Figure 6.9 Aircraft Longitudinal Static Stability

The above discussion of stable responses to disturbances leads to a criterion for positive longitudinal stability. This stability criterion is a condition which must be satisfied in order for an aircraft to be stable. Since, for positive static longitudinal stability, pitching moment must decrease with increasing angle of attack, and increase with decreasing angle of attack, the partial derivative of the coefficient of pitching moment about the center of gravity, C_Mcg = M_cg / q S c, with respect to angle of attack must satisfy:

A plot of pitching moment coefficient vs angle of attack or lift coefficient reveals the relationship between static stability and trim, and is usually called a trim diagram. It is convenient to plot the variation of C_{M cg} with respect to absolute angle of attack, _a = _{L = 0} , because _a = 0 when C_L = 0. Figure 6.10 illustrates a typical trim diagram for an aircraft with positive static longitudinal stability.