Dallas wrote:
Would anyone care to comment on the accuracy of this illustration of how
wing dihedral works from a 1981 Jeppesen Sanderson book.

http://makeashorterlink.com/?B25A35DCC

The accompanying statement reads:
"When an aircraft with dihedral rolls so that one wind is lower than the
other, the lower wing will have more effective lift than the raised wing
because it is not tilted from the horizontal as much. The imbalance in lift
tends to raise the lower wing and restore level flight."


Dallas


This is not quite correct, and most of the "pilot books" have it wrong
too. Here is a very nice explanation taken from the book titled
"Mechanics of Flight" by A.C. Kermode of the RAF.

"The most common method of obtaining lateral stability is by the use of
a dihedral angle on the main planes. Dihendral angle is taken as being
the angle betwen each plane and the horizontal, not the total angle
between the two planes, which is really the geometrical meaning of
dihedral angle. If the planes are inclined upwards towards the wing
tips, the dihedral is positive; if downwards, it is negative and called
anhedral; the latter arrangement is used in practice for reasons of
dynamic stability.

The effect of the dihedral angle in securing lateral stability is
sometimes dismissed by saying that if one wing tip drops the horizontal
equivalent on that wing is increased and therefore the lift is
increased, whereas the horizontal equivalent and the lift of the wing
which rises is decreased, therefore obviously the forces will tend to
right the airplane.

Unfortunately, it is not all quite so obvious as that.

Once the aircraft has stopped rolling, provided it is still travelling
straight ahead, the aerodynamic forces will be influenced only by the
airstream passing over the aircraft. This will be identical for both
wings and so no restoring moment will result.

What, then, is the real explanation as to why a dihedral angle is an
aid to lateral stability? When the wings are both equally inclined the
resultant lift on the wings is vertically upwards and will exactly
balance the weight. If, however, one wing becomes lower than the other,
then the resultant lift on the wings will be slightly inclined in the
direction of the lower wing, while the weight will remain vertical.
Therefore the two forces will not balance each other and there will be
a small resultant force acting in a sideways and downwards direction.
This force is temporarily unbalanced and therefore the aeroplane will
move in the direction of this force - i.e. it will sideslip - and this
will cause a fow of air in the opposite direction to the slip. This ahs
the effect of increasing the angle of attach of the lower plane and
increasing that of the upper plane. The lower plane will therefore
produce more lift and a restoring moment will result. Also the wing tip
of the lower plane will become, as it were, the leading edge so far as
the slip is concerned; and just as the center of pressure across the
chord is nearer the leading edge, so the center of the pressure
distribution along the span will now be on the lower plane; for both
these reasons the lower plane will receive more lift, and after a
slight slip sideways the aeroplane will roll back into its proper
position. As a matter of fact, owing to the protetcion of the fuselage,
it is probably that the flow of air created by the sideslip will not
reach a large portion fo the raised wing at all; this depends very much
on the position of the wing relative to the fuselage.

Both the leading edge effect on the lower wing, and the shielding of
the upper wing by the fuselage, occur on nearly all type of aircraft,
and may well mean that an aeroplane has a sufficient degree of lateral
stability without any dihedral angle, or too much if some of the
follwing effects also apply. Even if there is no actual dihedral angle
on the wings, these other methods of achieveing lateral stability may
be described as having a dihedral effect."