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The purpose of trailing edge flaps is to give the aircraft more lift at lower speeds.

But do simple flaps beneficent more than increasing the angle of attack?

enter image description here

The image looks like part of the wing just had it's angle of attack increased, and the other part did not.

Also considering flaps lower a wings critical angle of attack, and increasing the lift coefficient are they really just another way of changing the angle of attack?

If so why do smaller planes use them instead of setting up the landing gear to takeoff/land with greater angles of attack?

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    $\begingroup$ Not my area of expertise, but I think it doesn't really affect AoA so much. Instead the flaps (simple or complex) increase the curvature of the profile, and sometimes area, thus increasing lift. $\endgroup$ – Sami Jul 22 '18 at 10:12
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The ultimate goal is to reduce the landing speed and takeoff run. Not to get the higher angle of attack. The speed without flaps would not be low enough even at higher critical AoA. The key is to generate the most lift as possible, with all means available.

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