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I have been looking at the lift/drag polars for various airfoil profiles. The L/D ratio seems to improve at higher Reynolds numbers. Obviously different wings are optimized for different speeds, and there are many other factor to consider, but in general terms do wings get more efficient at higher speeds?

I believe a 747 is more efficient than a model airplane because of the higher Reynolds number it operates at. Is this correct?

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Yes, the boundary layer that surrounds the airfoil is known to decrease its thickness as the Reynolds number increases; its relative thickness to the characteristic length (the cord for example) scales as $Re^{-1/2}$ in steady flow, and the polar curve becomes more horizontal when Re increases. Meanwhile, lift coefficient increases just a little bit (check this post).

In result, lift-to-drag ratio increases with Re.

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An intuitive way to look at it, is that an increase in Reynolds number can be interpreted as a decrease in viscosity taking all other components constant.

$\mathrm{Re} = \frac{\rho u L}{\mu} = \frac{u L}{\nu}$

One can intuitively feel that an object moving through a less vicious fluid will experience less drag. While the lift induced by momentum change in the fluid remains similar (constant $u$ and $\rho$).

It should be noted that at higher Reynolds numbers, the eddy viscosity will increase the perceived viscosity due to turbulence. And at higher Mach numbers you'll experience drag due to compressibility.

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