Re: An-124 and wing dihedral

Date:         18 May 98 16:02:58 
From:         drela@mit.edu (Mark Drela)
Organization: Massachvsetts Institvte of Technology
References:   1
Followups:    1
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In article <airliners.1998.772@ohare.Chicago.COM>, kls@ohare.Chicago.COM (Karl Swartz) writes:

> I can see how "positive" dihedral (like the 777) might help cancel out
> unwanted roll.  This might also explain why the 777 has greater dihedral
> than the 747, since an engine failure on a 777 would produce greater yaw
> which in turn would trigger a roll.  (The same sort of yaw-induced roll
> which is one of the theories for the USAir 427 crash.)
>
> I can't see what "negative" dihedral (like the An-124) would accomplish,
> or why it would even be desireable.

The main effect of dihedral is to give a roll moment
in response to a yaw angle (Cn_beta stability derivative).

On most aircraft, having Cn_beta close to zero (i.e. little or no
"dihedral effect") is desirable, since this makes the aircraft
more controllable on crosswind landings and takeoffs.  Another
reason for having a near-zero Cn_beta is that a sudden yaw angle
from an engine failure should NOT produce a roll moment.  This
would only complicate life for the scrambling pilot.

On the other hand, having zero Cn_beta makes the airplane spirally
unstable, but this is easily countered by the pilot or by any
rudimentary wing-leveling autopilot.  Free-flight model aircraft
must have spiral stability, and hence always have large amounts
of dihedral.

On a low-winger, the flow around the fuselage at a yaw angle
acts on the wing which then generates a roll moment as though
the wing had negative dihedral (bad).  Hence, positive dihedral
is added to compensate and return Cn_beta close to zero.
On a high-winger, the effect is opposite, and negative dihedral
is added to compensate.

  Mark Drela                          First Law of Aviation:
  MIT Aero & Astro          "Takeoff is optional, landing is compulsory"