Alexander
McKee begins his fascinating book, Great
Mysteries of Aviation, with the observation
that the most puzzling
mystery in the history of aviation is why it took
so long for humankind to
learn to fly. With so much
intellectual and physical energy devoted to a single
problem for so long, one might
have expected someone to stumble
on the secret, if only by accident, long ago.
What was the obstacle?
The problem is that the physical principles that
lie at the foundation of
flight are counterintuitive; indeed, the
mechanics of flight were ultimately revealed after
some fancy manipulation of
the physics and mathematics created by Sir Isaac Newton in
the late 1600s. Not only were
the theories of Aristotle, Bacon, Leonardo, and the
rest all wrong, but the
true principles of flight, including
how birds stay aloft, were simply un-guessable
and un-observable.

It took
several remarkable scientists, including
members of a celebrated family of
scientific giants, to
piece together the puzzle. For all the triumphs of
Newtonian physics—from
explaining the tides to predicting comets—Newton had
little success in applying his
methods to fluids and fluid
dynamics. Along came the
Bernoullis, a Swiss family among
whom were some of the most
important contributors to the
development of mathematics and science in the seventeenth
and eighteenth centuries. The two key figures in
this family were Johann (1667—1
748), who made the
University of Basel in Switzerland the centre of European
science in its day, and
his son Daniel (1700—1782). In
1725, Daniel accepted an appointment in St. Petersburg,
Russia, where he stayed for eight years and did
some of his most important work.
He managed to take a friend
with him: the great mathematician Leonhard Euler,
who had been a student of
Johann Bernoulli back in Basel.

In 1734,
Daniel completed his famous work
Hydrodynamica, which was
not published until 1738. In
addition to coining the word “hydrodynamics,” Daniel
laid out the basic
principles of the new science, applying
Newton’s basic laws to simplified cases of
fluid dynamics. Out of this work came Bernoulli’s
Principle (or Law), which Euler
helped express as a mathematical
equation known as Bernoulli’s
Equation. What Bernoulli found
boiled down to this: when a
fluid is moving—through a pipe or conduit, or
simply over any surface—it
exerts pressure in all
directions: against anything
that is in the way of its flow, as well as
against any surface it
touches. For example, as water
flows through a garden hose, you can feel the pressure of
the water against the
inner wall of the hose if you try to
squeeze the hose. Now, if the fluid is
non-compressible
(meaning it can’t he squeezed into a smaller
volume, which is true of water,
in most ordinary circumstances),
and if there is no change in the amount of fluid
flowing (meaning
nothing is leaking out or coming in), then the
faster the fluid is flowing, the lower its pressure
against the surface it’s
flowing over will be.

That means
that when you pinch the garden
hose slightly in the middle
and the water keeps coming out of the end at the
same rate, then the water
must be travelling through the
pinched portion a little faster (since the same
amount of water is
passing through that section of the hose as
before). Our intuition is that faster water exerts
greater pressure (and it
does, but only in the direction of the
flow), but the pressure of the faster
water against the wall of
the hose (which is perpendicular to the direction of the
flow) is less—a total
surprise. Euler gave Bernoulli’s work
mathematical form (with the help of the work of
French mathematician Jean le
Rond d’Alembert), and Johann,
Daniel’s father, made it intuitively
palatable in his 1743
work, Hydraulica (which he tried to pass off as having
been written in 1728).

Now, as to
flying: if a sleek, symmetrical wing is in
an air flow so that air is passing over it and
under it, the flow can be
considered non-compressible and
a closed system—a few feet back
(if the wing is sleek enough and
the wind is not too strong), one wouldn’t even know
the air took a
little detour around the wing. As the air flows
over the wing’s surface, it too exerts pressure in
two directions—in the
direction of its flow (that’s the force of
the wind) and perpendicular to its
flow against the surface of the wing. But since the
air has to travel a greater
distance to flow around the
wing, it speeds up, and by
Bernoulli’s Principle it exerts less pressure on the
surface of the wing.

Since the
wing is symmetrical (a teardrop
shape in cross-section), the reduced
pressure is the same both
above and below. Now what
happens if we slice the wing in
half, so that the lower surface
is straight (and the air flows
across it in a straight
line), hut the upper surface is curved (and the
air speeds up only when
flowing over that surface)? The pressure of
the air on the upper
surface drops, making the
pressure of the air on the
underside greater. The
difference
between the pressure upward on the underside of
the wing and the force downward on
the top surface is called
“lift”; the curve of the top surface of a wing over
its under surface is
called its “camber.”

After centuries of believing the
very reasonable notion that, like ships
floating on the ocean,
birds flew in a sea of air, and that
a wing (of a bird or of a successful aircraft)
would have a
cross-section that, like a boat, would be curved on the
bottom and flat on top, the
exact opposite turned out to
he the case. Flight is made possible by the lift
created by the
pressure difference resulting from air flowing over
a wing with camber, and that’s
the secret of flight.

Bernoulli's principle thus says that a rise (fall) in
pressure in a flowing fluid must always be accompanied
by a decrease (increase) in the speed, and conversely,
if an increase (decrease) in , the speed of the fluid
results in a decrease (increase) in the pressure. This
is at the heart of a number of everyday phenomena. As a
very trivial example, Bernouilli's principle is
responsible for the fact that a shower curtain gets
"sucked inwards'' when the water is first turned on.
What happens is that the increased water/air velocity
inside the curtain (relative to the still air on the
other side) causes a pressure drop. The pressure
difference between the outside and inside causes a net
force on the shower curtain which sucks it inward. A
more useful example is provided by the functioning of a
perfume bottle: squeezing the bulb over the fluid
creates a low pressure area due to the higher speed of
the air, which subsequently draws the fluid up. This is
illustrated in the following figure.

Action of a spray atomizer

Bernouilli's principle also tells us
why windows tend to explode, rather than implode in
hurricanes: the very high speed of the air just outside
the window causes the pressure just outside to be much
less than the pressure inside, where the air is still.
The difference in force pushes the windows outward, and
hence explode. If you know that a hurricane is coming it
is therefore better to open as many windows as possible,
to equalize the pressure inside and out.

Another example of Bernoulli's principle at work is
in the lift of aircraft wings and the motion of ``curve
balls'' in baseball. In both cases the design is such as
to create a speed differential of the flowing air past
the object on the top and the bottom - for aircraft
wings this comes from the movement of the flaps, and for
the baseball it is the presence of ridges. Such a speed
differential leads to a pressure difference between the
top and bottom of the object, resulting in a net force
being exerted, either upwards or downwards. This is
illustrated in the following figure.

Lift of an aircraft wing