# What Is The Coanda Effect?

Mechanics

Feb 22, 2014 (4 years and 2 months ago)

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What Is The Coanda Effect?

The flow of gases is subject to a great many "effects" which have been observed and
documented over the years.

In many cases, the person responsible for making the first observations of a particular effect
has their name attribu
ted to it and then they become famous
--

albeit only amongst those who
are interested in such things.

One such effect is that observed and documented by
a Romamanian by the name of Henri
-
Marie Coanda
in the 1930s.

Coanda noted that a stream of fluid or
gas will tend to hug a convex contour when directed at a
tangent to that surface.

You can check this out for yourself by turning on a tap, so that there's a steady but gentle
continuous stream of water flowing. Now bring the back of a spoon into slight co
ntact with the
stream and you'll find that the water will no longer fall straight down but actually stick to the
curve of the spoon.

This rather unintuitive behavior is the Coanda effect in action.

It's pretty easy to understand why a flow would be defle
cted by a concave curve
--

the curve will
"push" the flow around the corner
--

but isn't it odd that the flow seems to be pulled by a curved
surface?

My own experiments indicate that a single curved surface will deflect a gasflow by a maximum
degrees
--

after which the flow detaches itself from the curve and travels at a
tangent to that curve.

How Can This Be Used In A Pulsejet?

Like all seemingly unnatural behaviors, the Coanda effect has been put to good use in a
number of applications.

Ind
eed, some of the gasflows within my
X
-
Jet engine

rely on the Coanda effect so I thought I'd
have a think about how the same effect could be applied to more traditional pulsejet engines.

Here's what

I've come up with:

The Combustion Phase

What we have here is a possible valveless pulsejet design using the Coanda effect to
significantly reduce the tendency for combustion gases to travel up the intake tube.

When the air
-
fuel ignites, some of the hot
gases travel out the tailpipe through the expected
route
--

but those which would be expected to travel out the intake tube (the left
-
most arrows)
are subjected to the Coanda effect produced by
the curved path at the mouth of that internal
tube.

The
se gases are further coerced down the tailpipe by another of these great "effects" first
observed by (and named after) Mr Bernoulli. Because the gases which enter the tailpipe
through the outermost path are travelling very fast, they produce a low
-
pressure

area at the
right
-
hand end of that internal tube. The flow entering the front of the internal tube is thus further
encouraged to exit through the rear of the engine thanks to this area of low
-
pressure.

Now, let's see what happens during the intake phase
of the engine's operation.

The Intake Phase

The incoming air is deflected towards the outside path by way of the diamond shape in the
middle of the intake tube.

Note that the diamond shape has sharp edges, not curves. If we made this a nicely curved
shap
e then the Coanda effect would work against us by pulling the incoming air back towards
the center of the internal tube. By using a sharp edge, the flow will separate and virtually all of it
will travel outwards and into the combustion area.

However, beca
use a vortex will form on the back
-
side of this diamond, a small amount of the
incoming air will travel into the internal tube
--

but that's not going to be a problem because it will
simply become extra mass for the engine to eject later.

The fuel will be

injected at the point where the incoming air passes over the circle at the front of
the combustion area.

When the fresh air
-
fuel mixture ignites, the whole cycle repeats again.

Will It Work?

Now all this looks fine on paper (or a webpage) but will it wo
rk as planned?

To be honest
--

I don't know, I haven't built it yet.

Based on my experience with the design of pulsejets I'd have to say that there's probably a devil
in the detail.

The precise angles and radius of the curves involved need to be establi
shed by a little
calculation and much empirical work, but I see no reason why the basic theory won't hold up.

Now this isn't going to stop all the hot gases from trying to exit through the intake tube
--

no
valveless system can actually do that but I hope

that it could provide enough flow control to
allow such an engine to provide a good measure of static thrust.

The advantage of not bending the engine in half and facing the intake in the same direction as
the exhaust is that you can then take much more a
dvantage of ram
-
effect to increase the power
of such an engine when it is operating at high speed.

The "Coanda Effect"

History of The "Coanda Effect"

I came across this device recently and hope you find it interesting also

In 1910 a young Romanian
born engineer named Henri Coanda tested a
the inventor. The engine was not a Turbo jet which was later invented by
Frank Whittle and Von Ohain, but had a gasoline engine driven centr
ifugal
compressor, a combustion chamber and nozzle.

Coanda placed metal plates between the hot jet gases and the plywood
fuselage. However instead of deflecting the jet away it deflected it onto the
plates, ran along them and set his plane alight. Fascina
ted, he failed to
notice he was approaching a wall at high speed until the last second, pulled
back on the stick, became airborne enough to clear the wall, crashed and
was thrown clear to watch his plane go up in flames.

More than 20 years later he came t
o understand precisely the phenomenon
which was named after him, the "Coanda Effect".

Coanda jets are generated by blowing a moderate to high pressure gas
(such as air) or liquid through a narrow slot over a surface which in some
cases may be convexly cur
ved.

The jet runs tangent to the surface and can circulate around 180° bends.
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jet to recirculate around 360°.

The Coanda jets are never laminar like the flow over an aircraft wing or fan
blade. The jets are always highly turbulent. The jet is composed of myriads
of localised eddy currents. The speed of the air in the swirling or rotating
currents is far higher than the linear velocity of the whole jet stream itself.

Pressure is related to speed as you are now aware of. A round jet issuing
from a nozzle entrains ambient air due to its high velocity lowering its
pressure which attracts the
ambient air by collision and entrapment of
molecules.

Coanda jets are ejected from slots and then traverse a hard surface or wall.
They are sometimes called a wall jet. This wall after the slot creates a non
-
symmetrical nozzle.

The velocity of the jet im
mediately evacuates the molecules between it and
the wall. This low pressure region cannot be relieved by ambient inflow as
ambient air is on the other side of the jet and so the jet quickly deflects
toward and runs tangent to the wall. The average pressur
e across a Coanda
jet is lower than the average pressure across an unbounded round jet.

This means that the average velocity at any point in the Coanda jet is higher
than in a conventional jet at the same distance from the slot. It follows then
that the p
ressure is lower at any comparable distance from the slot and the
momentum and mass flow are higher at the same points.

Flow augmentation by entrainment of ambi
ent air is also greater than with a
conventional jet because of the pressure gradient caused by the proximity of
the hard surface (the wall) tangent to the jet and this is a more efficient
means of momentum transfer than mere molecular collision and entrap
ment
as with conventional jets.

The Coanda Effect

The "Coanda Effect" is a fascinating, powerful phenomenon that has been
lying almost unused for decades waiting to be exploited commercially. The
new "Jet
-
Fan" now makes it possible to revive the effect in

domestic and
industrial applications.

Some good quality higher pressure fans and
applications over which the new "Jet
-
Fan" gives
superior performance are:
-

Tu
rbine compressors (as in jet engines),

Computer chip cooling fans.

Ducting for air
-
conditioning,

Vacuum Cleaners

Ventilation in buildings,

Superchargers for racing cars, aircraft and trucks.

Lift and drive fans for Hovercraft

Ducted fans for aircraf
t

Jet boats

Water pumps for industry, agriculture and automotive

Large mine and power station ventilation and cooling

Exotic new devices impos
sible or impractical before the "Jet
-
Fan".

The main advantages of the "Jet
-
Fan" are:
-

It is stall free.

It does not require a diffuser or stator blades to realise a pressure gain.

It is more efficient over a wider speed range.

It delivers relatively hi
gh pressure air at a high flow rate with high efficiency

with no surging and delivers it axially through a nozzle.

To achieve this the main differences are:
-

The blades converge, unlike other fans (Average 6% to 10%)

The "Jet
-
Fan" does not rotate airfo
il blades around but rather rotates
convergent passageways ie. each two blades define a passageway.

It has far more blades than a conventional fan.

It has blades that are much shorter and angled to the axis of rotation.

T
he new "Jet
-
Fan" is an entirely new concept.

The gap created by the convergent blades can change during runs.

Each blade has a spigot which extends into a bore in the hub which is
aimed at the imaginary dead centre of a sphere which the hub is sliced from
.
(It has a spherical hub and shroud.) Because high pressure fans tend to leak
air back the wrong direction the "Jet
-
Fan" employs a spherical hub and the
blade roots touch the hub for their full length preventing back
-
flow. The
inside of the shroud also ha
s the same spherical aspect which shares the
same dead centre as the hub. In this way back
-
flow near the blade tips is
prevented and as all blades overlap significantly any air return is minimised
and in fact over almost all its speed and pressure range ba
ck
-
flow is
prevented entirely.

When the blades change pitch during runs the blade roots always remain
touching the hub and the infinitesimal gap between the blade tips and
shroud is not altered.

The basic idea of the "Jet
-
Fan" is very simple.

Blade speed in all fans, especially the centrifugal fans compresses air to
some extent. This compression is inevitable and is detrimental to
performance as it can cause bl
ade stall by air circulating around the trailing
edges. In addition, the air must expand to the average low pressure as it
joins the higher speed, lower pressure flow at the trailing edges,
subsequently it must have its pressure raised again as it is decel
erated
through the diffuser or stators. These pressure fluctuations decrease
efficiency.

The "Jet
-
Fan" relies on the fact that the air will be compressed by blade
speed just as in all conventional fans but in the case of the "Jet
-
Fan" the
pressure generat
ed is retained without re
-
expansion.

Blade pitch is configured to maximise compression (with liquids the
pressure rises but liquids do not compress).

The blade dynamic pressure on the air can tend to rise by the square as the
air is swept further out and

toward the trailing edges to ease the pressure within the passageways. This
is to prevent back
-
flow along the passageways.

passageway that each pair of blades define is reduced in volume.

There is therefore a step
-
down in volume between the blades.

Significant useful pressure is generated by bl
increases by the square of the blade speed increase.

The passageway therefore along its length merely progressively conforms to
the lesser space the compressed air occupies and the air is discharged in a
pressurised state.

In prac
tice the pressure within the discharge apertures is found to be
identical to that immediately aft of the blades and before the air
straighteners.

This avoids the abrupt pressure fluctuations found with other fans, the
pressure being generated once only an
d maintained and this avoids the use
of a diffuser or stators.

As system resistance increases due to a variable choke in some
applications such as ducted fans, or jet boats the fan speed is increased
and blades are brought closer together to postpone the
stall.

How the "Jet Fan" Solves the problem

The new "Jet
-
Fan" is able to produce the same high pressures required for
all the applications listed but without th
e need for a diffuser or stators.

That pressure is delivered immediately from between the fan trailing edges.
This feat is achieved by the blade convergence of the "Jet
-
Fan" which is
unlike any other fan.

What all of this means is that the new "Jet
-
Fan"
is able to perform all of the
applications listed and many more, better than existing conventional fans.

In addition to producing high pressure air or liquids the "Jet
-
Fan" has
several extra features giving it even more advantages over other fans.

The ne
w "Jet
-
Fan" has blades that are arranged about a hub that is a slice
taken from a true sphere. The blades extend into bores aimed at the
blade pitch) to be changed during runs. This e
nables the fan to maintain
high pressure and efficiency over a wider RPM range and pressure duty than
conventional fans.

The new "Jet
-
Fan" is also able to do this in very small versions, an
achievement not seen before. This means that the existing applica
tions
already listed can be performed better by "Jet
-
Fans" as they are more
efficient with higher pressures in smaller diameters and do not require the
excess baggage, (diffusers or stators).

Tiny "Jet
-
Fans" are more efficient than existing computer fans
which are
normally only around 1% to 5% efficient. Marine And Aviation Transportation

Hovercraft require high volume air flow at moderate pressures. The "Jet Fan"
can provide higher pressure when needed such as in heavy seas as it does
not stall due to fl
uctuating back pressure, and it also occupies less space.

To whom it may concern,

The LMB Company welcomes the partnership we sealed in January with the
Austral
ian JET FAN Technology Company. We are looking forward to
developing further the JET FAN for our market in association with Mr Terry
Day, and to help him produce specific prototypes for other markets as well.

We have started our JET FAN R & D eight month
program and will be very
pleased to reveal these results, graphics and prototypes during the next
military EUROSTATORY International Expo in Paris in June 1996.

All genuine enquiries for fan production for the Defence and Avionics market
(such as cooling
systems and air
-
conditioning in cells, cockpits, shelters)
and for Medical and Transportation market s (such as air
-
conditioning and
air
-
renewal in buses, tramways, trains, subways, etc....) can be addressed
to:

Mr Chapalain / LMB Director

36 Ave Curie
-

Malemort

FRANCE

Fax: ± 33 55 92 29 00

Currently, LMB on behalf of JET FAN Technology is developing a computer
designing software package for these applications. The first JET FANS are
expected to be in production in the second half of 1996.

LMB is hap
py to have this statement published in future JET FAN
Technology brochures and will consider seriously any JET FAN production
enquiries concerning our specific market.

If you need further information please let me know.

Rene Chapalain

Managing Director

Interview with Terry Day

Is it noisy?

No. Noise from a fan is due to air turbulence. The "Jet Fan" drives high
pressure air into a high pressure area. This makes it much quieter than other
fans.

No. It will be no more expensive
than the present day conventional fans it
replaces. It may be less expensive due to it's smaller size and not needing a
diffuser.

Will electric motor manufacturers be resistant due to higher speed
requirements?

No. Almost all applications require no moto
r changes at all. Only a very few
situations where a brushless electric motor is required for noise
considerations will a one stage gearbox be needed to increase fan speed.

Will manufacturers resist change due to expensive plant changes?

No. Although the

"Jet Fan" is a vast improvement over todays conventional
fans, it is still after all only a fan from a manufacturing viewpoint.

With spherical hubs, shrouds and moveable blades, surely it is more
complex and therefore more difficult to produce?

No. The
more complex versions are for more exotic, high stress or special
situations, mainly transportational, where pressures and thrust requirements
change from second to second.

90% of applications including household ones need no speed change. The
rgence is matched to the fan speed and the blades are an
integral part of the hub and are cast or moulded in one piece as with other
fans.

Will it be expensive to run?

No. The "Jet Fan" gives higher efficiency than other fans of the same size.
In other w
ords it uses less electrical power or fuel than others to do the
same job.

Is there a lot more research and development needed before the fan is

No. Most applications of the fan are ready now. The pressure versus flow
r
ate, the pressure being developed between the blades and the high
efficiency in very small sizes, have all been proven. The "Jet Fan" is ready
for manufacturing now.

The more complex versions including multi
-
staging as a compressor need
more development t
ime. We believe this period will not be long.

Is its high speed dangerous or a disadvantage?

No. We have not run it as fast as many conventional domestic vacuum
cleaner fans yet.

What is the reaction from the engineers to such a simple improvement?

We
have had many fan engineers and other technical people witness our fan
demonstration test runs. We have had no negativity and only great
enthusiasm from all.

What does buying or using an appliance with the "Jet Fan" mean to the
average consumer?

The cons
umers work will be more efficient thus saving time and money. It
also means a reduction in the consumption of fossil fuels for the production
of electricity to supply appliances. The reduction of fossil fuel consumption
will have a positive effect on green

house gas emissions and the
environment.

MODEL AIRPLANES, THE
BERNOULLI EQUATION, AND THE
COANDA EFFECT

"In aerodynamics, theory is what makes
the invisible plain. Trying to fly an
airplane without theory is like getting
into a fi
stfight with a poltergeist."

--
David Thornburg [1992].

"That we have written an equation does
not remove from the flow of fluids its
charm or mystery or its surprise."

--
Richard Feynman [1964]

INTRODUCTION

A sound theoretical understanding of lift

the Wright brothers' first flight
(Prandtl's work was most influential
1
),
but the most common explanation of lift
seen in elementary texts and popular
articles today is

The common explanation, from
The Way Things Work
[Macaulay 1988]

The reasoning
--
though incomplete
--
i s based on the
Bernoulli effect, which correctly correlates the
increased
speed with which air moves over a surface
and the lowered air pressure measured at that surface.

In fact, most airplane wings do have considerably more
curvature on the top than the bottom, lending credence
to this explanation. But, even as a child, I foun
d
that it presented me with a puzzle: how can a plane
fly inverted (upside down). When I

1
Ludwig Prandtl (1875
-
1953), a German physicist, often ca
lled the "father of
aerodynamics." His famous book on the theory of wings,
Tragflü
geltheorie
, was published in 1918.

1

pressed my 6th grade science teacher on this
question, he just got mad, denied that planes
could fly inv
erted and tried to continue his
lecture. I was very frustrated and argued until
he said, "Shut up, Raskin!" I will relate what
happened next later in this essay.

A few years later I carried out a calculation
according to a naive interpretation of the commo
n
explanation of how a wing works. Using data from
a model airplane I found that the calculated lift
was only 2% of that needed to fly the model. [See
Appendix 1 for the calculation]. Given that
Bernoulli's equation is correct (indeed, it is a
form of the
law of conservation of energy), I was
left with my original question unanswered: where
does the lift come from?

In the next few sections we look at attempts to
explain two related phenomena
--
what makes a
spinning ball curve and how a wing's shape
influence
s lift
--
and see how the common
explanation of lift has led a surprising number
of scientists (including some famous ones)
astray.

THE SPINNING BALL

The path of a ball spinning around a vertical
axis and moving forward through the air is
deflected to the ri
ght or the left of a straight
path. Experiment shows that this effect depends
both on the fact it is spinning and that it is
immersed in a fluid (air). Non
-
spinning balls or
spinning balls in a vacuum go straight. You
might, before going on, want to decide

for
yourself which way a ball spinning
counterclockwise (when seen from above) will
turn.

Three are by physicists, one is a standard
reference work, and the last, just for kicks, is
from a book by my son's

soccer coach. We'll start
with physicist James Trefil, who writes [Trefil
1984],

Before leaving the Bernoulli effect, I'd like to
point out one more area where its consequences
should be explored, and that is the somewhat
unexpected activity of a basebal
l. Consider, if
you will, the curve ball. This particular pitch
is thrown so that the ball spins around an axis
as it moves forward, as shown in the top in
figure 11
-
4. Because the surface of the ball is
rough, the effect of viscous forces is to create
a t
hin layer of air which rotates with the
surface. Looking at the diagram, we see that the
air at the point labeled A will be moving faster
than the the air at the point labeled B, because
in the first case the motion of the ball's
surface is added to the ba
ll's overall velocity,
while in the second it is subtracted. The effect,
then is a 'lift' force, which tends to move the
ball in the direction shown.
2

2
The surface roughness is not essential. The effect is observed no
matter how
smooth the ball.

2

Trefil's figure 11
-
4. It does not agree with some other sources.

Baseball
would say that the ball curves
toward third base. Trefil then shows a diagram of
a fast ball, shown as deflecting downward when
spinning so that the bottom

of the ball is
rotating forward. It is the same phenomenon with
the axis of rotation shifted 90 degrees.

In
The Physics of Baseball
1990] imagines a ball thrown toward home plate, so
that it rotates counterclockwise as seen from
ab
ove
--
as in Trefil's diagram. To the left of the
pitcher is first base, to his right is third base.

We can then expect the air pressure on the third
-
base

side of the ball, which is travelling faster
through the

air, to be greater than the pres
sure on the on the

first
-
base side, which is travelling more slowly,
and

the ball will be deflected toward first base. This
is exactly the opposite of Trefil's conclusion
though they agree that the side spinning forward
is moving faster through the air. We

have learned
from these two sources that going faster through

the air either increases or decreases the pressure
on that side. I won't take sides in this argument
as yet.

The
Encyclopedia Brittanica
[1979] gives an
explanation which introduces the concept
of drag
into the discussion.

"The drag of the side of the ball turning into the
air

(into the direction the ball is travelling)
retards the

airflow, whereas on the other side the drag speeds
up

the airflow. Greater pressure on the side where
the

airflow is

slowed down forces the ball in the
direction

of the low
-
pressure region on the opposite side,
where a

relative increase in airflow occurs."

Now we have read that spinning the ball causes the
air to move either faster or slower past the side
spinning forwa
rd, and that faster moving air
increases or decreases the pressure, depending on
the authority you choose to follow. Speaking of
authority, it

3

might be appropriate to turn to one of the
giants of physics of this century, Ri
chard
Feynman. He takes the side of Trefil,and uses a
cylinder rather than a sphere [Feynman et. al.
1964. Italics are theirs. The lift force
referred to is shown pointing upwards.]:

"The flow velocity is higher on the upper side
of a

cylinder [shown rotat
ing so that its top is
moving in

the same direction as its forward travel] than
on the

lower side. The pressures are therefore
lower
on
the

upper
side than on the lower side. So when we
have a

combination of a circulation around a cylinder
and a net

horizont
al flow, there is a net
vertical
force
on the

cylinder
--
it is called a
lift force
."

Now for my son's coach's book. The coach in
this case is the world
-
class soccer player,
George Lamptey. There is almost no theory
given, but we can be reasonably sure that
L
amptey has repeatedly tried the experiment and
should therefore report the direction the ball
turns correctly. He writes[Lamptey 1985]:

"The banana kick is more or less an off
-
center
instep

drive kick which adds a spin to the soccer
ball. Kick

off center t
o the right, the soccer ball curves
to the

left. Kick off center to the left, the soccer
ball

curves to the right... The amount the soccer
ball curves

depends on the speed of the spin."

Lamptey, like Adair, has the high pressure on
the side moving into the air. I will not relate
more accounts, some having the ball swerve one
way, some the other. Some explanations depend
on
the author's interpretation of the Bernoulli
effect, some on viscosity, some on drag, some on
turbulence.

but we are not yet finished finding problems
with the common explanation of lift.

Thecommon explanation of how a wing works leads
us to conclude, for example, that a wing which

is somewhat concave on the bottom, often called
an "undercambered" wing, will always generate
less
lift (under otherwise fixed conditions) than
a flat

4

bottomed one. This conclusion
is wrong.

We then have to ask how a flat wing like tha
t of
a paper airplane, with no curves anywhere, can
generate lift. Note that the flat wing has been
drawn at a tilt, this tilt is called "angle of
attack" and is necessary for the flat wing to
generate lift. The topic of angle of attack will
be returned to

presently.

A flat wing can generate lift. This is a bit difficult to explain

T
he cross
-
sectional shapes of wings,like those
illustrated here, are called "airfoils." A very
efficient airfoil for small, slow
-
flying models
is an arched piece of thin sheet material, but
it is not clear at all from the common
explanation how it can gener
ate lift at all

since the top and bottom of the airfoil are the
same length.

If the common explanation is all there w
ere to
it, then we should be making the tops of wings
even curvier than they now are. Then the air
would have to go even faster, and we'd get more
lift. In this diagram the wiggliness is
exaggerated. More realistic lumpy examples will
be encountered in a f
ew moments.

If we make the top of the wing like this, the air on top has a

lot longer path to follow, so the air wil
l go even faster than

with a conventional wing. You might conclude that this kind

of airfoil should have lots of lift. In fact, it is a disaster.

Enough examples. While Bernoulli's equations are
correct, their proper application to aerodynamic
lift proceed
s quite differently than the common
explanation. Applied properly or not, the
equations result in no convenient visualization

5

shape of an airfoil with its lift, and reveal
-
visualized mental model, combined with the
prevalence of the plausible
-
sounding common
explanation, is probably why even some excellent
physicists have been misled.

ALBERT EINSTEIN'S WING

My friend Yesso, who works for the aircraft
industr
y (though not as a designer), came up with
a proposed improved airfoil. Reasoning along the
lines of the common explanation he suggested that
you should get more lift from an airfoil if you
restarted the top's curve part of the way along:

An extra lump for extra lift?

This is just a "reasonable" version of the lumpy
airfoil that I presented above. Yesso's idea was,
of c
ourse, based on the concept that a longer
upper surface should give more lift. I was about
to tell Yesso why his foil idea wouldn't work when
I happened to talk to Jö rgen Skogh
3
. He told me
of a humped airfoil Albert Einstein
4
designed
during WWI that was

based on much the same
reasoning Yesso had used [Grosz 1988].

Albert Einstein's airfoil. It had no

aerodynamic virt
ues.

This meant that instead of telling Yesso merely
that his idea wouldn't work, I could tell him
that he had created a modernized version of
Einstein's error! Einstein later noted, with
5
. [Skogh 1993]

EVIDENCE FROM EXPERIMENT
S

If it were the case that airfoils generate lift
solely because the airflow across a surface
lowers the pressure on that

3
Mr. Skogh worked on airc
raft design for Saab in Sweden and for Lockheed
in
the United States.

4
Albert Einstein [1879
-
1955], a German
-
American physicist, was one of
the
greatest scientists of all time. His small error in
wing design does not detract from the massive revolution
his

5
Jö rgen Skogh writes, "During the First World War Albert Einstein was
for a
time hired by the LVG (Luft
-
Verkehrs
-
Gesellshaft) as
a consultant. At LVG he designed an airfoil with a
pronounced mid
-
chord hump, an innovatio
n intended to
enhance lift. The airfoil was tested in the Gö ttingen
wind tunnel and also on an actual aircraft and found, in
both cases, to be a flop." In 1954 Einstein wrote
"Although it is probably true that the principle of
flight can be most simply ex
plained in this [Bernoullian]
way it by no means is wise to construct a wing in such a
manner!" See [Grosz, 1988] for the full text.

6

surface then, if the surface is curved, it does
not matter whether it is st
raight,concave, or
convex; the common explanation depends only on
flow parallel to the surface. Here are some
experiments that you can easily reproduce to
test this idea.

1. Make a strip of writing paper about 5 cm X 25
cm. Hold it in front of your lips so

that it
hangs out and down making a convex upward
surface. When you blow across the top of the
paper, it rises. Many books attribute this to
the lowering of the air pressure on top solely
to the Bernoulli effect.

blow
air

Now use your fingers to form the paper into a
curve that it is slightly concave upward along
its whole length

and again blow along the top of
this strip. The paper now bends downward.

2. As per the diagrams below, build a box of thin
plywood or cardboard with a balsa airfoil held in
place with pins that allow it to flap freely up
and down. Air is introduced with
a soda straw.
That's one of the nice things about science. You
don't have to take anybody's word for a claim,
you can try it yourself!
6
In this wind tunnel the
air flows only across the top of the shape. A
student friend of mine made another where a leaf
bl
ower blew on both top and bottom and he got the
same results, but that design takes more effort
to build and the airfoil models require leading
and trailing edge refinement. Incidentally, I
tried to convince a company that makes science
demonstrators to in
clude this in their offerings.
They weren't interested in it because "it didn't
give the right results.""Then how does it work?"

An experiment may be difficult to interpret but,
unless it is fraudulent, it c
annot give the wrong
results.

6
In some fields, e.g. the study of sub
-
atomic particles, you might
need
megabucks and a staff of thousands to bui
ld an
accelerator to do an independent check, but the
principle is still there.

7

CROSS
SECTION

SIDE
VIEW

AIRFOIL DEMONSTRATOR. These drawings are full
size, but the exact size and s
hape aren't
important. I made a number of airfoils to test.
Here are drawings of the ones I made:

8

NORMAL

CONCAVE

RECURVED

FLAT

FLAT WITH
DOWNTURN

FLAT W
ITH
UPTURN

EXPERIMENTAL RESULTS

When the straw is blown into, the normal airfoil
promptly lifts off the bottom and floats up. When
the blowing stops, it goes back down. This is
exactly what everybody expects. Now consider
theconcave shape; the curve

is exactly the same as
the first airfoil , though turned upside down. If
the common explanation were true, then, since the
length along the curve is the same as with the
"normal" example, you'd expect this one to rise,
too. After all, the airflow along th
e surface must
be lowering the pressure, allowing the normal
ambient air pressure below to push it up.
Nonetheless, the concave airfoil stays firmly down;
if you hold the apparatus vertically, it will be
seen to move
away
from the airflow.

In other words, a
n often
-
cited experiment which is
usually taken as demonstrating the common
explanation of lift does not do so; another effect
is far stronger. The rest of the airfoils are for
fun
--
try to anticipate the direction each will move
before you put them in the
apparatus. It has been
noted that "progress in science comes when
although in this case the science has been long
known, and the experiment contradicts not
aerodynamic theory, but the often
-

taught common
interp
retation. Nonetheless, even if science does
not progress in this case, an individual's
understanding of it may. Another simple experiment
will lead us toward an explanation that may help to
give a better feel for these aerodynamic effects.

THE COANDA EFFE
CT

9

If a stream of water is flowing along a solid
surface which is curved slightly away from the
stream, the water will tend to follow the surface.
This is an example of the Coanda effect
7
and is
easily demonstrated by holding t
he back of a spoon
vertically under a thin stream of water froma
faucet. If you hold the spoon so that it can
swing, you will feel it being pulled
toward
the
stream of water. The effect has limits: if you use
a sphere instead of a spoon, you will find that
the water will only follow a part of the way
around. Further, if the surface is too sharply
curved, the water will not follow but will just
bend a bit and break away from the surface.

The Coanda effect works with any of our usual
fluids, such as air at usual temperatures,
pressures, and speeds. I make these
qualifications because (to give a few examples)
liquid helium, g
asses at extremes of low or
high pressure or temperature, and fluids at
supersonic speeds often behave rather
differently. Fortunately, we don't have to
worry about all of those extremes with model
planes.

7
In the 1930's the Romanian aerodynamicist Henri
-
Marie Coanda(1885
-
1972)
observed that a stream of air (or other fluid) emerging
from a nozzle tends to follow a nearby curved or flat
surface,

if the curvature of the surface or angle the
surface makes with the stream is not too sharp.

10

A stream of air, such as
what you'd get if you blow
through a straw, goes in a
straight line

A stream of air alon
gside a
straight surface still goes in
a straight line

A stream of air alongside
a curved surface tends to
ature of the
surface. Seems natural
enough.

Strangely, a stream of air

alongside a curved surface

that bends away

from it still

of the surface. This is the

Coanda effect.

Another thing we don't
have
the Coanda effect works, we can take it as an
experimentally given fact. But I hope your
curiosity is unsatisfied on t
his point and that
you will seek further.

A word often used to describe the Coanda effect is
to say that the airstream is "entrained" by the
surface. One advantage of discussing lift and drag
in terms of the Coanda effect is that we can
visualize the force
s involved in a rather
straightforward way. The common explanation (and
the methods used in serious texts on aerodynamics)
are anything but clear in showing how the motion
of the air is physically coupled to the wing. This
is partly because much of the app
roach taken in
the 1920s was shaped by the need for the resulting
differential equations (mostly based on the Kutta
-

Joukowski theorem
8
) to have closed
-
form solutions
or to yield useful numerical results with paper
-
and
-
pencil methods. Modern approaches use

computers and are based on only slightly more
intuitive constructs. We will now develop an
alternative way of visualizing lift that makes
predicting the basic phenomena associated with it
easier.

8
Discovered independently by the German mathematician M. Wilheim Kutta
(1867
-

1944) and the Russian physicist Nikolai Joukowski
(1847
-
1921).

11

A MENTAL MODEL OF HOW A WING
GENERATES LIFT AND
DRAG

As is typical of physicists, I have often
spoken of the air moving past the wing. In
aircraft wings usually move through the air. It
makes no real difference, as flying a slow
plane into the wind so that the plane's ground
speed is
zero demonstrates. So I will speak of
the airplane moving or the wind moving
whichever makes the point more clearly at the
time.

In the next illustration , it becomes
convenient to look at

the air molecules, attracted to the

surface, are pulled down.

Think of the wing moving to the left, with the
air standing still. The air moves toward the wing
much as if it was attached

to the wing with
invisible rubber bands. It is often helpful to
think of lift as the action of the rubber bands
that are pulling the wing up.

Another detail is important: the air gets pulled
along in the direction of the wing's motion as
well. So the acti
on is really more like the
following picture.

The air is pulled forward as well

as down by the motion of the

wing.

If you were
in a canoe and tried pulling someone
in the water toward you with a rope, your canoe
would move toward the person. It is classic
action and reaction. You move a mass of air down
and the wing moves up. This is a useful
visualization of the
lift
generated by

the top of
the wing.

As the diagram suggests, the wing has also spent
some of its energy, necessarily, in moving the
air forward. The imaginary rubber bands pull it
back some. That's a way to think about the
drag
that is caused by the lift the wing
generat
es. Lift cannot be had without drag.

The acceleration of the air around the sharper
curvature near the front of the top of the wing
also imparts a downward and forward component to
the motion of the molecules of air (actually a
slowing of their upward and
backward motion,
which is equivalent) and thus contributes to

lift. The bottom of the wing is easier to
understand, and an explanation is left to the

The experiments with the miniature wind tunnel
described earlier are readily understood in terms
o
f the Coanda effect: the downward
-
curved wing
entrained the airflow to move downward, and a
force upward is developed in reaction. The
upward
-
curved (concave) airfoil entrained the
airflow to move upwards, and a force downward was
the result. The lumpy win
g generates a lot of
drag by moving air molecules up and down
repeatedly. This eats up energy (by generating
frictional heat) but doesn't create a net
downward motion of the air and therefore doesn't
create a net upward

12

movement of

the wing. It is easy, based on the
Coanda effect, to visualize why angle of attack
(the fore
-
and
-
aft tilt of the wing, as
illustrated earlier) is crucially important to
a symmetrical airfoil, why planes can fly
inverted, why flat and thin wings work, and
why
Experiment 1 with its convex and concave strips

of paper works as it does.

What has been presented so far is by no means a
physical account of lift and drag, but it does
tend to give a good picture of the phenomena.
We will now use this grasp to get a
reasonable
hold on the spinning ball problem.

WHY THE SPINNING BALL'S PATH CURVES, IN TERMS OF
THE COANDA EFFECT

The Coanda effect tells us the air tends to follow
the surface of the ball. Consider Trefil's side A
which is rotating in the direction of

flight. It
is trying to entrain air with it as it spins, this
action is opposed by the oncoming air. Thus, to
entrain the air around the ball on this side, it
must first decelerate it and then reaccelerate it
in the opposite direction. On the B side, whic
h is
rotating opposite the direction of flight, the air
is already moving (relative to the ball) in the
same direction, and is thus more easily entrained.
The air more readily follows the curvature of the
B side around and acquires a velocity toward the A
side. The ball therefore moves toward the B side
by reaction.

It is again time for a simple experiment. It is
difficult to experiment with baseballs because
their weight is large compared to the aerodynamic
forces on them and it is very hard to control the

magnitude and direction of the spin, so let us
look at a case where the ball is lighter and
aerodynamic effects easier to see. I use a cheap
beach ball (expensive ones are made of heavier
materials and show aerodynamic effects less).
Thrown with enough bo
ttom spin (bottom moving
forward) such a ball will actually
rise
in a curve
as it travels forward.The lift due to spin can be

so strong that it is greater than the downward
force of gravity! Soon, air resistance stops both
the spin and the forward motion of

the ball and it
falls, but not before it has shown that Trefil's
explanation of how spin affects the flight of a
ballis wrong.

The lift due to spinning while moving through the
air is usually called the "Magnus
9
effect." Some
books on aerodynamics also des
cribe the "Flettner
Rotor," which is a long
-
since abandoned attempt to
use the Magnus effect to make an efficient boat
sail. Many sources besides Trefil get the effect
backwards including the usually reliable Hoerner
[Hoerner 1965]. College
-

level texts te
nd to get
it right [Kuethe and Chow 1976; Houghton and
Carruthers 1982] but, as noted above, Feynman's
Lectures on Physics
has the rotation backwards. I
was relieved to see that the
classic
Aerodynamics
[von Ká rmá n 1954] gets the
lift force on a

9
H. G. Magnus (1802
-
1870), a German physicist and chemist, demonstrated
this
effect in 1853.

13

spinning ball in the correct directi
on though
the reasoning seems a bit strained.

I wish I could send this essay to the 6th grade
science teacher who could not take the time to
listen to my reasoning. Here's what happened: he
sent me to the principal's office when I came in
the next day with

a balsa model plane with dead
flat wings. It would fly with either side up
depending on how an aluminum foil elevator
adjustment was set. I used it to demonstrate
that the explanation the class had been given
must have been wrong, somehow. The principal,
however, was informed that my offense was
"flying paper airplanes in class" as though done
with disruptive intent. After being warned that
I was to improve my behavior, I went to my
beloved math teacher who suggested that I go to
the library to find out ho
w airplanes fly
--
only
to discover that all the books agreed with my
science teacher! It was a shock to realize that
my teacher and even the library books could be
wrong. And it was a revelation that I could
trust my own thinking in the face of such
concert
ed opposition. My playing with model
airplanes had led me to take a major step toward
intellectual independence
--
and a spirit of
innovation that later led me to create the
Macintosh computer project (and other, less
-
well
-

APPENDIX 1

A QUANTITATIVE APPLICATION OF THE COMMON (INCORRECT)
EXPLANATION

If the pressure, in Newtons per square meter (Nm
-
2
=
kgm
-
1
s
-

2
), on the top of a wing is notatedptop , the pressure on
the
bottomp
bottom
, the velocity (ms
-
1
) on the top of
the wi
ng v, and the velocity on
thebottomv
bottom
,andwhere__ is the
top

density of air (approximately 1.2 kgm
-
3)
, then the
pressure difference across the wing is given by the
first term of Bernoulli's equation:

p
top
-

p
bottom
= 1/2 _ (v
top
2
-

v
bottom
2
)

A rectangula
r planform (top view) wing of one meter
span was measured as having a length chordwise along
the bottom of 0.1624 m while the length across the
top was 0.1636 m. The ratio of the lengths is
1.0074. This ratio is typical for many model and
full
-

size aircra
ft wings. According to the common
explanation which has two adjacent molecules
separated at the leading edge mysteriously meeting
at the trailing edge, the average air velocities on
the top and bottom are also in the ratio of 1.0074.

A typical speed for a
model plane of 1m span and
0.16m chord with a mass of 0.7 kg (a weight of 6.9
N) is 10 ms
-
1
is 10 ms
-
1, so v

which makes v
top
10.074 ms
-
1
. Given these numbers,
we
bottom

find a pressure difference from the equation of
-
1
-

2
. The area of the win
g is 0.16 m
2
s

giving a total force of 0.14 N. This is not nearly
enough
--
it misses lifting the weight of 6.9 N by a
factor of about 50. We would need an air velocity
difference of

14

-
1
to lift the plane.

The calculation is, of cour
se, an
approximation since Bernoulli's equation
assumes nonviscous, incompressible flow and
air is both viscous and compressible. But
the viscosity is small and at the speeds we
are speaking of air does not compress
significantly. Accounting for these deta
ils
changes the outcome at most a percent or
so. This treatment also ignores the second
term (not shown) of the Bernoulli equation
-
-
the static pressure difference between the
top and bottom of the wing due to their
trivially different altitudes. Its
contri
bution to lift is even smaller than
the effects already ignored. The use of an
average velocity assumes a circular arc for
the top of the wing. This is not optimal
but it will fly. None of these details
affect the conclusion that the common
explanation of
how a wing generates lift
--
with its naï ve application of the
Bernoulli equation
--
fails quantitatively.

FURTHER READING: There are many fine books
and articles on the subject of model
airplane aerodynamics (and many more on
aerodynamics in general). Commen
dably
accurate and readable are books and
articles for modelers by Professor Martin
Simons [e.g. Simons 1987]. Much can be
learned from Frank Zaic's delightful, if
not terribly technical, series [Zaic 1936
to Zaic 1964] (Available from the Academy

5

of Model

Aeronautics in the United States),
and no treatments are more professional or
useful than those of Professor Michael
Selig and his colleagues [e.g. Selig et.
al. 1989]. All of these authors are also
well
-
known modelers. The other references
on aerodynamic
s, e.g. Kuethe and Chow
[1976] and Houghton and Carruthers [1982]
-
texts, they require a knowledge of physics
and calculus including partial differential
equations. Jones [1988] is an informal
treatment by a master
and Hoerner [1965] is
a magnificent compendium of experimental
results, but has little theory
--
practical
designers find his work invaluable.

15

REFERENCES

The Physics of Baseball
, Harper
a
nd Row, NY, 1990. pg. 13

* Feynman, R. et. al.
Lectures on Physics, Vol II
,
-
Wesley 1964 pg. 40
-
9, 40
-
10, 41
-
11

* Gleick, J.
Genius
. Pantheon Books, NY 1992 pg.
234 * Grosz, Peter M. "Herr Dr Prof Albert Who?
Einstein the Aerodynamicist, That's Who!
" WWI Aero
No. 118, Feb. 1988 pg. 42 ff * Hoerner, S.F.
Fluid
-
Dynamic Drag
, Hoerner Fluid Dynamics, 1965 pg. 7
-
11

* Houghton and Carruthers.
Aerodynamics for
Engineering Students
, Edward Arnold Publishers,
Ltd. London, 1982

* Jones, R.T.
Modern Subsonic Aer
odynamics
.
Aircraft Designs Inc., 1988. pg.36

* Lamptey, George.
The Ten Bridges to Professional
Soccer, Book 1: Bridge of Kicking
Santa Clara CA, 1985. * Levy, Steven. "Insanely
Great." Popular Science, February, 1994. pg. 56 ff.

* Linzmaye
r, Owen.
, Sybex
1994 * Kuethe and Chow.
Foundations of Aerodynamics
,
Wiley, 1976 * Macaulay, David.
The Way Things Work
.
Houghton Mifflin Co. Boston, 1988. pg. 115

* Selig, M. et. al.
Airfoils at Low Speeds
.
Soartech 8. Herk Stokely,

1504 Horseshoe Circle,
Virginia Beach VA 23451, 1989 * Simons, M.
Model
Aircraft Aerodynamics
, 2nd ed.. Argus Books Ltd.,
London, 1987.

* Skogh, Jö rgen.
Einstein's Folly and The Area of
a Rectangle
, in publication

* Thornburg, Dave.
Do You Speak Model Ai
rplane?
Pony
X Press, 5 Monticello Drive, Albuquerque NM 87123,
1992

* Trefil, James S.
A Scientist At The
Seashore.
Collier Books, Macmillan Publishing Co.,
1984, pp 148
-
149

* von Ká rmá n, T.
Aerodynamics
. Oxford Univ. Press
1954 pg. 33 * Zaic, Frank. Mode
l Aeronautic
Yearbooks. Published from the 30's to the 60's

* Zaic, Frank.
Circular Airflow
. Model Aeronautic
Publications, 1964.

ACKNOWLEDGMENTS

I am very appreciative of the suggestions I have
including Dr.

Bill Aldridge, Professors

16

Michael Selig, Steve Berry, and Vincent Panico,
and Linda Blum. They have materially improved
both the content and the exposition, but where I
have foolishly not taken their advice my own
errors
may yet shine through.

AUTHOR'S BIOGRAPHY

Jef Raskin was a professor at the University of
California at San Diego and originated the
Macintosh computer at Apple Computer Inc [Levy
1994; Linzmayer 1994]. He is a widely
-
published
writer, an avid model airpl
ane builder and
competitor, and an active musician and composer.

17