Iterations until condition is met

clear all; clc
ER = 50;
gamma = 1.4;
for M=1:0.01:10
    if (1/M) * ((2/(gamma+1))*(1+((gamma-1)/2)*(M^2)))^((gamma+1)/(2*gamma-2)) == ER
        mach = M
        break
    end
end

I am trying to iterate M from 1 to 10 in intervals of 0.01 until the equation value matches my value for ER. Can you please help me figure out where I went wrong?

Answer 1

[Torsten]

ER = 50;
gamma = 1.4;
M = 1:0.00001:10;
expr = (1./M) .* ((2/(gamma+1))*(1+((gamma-1)/2)*(M.^2))).^((gamma+1)./(2*gamma-2)) - ER;
[error,index] = min(abs(expr))

error = 1.6950e-04

index = 491378

Mstar = M(index)

Mstar = 5.9138

[aregr8]

Thank you very much for your help.

Answer 2

[the cyclist]

It is because of the accuracy of floating-point operations.

Instead of checking

if (1/M) * ((2/(gamma+1))*(1+((gamma-1)/2)*(M^2)))^((gamma+1)/(2*gamma-2)) == ER

you could do something like

tol = 1.e-6; % Choose a suitable tolerance here
if abs(((1/M) * ((2/(gamma+1))*(1+((gamma-1)/2)*(M^2)))^((gamma+1)/(2*gamma-2))) - ER) < tol

Probably even better would be to use a while loop instead of a for loop, which is the more natural construct for looping until a condition no longer holds. (But you may still need to be careful about floating point precision.)

[aregr8]

Thank you very much for your help.