# Geometry of the Tail Surfaces

The geometry of the horizontal and the vertical tails may be described basically like that of a wing (see Sec. 3-1). In general, the horizontal tail has a symmetric planform and the vertical has an asymmetric side elevation (Fig. 7-1).

The planform of the horizontal tail is defined, in analogy to Sec. 3-1, by the following main quantities:

*The conclusion should not be drawn that the fin setting angle does not affect the longitudinal stability, because the determination of the degree of stability must always be related to an equilibrium state. a b Figure 7-2 Wind tunnel measurements on an airplane (Messerschmitt model Me 109) with and without empennage. £fj= setting angle of the tail plane (see Fig. 7-6c). (a) Lift coefficient vs. angle of attack, (b) Lift coefficient vs. pitching-moment coefficient. |

Span of the horizontal tail bH

Area of the horizontal tail AH

Aspect ratio of the horizontal tail AH = bjj/Ajj

Setting angle of the tail plane (Fig. 7-6a) £H

Deflection of the elevator (Fig. 7-6a) rH

The position of the horizontal tail relative to the airplane is given by the lever arm Tfj of the horizontal tail, defined as the distance between the geometric neutral points of the horizontal tail and the wing. The geometric neutral point is defined in Sec. 3-1.

For some airplanes, the high position of the horizontal tail relative to the wing plays some role.

For the aerodynamic effects of the horizontal tail, the following two dimensionless quantities, which express size and location of the horizontal tail relative to the wing quantities, are particularly important: area ratio AHjA and relative tail-surface distance гн/сц. Here, A is the wing area and сц is the reference wing chord according to Eq. (3-5Й).

For a large number of airplanes, the area ratio lies between AHfA «0.15 and 0.25 and the relative tail distance between rH/c^ « 2 and 3.

The side elevation of the vertical tail is described by the following quantities (Fig. 7-1):

Height of the vertical tail h v Area of the vertical tail A v Deflection of the rudder 7]v

The location of the vertical tail relative to the airplane is given by the lever arm rv of the vertical tail, defined as the distance between the geometric neutral points of the vertical tail and the wing. A general definition of the aspect ratio of the vertical tail is not feasible because of the great variety of tail-surface shapes and the various positions of the vertical tail relative to the fuselage and to the horizontal tail (see Sec. 7-3-2).

For the aerodynamic effect of the vertical tail the following two dimensionless quantities are important, as for the quantities for the horizontal tail: area ratio Ay IA and relative tail-surface distance r-yjs, where s=b/ 2 is the wing semispan. Approximately, AvjA = 0.1-0.2 and rv]s = 0.5-1.0.

On many newer airplanes, the horizontal tail has been eliminated so that the airplane has only a vertical tail as shown in Fig. 7-3. Such an airplane is termed an all-wing airplane (flying wing). Here the function of the elevator (control about the lateral axis) has been assigned to a control surface (elevator) of width bH.

Besides the most commonly used central arrangement of the vertical tail as shown in Figs. 7-1 and 7-3, various other arrangements are also found. For instance, Fig. 7-4a shows two fins (vertical tail surfaces) at the tips of the horizontal tail. Figure 7-4b illustrates a tail surface with large dihedral (V tail surface), combining the functions of both the horizontal and the vertical tails.

Figure 7-3 The geometry of the empennage of an all-wing airplane.

For the aileron, to be discussed in more detail in Chap. 8, the aileron span sд as shown in Figs. 7-1 and 7-3 is important in addition to the aileron chord ratio.