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METODO DE LOS VORTICES DISCRETOS
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DESARROLLO DEL PERFIL AERODINAMICO POR EL METODO DE VORTICES DISCRETOS Ajustando la línea media (
) por mínimos cuadrados
Como ya se vio en los trabajos anteriores la curva de la línea media se ajusta a una ecuación polinomial cubica. Lo que haremos ahora es determinar determinar los coeficientes de dicha ecuación por el método de mínimos cuadrados para un polinomio. La ecuación inicial es:
Determinamos los coeficientes por mínimos cuadrados, suma de los cu adrados de los residuos
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Para desarrollar el método método de vórtices discretos primero planteamos una cantidad (en nuestro caso 1000) de hilos vorticosos a lo largo de la cuerda δ
1
PR1
δ2
PR2 …………………
Luego nos apoyamos de las formulas deducidas en clase para poder encontrar Cl:
Se calculó el coeficiente de sustentación (Cl) por el método de vórtices vórtices discretos apoyándonos de Matlab.
Los cálculos se hicieron para un ángulo de 25°.
Si comparamos este coeficiente con el que se obtuvo con el método de perfiles delgados
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ANEXO
1. CODIFICACION PARA LA MATRIZ
A = zeros(1000); b = 0; for i for i = 1:1000 for j for j = 1:1000 b =(1/(0.5+(j-i))); A(i,j)= b; end end A
2. CODIFICACION PARA LA MATRIZ
* + ,-
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CODIFICACION FINAL (CALCULO DE
*+
) )
dlm='0.1162351-0.002214*x-17.4*(10^(-7))*(x^2)' dlm='0.1162351-0.002214*x-17.4*(10^(-7))*(x^2)'; ; h=100; n=input('Ingrese n=input('Ingrese el número ded puntos: '); '); alpha=25*pi/180; for i=1:n for i=1:n Xi(i)=((1+4*(i-1))*h)/(4*n); Xj(i)=((3+4*(i-1))*h)/(4*n); i=i+1; end %Construyendo la matriz A; for i=1:n for i=1:n for j=1:n for j=1:n A(j,i)=1/(0.5+(j-i)); j=j+1; end i=i+1; end % hallando el Bi for i=1:n for i=1:n x=Xj(i); Bi(i)=eval(dlm); i=i+1; end A=inv(A); %hallando la matriz fc for i=1:n for i=1:n fc(i,1)=2*pi*(sin(alpha)-Bi(i));