In this article we discuss off-axis responses to pilot control inputs. Off-axis responses are typically undesirable side-effects of pilot control inputs. For example, a yaw that occurs when a pilot increases the collective and tries to climb. Other examples include helicopter roll when a pilot aims to change the pitch, and vice versa. The latter are sometimes called pitch-roll coupling. Sections are provided below for the major off-axis responses. We also include a brief discussion of how augmentation systems minimize or eliminate these responses.
There are two primary sources of off-axis pitch/roll responses: control coupling and rate coupling. Control coupling applies an off axis moment roughly proportional to the stick movement. For example, if the longitudinal cyclic is moved an amount \(\delta_x\) and results in a change of roll moment \(L_x\delta_x\). Rate coupling is a roll moment proportional to pitch rate. For example, a roll moment \(L_q q\) associated with a pitch rate \(q\). Hence we have a total off-axis roll moment \(L_x\delta_x + L_q q\) due to a longitudinal cyclic input \(\delta_x\).
Control coupling is associated with a combination of control rigging and rotor dynamics. Control rigging determines where, on the rotor azimuth, the largest blade feathering change occurs. For example, a forward cyclic input may provide maximum feathering at \(\Psi = 275^o\). Rotor dynamics will then determine where the peak flapping change occurs. For example, say \(80^o\) after peak feathering. In this case, peak flapping due to forward cyclic would be at \(\Psi =275^o + 80^o=355^o\) due to the forward cyclic input. With these example numbers, the forward longitudinal cyclic input would provide a small, positive roll moment.
Rate coupling is associated with aerodynamic changes due to the on-axis response. For example, consider a helicopter pitching nose down due to forward cyclic input. The front of the rotor, moving down, experiences an upward air velocity from this pitch motion. It also experiences an increase in induced velocity as it sinks into the rotor wake. The reverse is true for the aft portion of the rotor. These changes in aerodynamics induce a peak flapping change roughly \(90^o\) later on the azimuth. This changes lateral flapping and hence creates a roll moment.
For a long time these off-axis effects were poorly predicted by computer models, often even missing the direction of the movement. For example, many models would predict a right wing down roll motion after a longitudinal cyclic input when the real helicopter rolled left wing down. Models have improved in this regard, primarily due to better estimates of wake distribution over the main rotor disk.
In hover and low speed flight, the primary off-axis response to collective is yaw. Assuming the main rotor turns counterclockwise (CCW) when viewed from above, an increase in collective will cause a clockwise (CW) yaw response. Let's step through this to understand why. First, the collective increase pitches the main rotor blades up, adding lift and drag. The added drag requires the engine to provide more torque to the rotor, to prevent it from slowing down. The increased CCW torque to the main rotor imparts an equal and opposite reaction torque to the fuselage. Normally the tail rotor counters reaction torque to maintain fuselage heading. In this case, until the pilot adjusts the pedals, the tail rotor is only countering the original torque, before the collective increase. The increased reaction torque "overpowers" the tail rotor and yaws the fuselage CW. Pilots are accustomed to this, and often subconsciously add left pedal when increasing collective. This increases tail rotor thrust which counters the yaw response to collective. This allows a pilot to maintain heading.
At higher speeds the picture is different. Modern helicopters have large vertical fins that reduce the aforementioned yaw responses at high speed. However, there’s another effect that creeps in. At high speed, collective input adds more lift to the advancing side (right side for CCW) of the main rotor than to the retreating side. This follows from the fact that the advancing side operates at a larger airspeed / dynamic pressure. This lift imbalance changes rotor flapping, increasing it roughly 90 degrees later, over the nose. This causes the helicopter to pitch up when the collective is increased. Likewise, a helicopter will naturally pitch down when collective is lowered at high speed. This, like other off-axis responses, may be automatically countered by an AFCS.
Pressing the left pedal increases tail rotor thrust to the pilot's right side. Since a typical tail rotor is located above the helicopter CG, this creates a “right wing down” roll moment. However, with forward speed, this effect is quickly overcompensated by another effect. The left pedal input pushes the nose left and increases sideslip (the angle of the relative wind to the fuselage). This changes the main rotor flapping to be lower over the nose and higher over the pilots right side. This results in a left wing down roll and a nose down pitch.
The effects described above are the "raw" effects associated with the control movement. Helicopters with augmentation systems activated may partially or completely counter many of these effects. For example, most augmentation systems, upon detecting a pure longitudinal cyclic input, will adjust lateral cyclic "underneath the covers" to minimize roll.
A paper about modeling off-axis responses may be found here.