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From what I know, usually NACA9/12 or similar symmetrical airfoils are used for the tail.

Still some aircrafts use highly cambered airfoils for elevators.

What are some advantages and disadvantages of this configuration?

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It's done to get a little more lift coefficient, and hence more tail downforce power, at low speeds and there is a drag penalty to take depending on how much camber. The Zenith STOL family are the extreme example, and being draggy flying lunchboxes anyway, the penalty is minor in relation to the benefit and allows a smaller, lighter tail unit than would be needed otherwise.

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Some high performance and transport aircraft have cambered airfoils for the tail but the amount of camber is subtle (a bit more curvature on bottom than top) and you can only tell if you can see the actual airfoil profile, or examine the surface up close.

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For the same reasons as camber is used is the main wing: to extend the maximum lift coefficient and the stall angle of attack. The following figure is from Abbott & Von Doenhoff, and shows the pressure distributions over both a cambered and an un-cambered wing profile: higher pressure differential = more lift.

enter image description here

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