# Control Forces

For obvious reasons, in the design of an airplane’s control system, the stick or control wheel forces must lie within acceptable limits throughout the operating envelope (V-n diagram) of the airplane. In addition, the variation of these forces with airspeed about any trim point should be such as to give a proper “feel” to the pilot. Generally, this means that a push forward on the longitudinal control should be required to increase the airspeed, and a pull should be required to fly slower.

With regard to the longitudinal control forces, FAR Part 23 allows a maximum of 60 lb for a temporary application to a stick and 75 lb for a wheel.

A prolonged application is not allowed to exceed 101b for either type of control.

Gearing

The control force, P, is directly proportional to the control surface hinge moment, H.

P = GH (8.27)

G is referred to as the gearing. To determine G, refer to the sketch in Figure 8.8. Here a schematic of a control linkage is shown between a stick and an elevator. If the system is in equilibrium,

(8.28)

where the stick force, P, and the hinge moment, H, are shown in their positive directions. Now allow the stick at the point of application of P to move a distance s in the direction of P. In so doing the elevator will rotate through an angle S„ given by

s

LI,

Substituting this into Equation 8.28 gives

(8.29)

Comparing Equation 8.29 to Equation 8.27 gives

This result is general and independent of the details of the linkage. Since Se is negative for a positive stick displacement, it follows that G is positive. It can also be obtained simply by noting that if the system is in equilibrium throughout its displacement, the net work done on the system is zero. Hence,

Ps + HSe = 0

from which Equation 8.30 follows.