The equation of motion in the yaw plane can be set up similarly to the pitch plane. The weathercock stability of the V-tail contributes to the restoring moment.
Figure 12.4 depicts moments in the yaw plane. In the diagram, the aircraft is yawing to the left with a positive yaw angle в. This generates a destabilizing moment by the fuselage with the moment (NF = YF x lf), where YF is the resultant side force by the fuselage and lf is the distance of Lf from the CG. Contributions by the wing, H-tail, and nacelle are small (i. e., small projected areas and/or shielded by the fuselage projected area). The restoring moment is positive when it tends to turn the nose to the right to realign with the airflow. The weathercock stability of the V-tail causes the restoring moment (NVT = YT x lt), where YT is the resultant side force on the V-tail (for small angles of (в + a), it can be approximated as the lift generated by the V-tail, LVT) and lt is the distance of LT from the CG. Therefore, the total aircraft yaw moment, N (for conventional aircraft), is the summation of NF and NVT, as given in Equation 12.9:
Nacc = NF + NVT
At equilibrium flight:
Nacc = 0; i-e-, NVT = ~NF
In coefficient form, the fuselage contribution can be written as:
C„f = – k„kRlNF [(Sff )/(Sw Ь)]в
where kn = empirical wing-body interference factor kR = empirical correction factor Sf = projected side area of the fuselage lf = fuselage length b = wing span
In coefficient form, the V-tail contribution can be written as in Equation 12.11 (LVT is in the coefficient form CLVT):
CnVT = [(lt/Svt)/(Swc)]vvtClvt = Lvt Vv vvtClvt (12.12)
VV = V-tail volume coefficient = (lt/Svt)/(Swc) (12.13)
(introduced in Section 3.20, derived here).
Equation 12.9 in coefficient form becomes:
Cn_cg = – knkmNF[(Sflf)/(SwЬ)]в + LvtVv wtClvt (12.14)