Static Stability and Control

Part 1

2.1 General Remarks

A general treatment of the stability and control of airplanes requires a study of the dynamics of flight, and this approach is taken in later chapters. Much useful informa­tion can be obtained, however, from a more limited view, in which we consider not the motion of the airplane, but only its equilibrium states. This is the approach in what is commonly known as static stability and control analysis.

The unsteady motions of an airplane can frequently be separated for convenience into two parts. One of these consists of the longitudinal or symmetric motions; that is, those in which the wings remain level, and in which the center of gravity moves in a vertical plane. The other consists of the lateral or asymmetric motions; that is, rolling, yawing, and sideslipping, while the angle of attack, the speed, and the angle of elevation of the x axis remains constant.

This separation can be made for both dynamic and static analyses. However, the results of greatest importance for static stability are those associated with the longitu­dinal analysis. Thus the principal subject matter of this and the following chapter is static longitudinal stability and control. A brief discussion of the static aspects of di­rectional and rolling motions is contained in Secs. 3.9 and 3.11.

We shall be concerned with two aspects of the equilibrium state. Under the head­ing stability we shall consider the pitching moment that acts on the airplane when its angle of attack is changed from the equilibrium value, as by a vertical gust. We focus our attention on whether or not this moment acts in such a sense as to restore the air­plane to its original angle of attack. Under the heading control we discuss the use of a longitudinal control (elevator) to change the equilibrium value of the angle of attack.

The restriction to angle of attack disturbances when dealing with stability must be noted, since the applicability of the results is thereby limited. When the aerody­namic characteristics of an airplane change with speed, owing to compressibility ef­fects, structural distortion, or the influence of the propulsive system, then the airplane may be unstable with respect to disturbances in speed. Such instability is not pre­dicted by a consideration of angle of attack disturbances only. (See Fig. 1.3d, and identify speed with x, angle of attack with y.) A more general point of view than that adopted in this chapter is required to assess that aspect of airplane stability. Such a viewpoint is taken in Chap. 6. To distinguish between true general static stability and the more limited version represented by Cm vs. a, we use the term pitch stiffness for the latter.

Although the major portion of this and the following chapter treats a rigid air­plane, an introduction to the effects of airframe distortion is contained in Sec. 3.5.