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dihedral and insufficient vertical stabilizer area
cause Dutch roll. There is too much spiral
stability and insufficient directional stability.
The cure for spiral divergence, reducing vertical
stabilizer area and/or increasing dihedral, thus
makes the aircraft more prone to Dutch roll. The
cure for Dutch roll, increasing vertical stabilizer
size and/or reducing dihedral, makes the aircraft
more directionally stable and more prone to
spiral instability and spiral divergence. As is
usual when designing aircraft, some
compromise must be made, and the aircraft is
then designed around what is seen as the best
overall performance. Winglets produce a
substantial amount of effective dihedral. If
winglets are mounted on a plank planform wing,
and the wing is then yawed, the forward winglet
produces some amount of lift toward the wing.
The trailing winglet will produce lift away from
the wing. The side of the winglet that is facing
away from the oncoming flow therefore has an
area of reduced pressure. Adjacent areas of the
wing are affected as well. The gross result is a
rolling moment, which is directly related to the
amount of yaw. This effect is kept when the
wing is swept. From Nickel and Wohlfahrt, the
skid-roll moment for a wing with winglets is the
same as that of a conventional wing with the
equivalent dihedral angle, EDA:
s
h
EDA w 20
=
where
EDA = equivalent dihedral angle;
hw = the height of the winglet;
s = b/2 or wing’s semispan.
Wing sweep also contributes to increase the
effective dihedral angle. Swept wings,
particularly those that use winglets may suffer
from excessive effective dihedral and Dutch roll
effects.
Another important issue to be taken
into account is the impact of the winglets on the
flutter characteristics of the configuration.
According to Boeing Co.4, in order to meet
flutter requirements with minimal structural
changes for the Boeing 737-800 winglet
installation, additional wingtip ballast was
mounted on the front spar to counteract the
incremental weight of the winglet located aft on
the wing. The use of wingtip ballast depended
on the structural configuration of the wing. In
some cases, ballast was simpler and more cost
effective than structural modification of the
wingbox. No wingtip ballast is required for the
BBJ configuration; 75 lb of ballast per wing is
required for each production winglet on the
737-800 commercial airliner; 90 lb of ballast is
required per wing for 737-800 retrofit. For the
ERJ 145XR and Legacy business jet, which are
derived of the successful ERJ 145 regional jet,
the winglet installation required no addition of
ballast to the wings.
The design of the winglet airfoil
imposes a great challenge to the aerodynamicist
because the winglet surface is usually highly
loaded and works under a large range of Mach
number and lift coefficient. Because of the later
consideration, a slightly nose droop of the
airfoil is recommended to avoid unwanted
suction peaks and drag creep. It is also highly
desirable that the winglet starts to stall after the
wing stalls. Apart from the airfoil, there are few
key parameters that have to be taken into
account to optimize the winglet design: cant
angle, twist distribution, sweepback, taper ratio,
root incidence angle, and aspect ratio. For a
winglet configuration aimed to a transonic
wing, it is mandatory the absence of moderate
to strong shock waves or even Mach numbers
above 1.2 on the winglet surface. To accomplish
this, the aerodynamicist has to avoid high toe-in
and twist angles of the winglet planform.
However, for doing so, the lift produced by the
winglet and therefore the associated drag
reduction will diminish at lower speeds. That is
the point where CFD could help by enabling
fast parametric configuration studies. The CFD
solvers shall be able to correctly treat the
complex flow patterns found at wingtips.
There are some other considerations
not directly related to the drag reduction but
which can impact it somehow. For example, in
specific cases, the winglet may have to house
anti-collision and navigation lights (Fig. 8).
Winglets also require protection against
lightning, considering they exert some attraction
for them. Although winglets frequently cause an
increase in maximum lift coefficient, the final
configuration must keep the maximum lift
coefficient of the wing without winglets, at
least. The winglets appeared to prevent the wing
　
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