by Tommy H. Thomason

Tuesday, March 25, 2014

Anhedral/Dihedral and Wing Sweep

The question of how much anhedral the F3H Demon wing has came up on a modeling website recently. (Anhedral is the opposite of dihedral; instead of the wings angling up relative to the fuselage when viewed from the front, they angle down.)

The answer is, strictly speaking, none. However, it looks like it does have some and appears to depicted with anhedral in a front view. The reason is that the F3H wing is swept and also mounted to the fuselage at a non-zero angle of incidence relative to the fuselage reference line.
This also makes the wing look thicker than it actually is when viewed from the front.

The effect is even more pronounced in the front view of the A3D Skywarrior because its wing is not only mounted at an angle of incidence, it has a higher aspect ratio.
As a result, in a side view the leading edge of the wing tip is lower than the leading edge of the wing root and therefore has to be drawn that way in the front view. Nevertheless, the wing itself has no dihedral; in other words, a line drawn from tip to tip on a front view of the wing that is at zero angle of incidence would lie right down the middle of the leading edge.

Taper in airfoil thickness between the wing root and tip can also create an illusion of anhedral/dihedral or mask it. An example is the A4D Skyhawk. It looks like it has no dihedral. In fact it is almost three degrees. (Note that aerodynamicists do not measure dihedral with respect to either the upper or the lower surface of the wing. It is generally defined with respect to the chord line; in the case of the A4D, it is measured at the trailing edge of the wing.)

A line drawn from tip to tip with the A4D wing at a zero angle of incidence lies along the upper surface of the wing, because it is basically flat. The taper of the thickness of the wing from root to tip is all in the lower surface, which results in the wing having a little dihedral from an aerodynamicist's view point.

Some airplanes do have anhedral in the wing, of course. The F8U Crusader is one, although the actual angle might be exaggerated by the sit of the airplane relative to the camera and the raising of the wing for takeoff and landing. (You'll also note that the horizontal tail appears to have no dihedral.)

In this case, a front-view drawing can be relied on since the wing is mounted a zero angle of incidence.

Aerodynamicists also define wing-sweep angle in a very specific and even more non-intuitive way. It is not measured at the leading edge as you might think, but generally at the quarter chord, or 25% of the local chord back from the leading edge of the wing. In accordance with this convention, the A4D has a wing sweep of about 33 degrees, somewhat less than the sweep angle of the leading edge.

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