The aim of this text is to provide some understanding in the physics of
an airplane. This helps to design and tune little paper or balsa
gliders.
Warnings
The drawings do not always match real-world
proportions, angles or air streams. Their purpose is to make you
understand
the principles.
I did not experiment thoroughly with every variable or principle
I'm writing about. I made many experimentations and I went through
loads of books and web pages... But do not hesitate to question this
text. Besides, even if everything was accurate in this text, the real
world always adds layers to whatever you can theorize.
I'm currently in the process of writing this text, mostly from
memory. Some technical terms are probably misused, some wordings are
mangled...
Throwing the problem
The purpose of an airplane is to transport something through the air,
be it some cargo, people, or just itself. The aircraft uses the
air to fly, somehow like a boat uses water to float upon.
Let's start by focusing on the load that the aircraft transports; just
the mass of it. Let's imagine a little ball of lead; a mass almost
concentrated in a dot. Or say a coin...
We can possibly throw it some distance away,
like if it was a cannonball.
But that's not what we want. We want to
build something around the coin that will allow it to hang in the air
on a slow and straight path.
The most important part of an airplane are the wings. Some aircraft are
only one big wing with nothing else... So lets take a postcard (or a
rectangular sheet
of balsa wood) and latch the coin in the middle of it.
Then we
gently throw this assembly like we would do with a toy glider and...
the result is quite awful. One probable outcome is that the rectangle
rotates at a fast rate around its longest axis and "flies" towards the
ground at a straight angle. (Note that it didn't fall vertically
towards the ground... we had a sideways displacement... this is
encouraging!)
You may have the intuition that a solution would be to hang the coin
below the sheet of balsa, like a pilot hangs below a delta glider.
Maybe try this out using a rod of wood or ropes. Yet you won't get the
desired result. The thing will probably fall to the ground making
random movements. At best it will fall gently like a parachute. No
flight...
You may have yet another intuition: that you should add a tail. A
little rod that extends rearwards from the wing, with little surfaces
at the end, like the tail of an arrow. You try to launch
that like a toy glider... and still it's a catastrophe.
Placing the coin lower than the wing is good. Using a tail is
good. But you didn't have the physics of flight in mind...
Forces and torques
When you hold a sheet of cardboard or balsa in your hand, with your arm
extended, and you shear
it through
the air like a wing (with a slight upward tilt of the leading edge), it
is pushed upwards by an aerodynamic lift force.
The wing wings...
The air shearing along the wing, exerts relative pressure and suction
forces all
around the surfaces of the wing...
Every single little portion of surface, experiences a tiny aerodynamic
force. The force is different everywhere, and, what's even worse, it
constantly changes... It's like if little bees were pushing and pulling
everywhere on the wing. You easily can get the impression that no clear
understanding can be build out of this mess...
Yet scientists have ways to extract key information out of such mess.
The whole "mesh of bees", pushing and pulling all around the wing, can
be summarized
(averaged) to two things: one aerodynamic force and one aerodynamic
torque. The force is what tends to push the wing upwards. The torque is
what tends to make it turn around its main axis. (Remember that
experiment above, when the wing fell sideways to the ground while
turning at a fast rate around its main axis. The torque is responsible
for the rotation.) When you hold a piece of cardboard in your hand
and shear it through the air around you, you will easily feel the lift
force but not the rotation torque, because that torque is quite weak.
Anyway it is key for us.
The aerodynamic force "seemingly grasps" the wing at about 1/3 from the
leading
edge. So, our first reaction would be to put the coin at 1/3 from the
leading edge, expecting that now the force caused by the weight of the
coin will be aligned with the aerodynamic force:
Nice try. But there are two bold errors. The first one is that you
forgot to take into account the mass of the wing. The wing and the coin
are a whole. If you want the center of mass of that whole to be 1/3
from the leading edge, you have to place the coin further away than 1/3
length.
The other bold error is that the two forces (lift and weight) are not
aligned. So they cannot compensate each other exactly. The force caused
by the weight will always be directed vertically towards the ground. We
can only change the aerodynamic force, by rotating the whole system
counterclockwise. Now the wing flies slightly towards the ground.
That's what happens in the real world:
in still air, gliders slowly fly towards the ground.
Nice work. But the postcard and the coin still won't fly
correctly. That's because we forgot the aerodynamic torque. It's still
there and it
tends to make the thing flip upwards.
What can we do to counteract that torque? The most obvious proposal
would be to add a tail to the postcard. It would be a little horizontal
wing yet slightly turned so that it creates and aerodynamic force
towards the sky, that counterbalances the torque from the main wing.
You indeed can compensate the torque that way... But if you try this
out, by gluing a toothpick behind the postcard and a little square of
paper at
the end of the toothpick, you will *never* get a proper flight. Sure
you did
counterbalance the torque... but you created a highly unstable system.
In other words: that thing can fly if you add a computer to it, with
captors and actuators, and the computer constantly adapts the angle of
the tail in order to keep flying straight. It's like the broom you hold
vertically on your finger. You can hold it vertically quite a long
time... with great efforts. (The Wright Brother's Flyer from 1903 was
unstable too and the pilot constantly had to correct it's attitude.
That's why flying a replica of the Flyer requires autorisations and a
special training.)
We need another way to compensate the aerodynamic torque... The way
that's used in almost every airplane is to place the center of mass of
the system further ahead. The coin is placed even more forward. That
way a torque appears, because the force
of the weight is not aligned with the aerodynamic force.
You have to place the coin so that the center of mass of the whole is
1/4 from the leading edge. *Now* you have a real chance to get the
thing to fly correctly. Just a
postcard with a coin you taped underneath... If you made sure that the
center of
mass of the whole is 1/4 from the leading edge:
Remember that 1/4th chord forever. Since I use it, I never more had to
tune the
center of mass of a little glider. I always get a good flight from the
first throw on, provided the center of mass is at 1/4 chord.
Stability
Throwing that coined postcard may still not yield a flight...
because, though we have an equilibrium
of the forces and torques, that equilibrium can be a tiny little bit
unstable. No fuss... the
trick to make it stable is very simple. Just make sure that the
trailing edge is a tad upward. If you are using a postcard, bend it
very slightly (hardly visible). If you are using a sheet of balsa wood,
taper the underside
of the trailing edge, using some sandpaper. (That way you make what is
called a "flying wing airfoil profile". Guess why...)
You should get a straight flight. (You may have to correct a tendency
to turn, by slightly warping the rear ends of the wings, like
you
would do with a toy balsa or paper glider... Or cut out ailerons and
bend them. Possibly don't bend the whole trailing edge upwards, use
only ailerons, but only bend them upwards...)
It is very important to insist on the fact that the equilibrium of this
whole system is "stable". That's why you get a stable flight path, on a
straight line, with the system not accelerating nor decelerating. The
concept is called "self-regulation". Actually, the glider is constantly
slightly changing speed, course and attitude. But, the mechanisms of
the
stability will
bring the system back towards the position of equilibrium. For example,
if the speed of the glider increases, the torque that tends to lift
the nose upwards will gain slightly and the glider will both lift more
and drag more... which makes the speed decrease. In shorter words: an
increase of speed
ultimately leads to a decrease in speed. Conversely, a decrease of
speed ultimately leads to an increase of speed. That's how you get
stability in an otherwise quite random system.
If you built such an elementary cardboard glider and it flies more or
less correctly, you will probably notice that while flying it
oscillates constantly around its main axis. The nose slightly pitches
up and
down constantly. It oscillates... This does not hamper flight, though
it is not desirable because it makes the glider loose energy (drag
more). The oscillation is part of the equilibrium but we will try to
damp it down.
Yet another problem you will encounter with such simplified airplanes
is that they can fly correctly on some distance (if you threw them
well) then suddenly they go berserk and fall to the ground. They went
out of stability... Their flight equilibrium is fragile! In the real
world, when engineers build a new airplane, they have to prove that it
will never go out of stability. More precisely, they have to prove
that,
if the airplane comes to get in any possible position and speed that
disallows proper flight and stability, the aircraft will anyway always
tend to get back towards proper flight and stability. The
requirements are different for each kind of aircraft. Unpiloted
model
airplanes need to be firmly stable, in order to go on flying properly
whatever the gusts of wind. Airplanes with pilots will rather tend
to have a "neutral" equilibrium. This means that if you put them in a
given position, they will tend to stay in that position. Military
airplanes like fighter airplanes, can be slightly unstable because this
increases their reactivity. Military pilots are trusted to
be constantly focused on the attitude of the airplane and they are
trained to cope instantly with all kinds of instabilities. (Modern
fighter planes can be very easy to pilot, because they have onboard
computers hat control everything...)
While you can make a proper glider using almost no maths, if you want
to master all the problems of stability you will need
high levels of physics and mathematics. Since the Wright's Flyer in
1903, it took about 40 years before airplanes
could be build that were perfectly stable and reliable in all
circumstances. This problem of
stability is key to almost every technological endeavor, be it a
chemical plant, an artificial forest, a windmill, a rocket or a
political or economic system. Many
industrial accidents occur in developing countries, because to build a
machine is easy, yet to build a stable one requires extended knowledge
in several branches of Mathematics. Complex systems have been developed
using few or no maths, like the boomerang or the Moslim economic
system, but this often required centuries of experimenting and many
casualties...
Now back to our glider. It flies... It's a minimalistic shape to get
flight... But it has many problems. It does not fly very far... It
oscillates while flying...
Dampening the oscillation
Let's first try to cope with the oscillation. Many solutions exist...
It's much fun for model airplane builders, to conceive flying
wings that do not oscillate, thanks to minute details in the shape of
the wings. But the common solution will do: let's use a tail. Glue a
thin rod of wood to the postcard and at the end of it glue a horizontal
little
surface of paper. (The mass of this tail forces you to put the coin
even further ahead, in order to keep the center of mass of the whole at
1/4th chord of the wing.)
That little surface at the tail has only one purpose: to damp down the
natural oscillation of the system. (You will see such little surfaces
used in old clockworks, inside churches or museums.) Its purpose is by
no way to act like the tail of an arrow. It absolutely not has the
purpose to impose the angle at which the wing travels through the air.
If it would impose that angle, superseding the self-regulation
mechanism discussed above, there would be no more stable equilibrium,
hence no flight! That's why the surface of that tail has to be very
little, just enough to damp the oscillation.
Conversely, the angle at which the wooden rod emerges from the
postcard, and the angle of the little surface in the flow or air, have
almost no importance. Amongst toy glider builders, it is often tensely
discussed what angle the tail should have, compared to the wings. A
friend of mine makes much fun of this, as no angle at all perfectly
does the job. I suppose that the optimal layout is to have the wings
have some angle compared to the rod, but I never checked this out...
A quite natural rule is that if you put the horizontal tail closer to
the wing, you have to increase its surface. This is up to you. A big
horizontal tail surface, close to the wing, will be heavier, will
create more drag and will aerodynamically interfere with the wing. On
the other extreme, a very long tail with an infinitesimal surface at
its end, will be fragile or will cause a problem with the
center or mass... The compromise is in-between. Building an airplane is
the art of computing out compromises...
Weight
Many beginner are puzzled by the weight that their glider should have.
Actually, this is maybe the least important parameter of the system.
Most gliders will fly correctly if they are made two, three, sometimes
even ten times heavier. As long as the center of mass keeps being at
1/4th chord, you do what you want... Remember this system is
self-regulating. If you increase the weight, the glider will simply fly
faster, in order to generate enough lift to keep that weight in the
air. If you decrease the weight, the glider will fly slower. Now of
course there are practical limits. If the weight is so heavy
that the wings bend away under the aerodynamic forces, you won't get a
proper flight... A glider may be able to fly correctly but the high
speed makes it won't survive many landings... On the opposite, a glider
can also be too lightweight. At very low speed, the air will simply no
more follow the wing profile correctly. Hence you have no more
aerodynamic lift... (This depends on the chord of the wing. The longer
the chord, the more you are allowed to decrease the speed. Conversely,
if you want to make a glider that flies really slow, use wings with a
strong chord.)
Aerodynamic yield of
the wing
This postcard glider is
kind of a hybrid between a glider and a parachute... It does fly
but with a steep angle towards the ground.
Let's talk a little bit about air pressure and depressure. Imagine a
loose and heavy piston in the middle of a closed cylinder that contains
air. If you place the
cylinder vertically, the weight of the piston will make it descend
slightly towards the ground. The air below the cylinder will be
slightly compressed and the air above the cylinder is slightly
depressed. That keeps the piston aloft, like hovering.
Yet if there would be air leaking along the piston, the hoovering would
stop after some while, the piston would slowly fall to the end of the
cylinder closest to the ground.
The postcard glider can be viewed such way too. Throw the postcard, yet
between two vertical walls, in such a way that the walls close the port
and starboard sides of the postcard. This is hardly doable but let's
suppose that, like the piston in the cylinder, the sides of the
postcard are airtight closed by the walls and this causes no friction.
The air that shears above the postcard creates a depressure and the air
that shears under the postcard creates a pressure. That's what keeps
the postcard in the air, just like the piston stayed hovering inside
the cylinder.
But here we have something very different from the piston, namely the
fact that the leading edge and the trailing edge of the postcard are
open. Hence you may fear that the pressure below leaks towards the
depressure above
and reciprocally... This does not happen, because the postcard is
moving through the air and this dynamic system sustains the difference
of pressure despite the open leading and trailing edges. If it wasn't
for the frictions and turbulences (some of which are necessary to get
lift and flight...), the postcard can stay flying at a
constant altitude between the walls, just like the piston does inside
the cylinder.
But what if we remove the walls? Then, the air will massively leak
between the upper and down side of the postcard, along the port and
starboard edges of the postcard. The pressurized air from underneath
constantly filling the depression above the wing.
One first thought may
be that this is not so bad. There is a loss of lift force... well let's
compensate for this, by using a huger postcard... Actually, the problem
is that the exchange of air makes the air turn in a massive whirl (two
whirls, one on each side of the wing) and the rotation energy that
those
whirls contain... is drawn from the postcard. The whirls "suck" the
postcard backwards and this makes it quite quickly falls to the
ground. Poor flight... The potential energy the postcard had, due to
its height above the ground, is quickly transformed into whirl energy
(which ultimately becomes simple heat).
You got it: we need to prevent that sideways leak of pressure. To the
least we must diminish it. We cannot have airplanes and glider fly only
between walls... Your first thought could be to have the postcard carry
its own "walls". You would glue two other postcards aside of it,
vertically,
acting as embedded walls. The problems is that this creates a massive
drag on itself... It's not a good solution.
A far better solution is to use a wide postcard. You still get those
massive bleeds of air between the upside and the downside but as the
length of the sides decreased (compared to the width of the wing), the
loss is less severe. Closer to the
center of the wing, things will be like if flying between walls.
That's one reason why modern gliders have very wide wings, with a very
narrow chord especially at the tips. But do not forget that toy gliders
fly slow, hence they need chord. I once was very puzzled by this. I
build a very neat little balsa glider with extremely narrow and wide
wings, nearly like a modern sport glider. I expected it to have a
very good yield... but it almost parachuted to the ground.
To further regulate and decrease the whirls, you can cut "salmons" at
the ends of the wings. The decrease of the
turbulences and vibrations can even be felt in your fingers if you
shear such a wing through the air.
Such a wide wing with salmons would be what sea birds have.
The other
simple way to cope with the turbulences would be trapezoidal wings.
(With the delta wing being an extreme. Birds that live in cities and
forest, making short and agile flights, tend to use the delta shape
(include the tail and rotate 180°).)
The trapezoidal wing can be felt as ideal. It is widely used and
proven, it is close to optimal for the mechanical constraints, but it
is not as perfect as you may expect. At every zone of
say the downside of the wing, the air will slightly move towards the
zone aside of it that's closer to the wing tips. Because, that zone
creates less overall pressure because it has less surface. On the
whole length of the downside, there is constant movement of the air
towards the wing tips.
While reciprocally, on the upside, there is a constant movement of air
away from the wing tips. Those opposite movements meet behind the wings
and create whirls that ultimately unite in two huge whirls similar to
those spoken above for a rectangular wing.
Trapezoidal wings have some disadvantages, like the
fact that their stalls are deadlier, because the stall tends to occur
on
the whole surface of the wing at once. On rectangular wings, the strong
vortexes at the wing tips, ensure a correct air flow there, even when
the center part of the wing is in a severe stall. And... remember the
chord: if the ends of a
trapezoidal wing have a too narrow chord for the flight speed of the
glider...
Maybe try a trapezoidal wing with
salmons...
Stability 2
If you try out a glider with wide wings, it will probably succeed but
you will notice a
problem: the glider tends to turn itself to the right or to the left.
Even if it stays flying on a straight path, its nose starts heading
aside. It flies like a crab... Simple problem, simple solution: we now
add a vertical tail. But it's mandatory that you do not oversize its
surface. A tiny surface, much like the horizontal tail, will do. A huge
vertical surface would cause instabilities and you would get ugly
flights. (The common solution to use a tail with more surface without
creating instabilities is to reverse the tail: either place the
vertical surface below the horizontal surface or use and inverted V
tail (a /\ tail...).)
Oh, yeah, I forgot about the slight upward bend of the trailing edge.
Now that we're using that tiny horizontal tail surface, it is most
often no
more needed...
There remains one big potential source of instability. If you launch
this glider on a long flight, it may steadily tend to turn in a given
direction and then the turn rate will augment towards a catastrophe (I
rarely encounter that problem...) One common way to cope with this is
to
place the center of mass of the glider a little lower. That regulates
the problem by the "pendulum effect".
Or you can use a positive dihedral (bend the wings slightly
upward). (Sometimes, the conceivers of an airplane have no other choice
than to place the wings above the fuselage. A good example is the
British "Harrier" VTOL fighter plane. But the strong pendulum effect is
unwanted.
In order to decrease it, the wings will have a negative dihedral...)
Now your glider should have an efficient and stable flight. It should
glide far, on a straight line, with no oscillations. In order to
further better it, you can slightly streamline the wing airfoil
profile, using some high grain sandpaper.
Angle of attack
One more sophisticated tuning is the AOA; the angle of attack of
the wings. Try it out with the piece of cardboard that you hold in your
hand and shear through the air. If you hold it parallel to the flow of
air, there is no lift force. The more you pitch its leading edge
upward, the higher
the lift force. Till some high angle where the cardboard rather brakes
than lift. The angle between the stream of air and the surface of the
cardboard is the AOA.
One obvious reason to tune the AOA is that this has a direct impact on
the flight speed. If the AOA is low, the wings lift less, hence a
higher speed is needed to get the appropriate lift force to
counterbalance the weight of the glider. The self-regulation mechanism
will (should) ensure that this speed is attained. On the opposite, a
high angle will lead to a low speed of flight.
Some airplanes, like the flying flee, are driven (you don't pilot a
flying flee, you drive it...) by changing the incidence of the main
wing (the angle compared to the fuselage). The wing can rotate a few
degrees around
its main axis. The yoke that the pilot holds in his hands, is coupled
to a system of levers that slightly rotates the wing. The flying flee
has no horizontal tail surface...
Yet far out most airplanes are
piloted using the horizontal tail. The angle and curvature of the tail
surface
changes according to the position the pilot gives to the yoke (and to
the trim). This leads the airplane as a whole to pitch up or down,
which changes the angle the wings travel through the air
(the AOA). I was a little bit provocative on purpose, a while above, by
telling that the horizontal tail had no purpose at all regarding the
angle the glider travels through the air. Of course it has, in most
cases. But never forget that the tail should always be little, in order
not to supersede the self-regulation. (Airplanes do exist that have
such a huge horizontal tail that actually they have two pairs of wings,
but precise rules have to be followed to ensure stability.)
There is a second reason why you want to tune the AOA: there exist two
optimal angles. The one that's optimal for you depends on what specific
performance you want: that your glider flies the longest distance or
that it stays the longest time in the air.
If you want your glider to fly far, then you need the highest
aerodynamic yield. What you need is not the least wing drag... (You
would get that by using an AOA of zero, hence no lift at all, hence
only drag.) Rather, you need that the *ratio* between the wing lift and
the wing drag be as high as possible. In other words: as much possible
lift per unit drag. It seems that you get that by using an AOA of about
7°. I
did not verify...
On the other hand, if you want the glider to stay the longest time in
the air, then you
need it to fly slow. Hence you need a strong lift from the wings, as
long the drag is not too high. It seems that you get that by using an
AOA of about 14°. I didn't verify either... But here we have a problem:
a
flat airfoil profile like we're using, will simply "stall" at an AOA of
14°. It is so that the air has to follow a strange path around the
leading edge. Once this is exaggerated, due to the strong AOA, the air
stream will detach from the wing and there will be no more proper lift.
One solution would be to bend the leading edge downward, to allow/force
the air to follow the shape of the airfoil. Let's call it a beak.
(That's what the slats on
the wings of airliners are for, to allow a high AOA, in order to be
able to take off and land at a lower
speed.) Yet be careful: while such a beak can save the day at
a strong AOA, it is useless and it causes drag at a low AOA. (That's
why airliners retract the slats once in flight.)
If you seek performance, then you want the fuselage to travel through
the air with the least drag. Hence parallel to the stream. So simply
use the wing incidence that matches your needs, always make sure that
the center of mass is at 1/4th chord and tune the horizontal tail (the
elevator) to get the glider to travel at the wished angle through the
air.
About the elevator... Don't make some errors. You want it to travel
through the air without generating a high drag and without stalling.
(That's
why the tails of many airplanes have a delta shape; it's the shape
that's the most tolerant to steep angles of attack.) You need an
elevator that has enough surface to exert its desired control force
while
having
only a few degrees of AOA. See for example the glider below. A beginner
may claim that he managed to build a glider whose
wings have a very steep AOA. And indeed the glider flies. But... it
flies with the wings at a normal AOA and the rear tail bluntly braking.
The fuselage and the nose are braking too, by the way. The *incidence*
of
the wings is 30°, as this is the manufactured angle between the
fuselage and the wing plane, but the AOA in flight is just a few ° and
the aerodynamic yield of the whole is bad.
Cambered airfoils
We only talked about flat airfoils.
Now about cambered airfoils.
One first advantage of cambered airfoils is that they lift more. Hence
they allow to use wings with less surface, or reciprocally they allow
to fly slower with a given wing surface.
(This property is used by
ailerons and flaps. When the aileron is lowered at the end of a wing,
this increases both the AOA and the camber of the wing, hence its lift
force. This makes the airplane roll. The sideways movements of the yoke
command the ailerons. The flaps, on the other hand, are deployed
simultaneously on
both sides of the wings. They strongly increase the curvature and allow
to take off and land at a lower speed.)
The second advantage of the camber is that a slight camber allows for
an even better aerodynamic yield. The lift to drag ratio is slightly
better than that of a flat airfoil. (Yet a strong camber will brake a
lot; it creates a lot of drag. This is not a problem when an airplane
takes off with powerful engines and especially when it is landing.
Flaps are often designed to increase the drag when they are fully
deployed, to ensure a safe landing path. On most little airplanes, the
flaps will not increase the wing surface, only its camber. On the B-52
bomber, the flaps cause no camber but they increase the surface of the
wings. On modern airliners, the flaps both increase the curvature and
the surface of the wings.)
So, if you want a glider designed for distance, you would use a slight
camber, that yields the maximum efficiency. If you want a glider that
stays in the air for a long while, you would use a stronger camber,
that yields a lot of lift and allows to fly slower, hence stay longer
in the air even if the increased drag decreases the distance.
But... are you sure you need a camber? It can poison your glider... You
can get the same lift with a flat profile, simply by using a wider
chord. That compensates for the fact the flat profile lifts less.
And... there is an elephant of a good reason why you may want and
benefit from a wider chord. Remember that when the chord is little and
the flight speed is low, the air will no more follow the airfoil
properly. By using a wider chord, you get a cleaner behavior at a given
low speed. That's why butterflies have flat
wings.
Reciprocally, at very high speeds, some camber will allow a shorter
wing chord and this is much desirable because the problem with long
chords and high speed is that strong and useless turbulences appear on
the upside of
the trailing part of the wing. You *want* less chord, in order to have
less wing surface braked by turbulences.
One way to talk about it is that under a given chord x speed
product
you get no turbulence at all. That makes the air won't follow the wing
profile. (Unless you artificially produce turbulences, say using
turbulators, or widely flapping wings like little insects.) You need to
be
above a given chord x speed.
But, when your chord x speed
becomes very
high, you get a lot of turbulences, useless to get a proper air path
and that create a lot of drag.
Yet another advantage of flat profiles is that they have a neat
behavior. Their stability is quite neutral and constant at any AOA.
They simply lift proportionally to the AOA. Cambered airfoils tend to
have a more constant lift, less dependent of the AOA. When
using highly cambered airfoils, for example (don't), the AOA has few
impact on the lift (but don't, the drag is tremendous). Common cambered
airfoils lift even at a slightly negative AOA. (Consider that the AOA
lifts and that the camber lifts, the lift force of the wing being the
sum of the two.) But the real problem
with cambered airfoils is that they are more unstable. Hence, either
you *must* use a flying wing airfoil (with the end of the camber
inverting to a short and slight upward camber) (exagerated in the
picture below) or you must use an
appropriate horizontal tail. (That's why when a conventional airplane
looses its tail, no recovery is possible and the airplane will tumble
to the ground and crash.)
Thick airfoils
Whether they were flat, had a beak or
were cambered, till now we talked only about thin profiles.
Why use a thick profile? Thick brakes when pasing through the air...
Well, there is
a compromise. The early airplanes all had thin wings but that posed a
serious problem to have them be stiff. The use of steel spars or plain
wooden wings, would have made the wings far too heavy. Instead,
structures were used, with ropes and rods, stiffening the wings in a
biplane structure. It was both very rigid and very lightweight. But
those ropes and rods cause drag. And the biplane structure is not
aerodynamically optimal. By using a thick wing, you can put spars
trough it, that have a strong diameter, hence that can be both stiff
and reasonably lightweight. You still get a heavier wing, but you have
no ropes and rods and you need no biplane structure. The
overall result is better. And, it is so that a not too thick wing,
won't drag much more than a thin wing in normal circumstances of
flight, with a regular AOA. (The WWII Spitfire fighter plane used quite
thin wings anyway, in order to be able to fly at high speed at low
altitude. In such circumstances, the wings were more a hinder than a
necessary part of the airplane. Much littler wings would have allowed
far better performances. Yet the wings being quite flat, the impact of
the problem was reduced because they would brake less when almost
parallel to the airstream. (This caused yet another problem: the wings
being less
rigid, due to their flatness, at high speed they would twist when the
pilot used the ailerons. That was vicious: say when the aileron went
down, that would twist the wing to a lower AOA, hence the lift of the
wing decreased instead of increasing and the plane rolled the other
side.))
When something thick travels through the air, you must streamline it.
The fuselage of an airliner would be a good illustration for this. It's
a tube... yet the fore part is rounded and the aft is a soft cone.
The more progressive you can allow those fore and aft parts to be, the
better the result. So far the tube allows...
Oversimplifiedly put, the wing contains the shortest possible tube
because it's just the cross-section of a spar. So the airfoil will
be made of only the fore and aft parts and you get the best aerodynamic
shape.
Most wings use such a shape. But... a toy glider is an extreme, as we
already stated. Again, it's about turbulences. The fore part tends to
avoid turbulences, while the aft part will eagerly trigger them. That's
why the high-speed WWII P-51 Mustang fighter plane used an airfoil
profile with a
much shorter aft part. (Modern gliders have yet another way to shorten
the aft part of the wing: the airfoil as a whole is kept short. Their
wings have a short chord and that's one reason why they are so wide.)
On the other hand, a toy glider, that dearly needs some turbulence for
the wings to wing, may benefit from the longest possible aft part.
But... thick airfoils are reportedly no good at very low speed. That
would be because the leading edge of thin airfoils scrapes a little
unaerodynamically trough the air and creates turbulences. Those
turbulences then ensure that the stream of air correctly follows the
upper side of the airfoil. Some airfoil profiles exist that have a thin
leading edge, then swell aerodynamically to contain a spar. The airfoil
below would be a thin one, with both a curvature and a beak, and with a
swell to contain a spar.
Airfoil Algebra
All the thick airfoil profiles drawn till now are flat. But of course
they
can have a camber and a beak. You "bend" the thick airfoil to match the
desired camber. You "bend" its fore part to follow the desired beak
curve.
Say you want to make a glider that must stay the longest possible time
in the air. Low speed, high lift. Hence a long chord, a beak, some
thickness in
order to have lighter wings, a long aft part. You get this:
Now a common warning to beginners. Suppose you get excellent
results with the composite airfoil depicted above (then tell me, I
never tried it
out). You love it. Your glider flies wonderfully. You get another kind
of wood that's more rigid and you decide to make another wing, with a
two times thinner airfoil. But you want to keep the same aerodynamic
quality! If you just take the above shape and you
flatten it, halving every height, you're a beginner. Your glider will
*not* have the same characteristics. Let's explain why. The flight
characteristics are mostly imposed by the flat wing part, with the
beak. The flesh you put around it is a minor detail. When you halved
the airfoil, you changed the shape of the beak. Hence you changed the
behavior of the wing. You *must* keep the same flat profile. But you
are allowed to make the flesh around it thinner. So you get this:
This reasoning also yields that when you talk about wing incidence or
angle of attack, the reference plane of the airfoil will be that of the
virtual thin profile it contains. The picture below show the thick
airfoil from above laying flat in the airstream:
But wait a minute. A rounded leading edge may be no good at very low
speed. So let's use a sharp one:
Acknowledgments
I wish to thank:
The pioneers of flight, who made this dream reality and whose
research is still ongoing.
My friend Jacques Donneux, for his thrive and dedication. He
learned building gliders to many children.
My friends Didier Bizzarri and Yves-Dominique Franck,
whose advice and data I have been thoroughly using.
The many experimenters and model glider builders that made data
available on the Internet.
The NASA, for their excellent online documentation and tools.
My friend Frédéric Cloth, who hosts this page and many more.
