Aeronautics is the mathematics and mechanics of flying objects, in particular airplanes.
Straight and Level
In steady, level flight, an aircraft can be considered as being acted on by four forces in equilibrium: lift, weight, thrust, and drag. Thrust is the force generated by the engine and acts along the engine's thrust vector. Lift acts perpendicular to the motion of the airplane. Drag acts parallel to the motion of the airplane. Weight acts towards the centre of the Earth. Very roughly, in straight and level flight, lift can be assumed equal to weight and thrust equal to drag. By altering the balance of these basic forces, an aircraft can be manoeuvred in three dimensions.
Aircraft Control and Movement
There are three primary ways for an aircraft to move (apart from fore-and aft).... pitch (movement of the nose up or down ), roll (rotation around the longitudinal axis, that is, the axis which runs along the length of the aircraft) and yaw (swinging the nose left or right relative to the aircraft vertical axis). On commercial aircraft these are controlled using a handlebar or spectacle grip mounted on a control column in front of the pilot. Following the introduction of fly-by-wire, some commercial aircraft now use a small controller mounted on the side of the flight deck. With Fly by wire there is no mechanical connection from the flight deck to the control surfaces, electrical signalling is used instead.
On military aircraft, as on the earliest aircraft, a control stick or joystick is used.
Conventionally, pulling back causes a nose-up pitch action. Turning or moving the control to the right or left produces roll (and turn), turning the control affects the rate of roll rather than indicating the angle to which the aircraft will roll. Yaw is induced by foot pedals where pressure on the right or left pedal produces yaw in the indicated direction.
In micro-lights and hang gliders the pitch action is reversed - pulling back produces a nose-down pitch action.
Yaw is induced by a moveable rudder attached to a vertical fin at the rear of the aircraft. Sometimes the entire fin is movable. Movement of the rudder cambers the vertical surface producing force. Since the force is created a distance behind the centre of gravity this sideways force causes a yawing motion. On a large aircraft there may be several independent rudders on the single fin for both safety and to control the inter-linked yaw and roll actions.
It should be realised that an aircraft cannot execute a level turn by yaw alone - there is no surface to use to create cornering forces. A precise combination of bank and lift must be generated to cause the required centripetal forces without producing a sideslip.
Pitch is controlled by the rear part of the tailplane's horizontal stabiliser being hinged to create an elevator. By moving the elevator up (a position of negative camber) the tailplane is pulled down and the angle of attack on the wings increased so the nose is pitched up and lift is generally increased. There is however an initial period where lift is reduced, this is especially noticeable in larger aircraft which can drop some way before the increased angle of attack on the wings takes effect.
The system of a fixed tail surface and moveable elevators is standard in subsonic aircraft. Craft capable of supersonic flight often have a stabilator, an all-moving tail surface. Pitch is changed in this case by moving the entire horizontal surface of the tail. This seemingly simply innovation was one of the key technologies that made supersonic flight possible. In early attempts, as pilots exceeded Mach 0.9, a strange phenomena made their control surfaces useless, and their aircraft uncontrollable. It was determined that as an aircraft approaches the speed of sound, the air approaching the aircraft is compressed and shock waves are produced in a conical shape as the aircraft meets and exceeds the sound barrier. These shock waves made the elevator control surfaces freeze and so the problem was solved by moving the entire horizontal surface of the tail. Also, in supersonic flight the change in camber has less effect on lift and a stabilator produces less drag.
Aircraft that need control at extreme angles of attack are sometimes fitted with a canard configuration, in which pitching movement is created using a forward foreplane (roughly level with the cockpit). Such a system produces an immediate increase in lift and therefore a better response to pitch controls. This system is common in delta-wing aircraft, which use a stabilator-type canard foreplane. Another advantage of a canard configuration is improved behaviour at stall. Disadvantages of a canard configuration include that the requirements for efficiency and good handling qualities drive the design in opposite directions, and that the canard disturbs the airflow before it encounters the main wing.
A further design of tailplane is the vee-tail. So named because that instead of the standard inverted T there are two vertical fins angled away from each other in a V. To produce force, like a rudder, the two trailling edge control surfaces move in opposite directions. To act as a elevator both surfaces move together. The supposed advantage is the reduction in weight and drag from the reduction in the number of control surfaces from three to two.
Roll is controlled by movable sections on the trailing edge of the wings called ailerons. The ailerons move differentially - one goes up as the other goes down. The difference in camber cause a difference in lift and thus a rolling movement. As well as ailerons there are sometimes also spoilers - small hinged plates on the upper surface of the wing, originally used to produce drag to slow the aircraft down. On modern aircraft, which have the benefit of automation, they can be used in combination with the ailerons to provide roll control.
The earliest powered aircraft did not have ailerons. The whole wing was warped using wires. Wing warping is efficient since there is no discontinuity in the wing geometry. But as speeds increased unintentional warping became a problem and so ailerons were developed.
The actual linkages within the aircraft are discussed under:
aircraft mechanical control systems aircraft powered control systems