There are many
which influence the amount of aerodynamic
which a body generates. Lift depends
on the shape,
flow conditions of the air passing the object.
For a three dimensional wing, there is an additional effect
on lift, called downwash, which will be discussed on this page.
For a lifting wing, the
on the top of the wing is lower than the pressure below the wing.
Near the tips of the wing, the air is free to move from the region
of high pressure into the region of low pressure. The resulting
flow is shown on the figure at the left by the two circular blue lines with
the arrowheads showing the flow direction. As the aircraft moves to
the lower left, a pair of counter-rotating vortices are formed at the
wing tips. The lines marking the center of the vortices are
shown as blue vortex lines leading from the wing tips.
If the atmosphere has very high humidity,
you can sometimes see the vortex lines on an airliner
during landing as long thin "clouds" leaving
the wing tips.
The wing tip vortices produce a downwash
of air behind the wing which is very strong near the wing tips and
decreases toward the wing root. The local
angle of attack
of the wing is increased by the flow induced by the downwash,
giving an additional, downstream-facing, component to the
aerodynamic force acting over the entire wing.
of the force is called
because it faces
downstream and has been "induced" by the action of the tip vortices.
The lift near the wing tips is defined to be perpendicular to the local
flow. The local flow is at a greater angle of attack than the free stream
flow because of the induced flow.
Resolving the tip lift back to the free stream
reference produces a reduction in the
of the entire wing.
The analysis for the reduction in the lift coefficient is fairly tedious
and relies on some theoretical ideas which are beyond the scope
of the Beginner's Guide.
The result of the analysis is an equation for the reduction of the lift
The final wing lift coefficient Cl is equal to
the basic free stream lift coefficient Clo divided by the quantity: 1.0
the basic lift coefficient divided by pi (3.14159)
times the aspect ratio AR.
Cl = Clo / (1 + Clo /[pi * AR])
is the square of the span
s divided by the wing area A. For a
rectangular wing this reduces to the ratio of the span to the chord.
Long, slender, high aspect ratio wings have less lift reduction than
short, thick, low aspect ratio wings as shown in the graph on the
right of the figure.
Reduced lift coefficient is a three dimensional effect related to the wing tips.
The longer the wing, the farther the tips are from the main portion of
the wing, and the smaller the lift reduction.
dramatically shows airplane downwash. The picture
was sent to us by Jan-Olov Newborg, from Stockholm, Sweden, and was
originally taken by Paul Bowens. In the picture, the Cessna Citation
has just flown above a cloud deck shown in the background. The
downwash from the wing has pushed a trough into the cloud deck. The
swirling flow from the tip vortices is also evident.
Another slide describes the
interesting problems downwash caused for early aerodynamicists.
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