Closed spline fit of airfoil coordinates

Hi, I'm working on airfoil coordinates and trying to fit the data point to a single closed curve but now i need some help to extract the coordinate of some point lying on the curve and but the result using fnval (the coordinates of the green point are named "pin") is clarly wrong. How could I fix it? Here's my code:

coord=load('S823.txt'); x=coord(:,1); y=coord(:,2);

xy = coord';

t=linspace(0,1,66); airfoil = csapi(t,coord'); figure(2) fnplt(airfoil) hold on plot(x,y,'r*') axis equal

s1=0.1; s2=fnval(airfoil,s1) pin=[s1,min(s2)] plot(pin(1),pin(2),'og')

The S823 file could be found in the NREL website:

http://wind.nrel.gov/airfoils/Shapes/S823_Shape.html

Thanks in advance!

Answer 1

[Unai San Miguel]

You are working with curves, not functions.

Your airfoil is a (planar) curve, or in the Splines toolbox wording a 2-valued, 1-variate spline function. This function is composed by two 1-valued, 1-variate functions which interpolate the pairs(t(i), x(i)) and (t(i), y(i)). With fnval(airfoil, s1) you are asking for the (x, y) coordinates for a value of t = 0.1.

You can see this if you plot the two components

airfoil_x = fncmb(airfoil, [1, 0]);
airfoil_y = fncmb(airfoil, [0, 1]);

figure(3)
clf
h1 = subplot(2,1,1);
fnplt(airfoil_y)
hold on
plot(t, y, 'o')
xlabel('t'), ylabel('y')
h2 = subplot(2,1,2);
fnplt(airfoil_x)
hold on
plot(t, x, 'o')
xlabel('t'), ylabel('x')

The point you asked for is found in these plots

errorbar(h1, s1, s2(2), s2(2) - h1.YLim(1), 0, 'k*')
errorbar(h2, s1, s2(1), s2(1) - h2.YLim(1), 0, 'k*')

And also in your original plot

figure(2)
plot(s2(1), s2(2), 'gsq', 'MarkerFaceColor', 'g')

If you want the point(s) over the airfoil at x = 0.1 you can do this:

1. Find the zero(s) of the x-coordinate of your function minus the desired x-value
2. Evaluate your funtion in those values of t

x0 = 0.1;
t0 = mean(fnzeros(fncmb(airfoil_x, '-', x0)), 1);
y0 = fnval(airfoil_y, t0);
airfoil_0 = fnval(airfoil, t0);

plot(h2, [0, 1], [x0, x0], 'g-')
errorbar(h2, t0, [x0, x0], [-5, -5], [5, 5], 'gsq', 'MarkerFaceColor', 'g')
h2.YLim = [0, 1];

h1.YLim = h1.YLim;
errorbar(h1, t0, y0, [-5, -5], [0, 0], 'gsq', 'MarkerFaceColor', 'g')