MATLAB: How do i rotate an airfoil points? and plot.

airfoilnacawindturbine

How do I rotate an airfoil points? I have all the new chord lengths and the angles in which are needed to rotate. I need to plot all these airfoils 16 times together in respect to their new angle and chord length. I know I need a sort of for loop but evetrytime I plot, the figure is funky looking.

HELP ME PLEASE!!!

NEW Chord lengths and twist angle, R vaules

Chord length= [ 0 0.0082328 0.0164657 0.0246985 0.0329313 0.0411642 0.049397 0.0576298 0.0658626 0.07409548 0.08232831 0.09056114 0.09879397 0.1070268 0.11525963 0.12349246 ]

r =[ 0 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.3 0.33 0.36 0.39 0.42 0.45]

twist = [1.0471976 0.7561128 0.5465782 0.4134997 0.3278728 0.2699279 0.2286826 0.1980428 0.1744757 0.15582879 0.14072889 0.12826373 0.1178059 0.10891077 0.10125497 0.09459804]

BELOW

THIS IS THE CODE I STATRED WITH FOR NACA

THE PLOT SHOULD LOOK SOMETHING LIKE THIS BELOW


c1= 1;
%c1= [0,0.008232831,0.016465661,0.024698492,0.032931323,0.041164153,0.049396984,0.057629815,0.065862645,0.074095476,0.082328307,0.090561137,0.098793968,0.107026798,0.115259629,0.12349246];
angle =[1.047197551	0.756112778	0.546578176	0.413499657	0.327872784	0.269927858	0.228682627	0.198042808	0.174475668	0.155828787	0.140728889	0.128263734	0.117805904	0.108910765	0.101254972	0.094598036];
s=num2str(5410);
%4 digits
NACA=s; 
% m represents first digit out of the scalar
m =str2double(s(1))/100; 
%p pulls the second digit out of the scalar
p=str2double(s(2))/10;
%t pulls and represents the third and fourth digit out of the scalar
t=str2double(s(3:4))/100; 
% define x
r=linspace(0, c1, 250);
 %yt fuction including the coeffiencients 
 
yt =5*t*c1*(.2969*(sqrt(r/c1))+-.1260*(r/c1)+-.3516*(r/c1).^2+.2843*(r/c1).^3+-.1015*(r/c1).^4);
%yt2 =5*t*c2*(.2969*(sqrt(x/c2))+-.1260*(x/c2)+-.3516*(x/c2).^2+.2843*(x/c2).^3+-.1015*(x/c2).^4);
for k = 1:length(r)
      if r(k) <= p*c1
          yc(k)=m*(r(k)/p^2)*(2*p-(r(k)/c1));
          dx(k)=(2*m)/p^2*(p-(r(k)/c1));
      elseif r(k) > p*c1
          yc(k)=m*((c1-r(k))/(1-p)^2)*(1+(r(k)/c1)-(2*p));
          dx(k)=((2*m)/(1-p)^2)*(p-(r(k)/c1));
      end
      %upper and lower limits of the airfoil (xu,yu) ; (xl,yl)
      angle=atan(dx(k));
      xu(k)=r(k)-yt(k)*-sin(angle);
      yu(k)=yc(k)+yt(k)*cos(angle);
      xl(k)=r(k)+yt(k)*sin(angle);
      yl(k)=yc(k)-yt(k)*cos(angle);
end
  %plot of airfoil
  plot(xu,yu,xlabel('x'),ylabel('y'));
  title( ['NACA Airfoil ', NACA]);
  hold on
  plot(xl,yl,'r')
  plot(r,yc,'g')
  grid on
  axis equal
%--------------------------------------------------------------------------------------%  
  % Given data vectors X and Y.  
% Want to rotate the data  through angle "ang" about rotation center Xc, Yc
X = [xl,xu];
Y = [yl,yu];
ang = [254]; %	0.756112778	0.546578176	0.413499657	0.327872784	0.269927858	0.228682627	0.198042808	0.174475668	0.155828787	0.140728889	0.128263734	0.117805904	0.108910765	0.101254972	0.094598036];
% Specify the coordinates of the center of rotation
Xc = 0.25 ;  % Rotate about the 1/4 chord point
Yc = 0 ;
% The data is roated in a three-step process
% Step 1) Shift the data to the rotation center
Xs = X - Xc;  % shifted data
Ys = Y - Yc;
% Step 2) Rotate the data
Xsr =  Xs.*cos(ang) + Ys.*sin(ang);    % shifted and rotated data
Ysr = -Xs*sin(ang) + Ys*cos(ang);    %
% Step 3) Un-shift the data (back to the original coordinate system)
Xr = Xsr + Xc;  % Rotated data
Yr = Ysr + Yc;
hold on

Best Answer

Does this look better?

Some (small) changes to your code. I swapped your rotation direction to better follow your example plot. Probably not a good idea to call a variable angle.

c1= 1;
%c1= [0,0.008232831,0.016465661,0.024698492,0.032931323,0.041164153,0.049396984,0.057629815,0.065862645,0.074095476,0.082328307,0.090561137,0.098793968,0.107026798,0.115259629,0.12349246];
s=num2str(5410);
%4 digits
NACA=s; 
% m represents first digit out of the scalar
m =str2double(s(1))/100; 
%p pulls the second digit out of the scalar
p=str2double(s(2))/10;
%t pulls and represents the third and fourth digit out of the scalar
t=str2double(s(3:4))/100; 
% define x
r=linspace(0, c1, 250);
 %yt fuction including the coeffiencients 
 
yt =5*t*c1*(.2969*(sqrt(r/c1))+-.1260*(r/c1)+-.3516*(r/c1).^2+.2843*(r/c1).^3+-.1015*(r/c1).^4);
%yt2 =5*t*c2*(.2969*(sqrt(x/c2))+-.1260*(x/c2)+-.3516*(x/c2).^2+.2843*(x/c2).^3+-.1015*(x/c2).^4);
for k = 1:length(r)
      if r(k) <= p*c1
          yc(k)=m*(r(k)/p^2)*(2*p-(r(k)/c1));
          dx(k)=(2*m)/p^2*(p-(r(k)/c1));
      elseif r(k) > p*c1
          yc(k)=m*((c1-r(k))/(1-p)^2)*(1+(r(k)/c1)-(2*p));
          dx(k)=((2*m)/(1-p)^2)*(p-(r(k)/c1));
      end
      %upper and lower limits of the airfoil (xu,yu) ; (xl,yl)
      angle=atan(dx(k));
      xu(k)=r(k)-yt(k)*-sin(angle);
      yu(k)=yc(k)+yt(k)*cos(angle);
      xl(k)=r(k)+yt(k)*sin(angle);
      yl(k)=yc(k)-yt(k)*cos(angle);
end
%% plot of airfoil
clf; 
plot(xu,yu,xl,yl,r,yc); 
xlabel('x'),ylabel('y')
title( ['NACA Airfoil ', NACA]);
 
grid on; axis equal
%% --------------------------------------------------------------------------------------%  
  % Given data vectors X and Y.  
% Want to rotate the data  through angle "ang" about rotation center Xc, Yc
X = [xl,fliplr(xu)]; % watch this 
Y = [yl,fliplr(yu)];
% Specify the coordinates of the center of rotation
Xc = 0.25 ;  % Rotate about the 1/4 chord point
Yc = 0 ;
% The data is roated in a three-step process
% Step 1) Shift the data to the rotation center
Xs = X - Xc;  % shifted data
Ys = Y - Yc;
% Step 2) Rotate the data
angles =[1.047197551	0.756112778	0.546578176	0.413499657	0.327872784	... 
        0.269927858	0.228682627	0.198042808	0.174475668	0.155828787	0.140728889	...
        0.128263734	0.117805904	0.108910765	0.101254972	0.094598036];
hold on
for i=1:length(angles) 
  ang = -angles(i); % in radians ?? 
  Xsr =  Xs.*cos(ang) + Ys.*sin(ang);    % shifted and rotated data
  Ysr = -Xs*sin(ang) + Ys*cos(ang);    %
% Step 3) Un-shift the data (back to the original coordinate system)
  Xr = Xsr + Xc;  % Rotated data
  Yr = Ysr + Yc;
  plot(Xr, Yr)
end % for 
hold off

Related Solutions

MATLAB: Need help with 4 digit airfoil

You have an end in the wrong place, and you need to subscript some of your variables.

Correct those, and then it works:

c=1; %chord length
s=num2str(2412);
NACA=s; %4 digits
d1=str2double(s(1)); % pulls the first digit out of the scalar
d2=str2double(s(2));% pulls the second digit out of the scalar
d34=str2double(s(3:4)); % pulls the third and fourth digit out of the scalar
m=d1/100;
p=d2/10;
t=d34/100;
x=linspace(0, c, 250);
yt =5*t*c*(.2969*(sqrt(x/c))+-.1260*(x/c)+-.3516*(x/c).^2+.2843*(x/c).^3+-.1015*(x/c).^4);
for k = 1:length(x)
      if x(k) <= p*c
          yc(k)=m*(x(k)/p^2)*(2*p-(x(k)/c));
          dx(k)=(2*m)/p^2*(p-(x(k)/c));
      elseif x(k) > p*c
          yc(k)=m*((c-x(k))/(1-p)^2)*(1+(x(k)/c)-(2*p));
          dx(k)=((2*m)/(1-p)^2)*(p-(x(k)/c));
      end
      %upper and lower limits of the airfoil (xu,yu) ; (xl,yl)
      theta=atan(dx(k));
      xu(k)=x(k)-yt(k)*sin(theta);
      yu(k)=yc(k)+yt(k)*cos(theta);
      xl(k)=x(k)+yt(k)*sin(theta);
      yl(k)=yc(k)-yt(k)*cos(theta);
  end
  %plot of airfoil
  plot(xu,yu)
  hold on
  plot(xl,yl,'r')
  plot(x,yc,'g')
  axis equal

MATLAB: Surface between plot3 plots at different points along an axis

This is possible. I did it a while back with this code:

c=1; %chord length
s=num2str(2412);
NACA=s; %4 digits
d1=str2double(s(1)); % pulls the first digit out of the scalar
d2=str2double(s(2));% pulls the second digit out of the scalar
d34=str2double(s(3:4)); % pulls the third and fourth digit out of the scalar
m=d1/100;
p=d2/10;
t=d34/100;
x=linspace(0, c, 250);
yt =5*t*c*(.2969*(sqrt(x/c))+-.1260*(x/c)+-.3516*(x/c).^2+.2843*(x/c).^3+-.1015*(x/c).^4);
for k = 1:length(x)
      if x(k) <= p*c
          yc(k)=m*(x(k)/p^2)*(2*p-(x(k)/c));
          dx(k)=(2*m)/p^2*(p-(x(k)/c));
      elseif x(k) > p*c
          yc(k)=m*((c-x(k))/(1-p)^2)*(1+(x(k)/c)-(2*p));
          dx(k)=((2*m)/(1-p)^2)*(p-(x(k)/c));
      end
      %upper and lower limits of the airfoil (xu,yu) ; (xl,yl)
      theta=atan(dx(k));
      xu(k)=x(k)-yt(k)*sin(theta);
      yu(k)=yc(k)+yt(k)*cos(theta);
      xl(k)=x(k)+yt(k)*sin(theta);
      yl(k)=yc(k)-yt(k)*cos(theta);
  end
  %plot of airfoil
  plot(xu,yu)
  hold on
  plot(xl,yl,'r')
  plot(x,yc,'g')
  axis equal
  grid
figure(2)
hu = mesh([xu; xu], [yu; yu], [zeros(size(xu)); ones(size(xu))]);     % Upper Half Of 3-D Wing Section
hold on
hl = mesh([xl; xl], [yl; yl], [zeros(size(xl)); ones(size(xl))]);     % Lower Half Of 3-D Wing Section
hold off
grid on
axis([0  1    -0.4  0.4    0  1])
rotate(hu,[1 0 0], 90)
rotate(hl,[1 0 0], 90)
title('NACA 2412 Airfoil')

The code takes the idea for the cylinder function (not the cylinder function itself) and simply uses a different contour. I used a constant contour here since that was the request. It first plots the airfoil as vertical, then rotates the axes to present it horizontally. It should not be difficult to change the cross section of the airfoil with increasing height. For hints on how to do it, experiment with the cylinder function with a varying radius to see how that works. That’s what I did to arrive at this code. Then plot it with the surf function. You will have to experiment with it to get the result you want.

Best Answer

Related Solutions

MATLAB: Need help with 4 digit airfoil

MATLAB: Surface between plot3 plots at different points along an axis

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