Directional (yawing) static stability
Contributions to the directional stability of a helicopter arise from the tail rotor, the fin, the fuselage and the main rotor. Suppose the helicopter was in a sideslip to starboard, then for positive static stability there must be a yawing moment also to starboard which tends to align the aircraft with the relative wind direction. The change of yawing moment, N, due to sideslip velocity, v, is the derivative Nv, so for static stability, this must have a positive value.
126.96.36.199 Tail rotor contribution to Nv
The tail rotor always provides a stabilizing contribution to Nv, which arises from the change in tail rotor thrust with change in sideslip velocity. In steady forward flight, the thrust produced depends on the blade angle of attack. Consider a blade element at radius, r, from the tail rotor hub. In forward flight at speed Ue, the blade element experiences a velocity in the plane of rotation of Ue + )trr (where )tr, is the tail rotor rotational speed) and a velocity perpendicular to the plane of rotation, vtr, due to inflow. Now the angle of attack of the blade element is given by:
a = 9tr — ф
where 9tr is the tail rotor collective pitch angle and ф is the inflow angle given, on the advancing side, by:
In positive side-slipping flight with sideslip velocity v, the relative air flow direction now makes an angle p with the plane of rotation, given by p = tan~i (v/Ue). The inflow through the tail rotor is now increased by the value of the sideslip velocity and the inflow angle is now given by:
This changes the blade element angle of attack to:
as = 0tr — ф5
The angle of attack has therefore been reduced by the sideslip (assuming tail rotor collective remains constant) which in this case will result in a reduction in tail rotor thrust, *Ttr. Now the fuselage torque reaction, 2MR, is initially balanced by the tail rotor thrust moment. So:
2mr = Ttr ltr
where Ttr = tail rotor thrust and ltr = tail rotor moment arm. The reduction in tail rotor thrust caused by the positive sideslip means that this balance is no longer maintained (assuming no rapid change in main rotor torque) and an out-of-balance yawing moment Ntr, is produced that is given by:
Ntr = 2mr — (Ttr — *Ttr )ltr = *Ttr ltr
This yawing moment will cause the helicopter to yaw to starboard into the direction of the sideslip. Hence, the tail rotor contribution to Nv is positive and therefore stabilizing. This applies to both tractor and pusher tail rotors.