Help with iteration convergence.

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Terry Poole
Terry Poole on 16 Apr 2021
Commented: Terry Poole on 22 Apr 2021
So I have a system of equations that I need to iterate until convergence.
I've tried doing this with for loops, while loops, symbolicly, and lastly using approximation methods.
Maybe convergence doesnt mean what I think it means, maybe I'm just missing something.
Here is my code...
clear all; close all; clc;
%% Given Data.
T = 20000; % lb
rho = .002377; %slug/ft^3
A = 2827; % ft^3
v_tip = 650; % ft/sec
R = 30; %ft
a = 6; % Lift Curve Slope
Theta_Tw = -10*pi/180; % Radians Twist Rate
gamma = 8.1; % Blade Lock
Cd0 = 0.01;
Sigma = 0.085;
k = 1.15;
mu = linspace(0.05,0.3,26); % Advance Ratio
i_hp = [-10; 0; 10]*(pi/180); % Radians
phi_hp = 0; % Lateral Shaft Tilt
beta1C = 0;
beta1S = 0;
%% Derived Data.
Omega = v_tip/R; % Rad/sec
% Thrust Coefficient of Main Rotor During Trimming Process
CT = T/(rho*A*v_tip^2);
% Constant for Flapping Equations
delta = 1-mu.^2+9*mu.^4/4;
% Initial Conditons
lambda_i_initial = [sqrt(CT/2), CT./(2*mu(2:end))];
% Convergence Equations
lambda = mu.*tan(i_hp)+lambda_i(1,:);
lambda_i = CT./(2*(mu.^2+lambda.^2));
I need to take the initial solution for lambda_i and insert that into the equation for lambda, and then take the lambda solution and insert it into lambda_i, then lambda_i into lambda and so on until convergence.
Any help would be appreciated.
  4 Comments
Mathieu NOE
Mathieu NOE on 22 Apr 2021
Ok , so problem solved ?
Terry Poole
Terry Poole on 22 Apr 2021
Yes sir, turns out I knew what to do. I’m just bad at working a problem for hours at a time and I get mentally fatigued and then I just can’t think straight anymore.

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