Lift is the force that holds an aircraft in the air. How is lift generated? There are many explanations for the generation of lift found in encyclopedias, in basic physics textbooks, and on Web sites. Unfortunately, many of the explanations are misleading and incorrect. Theories on the generation of lift have become a source of great controversy and a topic for heated arguments.

The proponents of the arguments usually fall into two camps: (1) those who support the "Bernoulli" position that lift is generated by a pressure difference across the wing, and (2) those who support the "Newton" position that lift is the reaction force on a body caused by deflecting a flow of gas. So who is correct?

Let's start with short biographies of Bernoulli and Newton.
On the figure at the top of this page we show portraits of Daniel Bernoulli,
on the left, and Sir Isaac Newton, on the right.
Newton worked in many areas of mathematics and physics.
He developed the theories of gravitation
in 1666, when he was only 23 years old. Some twenty years later, in 1686, he
presented his
three laws of motion
in the *Principia Mathematica Philosophiae Naturalis *.
He and Gottfried Leibnitz are also credited with the development of the
mathematics of Calculus.
Bernoulli also worked in many areas of mathematics and physics and
had a degree in medicine. In 1724, at age 24, he had published a mathematical
work in which he investigated a problem begun by Newton concerning
the flow of water from a container and several other problems involving
differential equations. In 1738, he presented his
hydrodynamics equation
in the work *Hydrodynamica*.
He continued to work on a wide variety of math and physics problems with
his student, Leonard Euler.
** Neither Newton nor Bernoulli ever attempted to explain the
aerodynamic lift of an object**.

When a gas flows over an object, or when an object moves through a gas,
the molecules of the gas are free to move about the object; they are not
closely bound to one another as in a solid. Because the molecules move,
there is a velocity (speed plus direction) associated with the gas. Within
the gas, the
velocity can have very different values at different places near the object.
Bernoulli's equation relates the pressure on the
object to the local velocity; so as the velocity changes around the
object, the pressure changes as well. Adding up (integrating) the
pressure variation
times the area around the entire body determines the aerodynamic
force on the body. The
lift
is the component of the aerodynamic force
which is perpendicular to the original flow direction of the gas.
The
drag
is the component of the aerodynamic force
which is parallel to the original flow direction of the gas.
Now adding up the velocity variation around the object instead
of the pressure variation also determines the aerodynamic force.
The integrated velocity variation around the object produces a net
turning
of the gas flow. From
Newton's third law
of motion, a turning action of the flow will result in a re-action (aerodynamic
force) on the object.
*So both "Bernoulli" and "Newton" are correct*. Integrating the effects
of either the pressure or the velocity determines the aerodynamic force on
an object. We
can use equations developed by each of them to determine the
magnitude and direction of the aerodynamic force.

So where is the argument? Arguments arise because people mis-apply Bernoulli and Newton's equations and because they over-simplify the description of the problem of aerodynamic lift. The most popular incorrect theory of lift arises from a mis-application of Bernoulli's equation. The theory is known as the "equal transit time" or "longer path" theory which states that wings are designed with the upper surface longer than the lower surface, to generate higher velocities on the upper surface because the molecules of gas on the upper surface have to reach the trailing edge at the same time as the molecules on the lower surface. The theory then invokes Bernoulli's equation to explain lower pressure on the upper surface and higher pressure on the lower surface resulting in a lift force. The error in this theory involves the specification of the velocity on the upper surface. In reality, the velocity on the upper surface of a lifting wing is much higher than the velocity which produces an equal transit time. If we know the correct velocity distribution, we can use Bernoulli's equation to get the pressure, then use the pressure to determine the force. But the equal transit velocity is not the correct velocity. Another incorrect theory uses a Venturi flow to try to determine the velocity. But this also gives the wrong answer since a wing section isn't really half a Venturi nozzle. There is also an incorrect theory which uses Newton's third law applied to the bottom surface of a wing. This theory equates aerodynamic lift to a stone skipping across the water. It neglects the physical reality that both the lower and upper surface of a wing contribute to the turning of a flow of gas.

The real details of how an object generates lift are very complex and do
not lend themselves to simplification. For a gas, we have to simultaneously
conserve the
mass,
momentum, and
energy
in the flow. Newton's laws of motion are statements concerning the conservation
of momentum. Bernoulli's equation is derived by considering conservation of
energy. So both of these equations are satisfied in the generation of lift; both
are correct. The conservation of mass introduces a lot of complexity into the
analysis and understanding of aerodynamic problems.
For example, from the conservation of mass, a change in the velocity of a gas
in one direction results in a change in the velocity of the gas in a direction
perpendicular to the original change. This is very different from the motion of
solids, on which we base most of our experiences in physics.
The simultaneous conservation of mass, momentum,
and energy of a fluid (while neglecting the effects of
air viscosity)
is called the **Euler Equations** after Bernoulli's student,
Leonard Euler. If we include the effects of viscosity, we have the
**Navier-Stokes Equations** which are are named after two independent
researchers in France and in England. To truly understand the details of
the generation of lift, one has to have a good working knowledge of the
Euler Equations.

Navigation..

- Beginner's Guide to Aerodynamics
- Beginner's Guide to Propulsion
- Beginner's Guide to Model Rockets
- Beginner's Guide to Kites
- Beginner's Guide to Aeronautics

Go to...

- Beginner's Guide Home Page

*byTom
Benson
Please send suggestions/corrections to: benson@grc.nasa.gov *