As a wing moves through the air, the wing is inclined to the
flight direction at some angle.
The angle between the chord line
and the flight direction is called the angle of
attack and has a large effect on the
generated by a wing.
When an airplane takes off, the pilot applies as much
as possible to make the airplane roll along the runway. But
just before lifting off, the pilot
the aircraft. The nose
of the airplane rises, increasing the angle of attack and producing
the increased lift needed for takeoff.
The magnitude of the lift generated by
an object depends on the
of the object and how it moves through
the air. For thin airfoils, the lift is directly
proportional to the angle of attack
for small angles (within +/- 10 degrees). For
higher angles, however, the dependence is quite complex. As an
object moves through the air, air molecules
to the surface.
This creates a layer of air near the surface called a
that, in effect, changes the shape of the object. The
reacts to the edge of the boundary layer just as it would to the
physical surface of the object. To make things more confusing, the
boundary layer may lift off or "separate" from the body and create an
effective shape much different from the physical shape. The
separation of the boundary layer explains why aircraft wings will
abruptly lose lift at high angles to the flow. This condition is
called a wing stall.
On the slide shown above, the flow conditions for two airfoils are
shown on the left. The shape of the two foils is the same. The lower
foil is inclined at ten degrees to the incoming flow, while the upper
foil is inclined at twenty degrees. On the upper foil, the boundary
layer has separated and the wing is stalled. Predicting the stall
point (the angle at which the wing stalls) is very difficult
mathematically. Engineers usually rely on wind
tunnel tests to determine the stall point. But the test must be done
very carefully, matching all the important similarity
parameters of the actual flight hardware.
The plot at the right of the figure shows how the lift varies with
angle of attack for a typical thin airfoil. At low angles, the lift is
nearly linear. Notice on this plot that at zero angle a small amount
of lift is generated because of the airfoil shape. If the airfoil had
been symmetric, the lift would be zero at zero angle of attack. At
the right of the curve, the lift changes rather abruptly and the
curve stops. In reality, you can set the airfoil at any angle you
want. However, once the wing stalls, the flow becomes highly
unsteady, and the value of the lift can change rapidly with time.
Because it is so hard to measure such flow conditions, engineers
usually leave the plot blank beyond wing stall.
Since the amount of lift generated at zero angle and the location
of the stall point must usually be determined experimentally,
aerodynamicists include the effects of inclination
in the lift coefficient.
For some simple examples, the lift coefficient can
be determined mathematically. For thin airfoils at
subsonic speed, and small angle of attack,
the lift coefficient Cl is given by:
Cl = 2 * pi * a
where pi is 3.1415, and a
is the angle of attack expressed in radians:
pi radians = 180 degrees
Aerodynamicists rely on wind tunnel
testing and very sophisticated computer analysis to determine the
Let's investigate the dependence of lift on angle of attack using a Java
simulator which solves the
As an experiment, set the angle to 5.0 degrees and note the amount of lift.
Now increase the angle to 10 degrees. Did the lift increase or decrease?
Increase the angle again to 15 degrees. What do you notice in the view window?
Set the angle to 0 degrees. Is there any lift? What does this tell you
about the shape of the airfoil? Find the angle for which there is
You can download your own copy of the program to run off-line by clicking on this button:
You can further investigate the effect of angle of attack and the other
factors affecting lift by using the
FoilSim III Java Applet.
You can also
your own copy of FoilSim to play with