Organizing and double integrating a large function
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I am trying to build a function using nested functions rather than trying to write out the whole function (sure to make errors). Then I would like to integrate that function with respect to r and psi. How do I set this up so I can have visability to the functions inside while still being able to integrate it.
function [dH] = dHf(r,psi)
% set constants
rho = 1.225;
Xin = 0.3048;
Yin = 0;
R = 0.1524;
[Cl, Cd, Cm, Re_values] = nacaData('4412');
% Velocities at the hub
% p = roll rate, q = pitch rate, r = yaw rate
u = 0 ;v = 0;w = 0;p = 0;q = 0;yawr = 0;
% North Rotor
Vhubxn = u + Yin*yawr;
Vhubyn = v + Xin*yawr;
Vhubzn = w - Yin*p - Xin*q;
Omega = 1100;
lambda = 0.5;
% Define dH based on dFx
dFx = @Fx;
dH = (-1).*dFx(r,psi).*sin(psi);
% Define dFx based on phii, dL and dD
function [dFx] = Fx(r,psi)
dD = @dDr;
dL = @dLi;
phii = @phi;
dFx = dL(r,psi)*sin(phii(r,psi)) + dD(r,psi)*cos(phii(r,psi));
% define phii
function [Phi] = phi(r,psi)
UP = @up;
UT = @ut;
Phi = atan(UP(r,psi)/UT(r,psi));
function [upo] = up(r,psi)
upo = Omega*R* lambda + Vhubzn - ((-1).^0) * r * rho * sin(psi) - r*q*cos(psi);
end
function [uto] = ut(r,psi)
uto = Omega*r + Vhubxn*sin(psi) + ((-1).^0) * Vhubyn *cos(psi);
end
end
% Drag definition ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
function [D] = dDr(r,psi)
UP = @up;
UT = @ut;
c = @cb;
Cdr = @cDo;
D = 0.5*Cdr(r,psi)*rho*(UT(r,psi).^2+UP(r,psi).^2)*c(r);
function [CD] = cDo(r,psi)
alpha = @a;
Cda = Cd(95:201,3);
Cdaa = Cd(95:201,2);
Cdeq = polyfit(Cdaa,Cda,3);
CD = Cdeq(1,1)*((alpha(r,psi)).^3) + Cdeq(1,2)*((alpha(r,psi)).^2) + Cdeq(1,3)*(alpha(r,psi)) + Cdeq(1,4);
function [ao] = a(r,psi)
thetab = @theta;
phi = @phii;
ao = thetab(r) - phi(r,psi);
function [thetablade] = theta(r)
thetablade = -1.1896*r+0.375;
end
function [Phi] = phii(r,psi)
UP = @up;
UT = @ut;
Phi = atan(UP(r,psi)/UT(r,psi));
function [upo] = up(r,psi)
upo = Omega*R* lambda + Vhubzn - ((-1).^0) * r * rho * sin(psi) - r*q*cos(psi);
end
function [uto] = ut(r,psi)
uto = Omega*r + Vhubxn*sin(psi) + ((-1).^0) * Vhubyn *cos(psi);
end
end
end
end
function [upo] = up(r,psi)
upo = Omega*R* lambda + Vhubzn - ((-1).^0) * r * rho * sin(psi) - r*q*cos(psi);
end
function [uto] = ut(r,psi)
uto = Omega*r + Vhubxn*sin(psi) + ((-1).^0) * Vhubyn *cos(psi);
end
function [C] = cb(r)
C = -0.12467*r+0.031;
end
end
%~~ Lift ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
function [L] = dLi(r,psi)
UP = @up;
UT = @ut;
c = @cb;
Clo = @cLo;
L = 0.5*Clo(r,psi)*rho*(UT(r,psi).^2+UP(r,psi).^2)*c(r);
%~~~~~ Cl ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
function [CL] = cLo(r,psi)
alpha = @a;
Cla = Cl(95:201,3);
Claa = Cl(95:201,2);
Cleq = polyfit(Claa,Cla,3);
CL = Cleq(1,1)*((alpha(r,psi)).^3) + Cleq(1,2)*((alpha(r,psi)).^2) + Cleq(1,3)*(alpha(r,psi)) + Cleq(1,4);
function [ao] = a(r,psi)
thetab = @theta;
phi = @phii;
ao = thetab(r) - phi(r,psi);
function [thetablade] = theta(r)
thetablade = -1.1896*r+0.375;
end
function [Phi] = phii(r,psi)
UP = @up;
UT = @ut;
Phi = atan(UP(r,psi)/UT(r,psi));
function [upo] = up(r,psi)
upo = Omega*R* lambda + Vhubzn - ((-1).^0) * r * rho * sin(psi) - r*q*cos(psi);
end
function [uto] = ut(r,psi)
uto = Omega*r + Vhubxn*sin(psi) + ((-1).^0) * Vhubyn *cos(psi);
end
end
end
end
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
function [upo] = up(r,psi)
upo = Omega*R* lambda + Vhubzn - ((-1).^0) * r * rho * sin(psi) - r*q*cos(psi);
end
function [uto] = ut(r,psi)
uto = Omega*r + Vhubxn*sin(psi) + ((-1).^0) * Vhubyn *cos(psi);
end
function [C] = cb(r)
C = -0.12467*r+0.031;
end
end
end
end
3 Comments
Torsten
on 18 Oct 2022
If you like such a structure, use it. I don't.
integral2(@A, x1,x2,y1,y2)
function valueA = A(x,y)
valueA = B(x,y).*C(x,y)
end
function valueB = B(x,y)
valueB = y.*x;
end
function valueC = C(x,y)
valueC = x.*D(x,y);
end
function valueD = D(x,y)
valueD = y.*2x;
end
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