The basic principles that make an airplane fly apply to all airplanes, from the Wright
Brother's first machine to Concorde, and it's actually not difficult to
understand how and why airplanes fly.
There are 4 aerodynamic
forces that act on a plane in flight; these are lift, drag, thrust and gravity (or weight).
In simple terms, drag is the resistance of air (the backward force), thrust is the power of the airplane (the forward force), lift is the upward force and gravity is the downward force.
So for airplanes to fly, the thrust (engine power) must be
greater than the drag and the lift must be greater than the gravity (so as you can see, drag opposes thrust and
lift opposes gravity).
This is certainly the case when the plane takes off or climbs. However, when it
is in level flight both opposing forces are equal.
In a descent, gravity exceeds lift and to slow an airplane drag has to exceed
thrust.
The picture below shows how these 4 forces act on an airplane in flight:

The thrust is generated by the plane's engine (propeller or
jet), gravity is a natural force
acting upon the airplane and drag is a normal kind of friction caused by the
plane moving through air molecules.
Drag is also a reaction to lift, and this lift must be generated by the plane in flight. This is done
by the wing of the airplane.
A typical cross section of a wing will show the top surface to
be more curved than the bottom surface - this shaped profile is called an 'airfoil' (or 'aerofoil').
During flight air naturally flows over the top of and beneath the wing. The air
that passes over the top surface of the wing accelerates faster than the air
passing underneath, and this results in a lower air pressure above the wing than below.
In addition, the air that passes beneath the wing is deflected downward. This
causes an opposite upward force
(Newton's 3rd Law of Action &
Reaction) that acts upon the underside of the wing.
This upward push combined with
the lower air pressure above the
wing both generate the lift
needed to hold the airplane up as it flies.

The faster a wing moves through the air, so the actions are
exaggerated and more lift is generated.
However, the direct reaction to lift is the drag, and this too increases with airspeed. So airfoils need to be
designed in a way that maximizes lift but minimizes drag, in order to be
efficient.
Another crucial factor of lift generation is the angle of attack - this is the angle at
which the wing sits in relation to the horizontal airflow.
As the angle of attack increases, so more lift is generated - but only up to a
point until the smooth airflow over the wing is broken up and so the generation
of lift cannot be withheld. When this happens, the sudden loss of lift will
result in the airplane entering into a stall,
where the weight of the plane cannot be supported any longer.
For an airplane to be controllable, control surfaces are necessary.
The 4 basic surfaces are ailerons, elevator, rudder
and flaps as shown below:

To understand how each works upon the airplane, imagine 3 lines
(axis - the blue dashed lines in the picture
above) running through the plane. One runs through the center of the
fuselage from nose to tail (longitudinal
axis), one runs from side to side (lateral axis) and the other runs vertically (vertical axis). All 3 axis pass
through the center of gravity,
roughly in the centre of the cockpit for the plane in the picture.
The plane will rotate around each axis when movement to any control surface is
made by the pilot. The table below shows the appropriate actions:
|
Action |
Axis |
Controlled by |
|
Roll |
Longitudinal |
Ailerons |
|
Pitch |
Lateral |
Elevators |
|
Yaw |
Vertical |
Rudder |
The following sections explain how each control surface effects
the airplane:

Located close to each wingtip on the trailing edge (rear) of the
wing, the ailerons control the airplane's roll.
Each aileron moves at the same time but in opposite directions ie when the left moves up, the right
moves down and vice versa.
This movement causes a slight decrease in lift on the wingtip with the upward
moving aileron, while the opposite wingtip experiences a slight increase in
lift.
Because of this subtle change in lift on each wingtip, the plane is forced to
roll in the appropriate direction ie
when the pilot moves the stick left, the left aileron will rise and the
airplane will roll left.
The ailerons are controlled by a left/right movement of the control stick, or
'yoke'.

The rudder is located on the back edge of the stabilizer, or
fin, and is controlled by 2 pedals at the pilot's feet.
When the pilot pushes the left pedal, the rudder moves to the left and this in
turn causes the airplane to yaw to the left, because the air running over the
stabilizer and rudder is now pushing harder
on the left side of the rudder than on the right.

The elevators are located on the tailplane.
Like the ailerons, they cause a change in lift when movement is applied; moving
the elevator up (pulling back
on the yoke) will cause the airplane to pitch its nose up and climb, while
moving them down (pushing forward
on the yoke) will cause the airplane to pitch the nose down and dive.
Elevators are linked directly to each other, so work in unison unlike ailerons.

Flaps are located on the trailing edge of each wing, between the
fuselage and the ailerons, and extend outward and downward from the wing when
put into use.
The purpose of the flaps is to generate more lift at slower airspeed. This
enables the airplane to fly at a greatly reduced speed without the risk of
stalling. Flaps also generate a lot more drag which slows the plane down much
faster than just reducing throttle power.
The risk of stalling is always present though, but an airplane has to be flying
very slowly compared to its
normal flying speed, to stall when flaps are in use.
So these are the basic factors that make an airplane fly -
radio control model airplanes can be more simple - for example just have rudder
and elevator control - but the same principles always apply.
RC airplane
controls - which 'channels' do what on a model plane.
Flying
model airplanes - a basic introduction to flying a 1 or 2 channel electric
model.
How
helicopters fly - read how these machines stay in the air.