ROTORCRAFT AERODYNAMIC DERIVATIVES

In rotorcraft flight dynamics analysis, the same stability and control derivatives expressions as used in the aircraft analysis are used. Asymmetric cross-coupling derivatives are usually neglected in aircraft flight mechanics analysis; however, in rotorcraft analysis these are also used. For a rotorcraft, we have

1 dM

Iy dw

In this case, the controls are held at the trim values. Higher-order rotor DOFs are allowed to reach a new equilibrium. The conventional 6DOF derivative model is a poor approximation for rotorcrafts, since the dynamics of the rotor response are not well separated from airframe dynamic responses [7]. The use of the 6DOF quasi­static derivatives is found to give an impression of greater aircraft stability. This is so because the regressing flapping mode (of the rotor) is neglected. In flight, the rotor is continuously excited by control and turbulence inputs and the estimates from the flights might differ considerably from the analytical perturbation derivatives (e. g., WT derivatives). The main reason is that the linear rotor plus body models are not easily derived by analytical means. These models should be determined from more comprehensive nonlinear models. In addition, because of the lack of physical interpretation of the higher-order rotor plus body models, the use of quasi-static

TABLE 4.9 Most Important Missile Aerodynamic Derivatives With Respect to Component Velocities With Respect to Angular Velocities (Rates) With Respect to Control Surface Deflections Response Variables^ Forces/Moments, U V (Axial) (Side) w (Normal) p q r (Roll) (Pitch) (Yaw) Se (Elevator) 5a (Aileron) Sr (Rudder) X (axial) Y (side) Yv (—ve, 1/s) Cr, Yr (+ve, m/s) YSr (+ve, m/s2) CYSr Z (vertical/normal) Zw (-ve, 1/s) Zq (usually —ve, m/s) Zs, (-ve, m/s2) L (rolling) Lp (-ve) Cip (-ve, 1/s2) ClSp M (pitching) Mw (-ve, 1/m-s) СШа Mq (-ve, 1/s) Сша MS’ (—ve, 1/s2) cmst N (yawing) Nv (+ve, 1/m-s) C„ Nr (—ve, 1/s) c„r NSr (-ve, 1/ C„sr

derivatives persists in rotorcraft analysis [7]. In general forces/moments equations are given as follows, by representing the changes about the trim conditions as the linear functions of the rotorcraft’s states:

The first and second terms of Equation 4.45 are the perturbation accelerations due to the aerodynamic forces and moments. If the coupling between various axes is strong, then the rotorcraft has many more derivatives (say up to 36 force and moments derivatives and 24 control derivatives) than an aircraft. For example, if the coupling between roll and pitch axes is quite strong, then Lq and Mp will have significant values. Also, Xu is the drag damping derivative. The complete sets of EOMs of a rotorcraft were discussed in Chapter 3. The simplified equations and linear models that can be easily used for generating dynamic responses will be discussed in Chapter 5, where the meanings and utility of all these derivatives will become clear. It is emphasized again here that the meanings of these aerodynamic derivatives across aircraft, missile, and rotorcraft should remain the same, with some specific interpretations depending on the special interactions between various axes of the airplane. This will depend on the extra DOF entering the EOM, e. g., for a rotorcraft. As seen in Chapter 3, the longitudinal modes for helicopters with zero or low forward speeds are very different from the short period (SP) and phugoid modes (see also Chapter 5). This is because certain derivatives disappear for the hovering flight. The derivatives Xw, Mw, and Mw are negligible. Additionally, in the hovering condition, U0 = Np = Lr = Nv = Yp = Yr = 0, under certain conditions that will be discussed in Chapter 5. In Ref. [10] the numerical values of the 60 aerodynamic derivatives estimated from the flight test data using the parameter-estimation method for three helicopters (AH-64, BO 105, and SA-330/PUMA) are given. However, a good number of derivatives have very small or negligible values.