Basics of toy glider physics
The aim of this text is to provide some understanding in the physics
of an airplane, to help in the design and tuning of little paper or
The drawings do not always match real-world proportions, angles or
air streams. Their purpose is to make you understand the principles.
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 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
The most important part of an airplane are the wings. Some aircraft
are just 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 with 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 could 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
this 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 wood 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
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
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
Possibly use a toothpick to place the weight further frontwards,
ahead of the leading edge, in order to get the center of mass at
1/4th chord. But, keep in mind that the shape of the weight may
cause an aerodynamic instability.
There are several ways to throw such a postcard glider:
- Hold it loosely by the trailing edge and let it hang towards
the ground, like a pendulum. Just open your fingers. The glider
should accelerate while falling then bend its trajectory towards
a stable flight.
- Hold it by the nose but with your wrist turned towards you.
Your fingers point towards your face while gently pinching the
nose of the glider. Your eyes see the trailing edge. Make a
forward movement with your arm while releasing the glider. Try
to make sure that your fingers release the glider in its stable
flight attitude and at the correct flight speed.
- Glue a tiny vertical piece of balsa wood on the belly of the
postcard, so you can hold it like you would a conventional balsa
Don't be confused if you never manage to get a flight, even an awful
and oscillating one. I don't always make successful flying postcards
either. Just try to make another one with a different shape,
possibly after reading the next chapter.
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. Bend them only upwards,
in order to keep a globally upwards trailing edge.
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
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 damper 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
You may get yet another chance at getting the postcard to fly by slightly
bending the outer
triangles. Try to bend the two trailing triangles upwards... Try to
bend the two leading ones downwards or maybe upwards... Try
different triangle sizes and shapes...
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. After 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 yet stable systems have been developed using
few or no maths, like the boomerang, but this often required centuries of experimenting and
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...
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 damper 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 damper 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
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...
Many beginners 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
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.)
Even if the wings don't bend and the wing chord is not too short for
the flight speed, you still may experience very different behaviors
with different weights. I'd say that this is because your glider is
"borderline". It is stable by chance, on a narrow margin of flight
speeds. There is nothing wrong with this. I often build balsa
gliders that behave that way. Just, there is no chance that the
glider would be certified for manned flights...
Aerodynamic yield of
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
If there is air leaking along the piston, the piston will slowly
fall to the bottom of the cylinder.
The postcard glider can be viewed in much the same way. 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... 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 that 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 simply heat).
You got it: we need to prevent that sideways leak of pressure. To
the least we must decrease it. Yet we cannot have airplanes and
gliders 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
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 proportionally 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 slowly, 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
To further regulate and decrease the whirls, you can cut rounded
wing tips 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 tapered wing tips would be what sea birds have
(but the overall shape of their wings is ways more sophisticated
than what I drew above).
The other simple way to cope with the turbulences would be the
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
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 rounded wing tips...
Yet another optimal shape would be an almost rectangular wing with
"winglets". To see beautiful such wings look at photographs of
flying eagles. For example by using this image search page: http://www.google.be/images?q=eagle&biw=1272&bih=625
. How do winglets work? I can propose an explanation. Look at the
4:1 aspect ratio wing below. Let's arbitrarily decide that the
outermost squares cause the worst turbulence and braking. Let's
color them in red. They make half of the wing surface, so for sure
this is not an optimal wing.
A wing with a sixth of the chord, with both end squares considered
red zones, has proportionally much more efficient surface. It's a
"high aspect ratio wing".
Now, we can create the same wing shape as the awful rectangle above
but using efficient high aspect ratio wings. We "simply" put six of
them one after the other.
Of course this only makes sense if we separate them vertically,
creating an "hexaplane" structure.
But... biplane, triplane and for sure hexaplane wing structures are
complex and not optimal. So, we try to get the best of both systems.
We'll use a plain surface for the most, inside part. And, separate
little wings (winglets) for the outer parts.
This implies that those winglets each end separately, as in the
six-plane structure. That way we have a straight rectangular wing
for most of the surface yet with much less "red surface".
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 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
Actually, the concept of stability can be perceived in a broader
way. If you build a glider with a huge vertical tail (which should
bring stability), a strong dihedral or the wings high above the
center of gravity (which should bring stability), you probably will
have the glider fly a "Dutch roll", that is oscillating in a
corkscrew path. The Dutch roll... will be very stable. You do
but not the kind of stability that is required for a standard
airplane. (If you don't succeed in inducing the Dutch roll that way,
try to put the center of gravity slightly backwards.)
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
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. (FoilSim is a
great Java applet developped by NASA: http://www.grc.nasa.gov/WWW/K-12/airplane/foil3.html
(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
But... are you sure that 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 that 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
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 turbulence appear
on the upside of the trailing part of the wing. You want
less chord, in order to have less wing surface braked by turbulence.
One way to talk about it is that under a given chord x
(Unless you artificially produce turbulence, say using turbulators,
or widely flapping wings like little insects.) You need to be above
a given chord x
when your chord x
very high, you get a lot of turbulence, 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) (exaggerated 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.)
Whether they were flat, had a beak or were cambered, till now we
talked only about thin profiles.
Why use a thick profile? The thicker an object, the more it brakes
when passing through the air...
Early airplanes all had thin wings. This is desirable for very slow
aircraft. The air won't move correctly around a thick profile, at
very low airspeed. Yet the problem with thin profiles is the
difficulty to get stiff wings. More exactly: stiff and lightweight.
By using steel spars or plain wooden plates, the wings would be very
stiff yet far too heavy. Instead, a huge structure was used made out
of ropes and rods, to get something very lightweight and rigid. That
was the biplane shape, like shown on these pictures: https://www.google.be/search?tbm=isch&q=early+biplane
. But those ropes and rods cause drag. And two wings one above each
other 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 flapping in the airstream. The overall result is better. And...
if the wing is not too thick, it 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 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.))
Thick wing... 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 the transitions between the shapes, the better
For a wing profile, one tries to use an optimal aerodynamic shape,
typically with the spar in the thickest part.
Most wings use such a shape. But... a toy glider is an extreme, as
we already stated. Again, it's about turbulence. The fore part tends
to avoid creating turbulence, while the aft part will eagerly
trigger them. That's why the high-speed World War II P-51 Mustang
fighter plane used an airfoil profile with a longer fore part and a
shorter aft part; in order to minimise the part of the wing that
creates the dreaded turbulences.
(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 slow 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 not good at very low speed.
That would be because the leading edge of thin airfoils scrapes a
little un-aerodynamically trough the air and creates turbulence.
Those turbulence 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.
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
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 thinner airfoil, say two times thiner. 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:
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
- My friend Frédéric Cloth, who hosts this page and many more.
- Frank Armbruster for pointing out two misused technical
Eric Brasseur - November
21 2009 till October 12 2014