Longitudinal Stability and Trim

The drag of the system is dependent on the distribution of loads between the surfaces. In order to determine this, and to properly size the tail surface, we must consider the aircraft's stability and trim. Stability is the tendency of a system to return to its equilibrium condition after being disturbed from that point. Two types of stability or instability are important.

A static instability:

A dynamic instability:

An airplane must be a stable system (well, with some exceptions ) with acceptable time constants. To assure this, a careful analysis of the dynamic response and controllability is required, but here we look only at the simplest case: static longitudinal stability and trim. This will tell us something about the aerodynamic design of the surfaces -- the load they must carry, the effect of airfoil properties, and the drag associated with the surfaces.

If we displace the wing or airplane from its equilibrium flight condition to a higher angle of attack and higher lift coefficient:

we would like it to return to the lower lift coefficient.

This requires that the pitching moment about the rotation point*, C_m, become negative as we increase C_L:

Note that:

where x is the distance from the system's center of additional lift to the c.g.

So,

If x were 0, the system would be neutrally stable. x/c represents the margin of static stability and is thus called the static margin. Typical values for stable airplanes range from 5% to 40%. The airplane may therefore be made as stable as desired by moving the c.g. forward (by putting lead in the nose) or moving the wing back. One needs no tail for stability then, only the right position of the c.g..

Although this configuration is stable, it will tend to nose down whenever any lift is produced. In addition to stability we require that the airplane be trimmed (in moment equilibrium) at the desired C_L.
This implies that:

With a single wing, generating a sufficient C_m at zero lift to trim with a reasonable static margin and C_L is not so easy. (Most airfoils have negative values of C_m₀.) Although tailless aircraft can generate sufficiently positive C_m₀ to trim, the more conventional solution is to add an additional lifting surface such as an aft-tail or canard. The following sections deal with some of the considerations in the design of each of these configurations.

* The rotation point is the center of gravity (c.g.) for freely flying bodies.