# AERODYNAMICS OF THE VERTICAL TAIL

7- 3-1 Contribution of the Vertical Tail to the Aerodynamics of the Whole Airplane

The airplane in sideslipping flight The function and the geometry of the vertical tail have already been described in Sec. 7-1. As shown in Fig. 7-36, the vertical tail at asymmetric incident flow of the airplane of sideslip angle /1 is subject to a side force Yy. Because of its large lever arm, this side force generates the predominant portion of the yawing moment due to sideslip of the whole airplane. Moreover, the vertical tail also contributes to the side force due to sideslip and the rolling moment due to sideslip of the airplane. The contribution of the vertical tail to the yawing moment. due to sideslip of the airplane is

MzV=-rvYv (7-47)

where, from Fig. 7-36, r’v is the distance of the side force vector of the vertical tail from the moment reference axis that generally coincides with the vertical axis through the airplane center of gravity.

In analogy to Eqs. (7-2h) and {l-2b) for the horizontal tail, dimensionless coefficients may be introduced for the side force Yy and the yawing moment Mzy of the vertical tail by

Yy — CiyAyqy |
(7-48a) |

Mz у — cMz уАщж |
(7-486) |

Figure 7-36 Incident flow direction of the vertical tail. C. G. — center of gravity of the airplane.

Here qv is the dynamic pressure at the location of the vertical tail, which is generally smaller than the dynamic pressure of the undisturbed flow q« because of the interference of wing and fuselage with the vertical tail. The coefficient of the yawing moment of the vertical tail, referred to the wing quantities, is obtained from Eqs. (7-47M7-48&) as

The lift coefficient of the vertical tail CjV depends on the angle of attack (angle of sideslip Pv) and the rudder deflection qv of the vertical tail, in addition to its geometric data. The term dciy/dav stands for the lift slope of the interference-free vertical tail and (davldVy)Vv stands for the change in the zero-lift direction of the vertical tail caused by the rudder deflection.

In some cases the incident flow direction of the fin pv is considerably different from that of the airplane P because of the interference of wing and fuselage with the vertical tail. The two incident flow angles differ, as shown in Fig. 7-36, by the sidewash angle ft, = v/Uoo induced by the wing and fuselage at the location of the vertical tail:

(3y — (3 + (3V

Hence, for a rudder deflection of zero, the contribution of the vertical tail to the yawing moment is given as

It follows, then, that the change in yawing moment with the angle of sideslip (contribution of the vertical tail to the directional stability, Sec. 1-3-3) becomes

(7-52)* |

dCmzV___ dciy / f 3ft, qy A у r’y

3j3 dav ~r dp qx A s

The quantity

d&v _ і, Sft

dp dp

is designated as the efficiency factor of the vertical tail. From Eq. (7-52) it follows that the contribution of the vertical tail to the directional stability is proportional to the efficiency factor.

To establish the contribution of the vertical tail to the side force of the whole airplane, the coefficient of side force of the vertical tail is defined, in analogy to Eq. (7-9) for the horizontal tail, as

Yy — CyyAqc

In analogy to Eq. (7*52), the contribution of the vertical tail to the side force due to sideslip becomes

Hence, the contribution of the vertical tail to the side force due to sideslip, too, is proportional to the efficiency factor of the fin. Generally, the vertical tail also contributes to the rolling moment due to sideslip because the point of application of the vertical tail side force lies, in most cases, considerably above the airplane’s longitudinal axis.

The airplane in yawing motion Besides the sideslipping considered so far, the rotary motion of the airplane about the vertical axis (yawing motion) is also of great importance to the aerodynamics of the vertical tail. A rotary motion about the vertical axis with angular velocity coz generates a sideslip angle at the vertical tail

as the dimensionless angular sidesUp velocity. By introducing this expression for $v into Eq. (7-51) considering Eq. (7-50), the change in the coefficient of the yawing moment with the angular sideslip velocity becomes

This coefficient is termed the contribution of the vertical tail to the sideslip or yaw damping. Comparison of this formula with Eq. (7-52) shows that the contribution of the vertical tail to the directional stability is, in terms of the geometric quantities, proportional to (A y/A)(r’v/s) and that to the yaw damping is proportional to (A vJA)(r’y/s)2. The following discussions will be limited to incompressible flow.