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It is said that when the preceding airplane is heavy, clean, and slow, wake turbulence is much hazardous due to greater angle of attack is requried. However, why does increasing angle of attack result in increase in wake turbulence? (or wing tip vortices)

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It is not the angle of attack - downwash intensity grows with lift squared and inversely to the squares of wingspan and speed. Please read this answer on how wake turbulence forms. Now let's look at the parameters you listed:

  • Heavy: Yes, the heavier the aircraft, the more lift needs to be created. Induced drag grows with the square of lift.
  • Clean: Not really. With or without flaps the amount of lift is the same. Only the lift distribution over span might be different, but this does not make much of a difference for the wake.
  • Slow: Absolutely! Induced drag is proportional to the inverse of speed squared.

What is missing from the list is wing span which lets induced drag grow with the inverse of its square. The angle of attack is only indirectly responsible for induced drag because lift is (within limits) proportional to the angle of attack.

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Wake turbulence is proportional to lift, and lift increases as you increase the angle of attack. Assuming an identical weight and configuration, an airplane on approach will produce less wake turbulence than one in the flare for landing, and an airplane on its takeoff roll will produce less turbulence than one which has rotated.

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