From what I've read (I'm no aero engineer), anhedral is necessary aircraft due 'Too much' to the overall dihedral effect.
Ok so I manipulated your response slightly. You're spot on though, except for linking it to high wing birds. The vertical orientation of the wing, high wing vs low wing, comprises roughly 3 to 5 degrees of dihedral effect. In the design process various conditions are quantitatively compared to a degree of dihedral. We know dihedral as the degrees of upward sweep a wing has.
The effect of dihedral, as you accurately point out, effect lateral stability. More dihedral effect equates to greater lateral stability. More stability means less controllability; this part is stability and control 101. That is, stability and control is a spectrum, if you have more control you have less stability and vice versa.
Furthermore you have the coupled effects of dutch roll and spiral divergence. An aircraft with a dominating lateral stability will exhibit dutch role characteristics. Think v-tail bonanza, lacking a vertical rudder meant less yaw stability. Or in the case of a delta wing aircraft, lateral stability's increase is proportional to the angle of sweep back and the lift coefficient. At zero lift, or zero angle of attack, there is no dihedral effect. However, at high lift coefficients, such as during landing, an aircraft with a large sweep angle can exhibit too much dihedral effect.
To sum that up. You're spot on in your analysis, just remember that the vertical location of the wing merely contributes to dihedral effect; it is not the sole reason for requiring anhedral. It's the role of the designer to ensure there is not too much dihedral effect. The primary contributors to this effect are sweep back, vertical location of the wing, and dihedral/anhedral of the lifting surfaces.
In the case of the falcon jet, if a wing produces a high lift coefficient and has a large degree of sweep, even though it is a low wing, it may have too much dihedral effect. As a result anhedral or a straight wing might be necessary to achieve desired performance. Just to nit pick, if you view the falcon aircraft in flight you'll note that the main wing has a slight degree of dihedral when compared to sitting on the ramp.
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troopernflight,
Have a look at this:
http://www.faa.gov/regulations_policies/handbooks_manuals/aviation/media/00-80T-80.pdf
Page 297 is of importance. The first image is the answer to your confusion. The image completely ignores the idea of relative wind and a forward moving aircraft. Instead it's a wing, shaped like the letter 'v' with a wind striking it from the side. In the case of this side moving component of wind the upward swept wing has a clear positive angle of attack. The downward swept wing has a clear negative angle of attack.
Think for a moment an aircraft making a left turn, but the pilot does not use any rudder. We know this will cause the nose to swing right and some component of the relative wind will now move sideways from left to right across the aircrafts wing. For a moment, imagine that airplane doesn't have a fuselage. Instead it is just a wing. Look again to the picture on page 297 of that V shape with the relative wind. Here is what's happening, imagine the horizontal line as the relative wind:
- Whole wing: ____ V Here the left wing has a positive angle of attack, look:
- Left wing: ____ \ Here the wind is striking the bottom of this wing, giving it a positive angle. Where as the right wing has a negative angle, look:
- Right wing: ____/ Finally, here the right wing is experiencing wind striking the top of it's surface, similar to that of an airplane flying inverted. Or, a negative angle of attack.
I apologize for the crude pictures, hopefully with the reference picture from AFNA on page 297 you can see what is meant by these first grade representations. If it's still unclear please say so, I will draw up something more vividly accurate on a sketch pad for you.
