Compound Lateral-Directional Derivatives

Two important compound derivatives are defined as [8]

(a) Cnbdynamic Cn$ cos a (1zz = 1xx)Clp sin a (4-33)

This compound derivative contains Cn and Ci static stability derivatives. This derivative will be the same as the weathercock stability if the AOA is zero or negligibly very small. For reasonably small AOA we have

Cng dynamic Cng — (1zz/1xx)Clba

TABLE 4.6

Typical Values of Some L-D Derivatives for a Small Trainer Aircraft

TABLE 4.7

Typical Values of the Compound Derivatives for a Supersonic Fighter Aircraft

Flight condition: Mach — 0.55, altitude — 6 km, and trim AOA — 6°.

For Dutch-roll static stability should be positive. At high AOA it

might become negative as can be seen from the above expression, thereby affecting the stability adversely.

(b) Lateral control divergence parameter (LCDP)

LCDp — Cnp (CnSa =CiSa )Cib

This parameter should be positive to avoid reverse responses due to adverse aileron yaw.

The positive values of the compound derivatives are necessary up to a maximum AOA for ensuring departure-free behavior of the aircraft. For nonzero AOA both the derivatives should be studied and the stability should be guaranteed. Typical numer­ical values of these compound derivatives are given in Table 4.7.

DADs are directly related to the forces and moments as well as to the aircraft response variables. DADs are useful as they directly appear in the simplified EOM/differential equations, which describe the vehicle dynamic responses as will be seen in Chapter 5. That is to say that DADs appear in TF models that can be used to describe the dynamic responses/Bode diagrams for the aircraft in a particular axis in an approximate way. NDADs are directly related to the aerodynamic coefficients and nondimensional velocities (Tables 4.3 and 4.4). The merits of nondimensional forms are (1) easy correlation between the results from different test methods like WT, flight tests, theoretical predictions (CFD, DATCOM), (2) correlation between the results from different flight test conditions, and (3) possible comparison/correla – tion of the results of different configurations of the same aircraft or different aircraft of similar kind (or even other kinds). DADs and NDADs defined and studied here can be very conveniently used in aerodynamic models of atmospheric flight vehicles.