# Stick-Free Longitudinal Static Stability

Up to this point we have been concerned with “stick-fixed” longitudinal static stability. The pitching moment as a function of a has been determined assuming that the necessary force was applied to the control stick to hold the elevatdr (or other types of control surfaces) at its trimmed position. Suppose, however, that the pilot does not hold the stick fixed. Sometimes, in a cross-country flight, one likes to be able to trim the airplane and sit back and relax. The degree to which one can relax depends on the airplane’s stick-free static stability.

As we will see shortly, freeing the stick has the effect of changing the slope of the tail lift curve. Thus, the results that have been obtained for the stick-fixed case will still hold if an effective a, is used.

The stabilator and the stabilizer-elevator configuration will again be considered separately, since there are basic differences in the analyses. The final results from the two analyses will, however, be similar.

Elevator-Stabilizer Configuration

This is the easiest of the two tail configurations to treat. If the stick force is zero, it follows that the hinge moment of the elevator must be zero. From

Equation 8.37,

Or Se, the floating elevator angle, is related to a, and S, by

The lift coefficient of the tail is given by

CL, = aAatt + т 8)

with the small contribution from 8, being neglected. With 8e related to a„ CL, becomes

Thus,

(8.41) where Fe is called the free elevator factor and is defined by

(8.42)

Normally, as seen by a previous example, bx and b2 are both negative for the stabilizer-elevator combination. Thus Fe is typically less than one. For the earlier example, bx = -0.33 and b2 – -0.69. CJC was given as 0.37, so that r would equal approximately 0.58. For this particular tail the value of Fe becomes 0.72.