In order for an airplane to rise and fly in the air, a force must b...
**How Do Airplanes Fly?** A short and very interest explanation by ...
Bernoulli's Principle states that within a horizontal flow of fluid...
The principle of **"equal transit times"** states that the air goin...
The air going over the top of the wing reaches the trailing edge be...
If the principle of equal transit times and thus the Bernoulli effe...
"the wing of a typical small plane, whichhas a top surface that is ...
> The popular explanation also implies that inverted flight is impo...
The wing produces lift by diverting air down. The work produced by ...
![updownwash](https://i.imgur.com/E8b7xhw.jpg) **Upwash** When ...
> One observation that can be made from figure 7 is that the top su...
**The Coanda effect** was first discovered by a mathematician and e...
I'm not sure this is right. Flow bends around objects even in the a...
The Angle of attack (also known as AOA) is the angle between the on...
**The induced power** is the power required to redirect the air and...
In order to lower the induced power needed for lift one needs to im...
Visualization of the airflow with increasing angle of attack. W...
At the end of the wing the lift goes to zero very rapidly and there...
How Airplanes Fly: A Physical Description of Lift
David Anderson
Fermi National Accelerator Laboratory
Batavia IL 60510
dfa@fnal.gov
Scott Eberhardt
Dept. of Aeronautics and Astronautics
University of Washington
Seattle WA 91895-2400
scott@aa.washington.edu
Originally published in February 1999
I. INTRO
Almost everyone today has ﬂown in an airplane. Many
ask the simple question "what makes an airplane ﬂy"?
just plain wrong. We hope that the answers provided
here will clarify many misconceptions about lift and that
you will adopt our explanation when explaining lift to
others. We are going to show you that lift is easier to un-
derstand if one starts with Newton rather than Bernoulli.
We will also show you that the popular explanation that
most of us were taught is misleading at best and that lift
is due to the wing diverting air down.
Let us start by deﬁning three descriptions of lift com-
monly used in textbooks and training manuals. The ﬁrst
we will call the Mathematical Aerodynamics Description
which is used by aeronautical engineers. This description
uses complex mathematics and/or computer simulations
to calculate the lift of a wing. These are design tools
which are powerful for computing lift but do not lend
themselves to an intuitive understanding of ﬂight.
The second description we will call the Popular Expla-
nation which is based on the Bernoulli principle. The
primary advantage of this description is that it is easy
to understand and has been taught for many years. Be-
cause of its simplicity, it is used to describe lift in most
ﬂight training manuals. The major disadvantage is that
it relies on the "principle of equal transit times" which
is wrong. This description focuses on the shape of the
wing and prevents one from understanding such impor-
tant phenomena as inverted ﬂight, power, ground eﬀect,
and the dependence of lift on the angle of attack of the
wing.
The third description, which we are advocating here,
we will call the Physical Description of lift. This descrip-
tion is based primarily on Newton’s laws. The physical
description is useful for understanding ﬂight, and is ac-
cessible to all who are curious. Little math is needed
to yield an estimate of many phenomena associated with
ﬂight. This description gives a clear, intuitive under-
standing of such phenomena as the power curve, ground
eﬀect, and high-speed stalls. However, unlike the math-
ematical aerodynamics description, the physical descrip-
tion has no design or simulation capabilities.
II. THE POPULAR EXPLANATION OF LIFT
Students of physics and aerodynamics are taught that
airplanes ﬂy as a result of Bernoulli’s principle, which
says that if air speeds up the pressure is lowered. Thus
a wing generates lift because the air goes faster over the
top creating a region of low pressure, and thus lift. This
explanation usually satisﬁes the curious and few chal-
lenge the conclusions. Some may wonder why the air
goes faster over the top of the wing and this is where the
popular explanation of lift falls apart.
In order to explain why the air goes faster over the
top of the wing, many have resorted to the geometric
argument that the distance the air must travel is directly
related to its speed. The usual claim is that when the air
separates at the leading edge, the part that goes over the
top must converge at the trailing edge with the part that
goes under the bottom. This is the so-called "principle
of equal transit times".
As discussed by Gail Craig (Stop Abusing Bernoulli!
How Airplanes Really Fly, Regenerative Press, Anderson,
Indiana, 1997), let us assume that this argument were
true. The average speeds of the air over and under the
wing are easily determined because we can measure the
distances and thus the speeds can be calculated. From
Bernoulli’s principle, we can then determine the pressure 2
forces and thus lift. If we do a simple calculation we
would ﬁnd that in order to generate the required lift for
a typical small airplane, the distance over the top of the
wing must be about 50% longer than under the bottom.
Figure 1 shows what such an airfoil would look like. Now,
imagine what a Boeing 747 wing would have to look like!
FIG. 1: Shape of wing predicted by principle of equal transit
time
If we look at the wing of a typical small plane, which
has a top surface that is 1.5 - 2.5% longer than the bot-
tom, we discover that a Cessna 172 would have to ﬂy at
over 400 mph to generate enough lift. Clearly, something
in this description of lift is ﬂawed.
But, who says the separated air must meet at the trail-
ing edge at the same time? Figure 2 shows the airﬂow
over a wing in a simulated wind tunnel. In the simula-
tion, colored smoke is introduced periodically. One can
see that the air that goes over the top of the wing gets
to the trailing edge considerably before the air that goes
under the wing. In fact, close inspection shows that the
air going under the wing is slowed down from the "free-
stream" velocity of the air. So much for the principle of
equal transit times.
The popular explanation also implies that inverted
ﬂight is impossible. It certainly does not address acro-
batic airplanes, with symmetric wings (the top and bot-
tom surfaces are the same shape), or how a wing adjusts
for the great changes in load such as when pulling out of
a dive or in a steep turn.
So, why has the popular explanation prevailed for so
long? One answer is that the Bernoulli principle is easy to
understand. There is nothing wrong with the Bernoulli
principle, or with the statement that the air goes faster
over the top of the wing. But, as the above discussion
suggests, our understanding is not complete with this
FIG. 2: Simulation of the airﬂow over a wing in a wind tunnel,
with colored "smoke" to show the acceleration and decelera-
tion of the air.
explanation. The problem is that we are missing a vi-
tal piece when we apply Bernoulli’s principle. We can
calculate the pressures around the wing if we know the
speed of the air over and under the wing, but how do we
determine the speed?
Another fundamental shortcoming of the popular ex-
planation is that it ignores the work that is done. Lift
requires power (which is work per time). As will be seen
later, an understanding of power is key to the under-
standing of many of the interesting phenomena of lift.
III. NEWTON’S LAWS AND LIFT
So, how does a wing generate lift? To begin to un-
review Newton’s ﬁrst and third laws. (We will introduce
Newton’s second law a little later.) Newton’s ﬁrst law
states a body at rest will remain at rest, and a body in
motion will continue in straight-line motion unless sub-
jected to an external applied force. That means, if one
sees a bend in the ﬂow of air, or if air originally at rest
is accelerated into motion, there is a force acting on it.
Newton’s third law states that for every action there is an
equal and opposite reaction. As an example, an object
sitting on a table exerts a force on the table (its weight)
and the table puts an equal and opposite force on the ob-
ject to hold it up. In order to generate lift a wing must
do something to the air. What the wing does to the air
is the action while lift is the reaction.
Let’s compare two ﬁgures used to show streams of air
(streamlines) over a wing. In ﬁgure 3 the air comes
straight at the wing, bends around it, and then leaves
straight behind the wing. We have all seen similar pic-
tures, even in ﬂight manuals. But, the air leaves the wing
exactly as it appeared ahead of the wing. There is no net 3
action on the air so there can be no lift! Figure 4 shows
the streamlines, as they should be drawn. The air passes
over the wing and is bent down. The bending of the air
is the action. The reaction is the lift on the wing.
FIG. 3: Common depiction of airﬂow over a wing. This wing
has no lift.
FIG. 4: True airﬂow over a wing with lift, showing upwash
and downwash.
IV. THE WING AS A PUMP
As Newton’s laws suggest, the wing must change some-
thing of the air to get lift. Changes in the air’s momen-
tum will result in forces on the wing. To generate lift a
wing must divert air down, lots of air.
The lift of a wing is equal to the change in momentum
of the air it diverts down. Momentum is the product of
mass and velocity. The lift of a wing is proportional to
the amount of air diverted down times the downward ve-
locity of that air. Its that simple. (Here we have used
an alternate form of Newton’s second law that relates the
acceleration of an object to its mass and to the force on it,
F = ma) For more lift the wing can either divert more air
(mass) or increase its downward velocity. This downward
velocity behind the wing is called "downwash". Figure
5 shows how the downwash appears to the pilot (or in
a wind tunnel). The ﬁgure also shows how the down-
wash appears to an observer on the ground watching the
wing go by. To the pilot the air is coming oﬀ the wing
at roughly the angle of attack. To the observer on the
ground, if he or she could see the air, it would be coming
oﬀ the wing almost vertically. The greater the angle of
attack, the greater the vertical velocity. Likewise, for the
same angle of attack, the greater the speed of the wing
the greater the vertical velocity. Both the increase in the
speed and the increase of the angle of attack increase the
length of the vertical arrow. It is this vertical velocity
that gives the wing lift.
FIG. 5: True airﬂow over a wing with lift, showing upwash
and downwash.
As stated, an observer on the ground would see the
air going almost straight down behind the plane. This
can be demonstrated by observing the tight column of
air behind a propeller, a household fan, or under the
rotors of a helicopter, all of which are rotating wings. If
the air were coming oﬀ the blades at an angle the air
would produce a cone rather than a tight column. If a
plane were to ﬂy over a very large scale, the scale would
register the weight of the plane.
If we estimate the average vertical component of the
downwash of a Cessna 172 traveling at 110 knots to be
about 9 knots, then to generate the needed 2,300 lbs of
lift the wing pumps a whopping 2.5 ton/sec of air! In fact,
as will be discussed later, this estimate may be as much
as a factor of two too low. The amount of air pumped
down for a Boeing 747 to create lift for its roughly 800,000
pounds takeoﬀ weight is incredible indeed.
Pumping, or diverting, so much air down is a strong
argument against lift being just a surface eﬀect as implied
by the popular explanation. In fact, in order to pump 2.5
ton/sec the wing of the Cessna 172 must accelerate all of
the air within 9 feet above the wing. (Air weighs about 2
pounds per cubic yard at sea level.) Figure 6 illustrates
the eﬀect of the air being diverted down from a wing. A
huge hole is punched through the fog by the downwash
from the airplane that has just ﬂown over it.