Analysis
Near the cruise condition most of the lift force is generated by the wings, with ideally only a small amount generated by the fuselage and tail. We may analyse the longitudinal static stability by considering the aircraft in equilibrium under wing lift, tail force, and weight. The moment equilibrium condition is called trim, and we are generally interested in the longitudinal stability of the aircraft about this trim condition.
Equating forces in the vertical direction:
where W is the weight, is the wing lift and is the tail force.
For a symmetrical airfoil at low angle of attack, the wing lift is proportional to the angle of attack:
where is the wing area is the (wing) lift coefficient, is the angle of attack. The term is included to account for camber, which results in lift at zero angle of attack. Finally is the dynamic pressure:
where is the air density and is the speed.
Read more about this topic: Longitudinal Static Stability
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