AERODYNAMICS OF THE STABILIZERS
7- 1 INTRODUCTION
6- 1-1 Function of the Stabilizers
and Control Surfaces
The main parts of an airplane are the wing, the fuselage, and the tail unit or empennage. The aerodynamics of the wing has been discussed in detail in Chaps. 2-4, and that of the fuselage alone and the interaction between the wing and fuselage in Chaps. 5 and 6, respectively. Now, in Chaps. 7 and 8, the aerodynamics of the stabilizing and control surfaces will be discussed. Generally, an airplane has (see Fig. 7-1) a horizontal tail consisting of a horizontal stabilizer (tail plane) with an elevator, a vertical tail consisting of a vertical stabilizer (fin) with a rudder, and two ailerons.
A primary purpose of the tail unit is the stabilization of the airplane. This means that the airplane should have the tendency to return to a stationary flight attitude after a small disturbance. This process should take place “by itself’; that is, the aerodynamic forces should move the airplane back to the original attitude without application of the control surfaces.
Another equally important function of the tail unit is control of the airplane. Whereas the horizontal stabilizer and the elevator control the motion about the lateral axis, the vertical stabilizer with the rudder and the ailerons control that about the vertical and longitudinal axes (Fig. 1-6). The control of the airplane requires establishment of an equilibrium of the moments about the three axes. Here,
Figure 7-1 The geometry of the tail surfaces (empennage).
in addition to the moments of the aerodynamic forces, those of the inertia forces play a role.
As has already been pointed out in Sec. 1-3-3, the motion of the airplane about the lateral axis is termed longitudinal motion, that about the vertical and longitudinal axes lateral motion (side motion). Consequently, the horizontal stabilizer and the elevator stabilize and control the longitudinal motion. The vertical stabilizer and the rudder stabilize and, together with the ailerons, control the lateral motion.
Generally, each of the three control assemblies has the form of a wing with a control surface as shown in Fig. 2-24. It consists of a fixed and a movable part. The fixed part is termed a fin or vertical stabilizer at the vertical tail and a horizontal stabilizer or tail plane at the horizontal tail. The movable part is the control surface. It is termed a rudder at the vertical tail and an elevator at the horizontal tail. In Fig. 7-1, the horizontal stabilizer and the elevator and the vertical fin and the rudder are indicated by hatches. The changes of the moments required for control are effected by deflections of the control surfaces. At the horizontal and vertical tail assemblies, the moments may also be controlled by a stabilizer adjustment (stabilizer trim). The horizontal tail of many airplanes does not have a separate stabilizer and elevator. Here, the change of the moment about the lateral axis is achieved by displacement of the entire horizontal surface.
The aerodynamic effect of the horizontal tail is illustrated in Fig. 7-2 for an airplane with and without a horizontal tail. The lift coefficient is plotted against both the angle of attack and the moment coefficient. According to Fig. 7-2u, the contribution of the horizontal tail to the total lift is relatively small. Figure 7-26 gives the moment curves for several setting angles at the tail plane. Comparison
with the curves for the airplane without a horizontal tail shows that at all setting angles of the tail plane, the horizontal tail causes a considerable increase in the stability coefficient dcM/dcL, as defined-in Sec. 1-3-3. A change in the tail-plane setting angle zH causes a parallel shift of only the moment curve cM(cL)* When the moment reference axis passes through the center of gravity at a steady flight attitude, the equation cM = 0 describes the moment equilibrium about the lateral axis. Figure l-2b shows that this condition can always be satisfied by choosing the proper setting angle eH of the tail plane for a given lift coefficient. The results on wing-fuselage-tail systems at subsonic, transonic, and supersonic incident flows reported by Pitts et al.  should be pointed out. Schlichting  gives a summary of the importance of the interference among wing, fuselage, and tail unit for the stability coefficients of the airplane.
The aerodynamics of the tail units will be treated in two parts: The problems concerning the. tail surfaces without deflection of the control surfaces (stabilization) will be covered in Chap. 7, those concerning the effect of the control surfaces (control) and of the flaps (lift increase) will be discussed in Chap. 8.