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I'd get rid of rho.TAS^2 and instead use rho_0.EAS^2 which is the same thing
So, W.Nz = 0.5 rho_0.EAS^2 S a.AoA
Which will give you AoA = (2.W.Nz)/(rho_0.EAS^2 . S .a)
So, you need:
W = aircraft weight, from operational plan and fuel state
Nz = normal acceleration, from INS, g-meter, etc.
EAS = equivalent airspeed, from FMS, or derived from IAS via CAS
S= wing area
a = lift curve slope, hopefully available from wind tunnel data for the whole aeroplane (DO NOT just use aerofoil data, because the tailplane and fuselage have a significant effect). You might be able to come up with an estimate of this, if you don't have wind tunnel data, using ESDU data sheets - but that can only be an approximation.
Obvious cautions to this:
- CL=a.AoA assumes that CL=0 when AoA=0, if it's more complex than that, which it may well be, you need to modify the formulae.
- It'll only work in steady state conditions (so Nz, EAS, bank, sHp are all constant for any given data point)
- It'll still be an approximation, and no substitute for flying an external air data sensor in clear air.
(Edited 18/5/11 because I realised I'd missed a Rho_0 out of the formulae)
It varies with Reynolds number (rho .TAS. L / mu), which is a function of density. But, the dependency is small.
My suggestion would be that you look at the variation in "a" with Reynolds number, over the range of tested conditions, and include that (along with IAS accuracy, altitude accuracy, Nz accuracy...) in a reasonably robust error analysis of the eventual derived AoA. Using multiple test points, you can then plot through well argued error bars.
Look at the paper here for one example of how to do the error analysis in a derived quantity. It's a bit labour intensive to derive, but then easily automated on a spreadsheet.
You might want to get an aeronautical engineer, better still a Flight Test Engineer to work with - this sort of data analysis is fraught with problems for somebody lacking the right professional skills and training.
thanks again. I have one more doubt related to matlab.
I have actually written a code which uses syms function.I want to use this code in simulink,but there seems to be a problem. Is there any alternative for syms function in simulink??.please help.... my code is: function [CL] = attack(m,h,v,s,alpha0) clc syms x; CL=zeros(300,1); AOA=zeros(300,1); ro=zeros(300,1); for i=1:300 ro(i)=1.225.*((1-(.0065.*h(i)./288.15)).^4.258644); AOA(i,1)=solve((0.5.*ro(i).*v(i).*v(i).*s.*.1.*(x-alpha0))-(m.*9.81.*cos(x.*pi./180))); AOA(i,1)=AOA(i,1).*1; end