Small amplitude/low to moderate frequency: dynamic stability
Stability is important in any dynamic system, and for helicopters this is reflected in the need for the aircraft to not diverge from its trim condition if the pilot’s controls are left momentarily unattended. The theoretical foundation for dynamic stability has already been covered in detail in Chapter 4, and the reader is referred there for discussions on modes of motion and associated eigenvalues. Stability was discussed in terms of the character of the response to small disturbances and the tendency of the aircraft to return to or depart from equilibrium. One of the problems encountered when discussing stability criteria in separated axes form is that the natural modes of motion are generally coupled and the roll DoF actually appears in most. However, there is often, but not always, a single dominant axis per mode and this appears the most logical manner by which to approach the discussion. With this rationale we discuss the lateral/directional oscillatory mode under the yaw axis stability and the pitch-roll long period oscillation under pitch axis stability, although both have implications on roll stability. The remaining mode for which there are stability concerns is the roll-yaw spiral and we choose to discuss relevant criteria in this section.
The characteristics of the spiral mode will determine the tendency of the aircraft to return to or depart from a level trim condition following a perturbation in roll. Spiral and Dutch roll stability are naturally at variance with one another so that a strongly stable spiral mode will result in an attitude command response type in roll, accompanied by a strong excitation of a weakly stable, or even unstable, roll-sideslip oscillation during simple uncoordinated turns. Criteria relating to the roll-sideslip coupling are discussed in Section 6.7 and, of course, the Dutch roll stability itself in Section 6.5. ADS-33 sets the handling boundaries on the time-to-double amplitude of the roll angle following a pulse input in lateral cyclic; i. e.
Level 1: td > 20 s
Level 2: td > 12 s
Level 3: td > 4 s
The degree of spiral stability can be demonstrated qualitatively by the ‘turns on one control’ technique. Having established a trim condition, lateral cyclic is used to roll the aircraft to a small bank angle. Speed is held constant with longitudinal cyclic and the lateral cyclic retrimmed to hold the new bank angle and turn rate; pedal and collective are held fixed. The manoeuvre is repeated in the opposite direction and for a range of increasing bank angles. Similar tests can be performed using yaw pedals to initiate and trim in the turn. For both tests, the control deflexion required to maintain the steady turn gives a direct indication of the spiral stability. If out-of-turn control is required then the aircraft exhibits spiral instability; conversely, if into-turn control is required then the aircraft is spirally stable. Recalling the linearized derivative theory in Chapter 4 and combining terms in the rolling and yawing equations of motion in a steady turn, the control perturbations can be written as
Here r is the yaw rate in the turn and an additional assumption is made that rolling moments generated by the helicopter’s pitch rate in the turn can be neglected. The numerator in the above equations is the spiral stability parameter derived in Chapter 4. From the test results, only the ratio of this parameter with the control derivatives can be obtained as a function of flight condition, and the inclusion of the rolling moment due to pedal complicates the analysis. The spiral stability test technique recommended by the FAA (Refs 6.10, 6.13) involves establishing an out-of-balance trim, returning controls to the level trim position and measuring the bank angle response. Reference 6.13 states that the time for the bank angle to pass 20° should not be so short as to cause the aircraft to have objectionable flight characteristics in the IFR environment (UCE >1). For unstable aircraft, the time-to-double amplitude should be at least 9 s.
As we examine handling qualities boundaries based on stability for other axes, we shall see that pilots can tolerate some degree of instability in the long period modes of helicopter motion, particularly during attentive flight phases. But before the aircraft even moves, the pilot will be concerned about the ability to establish and maintain trim. We now come to the final area on our response diagram, encompassing trim and classical quasi-static stability.