Pitch Stiffness

Suppose that the airplane of curve a on Fig. 2.3 is disturbed from its equilibrium attitude, the angle of attack being increased to that at В while its speed remains unal­tered. It is now subject to a negative, or nose-down, moment, whose magnitude corre­sponds to BC. This moment tends to reduce the angle of attack to its equilibrium value, and hence is a restoring moment. In this case, the airplane has positive pitch stiffness, obviously a desirable characteristic.

On the other hand, if Cm were given by the curve b, the moment acting when dis­turbed would be positive, or nose-up, and would tend to rotate the airplane still far­ther from its equilibrium attitude. We see that the pitch stiffness is determined by the sign and magnitude of the slope dCJda. If the pitch stiffness is to be positive at the equilibrium a, Cm must be zero, and dCJda must be negative. It will be appreciated from Fig. 2.3 that an alternative statement is “Cmo must be positive, and dCm/da neg­ative if the airplane is to meet this (limited) condition for stable equilibrium.” The various possibilities corresponding to the possible signs of Cmo and dCJda are shown in Figs. 2.3 and 2.4.