LATERAL AND DIRECTIONAL STATIC STABILITY AND CONTROL
We now turn our attention to the static forces and moments that tend to rotate the airplane about its x – and 2-axes or translate it along its у-axis. First consider directional stability and control about the z-axis.
Directional Static Stability
Figure 8.25 illustrates an airplane undergoing a positive sideslip. In this case, the component of its velocity vector along the у-axis is nonzero and positive. The airplane is “slipping” to the right. This results in a positive sideslip angle, /3, being defined as shown. As a result of the velocity vector no longer lying in the plane of symmetry, a yawing moment, N, is produced by the fuselage and by the side force on the vertical tail. The airplane will possess positive static directional stability (sometimes called weathercock stability, after the weathervane) if
Figure 8.25 An airplane having a positive sideslip.
The criterion for longitudinal static stability required the slope of the moment curve to be negative. In this case, the sign is opposite because the yawing moment is opposite in direction to the angle fi.
Generally, the yawing moment from the fuselage is destablizing. However, it is usually small and easily overridden by the stabilizing moment contributed by the vertical tail, so airplanes generally possess static directional stability. However, the vertical tail is not normally sized by any considerations of static directional stability. Instead, the minimum tail size is determined by controlability requirements in the event of an asymmetric engine failure or flying qualities requirements related to dynamic motion.
The yawing moment is expressed in coefficient form by
N = CsqSb (8.88)
The contribution to CN from the fuselage can be estimated on the basis of Equation 8.72. However, in calculating CNfB corresponding to CMaB, the difference in signs and reference lengths must be remembered. CygB will also be of opposite sign to Cl»b.
The contribution of the vertical tail to the static directional stability is formulated in a manner similar to that followed in determining the horizontal
tail’s effect on longitudinal stability. If the aerodynamic center of the vertical tail is located a distance of lv behind the center of gravity, then
Nv = r)tqSJvav[(3( – e„)] or
CN = T,’f ьаЛ1~€^ (8 89)
The vertical tail volume, Vv9 is defined by
X/ = v —
v~ S b
so that Equation 8.89 becomes
С» = v, VvavO – єр) (8.90)
av is the slope of the lift curve for the vertical tail. An estimate of this quantity is made more difficult by the presence of the fuselage and horizontal tail. If the vertical tail is completely above the horizontal tail, then it is recommended that an effective aspect ratio be calculated for the vertical tail equal to the geometric aspect ratio multiplied by a factor of 1.6. If the horizontal tail is mounted across the top of the vertical tail (the so-called T-tail configuration), this factor should be increased to approximately 1.9 to allow for the end-plate effect of the fuselage on the bottom of the vertical tail and the horizontal tail on the top. This latter factor of 1.9 is only typical of what one might expect for an average ratio of fuselage to tail size. For a more precise estimate of this factor, one should resort to wind tunnel tests or Reference 8.3 or 5.5.
The sidewash factor, ep, is extremely difficult to estimate with any precision. For preliminary estimates, it can be taken to be zero. However, one should be aware of its possible effects on Nv.