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How I understand a flat (rudder-only) turn:

  1. AOA between relative wind and the fuselage of the airplane causes a sideslip in the direction of yaw.
  2. Vertical stabilizer weathervanes into the relative wind to cause a turn.

Credit: Pilot Effect (YouTube)

The only difference I see between a coordinated turn and flat turn is that the horizontal lift component comes from the wing in a coordinated turn but from the fuselage "airfoil" in a flat turn.

Why is the flat turn less efficient, if both methods of turning work the same in principle?

Picture credit: Pilot Effect (YouTube)

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    $\begingroup$ FWIW, there's a teensy bit of an edge case known to glider pilots: because of the tendency for a plane to fall deeper into a steep turn, thus requiring opposite aileron to stabilize, a slight slip winds up being marginally more efficient than a purely coordinated turn. $\endgroup$
    – Kenn Sebesta
    Commented Oct 14, 2023 at 12:03
  • $\begingroup$ Who said it was less efifcient? $\endgroup$
    – copper.hat
    Commented Oct 15, 2023 at 21:42
  • $\begingroup$ This answered question details turning with rudder only as inefficient (higher drag): aviation.stackexchange.com/questions/55597/… $\endgroup$
    – astroball
    Commented Oct 16, 2023 at 20:23
  • $\begingroup$ "The only difference I see between a coordinated turn and flat turn is that the horizontal lift component comes from the wing in a coordinated turn but from the fuselage "airfoil" in a flat turn." -- exactly. The purpose of a wing is to generate force efficiently, i.e. with a minimum of drag. You are confused about why a wing does a better job of simulating a wing than a fuselage does? You have no doubt noticed that they are shaped a little differently, right? $\endgroup$
    – quiet flyer
    Commented Oct 17, 2023 at 14:22

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I don't believe Chris's answer is incorrect, however I'd like to pose an alternate way of explaining what happens:

As you have noted, turning requires a horizontal force perpendicular to velocity, and this can come either from the wing or the side of the fuselage. Although the wing's lift must be increased to provide a horizontal component of lift without reducing the vertical component (since that would make the plane descend), the lift-to-drag ratio generally will remain high. The body has a much lesser L/D since it is not designed to be a lifting surface.

Thus much greater turning force can be generated for the same drag when using the wing.

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  • $\begingroup$ Thanks, that was my hypothesis, and now I can see how both answers are true. Fuselage requires a high AOA for a small amount of horizontal lift, and resulting AOA in the slip doesn’t change much, increasing induced drag. $\endgroup$
    – astroball
    Commented Oct 14, 2023 at 6:48
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    $\begingroup$ I would think another factor would be that wings are curved so as to operate most efficiently with a fore-to-aft airflow. If a plane were to yaw fast enough that its fuselage was pointed 90 degrees away from its velocity through the air, it wouldn't really be "flying" anymore. A smaller amount of law wouldn't totally negate lift, but I would think it would still reduce lift unless the angle of the relative velocity through the air was close enough to fore/aft that the plain wouldn't be providing much sideways acceleration. $\endgroup$
    – supercat
    Commented Oct 15, 2023 at 16:17
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The sideslip angle. An airplane's drag increases with sideslip angle. In a coordinated turn, the nose is always pointed into the relative wind, and so there is not as much of an increase in drag.

Essentially, in a coordinated turn you are generating lift primarily from the part of the plane that is designed to create lift with a minimum of drag, the wings.

In a flat turn, the required horizontal force to turn comes directly from the aerodynamic forces acting on the fuselage. Essentially, the fuselage is acting as (rather poor) airfoil, producing "horizontal lift." To generate the same amount of horizontal force requires more drag than doing it with the wings, as you don't benefit from the high ratio of lift to drag of the wings.

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  • $\begingroup$ Does your answer consider rudder weathervaning? I can only think of a dampening effect from the fuselage keeping some sideslip in. $\endgroup$
    – astroball
    Commented Oct 14, 2023 at 5:31
  • $\begingroup$ @astroball You need to keep the sideslip angle in the whole time you are turning. Meanwhile, the relative wind is no longer directly down the nose. Aircraft are aerodynamically slickest when pointed directly into the wind, so the drag is higher in a sideslip. The extra drag is not even on both sides of the aircraft, and this is what causes the aircraft to yaw into the relative wind. $\endgroup$
    – Chris
    Commented Oct 14, 2023 at 6:01
  • $\begingroup$ This answer isn't exactly wrong, but it doesn't do anything to support why it's right. The sideslip angle is not the problem, as fish show ably. The issue is that a change of direction requires a force derived from lift, and wings are much more efficient at making lift forces than fuselages. FWIW, this answer is wrong, however, in stating that drag does not increase. In a level turn it absolutely does, as the additional lift required to turn generates additional drag. $\endgroup$
    – Kenn Sebesta
    Commented Oct 14, 2023 at 11:58
  • $\begingroup$ @KennSebesta how do fish "ably show" that side slip angle is not the problem? Millions of years of trial and error have created hydrodynamic masterpieces that only propel themselves by moving out of alignment with the freestream flow. It is a delight to watch aquarium fish do this only by undulating their forefins (like birds?) to slow cruise around (its great to be bouyant too). $\endgroup$
    – Robert DiGiovanni
    Commented Oct 14, 2023 at 19:42
  • $\begingroup$ @RobertDiGiovanni because fish turn without banking, so the lift forces are derived 100% from their β. To build on your comment, check out youtube.com/watch?v=_ZBWnhzYvts. In it, a dead trout in a current is shown to still flop like a fish, capturing energy from the moving water. It sometimes even propels itself forward to such an extent that the tow line goes slack. Their bodies are amazing! $\endgroup$
    – Kenn Sebesta
    Commented Oct 14, 2023 at 19:52

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