MATLAB: Error using integral (line 85) A and B must be floating point scalars. Error in hawt3 (line 30) Torque(i)= integral(fun,’r’,a1,b1);

' fun = @(r)(sigmaprime*pi*rho*((vwind^2)*(1-a)^2/cos(bladeangle)^2)*(cl*cos(bladeangle)-cd*sin(bladeangle))*r^2) '

code:
close all
clear all
Vwind=10;
BladeRadius=40;
% aoa=5 deg
TSR=[2 3 4 5 6 7 8 9];
Numblades=3;
n= length(TSR);
Power= zeros(1,n);
rpm= zeros(1,n);
Torque= zeros(1,n);
Vtip=TSR.*Vwind;
for i=1:n
      Vr= @(r)Vtip(i)*(r/BladeRadius);
      BladeAngle =@(r) pi/2-2/3*atan(Vwind/Vr);
      BladeChord =@(r) 8*pi*r*Vwind*cos(BladeAngle)/(3*Vr*Numblades);
sigmaprime=@(r) Numblades*BladeChord/(2*pi*r);
rho=1.23;
Cl=1.125;
Cd=0.03;
a1 =0.001;
b1= 40.00;
a=@(r)(1+4*cos(BladeAngle)^2/(sigmaprime*Cl*sin(BladeAngle)))^(-1);
syms r
fun = @(r)(sigmaprime*pi*rho*((Vwind^2)*(1-a)^2/cos(BladeAngle)^2)*(Cl*cos(BladeAngle)-Cd*sin(BladeAngle))*r^2);
Torque(i)= integral(fun,'r',a1,b1);
rpm(i)=Vtip(i)/BladeRadius;
Power(i)=rpm(i)*Torque(i);   
end

Best Answer

close all
clear all
Vwind=10;
BladeRadius=40;
% aoa=5 deg
TSR=[2 3 4 5 6 7 8 9];
Numblades=3;
n= length(TSR);
Power= zeros(1,n);
rpm= zeros(1,n);
Torque= zeros(1,n);
Vtip=TSR*Vwind;
for i=1:n
  Vr= @(r)Vtip(i)*(r/BladeRadius);
  BladeAngle =@(r) pi/2-2/3*atan(Vwind./Vr(r));
  BladeChord =@(r) 8*pi.*r.*Vwind.*cos(BladeAngle(r))./(3*Vr(r)*Numblades);
  sigmaprime=@(r) Numblades*BladeChord(r)./(2*pi*r);
  rho=1.23;
  Cl=1.125;
  Cd=0.03;
  a1 =0.001;
  b1= 40.00;
  a=@(r)(1+4*cos(BladeAngle(r)).^2./(sigmaprime(r).*Cl.*sin(BladeAngle(r)))).^(-1);
    fun = @(r)(sigmaprime(r).*pi.*rho.*((Vwind.^2).*(1-a(r)).^2./cos(BladeAngle(r)).^2).*(Cl.*cos(BladeAngle(r))-Cd.*sin(BladeAngle(r))).*r.^2);
    Torque(i)= integral(fun,a1,b1);
    rpm(i)=Vtip(i)/BladeRadius;
    Power(i)=rpm(i)*Torque(i);   
  end
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