What "designs" the dihedral angle in modern airliners?

Question

Is this an accurate description of the design process for modern jet airliners?

If not, why not? What other factors come into play in determining the choice of dihedral angle?

1. Designer starts by assuming that aircraft's automated systems will maintain zero sideslip (defined as zero "yaw string" deflection) at virtually all times, except in rare cases such as when pilot is using rudder to (perhaps only partially) "kick out the crab" just before touchdown in a crosswind landing

2. Therefore effect of dihedral on lateral stability, yaw-roll coupling, "Dutch roll" oscillations, etc is essentially irrelevant (i.e. can be assumed to be zero, so long as the automation keeps working as described above)

3. Therefore choice of dihedral angle is based entirely on a) structural considerations-- what geometry is most compatible with a lightweight, strong structure and b) wingtip and engine nacelle clearance considerations-- what geometry allows adequate wingtip and engine nacelle clearance at bank angles likely to be encountered during takeoff and landing

Answer 1

Look at the A380: The inner engines must be high enough so they don't suck in every little piece of dirt on run- and taxiways. Therefore, the inner wing has more dihedral and the outer wing adds just enough to give sufficient dihedral effect overall. Low wing airplanes in general need some positive dihedral in order to compensate for the opposing influence of the fuselage.

A380 front view (picture source).

The tail dihedral is selected such that even with a tailstrike the tips of the horizontal tail will just stay above ground. This adds a bit dihedral effect of its own, so wing dihedral must be a bit smaller in order to produce the desired dihedral effect overall.

While Fly-by-Wire systems allow to fly unusual dihedral angles and dynamically compensate for almost any deficiencies, the regulations for airliners require them to be still flyable when the FCS has failed. Therefore, the electronics cannot remove the responsibility of the design engineers to choose the correct dihedral for agreeable flight characteristics.

Answer 2

Designer starts by assuming that aircraft's automated systems will maintain zero sideslip (defined as zero "yaw string" deflection) at virtually all times,

Civil passenger jet design starts with making sure that any failure has no catastrophic effects. If the automated system fails, the aeroplane geometry must ensure Dutch roll behaviour that is acceptable for pilots to land the plane - with failed systems, in gusty stormy conditions, in a manner that the pilot can cope with in these difficult circumstances.

Only when it can be shown to authorities that the chance of automated system failure is smaller than $10^{9}$ flying hours, will the method in the question be allowed. Final proof will require a substantial fleet of aeroplanes making a couple of billion flying hours without total failure of the systems. In the mean while, dihedral angles will be such that good Dutch Roll behaviour is guaranteed when all automated systems are down.

Answer 3

The driving factor may be desired roll stability to counteract transient non zero sideslip conditions from variations in wind, weight shift of fuel or passengers, and degree of spiral stability desired.

One may start by observing dihedral built in a high wing 172 and a low wing Piper Chorokee. Essentially, dihedral is a passive roll stability system to damp and reverse an unwanted roll force.

One can see the top graph has no stabilizing force, resulting in progressively worse stability as bank angle increases, better for hang gliders. The bottom graph restores wings level from a minor upset if bank angle is not excessive or ailerons are not deliberately applied, better for cruising aircraft.

Yes, dihedral contributes to "dihedral effect" but serves as a roll damper$^1$. "Dihedral effect" (to crosswinds) can be mitigated by raising vertical CG, raising the wing, or by adding side area (such as ventral fins) beneath the CG, and, as the OP suggests, flying in with "zero sideslip" as much as possible.

Additionally, with swept wings, yaw contributes to roll, so now a large vertical stabilizer is need as well and a yaw damper. The vertical stabilizer also contributes to dihedral effect.

Perhaps we can look at the B-52 and the B-2 as a progression towards what birds do, control yaw and roll with their wings. This does require a computer, with sufficient redundancy for safety.

$^1$ a footnote for those who feel dihedral stabilization is a "fallacy": combined with side slip (which it creates) it is not. The roll from a crosswind gust applies force from drag, whereas the vertical lift differential and slip effectively counteract it with straight wings. Yaw is more of a problem with swept wings because dihedral is now counteracting lift differential (from sweep) as well as crosswind. As dihedral alone can be insufficient, the yaw damper must be added.

Food for thought: this

outperforms this

in a crosswind!