so far I have an airfoil file, S823, which has following coordinates.
1.000000 0.000000
0.996260 0.000570
0.985390 0.002590
0.968200 0.006440
0.945590 0.012020
0.918230 0.018900
0.886490 0.026690
0.850640 0.035270
0.811260 0.044730
0.769210 0.054910
0.725320 0.065490
0.680480 0.075890
0.635300 0.085260
0.589910 0.092770
0.544140 0.097990
0.497850 0.100890
0.451090 0.101740
0.404250 0.100920
0.357860 0.098640
0.312450 0.095050
0.268520 0.090260
0.226560 0.084410
0.187020 0.077610
0.150340 0.070010
0.116930 0.061730
0.087140 0.052940
0.061300 0.043770
0.039710 0.034410
0.022590 0.025040
0.010170 0.015870
0.002610 0.007130
0.000000 0.000000
0.000020 -0.000570
0.003550 -0.007470
0.013320 -0.014500
0.028210 -0.021620
0.047970 -0.028480
0.072370 -0.034920
0.101170 -0.040770
0.134060 -0.045950
0.170710 -0.050360
0.210750 -0.053940
0.253750 -0.056640
0.299260 -0.058430
0.346770 -0.059270
0.395780 -0.059140
0.445720 -0.058010
0.496040 -0.055800
0.546170 -0.052370
0.595730 -0.047450
0.644760 -0.040840
0.693550 -0.033050
0.741760 -0.025080
0.788480 -0.017710
0.832770 -0.011380
0.873640 -0.006380
0.910130 -0.002830
0.941340 -0.000660
0.966490 0.000320
0.984930 0.000470
0.996200 0.000190
1.000000 0.000000
The coordinate starts from trailing edge to leading edge then back to trailing edge again.
Due to the fact that the x-coordinates are not the same as the points above and below the x-axis (there is no x=0.002610 when the coordinates moves back from leading to trailing edge). It is hard for me to just subtract the coordinates, straight away, to get my maximum thickness.
I am wondering if there is a way that I can smooth the airfoil coordinates and get the maximum thickness?
Yes, you normally want to use something like cubic B-splines to smooth the curves. Note that a B-spline won't normally go precisely through each point you specify. Along the top/bottom sides, the you typically have a large enough curve that it's little problem.
Near the leading edge, you frequently need to fill in some points for things to work well. Unfortunately in most cases (probably including this one, with only 62 points) it's hard to be at all sure where those points you're trying to fill in should go.
When I've had to do this, I've used xfoil to simulate the airfoil, and played with the LE until I got the drag bucket/LD/Cp curves to match (at least pretty closely) with those given for the design. Not always easy to do that though.