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I have noticed and read in books that low wing aircraft have higher dihedral than high wing aircraft. Dihedral is design feature for lateral stability so should be needed for both designs. So why is it more pronounced in low wing designs?

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There are several sources for a sideslip-induced rolling moment:

  1. The dihedral angle $\nu$ of the wing, which will increase the local angle of attack $\alpha$ on the windward wing according to $\Delta\alpha = \beta\cdot sin\nu$; $\beta$ being the angle of sideslip,
  2. The sweep angle $\varphi$ of the wing, which in a sideslip causes a de-sweeping of the airflow over the windward wing (and an increased sweep effect on the leeward wing). The local change in angle of attack is $\Delta\alpha = (cos(\varphi±\beta)-cos\varphi)\cdot(\alpha-\alpha_0)$ and is proportional to the angle of attack,
  3. The crossflow around the fuselage (see sketch below for illustration, sorry, no simple formula here), and
  4. The location of the vertical tail, or more precisely, the side force created on it by a sideslip angle in relation to the location of the center of gravity. This effect dictated the anhedral of aircraft like the F-104 Starfighter.

Please see this answer for a more complete explanation of effect 3. The sketch below is taken from the linked answer and shows a high and a low wing configuration in sideslip. The thin blue arrows indicate the sideways component of airflow $v_{\infty}\cdot sin\beta$.

In the end, some rolling due to sideslip is good, but too much must be avoided, and dihedral is used to complement the other effects such that the total is just right. A high wing already provides some positive rolling moment due to sideslip (negative $c_{l_{\beta}}$: When you deflect rudder to the left, the resulting sideslip should roll the aircraft to the left, too), so the wing doesn't need to contribute as much (by means of dihedral) as in low wing aircraft.

Dihedral (or for that matter, even a low center of gravity) will not roll the aircraft level: There is no aerodynamic way to achieve that! Dihedral will only give you a rolling moment when the aircraft sideslips.

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  • $\begingroup$ Peter, Thanks for the reply. A clarification....both cases represent right bank, is that correct? So in a low wing craft, right bank (clockwise force) is opposed by rolling moment (counterclockwise force) due to dihedral which stabilizes the plane. Guessing from direction of rolling moment arrow in high wing craft, this would cause instability, hence lack of dihedral??? The blue arrows are confusing me. Is it meant to indicate direction of relative wind? $\endgroup$ – yankeemike Jan 28 '15 at 19:22
  • $\begingroup$ @yankeemike: Yes, the blue arrows indicate the sideways component of airflow. Both cases represent right sideslip, however. Dihedral or a high wing will not get you out of a bank, instead they will roll the aircraft away from the sideslip. $\endgroup$ – Peter Kämpf Jan 28 '15 at 21:39
  • $\begingroup$ Yes but banking causes turning causes sideslip, therefore the roll torque generated by dihedral DOES tend to roll the aircraft towards wings-level. A model glider with lots of dihedral will fly for hours with the average bank angle remaining near zero even with no pilot input. Dihedral or high wing placement absolutely does tend to roll an aircraft out of a bank. $\endgroup$ – quiet flyer May 16 at 22:20
  • $\begingroup$ @quietflyer Right, but in inhabited aircraft too much dihedral quickly becomes uncomfortable. $\endgroup$ – Peter Kämpf May 17 at 8:09
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High-wing aircraft already have better roll stability due to their vertical center of gravity located under the wing than low-wing aircraft (with vertical CG located above the wing).

From a source other than Wikipedia:

If the center of gravity is below the wing, the weight tends to restore the upright position. This is known as pendulum stability or the keel effect. If the CG is above the wing, the weight is destabilizing.

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    $\begingroup$ Wikipedia is not always right. $\endgroup$ – Peter Kämpf Jan 28 '15 at 5:50
  • $\begingroup$ Also, more ground clearance. $\endgroup$ – copper.hat Feb 2 '15 at 5:03
  • $\begingroup$ "the weight tends to restore the upright position" - That's not true; gravity never exerts torque on an aircraft, or, for that matter, on anything else. (The exception is when tidal forces become significant, which never happens in Earth's atmosphere.) Aerodynamic forces can push an aircraft upright, but gravity cannot. $\endgroup$ – Terran Swett yesterday
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Peter Kampf is right--the airplane does not know the difference between gravity and the g forces (acceleration) that it experiences in a turn. When the ball is centered, that means "gravity/acceleration" is pulling "straight down" on the airframe ("down" from the perspective of the airplane, not from the perspective of the horizon). The airplane is not capable of "seeing" any other gravity, because gravity is the same as acceleration. So when you are in a perfectly balanced turn, with the ball centered, the gravitational pull coming from earth is not relevant except as it is joined with the acceleration of the turn to create a new "down" direction for the airplane.

To understand this better, you need to visualize the same "mind experiment" that Einstein used when he came to understand gravity as merely acceleration and not anything more. He put a man inside a closed box floating in space, with the man floating in the middle of the box. Then he hooked a rope to the box and accelerated the box smoothly in one direction, simulating gravity. From the perspective of the man inside the closed box, it could have been sitting on the surface of the earth. Everything about acceleration and gravity, from the perspective of the man in the box, was identical. This helped Einstein to see that gravity was not "like" acceleration. Gravity IS acceleration. So when you use acceleration (changing directions in a turn; centrifugal force) to change the direction of "down" in a turn, the airplane absolutely does not know the difference between true "down" and its new "down" as adjusted by the turning acceleration. Gravity can not "pull" the pendulum of the fuselage down in any other direction than the direction of "down" as indicated by the ball in your turn and bank indicator. So the only way dihedral and the pendular effect of the fuselage can roll the wings back to level, is if the turn is not perfectly coordinated, i.e., the ball has rolled in the direction true "down" not the airplane's "down". So maybe feet-flat-on-the-floor flying is not such a bad thing after all.

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