Speed Stability

The longitudinal trim equations can be used to evaluate speed stability, or, as it is sometimes confusedly called, "longitudinal static stability.” The question here is whether with an inadvertent increase in speed with controls held fixed, the helicopter will pitch up and slow down, exhibiting speed stability, or pitch down and speed up in an unstable manner. The rotor flapping is always stabilizing, producing increased longitudinal flapping with increasing speed and a resulting nose-up moment, but the effect of the other components of the aircraft may be either stabilizing or destabilizing. The most important component in this regard is the horizontal stabilizer. If it is carrying a download at the initial trim condition, it should develop more of a download as speed is increased, thus producing a stabilizing nose-up pitching moment. Figure 8.26 summarizes the possibilities for several initial stabilizer loadings. In reality, the contribution of the horizontal stabilizer is modified by changes in angle of attack which accompany the changes in speed. For example, the helicopter’s rate of descent that will exist at the higher- than-trim speed with the collective fixed at its trim value will increase the stabilizer’s angle of attack. This is destabilizing. The draggier the helicopter, the more destabilizing is this effect, since a higher speed will require a higher rate of descent to achieve it. Another destabilizing change in angle of attack can be traced to the decrease in main rotor downwash at the horizontal stabilizer at the higher speed. This effect is especially significant on tandem rotor helicopters where the aft rotor is directly affected by what the front rotor is doing.

FIGURE 8.26 Illustration of Possible Speed Stability Results

The magnitude of the stability—or the instability—in terms of the change in moment per unit change of speed can be found using the charts of Chapter 3 along with the longitudinal equilibrium equations. For this calculation, the equilibrium conditions are determined in level flight as has just been done and then recalculated at a slightly higher (or lower) speed assuming no change in collective pitch to represent an inadvertant speed change. A change, however, in tail rotor pitch is allowed to maintain zero sideslip as a pilot would do by instinct. For this recalculation, the seventh illustrative example, "Helicopter in Dive at Constant Collective Pitch” of Chapter 3 can be used to establish the new conditions including the angle of climb, yc (or dive, yD). The new trim condition for the example helicopter at 135 knots (p = 0.35) with the same collective pitch as at 115 knots (p = 0.30) are listed in Table 8.6.

Solving for the trim solutions as was done at 115 knots gives:

TM = 20,496 lb

From the chart of Chapter 3 for a tip speed ratio of 0.35 and the trim collective pitch and thrust coefficient:

й, + В, — 8.6

SM

TABLE 8.6 Elements of the Longitudinal Equilibrium Equations for the Example Helicopter at 135 Knots Flight Conditions Initial Trim Forces Condition Symbol Units Value Force Symbol Units Value Gross weight G. W. lb 20,000 Main rotor thrust Tw lb 20,618 Climb angle Ъ rad .049* Main rotor H-Force lb -72 Dynamic pressure Я lb/ft2 61.5 Antitorque force Ом/h lb 882 Drag of H + V + F DH + Dy + Dp lb 1,193 Lift of H + F LH + LF lb -584 Resultant Component Trim Forces Tail rotor thrust TT lb 428 Tail rotor total H-Force HT lb 34 Tail rotor torque 2t ft-lb 164 v -.052 Horiz. stab lift T/f lb -334 у .023 Horiz. stab, drag Dh lb 16 К -.012 Vert. stab, lift Lv lb 480 ST Vert. stab, drag Dv lb 128 Fuselage lift Lf lb -250 Fuselage drag Df lb 1,049 Fuselage moment MF ft lb -14,268 aUsing method of Chapter 3.

Thus the longitudinal cyclic pitch is

= 8.6 + .7 = 9.3°

The comparable value at 115 knots was 8.9°. Thus the calculations have demonstrated that in this speed regime, the example helicopter has speed stability since the pilot must hold more forward cyclic stick to dive at 135 knots than to fly level at 115 knots. Had he not done so, the increase in speed would have resulted in a nose-up maneuver with a subsequent decrease in speed. Figure 8.27 shows the results of this analysis in terms of stick position. The rigging curves of Appendix A have been used to convert cyclic pitch to stick position.

The curvature of the collective-Fixed speed sweep line on Figure 8.27 can be traced to the two destabilizing effects of the change in angle of attack discussed earlier. For this example, the dynamic pressure increased by 37% in going from 115 to 135 knots, but the download on the horizontal stabilizer increased only by 10%. This type of curvature is often seen in flight test results.

To a pilot, speed stability is seen as the change in stick position required to maintain a new speed. For example, on an unstable helicopter, an increase in speed

Full Aft FIGURE 8.27 Speed Stability Calculation for Example Helicopter

will initially require a forward stick motion to accelerate; but when finally trimmed out at this new speed, the stick will be aft of its initial trim point. Such a helicopter is possible to fly, but will tend to wander off its trim point unless constantly corrected. This may not be much of a problem in normal flight, but it is generally considered unacceptable for instrument flight, where the cues are poor and the pilot has other things to worry about. As a general rule, pilots prefer a level of speed stability which is just slightly positive. Too much speed stability could result in running out of forward stick travel—or at least putting the stick into an uncomfortable far-forward position at high speeds.

It should be pointed out that the change in pitching moment with speed is unique to rotary-wing aicraft and does not normally exist for fixed-wings. For airplanes, any change in control position while changing speed is due only to the resulting change in angle of attack and not to the change in speed itself (except for high-speed airplanes, for which compressibility effects might be important). Airplanes also have inherent speed stability through another mechanism, however. For a given propeller pitch or jet power setting, the change in forward propulsive force is stabilizing; that is, if the airplane slows down, the propulsive force increases, thus accelerating the aircraft to its original trim speed—an automatic "cruise control.” A rotary wing aircraft that has auxiliary propulsion, such as an

autogiro or a compound helicopter, will also benefit from this inherent speed stability and need not be subjected to the analysis and tests that are necessary on a pure helicopter, which gets its propulsive force from tilt of the rotor.