*c))/(uo*Iy);
Mwdot = Cmadot*(c/(2*uo))*((Q*S*c)/(uo*Iy));
Mq = Cmq*(c/(2*uo))*((Q*S*c)/Iy);
Mdele = (Q*S*c*Cmdele)/Iy;

A = [ Xu Xw 0 -g ; Zu Zw uo 0 ; Mu+(Mwdot*Zu) Mw+(Mwdot*Zw) Mq+(Mwdot*uo) 0 ;


0 0 1 0 ]
B = [ Xdele ; Zdele ; Mdele+(Mwdot*Zdele) ; 0 ]
C = [ 1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1 ];
D = 0;
sys = ss(A,B,C,D);
pzmap(sys)

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2.6.2 Pole-zero Graphs

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