How to use the Sum function in this instance

Hello, Ive been writing code for one of my modules and came across a formula that I dont understand how to put it in matlab, it is this equation below:

My problem is that I dont understand how to use the sum function in this instance

[John D'Errico]

Is x known? Is z known? Is Ar known? What are they? Are they variables, constants? Symbolic? What?

Is the sum taken as 5:1:85? I find it strange that the sum does not go all the way down to 0 or up to 90, since this is clearly an angle, represented in degrees.

It is easer to help you if you tell us enough to know what form are the variables in that expression.

[Ahmed Alzaabi]

Ah Sorry about that Ill post those values:

%A symmetric Trim Calculator for Subsonic Flight Conditions
% Aircraft Flight Conditions (Make sure to check if unit change is needed
% for ft to meter and degrees to radians
Alt = 0; %Altitude (ft)
A_Mass = 0; %Aircraft Mass (kg)
cg_p = 0; % cg Position (%c)
Flight_path_angle = 0; % Flight Path angle in Degrees 
G0 = 9.81; %Gravity Constant

%Air Density calculation - Valid for tropospwhere only up to 36,000ft
R = 287.05 % Gas Constant
L_R = -0.0065; %Lapse rate
Temp = 288.16 + (L_R * Alt); %Temperature
rho = 1.225 * ((Temp)/288.16)^(-((G0)/(L_R * R)+1))
sigma = rho/1.225 %Density ratio
 %Setting up the Velocity Range for Computations
 %Setting the counter i from 0 - 10
 counter = 0:10
 %Setting up the array to save result for wach itteration
 results = zeros(1, length(counter));
 %Loop Itteration
 for i = 1:length(counter)
     results(i) = 100 + (15*i); %Outputs the True airspeed range in Knots
 end
V_TAS = results .*0.515;
Eq_airspeed = results .*sqrt(sigma);
%Aircraft Geometry Constant
%Wing Geometry
% Aircraft Geometry- Constants
S = 0; % Wing Area m^2
b = 0; % Wing Span
cw = 0; % Wing mean chord
sweep = 0; %Sweep 1/4cw
zw = 0; % Z coordinate of 1/4wc point above (-ve) or below (+ve) ox body axis (m)
alpha_wr = 0; % Wing Rigging
%Tailplane Geometry
St = 0; % Tailplane area
bt = 0; % Tailplane span
It = 0; % Tail arm, 1/4cw to 1/4ct
Zt = 0; % Z coordinate of 1/4wc point above (-ve) or below (+ve) ox body axis (m)
nt = 0; %Tail setting angle
Fd = 0; % Fuselage Diameter
%Engine Installation
zt = 0; %Thrust line z coorrdinate  above (-ve) or below (+ve) ox body axis (m)
k = 0; %Engine thrust line angle relative to ox body axis (+nose up)
Wing-body aerodyanmics
a = 0; %Wing-body CL - alpha (per rad)
CL_max = 0; % Maximum Lift Coefficient
Cm_0 = 0; % Zero lift pitching moment
CD_0 = 0; % Zero lift drag coefficient
AOA_0 = 0; %Zero lift angle of attack 
h_0 = 0; %Wing-body aero centre
%Tailplane aerodynamics
a1 = 0;% TailplaneCL-α (per rad)
a2 = 0;% ElevatorCL-η (per rad)
e0 = 0;%Zero lift downwash angle(deg)
%Wing and Tailplane Calculations
Ar = (b^2)/(S); % Aspect ratio
wing_semi = b/2 ; % Wing Semi Span
Tail_arm = It - cw *(cg_p - 0.25) ; % Tail arm, cg to 1/4ct
V_T = ((St *Tail_arm)/(S*cw)); % Tail Volume

[Torsten]

Are you sure you included the correct code ?

And you didn't tell us about x and z.

So far I can see that if a = 0 as in your code, d_eps_alpha will also be 0.

[Ahmed Alzaabi]

I didn't put the values in yet that's why all of the variables are 0. All of the values are scalar meaning they will hold 1 value only, that's why initially I didn't put my code as I have all of the values of the variable shown in the equation above. I just need help setting that equation in terms of matlab code.

Answer 1

[Image Analyst]

Take it one term at a time, like

fi = 5 : 85;
term1 = 0.5 * cosd(fi) .^ 2
term2 = whatever
numerator = whatever
denominator = whatever
d = scalingFactor * sum(numerator ./ denominator);

I know you can do it. I have confidence in you.

Answer 2

[Matt J]

Assuming all your variables (x,z,Ar, etc...) are scalars, then,

fi=5:85;

q1=0.5*cosd(fi).^2;
q2=q1+z^2;
q3=sqrt(x^2+q2);

d=(a/pi^2/Ar)*sum(  (q1./q3).*(  (x+q3)./q2 +x./(x^2+z^2)  )  ) * pi/180

[Paul]

Missing "a" out front?

[Matt J]

Yep. Fixed it.