Tutorial

5. The Use of Coordinate Axes in Aeronautics

For purposes of basic understanding all references to motion and direction will be made using an imaginary three-dimensional coordinate system. This coordinate system will help to describe the motions of an aircraft in three-dimensional space. The center of the coordinate system is found at the centroid of the aircraft - roughly between the wings in the middle of the fuselage. A centroid is an imaginary point around which all rotation takes place. The three axes intersect at the centroid at right (90 degree) angles to each other. The longitudinal axis runs the length of the aircraft from the nose through the tail. The lateral axis runs across the wings from tip to tip. The vertical axis runs from the top (ceiling) of the airplane to the bottom (floor). These axes extend indefinitely from the center of the aircraft (see figure). Movement along or around one axis does not necessarily involve any movement on or around the other two.

Moving on Three Axes

Once in flight, an airplane can have six motions along and around the three axes. Mathematically speaking, all possible movements that an airplane can make can be defined in terms of these six directions. This is the basis of the mathematical modeling of airplanes and flight. Three of the movements are linear: front and back along the longitudinal axis; side to side along the lateral axis; up and down along the vertical axis. The other three movements are rotational: movement around the longitudinal axis, called roll; movement around the lateral axis, called pitch; Ñmovement around the vertical axis, called yaw.

An interesting exercise is to make a comparison between the movements an airplane can make with the movements a car can make. Of the linear motions, a car can obviously move along the longitudinal axis. It can not move laterally, (except on ice) but it can rotate (yaw). Cars cannot move up and down vertically on their own. Of the rotational motions, a car is limited to only one, yaw. A car will pitch slightly when the brakes or the accelerator are applied. A car will not roll Ñ or at least it's not supposed to! So, under normal driving conditions a car has only two motions: forward/back and yaw.

An airplane, in contrast, can roll, pitch and yaw through the use of its control surfaces. It can move forward and backward by using its engines. However, unlike a car, it can move side to side or up and down by using the three rotational motions. We use stabilizers to keep the airplane flying primarily longitudinally. This is why mathematical modeling or even a simple description of airplane movement can become very complex.

Stability

Stability is the ability of an airplane to return, of its own accord, to its original attitude in flight after it has been disturbed by some outside force, like wind gusts. Stability also refers to an airplane's response to the pilot's use of the controls.

The usable center of gravity range of this airplane is greater when it is gliding in stable horizontal flight with the engine off (TOP) than it is when the engine is on and the landing gear is down (BOTTOM).

The empennage plays an important role in the stability of an airplane Ñ much like the tail feathers of an arrow are critical to the stability of the arrow. If an arrow is shot without its tail feathers, it will wobble. The tail feathers keep the arrow stable and help it to stay on course. The empennage works the same way. The vertical fin helps to maintain stability in the direction of yaw. The horizontal stabilizer helps to maintain stability in the directions of pitch and roll. The empennage structures do produce drag, however. Researchers have developed ways to fly tail-less airplanes, but the airplanes must use computer-based control systems to maintain their stability. While the empennage structures of different airplanes can be very dissimilar, most modern airplanes still do have some form of fin and horizontal stabilizer.

An important component of stability for an airplane is the center of gravity (cg). The cg is an imaginary point about which the weight of an airplane balances. If you put a ruler across your finger and place it so it balances, your finger is at the cg of the ruler. The cg in an airplane does not stay in the same place at all times. A load of heavy cargo may shift the cg as will the drainage of fuel from the tanks during flight. Pilots have to recognize shifts in the cg and respond accordingly. Sudden shifts in the cg can be catastrophic. If an airplane experiences turbulence during flight and a large cargo load shifts, the pilot may have trouble reacting quickly enough to the shift to maintain stability of the airplane.

Controlling Motion

An airplane has three control surfaces: ailerons, elevators and a rudder. Within the cockpit, two controls operate the control surfaces. The control stick controls the ailerons and elevators. The rudder pedals control the rudders.

 

The table below explains flow from pilot controls to control surface to motion.

control in cockpit	control surface	motion
control stick (right and left)	ailerons	roll
control stick (front and back)	elevators	pitch
rudder pedals	rudder	yaw

The ailerons are flap-like structures on the trailing edge of the wings -one on each side. When the pilot moves the control stick to the right, the right aileron will tilt up and the left aileron will tilt down. This will cause the airplane to roll to the right. When the pilot moves the control stick to the left, the left aileron tilts up, the right aileron tilts down and the airplane rolls to the left. This happens because as the aileron tilts downward (effectively increasing camber) more lift is created and the wing rises. As it tilts upward, less lift will be created and the wing will descend. If the wing on one side of the airplane rises and the other descends, the airplane will roll towards the side of the decrease in lift.

The elevators are also flap-like structures that are mounted on each side of the horizontal stabilizer. When the pilot pushes the control stick forward, the elevators tilt downward. This causes the tail of the airplane to rise and the fuselage to tilt down - this is called pitching down. When the pilot pulls the control stick back, the elevators tilt upward, the tail goes down and the fuselage pitches nose-up. When the elevator tilts downward more lift is created (like the ailerons) and the tail rises. When the elevator tilts upward, less lift is created and the tail descends.

The rudder is located on the fin. The two rudder pedals are located at the pilot's feet. When the pilot pushes on the right rudder pedal, the rudder tilts to the right and the airplane yaws "nose-right." When the pilot pushes on the left rudder pedal, the rudder tilts to the left and the airplane yaws "nose-left." Again this is due to lift. However, the direction of this lift force is different than the lift force that causes the airplane to rise. When the rudder tilts to the right, more lift is created on the right, which "lifts" or pushes the vertical stabilizer to the left. This, in turn, causes the airplane to yaw nose-right. The opposite motion occurs when the rudder tilts to the left.

In trying to figure out all of this tilting right and left, remember that if the rudder is extended so that it obstructs the airflow, then the airflow is going to push hard on that rudder. An imbalance will be created between the side where the rudder is obstructing the airflow and the side where it isn't. This will cause the airplane to move away from the side where the rudder is extended. That is why when a pilot pushes the right rudder pedal, the rudder tilts to the right - the air will push harder on the right side of the tail causing the tail to swing left, which will cause the nose to swing right.

NASA Research At the dawn of powered flight, the Wright brothers used the method of actively warping an aircraft's wings to turn their aircraft. Now NASA researchers are teaming up with the U.S. Air Force Research Laboratory and Boeing's Phantom Works to develop a new high-tech version of this method. The Active Aeroelastic Wing (AAW) concept has been tested at NASA's Dryden Flight Research Center using an F/A-18A Hornet. The aircraft's wings were modified to enhance flexibility and to take advantage of a new actuator and flight control computer system. The program investigated the potential of aerodynamically twisting flexible wings to improve roll maneuverability of high-performance aircraft at transonic and supersonic speeds. Because this type of wing would require fewer moving parts for controlling flight, wings could be made thinner, lighter, and more aerodynamically efficient—translating to more economical operation and greater payload capability. Data obtained from these tests will aid in the design of a wide variety of future aircraft including high-performance fighters to high altitude, long endurance unmanned aerial vehicle (UAV) concepts, large transport aircraft, and high-speed, long-range aircraft.

Maneuverability

There is often a trade-off between stability and maneuverability. An airplane that is highly maneuverable and can do amazing things in the air is probably not very stable. Sometimes we refer to an automobile as having "tight" steering. That means that the car responds readily to movements of the steering wheel. There is no slack or lag. On the other hand, it also means that the automobile responds quickly and decisively, but does not over-respond. It does precisely what the driver tells it to do through the steering wheel - no more, no less. An airplane works the same way. "Tight" stability means the airplane responds precisely to the pilot's controls. The X-29 is a good example of this. The X-29, with its forward-sweep wing, is amazingly maneuverable. It can move like no other aircraft. However, the X-29 is also very unstable. A computer-based control system is required to help the pilot keep the airplane under control. The control system operates all the control surfaces based on a combination of what the pilot tells it to do and what its sensors say the airplane is doing. It makes minute and extremely rapid changes in the control surface positions to maintain the stability of the airplane. A human cannot perceive, absorb and react to this much information in the infinitesimally short time required Ñ computer help is needed.

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