Christian O’Toole
English 202C
Professor Peacock
March 25, 2015
Audience: Junior year aerospace engineering students.
How an Airfoil Generates Lift
Introduction:
Pioneers of aviation such as Otto Lilienthal and the Wright brothers made the connection
between curved surfaces and the effect they have to produce lift. At the heart of their flying
contraptions was a functional airfoil which ultimately led to their success in flight. The
generation of lift is an aerospace phenomenon that occurs when airflow is streamlined over an
airfoil. Six causal relationships are responsible for producing lift on a wing. The process is
related to the geometry and orientation of an airfoil, circulation caused by viscous effects on the
body and conservation of momentum inducing a clockwise vortex. Furthermore, effects on the
streamwise velocity from vortex shedding, pressure distribution effects around an airfoil and the
net perpendicular force created by the system to sustain equilibrium account for producing lift.
Geometry and Orientation of an Airfoil:
The geometry and orientation of an airfoil play a crucial role in satisfying the conditions
for lift. In order to streamline airflow around a wing the body shape must be cambered or placed
at an inclined angle of attack relative to the wind direction. In Figure 1 the camber line is in blue
and the green α symbol represents a positive angle of attack with the leading edge up. The figure
below also highlights additional airfoil characteristics referenced in this document such as the
trailing edge, leading edge, upper surface and lower surface in grey and the chord line in red.
Figure 1: Airfoil Nomenclature by Olivier Cleynen on
http://commons.wikimedia.org/wiki/File:Wing_profile_nomenclature.svg
The degree of curvature between the upper and lower surface with respect to the chord
line is different. The camber line illustrates this point in the form of an upward arc. As a result
the distance an air molecule travels on the upper surface is greater than that of the lower surface.
An increase in angle of attack is directly proportional to an increase in this imbalance between
the velocity on the top side and bottom side of the wing. This linear relationship plays a crucial
role in the beginning steps to produce lift.
Viscous Effects Cause Circulation:
The aerodynamic shape of an airfoil satisfies the Kutta Condition since the freestream
velocity contours around its body. Friction is created on the upper and lower surfaces as air
molecules flow over the wing and smoothly off the trailing edge. Circulation in the form of a
vortex forms as a consequence of these viscous effects. Since airflow over the upper surface
travels further, the total frictional force resisting air molecules above the camber line is greater in
comparison to the force below it. As a result a counter-clockwise vortex is formed to compensate
for the difference in viscous effects between the two surfaces.
Conservation of Momentum Induces a Clockwise Vortex:
As an airfoil moves through the air a counter-clockwise vortex is shed off the trailing
edge. According to the conservation of momentum, the momentum of a system is constant if no
external forces act on the system. It is true air molecules impose a force on the system, however
this reaction force is negligible since an air molecule’s mass is approximately zero relative to the
aircraft’s weight. When a vortex sheds off the trailing edge another vortex of equal magnitude is
induced to conserve momentum in the system. The vortex formed is in the opposite direction
which rotates clockwise around the airfoil. The red, counter-clockwise shed vortex and blue,
clockwise induced vortex illustrate this phenomenon in Figure 2.
Figure 2: Shed and Induced Vortices on an Airfoil by Ludwig Prandtl on www.dlr.de
Circulation Influences the Streamwise Velocity:
An induced clockwise vortex around an airfoil alters the streamwise velocity flowing
near the surface. Airflow passing under the wing is impeded while it is assisted on the upper
surface by this circulating vortex. These disturbances cause a velocity difference between the
two surfaces. A fundamental concept of fluid mechanics is that a change in velocity causes a
change in pressure. Since the velocity below the camber line relative to the upper surface of the
wing is lower it ultimately causes a pressure gradient between the two surfaces to form.
Induced Pressure Distribution:
A positive angel of attack generates a low pressure system on an airfoil’s upper surface.
This is due to the fact that the air molecules are traveling at a greater velocity relative to the ones
on the lower surface. Below the camber line a high pressure system forms as a consequence of
the low speed air molecules. This difference in pressure results in a pressure distribution over an
airfoil’s body. An increase and decrease in angle of attack are directly proportional to the
pressure envelope formed. In steady level flight the force provided by the high and low pressure
system counters the weight of the aircraft. As α, the angle relative to the wind speed, fluctuates
the pressure distribution created grows in magnitude. The pressure envelopes formed at various
angles of attack are illustrated in Figure 3.
Figure 3: Pressure Distribution over an Airfoil Provided by www.pilotsweb.com
Resultant Force to Maintain Equilibrium:
A fundamental concept of fluid dynamics is air flows from high pressure to low pressure
in order to reach equilibrium. Air molecules under the wing must travel upwards because of this
principle. Another concept that factors into lift generation is Newton’s Third Law which states,
for every action there is an equal and opposite reaction. The streamwise airflow below the chord
line imposes a net upward force to balance the pressure distribution between the airfoil’s upper
and lower surfaces. This resultant force ultimately places the system back in equilibrium. The
vertical component of the resultant force as shown in Figure 4 is categorized as lift.
Figure 4: Resultant Force on an Airfoil by Praba Karan on www.aeronauticallecture.blogspot.com
Limiting Constraints:
There is a limiting case for how great an angle of attack can be in order to generate lift.
As the angle of attack increases above 15 degrees for most airfoils flow separation begins to
occur. This reduces circulation which decreases the pressure distribution around the airfoil.
Consequently, the resultant force perpendicular to the body decreases and when the vertical
component of lift is less than the weight of the aircraft an aerodynamic stall occurs.
Conclusion:
As a symmetric airfoil’s angle of attack is increased or when a cambered body shape is
placed in a freestream velocity the flow is streamlined. As air flows over a wing viscous effects
on the upper and lower surface cause circulation around the body. This clockwise circulation
counters the streamwise velocity below the camber line and assists the streamwise velocity
above this line. In turn a pressure distribution is induced between the upper and lower curved
surfaces of the airfoil. As a result a net resultant force perpendicular to the body of the airfoil
balances the pressure difference. The vertical component of the net force required to achieve
equilibrium is lift.
Glossary
A
M
Airfoil: Any surface such as a wing, aileron, or
stabilizer, designed to aid in lifting or
controlling an aircraft by making use of the air
currents through which it moves.
Momentum: A quantity expressing the motion
of a body or system, equal to the product of
the mass of a body and its velocity.
P
Angle of attack: The acute angle between the
chord of an aircraft wing or other airfoil and
the direction of the relative wind.
Perpendicular: Meeting a given line or surface
at right angles.
C
S
Camber line: The curve that is halfway
between the upper and lower surfaces of the
airfoil.
Streamlined: A current of air optimally shaped
for motion by having a contour design to offer
the least possible resistance.
Chord line: The imaginary straight line joining
the leading and trailing edges of an airfoil.
T
E
Equilibrium: A state of rest or balance due to
the equal action of opposing forces.
F
Freestream velocity: Air traveling far upstream
of an aerodynamic body, that is, before the
body has a chance to deflect, slow down or
compress the air.
K
Kutta Condition: The circulation of the flow
causes a streamline to leave the trailing edge
of an airfoil smoothly, or, equivalently, that
the fluid velocity at the trailing edge be finite.
L
Leading edge: The foremost edge of an airfoil
where flow separation occurs.
Trailing edge: The rear edge of an airfoil,
where the airflow separated by the leading
edge rejoins.
V
Viscous: Of a glutinous nature or consistency;
sticky; thick; adhesive.
Vortex: A whirling clockwise or counterclockwise mass of air.