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
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-
derstand lift we must return to high school physics and
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