When you launch a paper airplane, the most frequent cause of an unsuccessful flight is that the airplane flips out of control. This is usually because the airplane is not statically stable. If we could carefully adjust the weight distribution, or deflect some control surfaces, the flight characteristics can be greatly improved.

The control surfaces may be placed in various ways, as seen in these pictures

F-15 with  close-coupled canards and all-moving tails.

Translation (movement of the center of gravity) along:

x: forward (or rearward) motion U

y: sideslip : V

z: climb or descent (assuming airplane level): W

Rotation about axes passing through the center of gravity:

l: roll f

m: pitch q

n: yaw e

Longitudinal degrees of freedom are: u,v,w,q

Lateral: v,f,e

An aircraft is statically stable if it recovers from a small disturbance by itself. It is statically unsable if the disturbance gets amplified and the aircraft does not recover.

Example:

Statically Unstable:  Center of pressure is ahead of the center of gravity. Say a increases. C_L increases, so lift L increases. The change in pitching moment  is nose-up, which increases a further: this is unstable.

Thus, center of pressure behind center of gravity is stable.

Vertical tail is for directional stability for a given c.g. range.

Horizontal tail is for pitch stability and pitch control for a given c.g. range.

Empennage is for stability and control.

Pitch, Roll and Yaw: 3 basic controls are : ailerons for roll, elevator for pitch and rudder for yaw.

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