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How does one determine the optimal cross sectional geometry to maximize Cl/Cd?

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  • $\begingroup$ Basically I want to be able to know (or at least get a general idea for) the best airfoil geometry for a given airspeed to get the right lift with the smallest drag $\endgroup$ – Daniel Caoili Nov 26 '16 at 22:23
  • $\begingroup$ Are there any equations that can relate these? $\endgroup$ – Daniel Caoili Nov 26 '16 at 22:33
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The optimum airfoil is a cambered line of zero thickness. If operated at just the correct angle of attack, it will produce the highest L/D possible. It's cross section is trivial: It has none. However, it will not allow to build a clean wing since it has no space for a spar. It would need to be kept in shape by lots of wire bracing, and then the overall L/D of the resulting aircraft would be horrible.

Next, if the angle of attack is only slightly different from the optimum value, the sharp leading edge will cause early separation on one side, causing the L/D figure to plummet. This airfoil will not be practical for any purpose other than establishing a theoretical optimum figure.

Real airfoils need a blunt nose and some thickness. There are plenty enough airfoils to choose from already. All of them were designed not just for one single design point, but as an overall compromise to cover a wider range of parameters in real-world operation.

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  • $\begingroup$ I suppose this optimum airfoil should have the most camber possible that maintains laminar flow over the surface. $\endgroup$ – Daniel Caoili Nov 28 '16 at 12:41
  • $\begingroup$ @DanielCaoili: Depends on the Reynolds number. Most likely it will be laminar for 30% - 70% on the upper and 100% on the lower side. The turbulent transition is needed to achieve a steeper pressure recovery - with laminar flow alone you simply cannot get much lift out of the airfoil. $\endgroup$ – Peter Kämpf Nov 28 '16 at 12:43

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