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Since a horizontal wing generates lift in a vertical direction, a vertical wing (the propeller), if spinning, would generate thrust in a horizontal direction.
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When spinning, the sections of the propeller blade closer to the center move slower than those at the tips.
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A wing meets the air at an angle called the angle of attack. The slower the speed, the steeper the angle of attack must be to generate lift. Therefore, the shape of the propeller's airfoil (cross section) must change from the center to the tips.
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The changing shape of the airfoil (cross section) across the blade results in the twisting shape of the propeller.
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