Airplane control surfaces

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For an airplane to be controllable, control surfaces are necessary. The 4 main surfaces are ailerons, elevator, rudder and flaps as shown below:
 Focus on the 4 control surfaces ailerons, elevator, rudder and flaps
Before i discuss how every surface effect the plane motion you must know the center of gravity of the plane ( The point from which the weight of the plane effect downwards ) . From this point we can take three axis as shown below .(All 3 axis pass through the Center of Gravity)
As shown  the orange axis (z) When the plane rotates about it then the plane can be turned right or lift .
The  green axis (y) when the plane rotates about it then the plane can move upward or downward .
 The blue axis (x) rotating about it makes the plane roll .

Let's talk about the surfaces ( in the designing of the plane ) that controls these motions . 

1- Elevator:

The elevators control the movement of the airplane about its lateral axis. This motion is called pitch. The elevators form the rear part of the horizontal tail assembly and are free to swing up and down. They are hinged to a fixed surface—the horizontal stabilizer. Together the horizontal stabilizer and the elevators form a single airfoil. A change in the elevator's position modifies the camber of the airfoil, increasing or decreasing lift.
The elevators are connected to the control stick by control cables. Pushing the stick forward moves the elevators downward. This increases the lift produced by the horizontal tail surfaces and causes the nose to drop. Pulling back on the stick causes the elevators to move upward, decreasing the lift produced by the horizontal tail surfaces and forcing the nose upward.

 2 - FLAPS
Flaps slow the plane
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, which enables the airplane to fly at a greatly reduced speed with a lower risk of stalling. When extended further flaps also generate more drag which slows the airplane down much faster than just reducing throttle power.
Although the risk of stalling is always present, an airplane has to be flying very slowly to stall when flaps are in use at, for example, 10 degrees deflection.
So all these factors are why and how airplanes fly. Radio control model airplanes can of course be more simple - for example, just have rudder and elevator control or perhaps just rudder and motor control. But the same fundamental principles always apply to all airplanes, regardless of size, shape and design.

  3- Ailerons :
Ailerons can be used to generate a rolling motion for an aircraft. Ailerons are small hinged sections on the outboard portion of a wing. Ailerons usually work in opposition: as the right aileron is deflected upward, the left is deflected downward, and vice versa. This slide shows what happens when the pilot deflects the right aileron upwards and the left aileron downwards.
The ailerons are used to bank the aircraft; to cause one wing tip to move up and the other wing tip to move down. The banking creates an unbalanced side force component of the large wing lift force which causes the aircraft's flight path to curve. (Airplanes turn because of banking created by the ailerons, not because of a rudder input). 

 4 - rudder

 for Airplane The rudder is located on the back edge of the vertical 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. The air flowing over the fin now pushes harder against the left side of the rudder, forcing
the nose of the airplane to yaw round to the left .And the same thing happen when the pilot pushes the right pedal but to right .

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