I need a help 3. The figure shows the forces acting on an aircraft flying in ste

Question

I need a help

3. The figure shows the forces acting on an aircraft flying in steady flight (no acceleration) The steady flight (or trim) equations can be expressed in a coordinate system aligned with the flight path as F cos a W sin (3) T (4) (5) HLH NTT Note that hr is not shown in the figure, but it represents the vertical distance between the center of gravity (the origin of the coordinate and the thrust vector. In these equations, T e ust We aircraft weight D E aircraft drag Lw wing lift LH horizontal tail lift E ight-path angle a E aircraft angle of attack First, we must determine what is unknown. The unknown quantities depend on the problem to be solved, but a typical situation may be that the aircraft properties are known and a certain flight

Explanation / Answer

MATLAB fiunction to calculate the equation value is given below:

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function F_out = sys_fun(F_in)

T = F_in(1);
L_w = F_in(2);
L_h = F_in(3);
D = F_in(4);
alpha = F_in(5);

% for gamma = 0 , 10 deg, and -3 deg

gamma = 10*(pi/180) ;

W = 410000 ; % N
V = 250 ;    % m/s
rho = 0.228 ;% kg/m^3
C_d0 = 0.02 ;
a_w = 4.8 ;
S = 119 ;    % m^2
K = 1.08 ;
l_w = 0.25 ; % m
l_h = 15 ;   % m
h_t = 0.5 ; % m

f1 = T*cos(alpha)-W*sin(gamma)-D ;
f2 = -T*sin(alpha)+W*cos(gamma)-L_w-L_h ;
f3 = -l_w*L_w-l_h*L_h-h_t*T ;
f4 = L_w -(0.5*rho*(V^2)*a_w*alpha);
f5 = 0.5*rho*(V^2)*S*(C_d0+(K*(alpha^2)));

F_all = [f1;f2;f3;f4;f5] ;

F_out = max(F_all);

end

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To use this function in FSOLVE, script given below is useful.

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% solution script:
% sys_fun(T,L_w,L_h,D,alpha)

% use fsolve function to solve the system of non linear equations:
% To evaluate function at different value of gamma,
% please change the value of gamma from function sys_fun

clear all
clc

% inital guess
x_initial = [2000,1000,150,3000,0.05];

options = optimoptions('fsolve','Display','iter'); % Option to display output

[x,fval] = fsolve(@sys_fun,x_initial,options); % Call solver

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Have a Nice Day ...

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