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 ...
**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"?
The answer one frequently gets is misleading and often
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-
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
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.
4
FIG. 6: Downwash and wing vortices in the fog. (Photogra-
pher Paul Bowen, courtesy of Cessna Aircraft, Co.)
So how does a thin wing divert so much air? When
the air is bent around the top of the wing, it pulls on the
air above it accelerating that air down, otherwise there
would be voids in the air left above the wing. Air is
pulled from above to prevent voids. This pulling causes
the pressure to become lower above the wing. It is the
acceleration of the air above the wing in the downward
direction that gives lift. (Why the wing bends the air
with enough force to generate lift will be discussed in the
next section.)
As seen in figure 4, a complication in the picture of
a wing is the effect of "upwash" at thae leading edge
of the wing. As the wing moves along, air is not only
diverted down at the rear of the wing, but air is pulled
up at the leading edge. This upwash actually contributes
to negative lift and more air must be diverted down to
compensate for it. This will be discussed later when we
consider ground effect.
Normally, one looks at the air flowing over the wing in
the frame of reference of the wing. In other words, to the
pilot the air is moving and the wing is standing still. We
have already stated that an observer on the ground would
see the air coming off the wing almost vertically. But
what is the air doing above and below the wing? Figure
7 shows an instantaneous snapshot of how air molecules
are moving as a wing passes by. Remember in this figure
the air is initially at rest and it is the wing moving. Ahead
of the leading edge, air is moving up (upwash). At the
trailing edge, air is diverted down (downwash). Over
the top the air is accelerated towards the trailing edge.
Underneath, the air is accelerated forward slightly, if at
all.
FIG. 7: Direction of air movement around a wing as seen by
an observer on the ground.
In the mathematical aerodynamics description of lift
this rotation of the air around the wing gives rise to the
"bound vortex" or "circulation" model. The advent of
this model, and the complicated mathematical manipu-
lations associated with it, leads to the direct understand-
ing of forces on a wing. But, the mathematics required
typically takes students in aerodynamics some time to
master.
One observation that can be made from figure 7 is that
the top surface of the wing does much more to move
the air than the bottom. So the top is the more critical
surface. Thus, airplanes can carry external stores, such
as drop tanks, under the wings but not on top where
they would interfere with lift. That is also why wing
struts under the wing are common but struts on the top
of the wing have been historically rare. A strut, or any
obstruction, on the top of the wing would interfere with
the lift.
V. AIR HAS VISCOSITY
The natural question is "how does the wing divert the
air down?" When a moving fluid, such as air or water,
comes into contact with a curved surface it will try to
follow that surface. To demonstrate this effect, hold a
water glass horizontally under a faucet such that a small
stream of water just touches the side of the glass. Instead
of flowing straight down, the presence of the glass causes
5
the water to wrap around the glass as is shown in figure
8. This tendency of fluids to follow a curved surface is
known as the Coanda effect. From Newton’s first law we
know that for the fluid to bend there must be a force
acting on it. From Newton’s third law we know that the
fluid must put an equal and opposite force on the object
that caused the fluid to bend.vis
FIG. 8: Coanda effect.
Why should a fluid follow a curved surface? The an-
swer is viscosity: the resistance to flow which also gives
the air a kind of "stickiness." Viscosity in air is very small
but it is enough for the air molecules to want to stick to
the surface. The relative velocity between the surface
and the nearest air molecules is exactly zero. (That is
why one cannot hose the dust off of a car and why there
is dust on the backside of the fans in a wind tunnel.) Just
above the surface the fluid has some small velocity. The
farther one goes from the surface the faster the fluid is
moving until the external velocity is reached (note that
this occurs in less than an inch). Because the fluid near
the surface has a change in velocity, the fluid flow is bent
towards the surface. Unless the bend is too tight, the
fluid will follow the surface. This volume of air around
the wing that appears to be partially stuck to the wing
is called the "boundary layer".
VI. LIFT AS A FUNCTION OF ANGLE OF
ATTACK
There are many types of wing: conventional, sym-
metric, conventional in inverted flight, the early biplane
wings that looked like warped boards, and even the
proverbial "barn door." In all cases, the wing is forc-
ing the air down, or more accurately pulling air down
from above. What all of these wings have in common
is an angle of attack with respect to the oncoming air.
It is this angle of attack that is the primary parameter
in determining lift. The lift of the inverted wing can
be explained by its angle of attack, despite the apparent
contradiction with the popular explanation involving the
Bernoulli principle. A pilot adjusts the angle of attack
to adjust the lift for the speed and load. The popular ex-
planation of lift which focuses on the shape of the wing
gives the pilot only the speed to adjust.
To better understand the role of the angle of attack it is
useful to introduce an "effective" angle of attack, defined
such that the angle of the wing to the oncoming air that
gives zero lift is defined to be zero degrees. If one then
changes the angle of attack both up and down one finds
that the lift is proportional to the angle. Figure 9 shows
the coefficient of lift (lift normalized for the size of the
wing) for a typical wing as a function of the effective angle
of attack. A similar lift versus angle of attack relationship
is found for all wings, independent of their design. This
is true for the wing of a 747 or a barn door. The role of
the angle of attack is more important than the details of
the airfoil’s shape in understanding lift.
FIG. 9: Coefficient of lift versus the effective angle of attack.
Typically, the lift begins to decrease at an angle of
attack of about 15 degrees. The forces necessary to bend
the air to such a steep angle are greater than the viscosity
of the air will support, and the air begins to separate from
the wing. This separation of the airflow from the top of
the wing is a stall.
6
VII. THE WING AS AIR "SCOOP"
We now would like to introduce a new mental image of
a wing. One is used to thinking of a wing as a thin blade
that slices through the air and develops lift somewhat
by magic. The new image that we would like you to
adopt is that of the wing as a scoop diverting a certain
amount of air from the horizontal to roughly the angle
of attack, as depicted in figure 10. The scoop can be
pictured as an invisible structure put on the wing at the
factory. The length of the scoop is equal to the length
of the wing and the height is somewhat related to the
chord length (distance from the leading edge of the wing
to the trailing edge). The amount of air intercepted by
this scoop is proportional to the speed of the plane and
the density of the air, and nothing else.
FIG. 10: The wing as a scoop.
As stated before, the lift of a wing is proportional to the
amount of air diverted down times the vertical velocity
of that air. As a plane increases speed, the scoop diverts
more air. Since the load on the wing, which is the weight
of the plane, does not increase the vertical speed of the
diverted air must be decreased proportionately. Thus,
the angle of attack is reduced to maintain a constant lift.
When the plane goes higher, the air becomes less dense
so the scoop diverts less air for the same speed. Thus, to
compensate the angle of attack must be increased. The
concepts of this section will be used to understand lift in
a way not possible with the popular explanation.
VIII. LIFT REQUIRES POWER
When a plane passes overhead the formerly still air
ends up with a downward velocity. Thus, the air is left
in motion after the plane leaves. The air has been given
energy. Power is energy, or work, per time. So, lift must
require power. This power is supplied by the airplane’s
engine (or by gravity and thermals for a sailplane).
How much power will we need to fly? The power
needed for lift is the work (energy) per unit time and
so is proportional to the amount of air diverted down
times the velocity squared of that diverted air. We have
already stated that the lift of a wing is proportional to
the amount of air diverted down times the downward ve-
locity of that air. Thus, the power needed to lift the
airplane is proportional to the load (or weight) times the
vertical velocity of the air. If the speed of the plane is
doubled the amount of air diverted down doubles. Thus
the angle of attack must be reduced to give a vertical ve-
locity that is half the original to give the same lift. The
power required for lift has been cut in half. This shows
that the power required for lift becomes less as the air-
plane’s speed increases. In fact, we have shown that this
power to create lift is proportional to one over the speed
of the plane.
But, we all know that to go faster (in cruise) we must
apply more power. So there must be more to power than
the power required for lift. The power associated with
lift, described above, is often called the "induced" power.
Power is also needed to overcome what is called "para-
sitic" drag, which is the drag associated with moving the
wheels, struts, antenna, etc. through the air. The en-
ergy the airplane imparts to an air molecule on impact
is proportional to the speed squared. The number of
molecules struck per time is proportional to the speed.
Thus the parasitic power required to overcome parasitic
drag increases as the speed cubed.
Figure 11 shows the power curves for induced power,
parasitic power, and total power which is the sum of in-
duced power and parasitic power. Again, the induced
power goes as one over the speed and the parasitic power
goes as the speed cubed. At low speed the power require-
ments of flight are dominated by the induced power. The
slower one flies the less air is diverted and thus the angle
of attack must be increased to maintain lift. Pilots prac-
tice flying on the "backside of the power curve" so that
they recognize that the angle of attack and the power
required to stay in the air at very low speeds are consid-
erable.
At cruise, the power requirement is dominated by par-
asitic power. Since this goes as the speed cubed an in-
crease in engine size gives one a faster rate of climb but
does little to improve the cruise speed of the plane.
Since we now know how the power requirements vary
with speed, we can understand drag, which is a force.
Drag is simply power divided by speed. Figure 12 shows
the induced, parasitic, and total drag as a function of
speed. Here the induced drag varies as one over speed
squared and parasitic drag varies as the speed squared.
Taking a look at these curves one can deduce a few things
about how airplanes are designed. Slower airplanes, such
7
FIG. 11: Power requirements versus speed.
as gliders, are designed to minimize induced drag (or in-
duced power), which dominates at lower speeds. Faster
airplanes are more concerned with parasitic drag (or par-
asitic power).
FIG. 12: Drag versus speed.
IX. WING EFFICIENCY
At cruise, a non-negligible amount of the drag of a
modern wing is induced drag. Parasitic drag, which dom-
inates at cruise, of a Boeing 747 wing is only equivalent
to that of a 1/2-inch cable of the same length. One might
ask what affects the efficiency of a wing. We saw that the
induced power of a wing is proportional to the vertical
velocity of the air. If the length of a wing were to be
doubled, the size of our scoop would also double, divert-
ing twice as much air. So, for the same lift the vertical
velocity (and thus the angle of attack) would have to be
halved. Since the induced power is proportional to the
vertical velocity of the air, it too is reduced by half. Thus,
the lifting efficiency of a wing is proportional to one over
the length of the wing. The longer the wing the less in-
duced power required to produce the same lift, though
this is achieved with an increase in parasitic drag. Low
speed airplanes are affected more by induced drag than
fast airplanes and so have longer wings. That is why
sailplanes, which fly at low speeds, have such long wings.
High-speed fighters, on the other hand, feel the effects of
parasitic drag more than our low speed trainers. There-
fore, fast airplanes have shorter wings to lower parasite
drag.
There is a misconception held by some that lift does
not require power. This comes from aeronautics in the
study of the idealized theory of wing sections (airfoils).
When dealing with an airfoil, the picture is actually that
of a wing with infinite span. Since we have seen that the
power necessary for lift is proportional to one over the
length of the wing, a wing of infinite span does not re-
quire power for lift. If lift did not require power airplanes
would have the same range full as they do empty, and he-
licopters could hover at any altitude and load. Best of all,
propellers (which are rotating wings) would not require
power to produce thrust. Unfortunately, we live in the
real world where both lift and propulsion require power.
X. POWER AND WING LOADING
Let us now consider the relationship between wing
loading and power. Does it take more power to fly more
passengers and cargo? And, does loading affect stall
speed? At a constant speed, if the wing loading is in-
creased the vertical velocity must be increased to com-
pensate. This is done by increasing the angle of attack.
If the total weight of the airplane were doubled (say, in
a 2-g turn) the vertical velocity of the air is doubled to
compensate for the increased wing loading. The induced
power is proportional to the load times the vertical ve-
locity of the diverted air, which have both doubled. Thus
the induced power requirement has increased by a factor
of four! The same thing would be true if the airplane’s
weight were doubled by adding more fuel, etc.
One way to measure the total power is to look at the
rate of fuel consumption. Figure 13 shows the fuel con-
sumption versus gross weight for a large transport air-
plane traveling at a constant speed (obtained from ac-
tual data). Since the speed is constant the change in fuel
consumption is due to the change in induced power. The
data are fitted by a constant (parasitic power) and a term
that goes as the load squared. This second term is just
what was predicted in our Newtonian discussion of the
effect of load on induced power.
8
FIG. 13: Fuel consumption versus load for a large transport
airplane traveling at a constant speed.
The increase in the angle of attack with increased load
has a downside other than just the need for more power.
As shown in figure 9 a wing will eventually stall when the
air can no longer follow the upper surface, that is, when
the critical angle is reached. Figure 14 shows the angle
of attack as a function of airspeed for a fixed load and for
a 2-g turn. The angle of attack at which the plane stalls
is constant and is not a function of wing loading. The
stall speed increases as the square root of the load. Thus,
increasing the load in a 2-g turn increases the speed at
which the wing will stall by 40%. An increase in altitude
will further increase the angle of attack in a 2-g turn.
This is why pilots practice "accelerated stalls" which il-
lustrate that an airplane can stall at any speed. For any
speed there is a load that will induce a stall.
XI. WING VORTICES
One might ask what the downwash from a wing looks
like. The downwash comes off the wing as a sheet and is
related to the details of the load distribution on the wing.
Figure 15 shows, through condensation, the distribution
of lift on an airplane during a high-g maneuver. From the
figure one can see that the distribution of load changes
from the root of the wing to the tip. Thus, the amount
of air in the downwash must also change along the wing.
The wing near the root is "scooping" up much more air
than the tip. Since the root is diverting so much air the
net effect is that the downwash sheet will begin to curl
FIG. 14: Angle of attack versus speed for straight and level
flight and for a 2-g turn.
outward around itself, just as the air bends around the
top of the wing because of the change in the velocity of
the air. This is the wing vortex. The tightness of the
curling of the wing vortex is proportional to the rate of
change in lift along the wing. At the wing tip the lift
must rapidly become zero causing the tightest curl. This
is the wing tip vortex and is just a small (though often
most visible) part of the wing vortex. Returning to figure
6 one can clearly see the development of the wing vortices
in the downwash as well as the wing tip vortices.
FIG. 15: Condensation showing the distribution of lift along
a wing. The wingtip vortices are also seen. (from Patterns in
the Sky, J.F. Campbell and J.R. Chambers, NASA SP-514.)
Winglets (those small vertical extensions on the tips
of some wings) are used to improve the efficiency of the
wing by increasing the effective length of the wing. The
lift of a normal wing must go to zero at the tip because
the bottom and the top communicate around the end.
The winglets blocks this communication so the lift can
9
extend farther out on the wing. Since the efficiency of a
wing increases with length, this gives increased efficiency.
One caveat is that winglet design is tricky and winglets
can actually be detrimental if not properly designed.
XII. GROUND EFFECT
Another common phenomenon that is misunderstood
is that of ground effect. That is the increased efficiency
of a wing when flying within a wing length of the ground.
A low-wing airplane will experience a reduction in drag
by 50% just before it touches down. There is a great
deal of confusion about ground effect. Many pilots (and
the FAA VFR Exam-O-Gram No. 47) mistakenly believe
that ground effect is the result of air being compressed
between the wing and the ground.
To understand ground effect it is necessary to have an
understanding of upwash. For the pressures involved in
low speed flight, air is considered to be non-compressible.
When the air is accelerated over the top of the wing and
down, it must be replaced. So some air must shift around
the wing (below and forward, and then up) to compen-
sate, similar to the flow of water around a canoe paddle
when rowing. This is the cause of upwash.
As stated earlier, upwash is accelerating air in the
wrong direction for lift. Thus a greater amount of down-
wash is necessary to compensate for the upwash as well
as to provide the necessary lift. Thus more work is done
and more power required. Near the ground the upwash
is reduced because the ground inhibits the circulation of
the air under the wing. So less downwash is necessary to
provide the lift. The angle of attack is reduced and so is
the induced power, making the wing more efficient.
Earlier, we estimated that a Cessna 172 flying at 110
knots must divert about 2.5 ton/sec to provide lift. In
our calculations we neglected the upwash. From the mag-
nitude of ground effect, it is clear that the amount of air
diverted is probably more like 5 ton/sec.
XIII. CONCLUSIONS
Let us review what we have learned and get some idea
of how the physical description has given us a greater
ability to understand flight. First what have we learned:
• The amount of air diverted by the wing is propor-
tional to the speed of the wing and the air density.
• The vertical velocity of the diverted air is propor-
tional to the speed of the wing and the angle of
attack.
• The lift is proportional to the amount of air di-
verted times the vertical velocity of the air.
• The power needed for lift is proportional to the lift
times the vertical velocity of the air.
Now let us look at some situations from the physical
point of view and from the perspective of the popular
explanation.
• The plane’s speed is reduced. The physical view
says that the amount of air diverted is reduced so
the angle of attack is increased to compensate. The
power needed for lift is also increased. The popular
explanation cannot address this.
• The load of the plane is increased. The physical
view says that the amount of air diverted is the
same but the angle of attack must be increased to
give additional lift. The power needed for lift has
also increased. Again, the popular explanation can-
not address this.
• A plane flies upside down. The physical view has
no problem with this. The plane adjusts the angle
of attack of the inverted wing to give the desired
lift. The popular explanation implies that inverted
flight is impossible.
As one can see, the popular explanation, which fix-
ates on the shape of the wing, may satisfy many but it
does not give one the tools to really understand flight.
The physical description of lift is easy to understand and
much more powerful.
Visualization of the airflow with increasing angle of attack.
When the angle of attack is too high the airflow over most of the top of the wing has separated and there is **no noticeable downwash thus there is no lift and the wing stalls**.
I'm not sure this is right. Flow bends around objects even in the absence of viscosity. What determines bending is actually pressure gradients that develop due to local accelerations and decelerations of the fluid.
**@Prof. Rod Burton** That's correct. The authors are simply assuming no angle of attack and the principle of equal transit times. Here is an interesting visualization showing the airflow over and under the wing with increasing angle of attack - one can also see the change in the leading edge stagnation point.
> The popular explanation also implies that inverted flight is impossible. It certainly does not address acrobatic airplanes, with symmetric wings (the top and bottom surfaces are the same shape)
> One observation that can be made from figure 7 is that the top surface of the wing does much more to move the air than the bottom. So the top is the more critical surface. Thus, airplanes can carry external stores, such as drop tanks, under the wings but not on top where they would interfere with lift. That is also why wing struts under the wing are common but struts on the top of the wing have been historically rare. A strut, or any obstruction, on the top of the wing would interfere with the lift.
**The Coanda effect** was first discovered by a mathematician and engineer named Henri Coanda in 1910. Coanda observed that when air was ejected from a rectangular nozzle, it would attach itself to an inclined flat plate connected to the nozzle exit. He stated that *“when a jet of fluid is passed over a curved surface, it bends to follow the surface, entraining large amounts of air as it does so”*. He applied this principle to a series of different surfaces, each at a sharp angle to the previous one, and succeeded in turning flows through angles as large as 180$^{\circ}$.
He was the first to recognize the practical application of the phenomenon in aircraft design.
At the end of the wing the lift goes to zero very rapidly and there is some airflow around the wingtip. This causes the tightest curl in the wing vortex, creating the wingtip vortex. See below.
The Angle of attack (also known as AOA) is the angle between the oncoming air or relative wind and a reference line on the airplane or wing. See a few examples below.
Fig: Illustartion of 3 different angles of attack: 5$^{\circ}$, 10$^{\circ}$, 20$^{\circ}$
In order to lower the induced power needed for lift one needs to improve the efficiency of a wing. The easiest way to increase the efficiency of a wing is to increase the amount of air diverted by the wing. If the wing is able to divert more air, then the vertical velocity of the air is reduced for the same lift and so is the induced power. An "easy" way to accomplish this is by increasing the size of the wing.
At low speeds induced drag dominates so for example sailplanes have longer wings and at high speeds parasitic drag dominates reason why high speed fighters have shorter wings.
**The induced power** is the power required to redirect the air and generate lift.
**The parasitic power** is the power needed to overcome the drag when an object is moving through a fluid (in the case of a plane that fluid is the atmosphere). The power required to overcome the parasitic drag is given by:
$P_d = \mathbf{F}_d \cdot \mathbf{v} = \tfrac12 \rho v^3 A C_d$
where $F_{D}$ is the drag force, $\rho$ is the density of the fluid $v$ is the speed of the object relative to the fluid, $A$ is the cross sectional area, and $C_{D}$ is the drag coefficient.
At cruise, the total power requirement is dominated by parasitic power since it is proportional to $v^3$.
The total power is the sum of the induced and parasitic power.
The air going over the top of the wing reaches the trailing edge before the air that goes under the wing. The air that passed under the wing has a somewhat retarded velocity compared to the velocity of air some distance from the wing. See the video below for a better visualization of this effect:
[](https://www.youtube.com/watch?v=UqBmdZ-BNig)
If the principle of equal transit times and thus the Bernoulli effect were the only contributing factors to generate lift than the air would have to travel a distance over the wing $L_{over}$ that is 50% longer than that traveled under the wing $L_{under}$ which would produce "weirdly" shaped wings.
"the wing of a typical small plane, whichhas a top surface that is 1.5 - 2.5% longer than the bottom," is incorrect. As the angle of attack increases, the leading edge stagnation point moves rearward along the underside of the wing, which lengthens the distance over the top and shortens the distance along the underside. Thus Fig. 1 is distorted.
In order for an airplane to rise and fly in the air, a force must be created that equals or exceeds the force of gravity. This force is called lift.
The popular explanation for lift is based on Bernoulli's principle. This explanation relies on the "principle of equal transit times" - air travelling over and under the wing will do so in the same amount of time.
This explanation falls short when it comes to explain simple things like inverted flight or flat/symmetric wings. This paper provides a general overview of all the effects that contribute to the lift generated by wings and thus provides a better explanation of how planes really fly.
If you are interested in learning more, the authors of this paper also wrote a book describe the phenomenon of flight: [Understanding Flight, by David W. Anderson, Scott Eberhardt](https://www.goodreads.com/book/show/26251943-understanding-flight-second-edition)
**How Do Airplanes Fly?** A short and very interest explanation by Minute Physics:
[](https://www.youtube.com/watch?v=Gg0TXNXgz-w)
**Upwash**
When a plane is flying the air approaches the front of wings from below due to the wings angle of attack and is. This air is diverted upwards: upwash.
**Downwash**
The air splits around the wing and it will leave the wing with a downward angle. This downward-traveling air is the downwash and is the action that creates lift as its reaction.
There has been a change in the air after passing over the wing. Lift is created via a force acting on the air and a reaction force acting on the wing.
A better visualization of the downwash and upwash zones can be seen below.
The principle of **"equal transit times"** states that the air going around a wing, whether going over or under, must do so in equal time. For a curved wing the air has to travel farther over the top of the wing it has to go faster which produces a difference in pressure that will generate lift (Bernoulli’s principle).
The notion that the air passing above and below the wing must do so in equal time is a common misconception that is usually used to explain how wings work. For a detailed and visual explanation of how wings generate lift see the video below **"How Does A Wing Actually Work?"**.
[](https://www.youtube.com/watch?v=aFO4PBolwFg)
The wing produces lift by diverting air down. The work produced by the wing when it diverts the air downs produces lift. The lift produced by a wing $L_{wing}$ is the proportional to the product of the amount of air $V_{air}$ diverted down and the speed of that air $v_{air}$:
$$L_{wing} \propto V_{air} \cdot v_{air}$$
Bernoulli's Principle states that within a horizontal flow of fluid, points of higher fluid speed will have less pressure than points of slower fluid speed - an increase in velocity leads to an decrease in pressure.
Bernoulli's equation can be considered as a statement of the conservation of energy for flowing fluids and can be written as follows:
$$P+\dfrac{1}{2}\rho v^2+\rho gh=\text{constant}$$
Applying this principle to the wing of an airplane we get that the air flowing over an airfoil will decrease in pressure. The difference in pressure between the top surface and the bottom surface creates a net pressure force in the upward direction. This pressure force is lift.
