Use result of the for ith iteration of the for loop to compute the i+1 iteration

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Konstantinos Tsitsilonis
回答： Ameer Hamza 2018-5-1
Hi all,
I am using relatively complex equations in order to derive the values of the variables: a and a_prime. These variables are derived following an iterative approach, starting with a = a_prime = 0 , and going through the for loop to obtain better values.
I am having however difficulty with using the final result of the a and a_prime as derived at the end of each for loop, in order to re-run the for loop with that value. Below is the code:
% Input Data
R = 5 ; % m
V = 10 ; % m/s
B = 3 ; % blades
lambda = 6 ; % tip speed ratio
% Input Matrix
% r(m) g(deg) c(m)
M = [ 0.20 53.0 0.65 ; ...
0.15 74.3 0.76 ; ...
2.50 84.9 0.44 ; ...
3.75 89.1 0.30 ; ...
5.00 92.6 0.19 ] ;
% Variables
r = M(:,1) ;
gamma = M(:,2) ;
c = M(:,3) ;
% Calculations
Omega = lambda * V / R ; % rad/s
% First guesses
a = 0 ;
a_prime = 0 ;
% Iterations
for k = 1:2 %length(M)
% Local factors
sigma = B * c(k) / (2 * pi * r(k)) ; % Local solidity
lambda_r = Omega * r(k) / V ; % Local tip speed
beta = atan(lambda_r * (1 + a_prime) / (1 - a) ) ; %relative flow anlge onto the blades
i = gamma(k) - beta * 180/pi ; % angle of incidence
C_L = 0.327 + 0.1059 * i - 0.0013 * i^2 ; % lift coefficient
% New a and a'
a = 1 / (1 + (4 * cos(beta)^2 ) / (sigma * C_L * sin(beta) )) ;
a_prime = (sigma * C_L / 4 / lambda_r / cos(beta) ) * (1 - a) ;
end
Any help would be appreciated.
Kind Regards,
KMT.

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采纳的回答

Ameer Hamza
Ameer Hamza 2018-5-1
Instead of overwriting the variables, create an array. In the end, it will also help you to look at values of a and a_prime during each iteration.
a = zeros(1, length(M)+1) ;
a_prime = zeros(1, length(M)+1) ;
% Iterations
for k = 1:2 %length(M)
% Local factors
sigma = B * c(k) / (2 * pi * r(k)) ; % Local solidity
lambda_r = Omega * r(k) / V ; % Local tip speed
beta = atan(lambda_r * (1 + a_prime(k)) / (1 - a(k)) ) ; %relative flow anlge onto the blades
i = gamma(k) - beta * 180/pi ; % angle of incidence
C_L = 0.327 + 0.1059 * i - 0.0013 * i^2 ; % lift coefficient
% New a and a'
a(k+1) = 1 / (1 + (4 * cos(beta)^2 ) / (sigma * C_L * sin(beta) )) ;
a_prime(k+1) = (sigma * C_L / 4 / lambda_r / cos(beta) ) * (1 - a(k)) ;
end

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